pages/docs website/publications...LETTERS PUBLISHEDONLINE:21SEPTEMBER2015|DOI:10.1038/NPHYS3469 Propagatinggeneexpressionfrontsina one-dimensionalcoupledsystemofartiﬁcialcells AlexandraM.Tayar

LETTERSPUBLISHED ONLINE 21 SEPTEMBER 2015 | DOI 101038NPHYS3469

Propagating gene expression fronts in aone-dimensional coupled system of artificial cellsAlexandra M Tayar1dagger Eyal Karzbrun1dagger Vincent Noireaux2 and Roy H Bar-Ziv1Living systems employ front propagation and spatiotemporalpatterns encoded in biochemical reactions for communica-tion self-organization and computation1ndash4 Emulating suchdynamics in minimal systems is important for understandingphysical principles in living cells5ndash8 and in vitro9ndash14 Here wereport a one-dimensional array of DNA compartments in asilicon chip as a coupled system of artificial cells oering themeans to implement reactionndashdiusiondynamicsby integratedgenetic circuits and chip geometry Using a bistable circuitwe programmed a front of protein synthesis propagating inthe array as a cascade of signal amplification and short-rangediusion The front velocity is maximal at a saddle-nodebifurcation from a bistable regime with travelling fronts toa monostable regime that is spatially homogeneous Nearthe bifurcation the system exhibits large variability betweencompartments providing a possible mechanism for populationdiversity This demonstrates that on-chip integrated gene cir-cuits are dynamical systems driving spatiotemporal patternscellular variability and symmetry breaking

Sharp travelling fronts are prevalent in nature and emerge whennonlinear and dispersive effects combine for example solitarywavesin nonlinear optics fluid convection and chemical reactions15Biological multicellular systems use travelling fronts of molecularsignals as a means for computation and communication over longdistances when signalling by diffusion is inefficient In these sys-tems cells can be described as autocatalytic units that amplify andtransmit signals beyond a threshold Because signals dissipate inthe medium over short distances long-range information transmis-sion is achieved by consecutive local cellndashcell interactions Signalpropagation has been measured over orders of magnitudes in avariety of biological processes ranging from fast action potentialsin neuron networks with typical velocities16 of vasymp107 mmhminus1 toslow gene expression fronts in development3 with vasymp 01mmhminus1Although some systems have a linearly unstable initial state andthus can be treated as Fisher waves17 the majority of biologicalexamples require more complex models including the cable equa-tion and HodgkinndashHuxley model18 These systems raise questionsconcerning the selected speed bifurcations fluctuations and sta-bility in parameter space15 which are challenging to study in aliving organism

Front propagation has been extensively studied in chemicalreactions1619 and more recently in reconstituted biological systemsincluding the bacterial cell division network10 the Xenopus laeviscell cycle11 and RNA (ref 20) and DNA (ref 14) catalyticreactions In the past decade cell-free transcriptionndashtranslationreactions have been used to advance the design of programmableartificial gene systems including bulk solution21 gels9 membranevesicles22 water-in-oil drops23 microfluidic devices24 and on-chip

DNA compartments13 So far however a synthetic spatially coupledcellular system driven by integrated programmable gene expressioncircuits and capable of long-range communication has not beenreconstructed Here we used our recently developed on-chip DNAcompartments13 to design a one-dimensional array of coupledartificial cells programmed with a bistable genetic circuit to exhibitfront propagation

The array consisted of 15 compartments connected to a mainflow channel and interconnected by fork-shaped capillaries Thearray was carved in silicon to a shallow depth h= 2ndash3 microm withcompartment radius R = 50 microm capillary lengths L1 = 150 micromL2=400microm L3 = 50 microm and width W = 10 microm The mainflow channel was 50 microm deep and 900 microm wide (Fig 1a andSupplementary Fig 1) Gene circuits were patterned in everycompartment the device was sealed and Escherichia coli cell extractcontinuously flowed through the main channel13 Protein synthesisinitiated by diffusion of cell extract from the flow channel throughthe capillaries and into the compartments (Methods) Synthesizedproteins were evacuated at the capillary opening to the flow channelsetting a boundary condition of zero protein concentration

The expressionndashdiffusion dynamics were characterized by aseparation of timescales between the diffusion of proteins alongthe capillaries which reached steady-state profiles within minutesand the gene expression dynamics which changed over hours13(Supplementary Information) Thus we observed steady-state lin-ear concentration gradients along the capillaries and a homoge-neous protein concentration pi within each compartment i=1ndash15throughout the expression dynamics (Supplementary Fig 2) Theprotein flux out of each compartment can be derived by Fickrsquoslaw J = minusD0nablapi = minuspiτ setting a geometrically defined pro-tein lifetime τ = (πR2L1D0W )Φ1(L1L2 L2L3) asymp 04 h whereD0asymp0126mm2 hminus1 (35 times 10minus7 cm2 sminus1) is the protein diffusionconstant and Φ1 asymp 05 (Supplementary Equations 1ndash20) In gen-eral 0ltΦ1lt1 depends on the inter-compartment connectionsand for the case of isolated compartments Φ1(L2L1 1) = 1(Supplementary Equation 20)

The diffusion flux between compartments is determined bythe fork-shaped capillaries (L2 L3) and can be estimated by ap-plying Kirchhoff current conservation law at each junction andFickrsquos law with a linear concentration gradient along the capil-laries (Supplementary Equations 8ndash21) This leads to a discreteone-dimensional diffusion term for pi in the ith compartment1pi=D((piminus1+pi+1minus2pi)L2

2) with an effective diffusion coeffi-cient D=D0(L2WπR2)Φ2(L2L3)asymp 002mm2 hminus1 and Φ2= 028(Supplementary Equation 21) For short shunts Φ2(L3L2)rarr0diffusion between compartments is negligible compared to dif-fusion to the main channel which approached the limit of iso-lated compartments13

1Department of Materials and Interfaces Weizmann Institute of Science Rehovot 76100 Israel 2Department of Physics University of MinnesotaMinneapolis Minnesota 55455 USA daggerThese authors contributed equally to this work e-mail roybar-zivweizmannacil

NATURE PHYSICS | ADVANCE ONLINE PUBLICATION | wwwnaturecomnaturephysics 1

copy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reservedcopy 2015 Macmillan Publishers Limited All rights reserved

LETTERS NATURE PHYSICS DOI 101038NPHYS3469

Bistable DNA compartmenta

WDiffusion

Flow channel

001 2 3 4 5 6

Single DNA sourceeminusxλ

minus1)

10minus2

10minus22

4 6 100 102

SomitogenesisDNA compartments

Calciumwaves

Actionpotentials

Mitosiswaves

DNAcatalysers

cAMPwaves

104 106 108

minus16 minus08 00 = x minus vt (mm)ξ

08 162 4 6Time (h)

(times10

) (times

Tanh( )ξ η

v prop radickD

radickD (mm hminus1)x (mm)x (mm)

v = 062 mm hminus1

DNAstarter

Figure 1 | Travelling gene expression front in an array of coupled DNA compartments a Overlay image of expressed GFP and fluorescently labelled DNApatterns (white squares) Compartments 2ndash15 (from left) were patterned with a bistable gene circuit the first one patterned with a small amount of starterconstruct to initiate propagation Scale bar 100 microm Inset single compartment overlaid with the self-activatorinhibitor (AI) scheme using activator σ 28

and inhibitor Aσ 28 b GFP concentration profile in arbitrary units (au) along 15 compartments formed from a single DNA source in the first compartmentSolid line is an exponential fit eminusxλ with λ=0416plusmn0016mm (104plusmn 004 compartments) averaged over 4 h of expression c Expression dynamics ofthe propagator during 9 h of experiment Each graph represents the profile in a compartment according to their order in the array d A spacetime image ofGFP in the array propagating at a constant velocity of v=062 mm hminus1 (155 compartment hminus1) e Collapse of fronts in the travelling frame of referenceξ=xminusvt Protein levels are normalized to the maximal protein value in the array for each time point (Supplementary Information) Red line is a fit toTanh(ξη) with ηasymp02 mm (05 compartment) f Propagation velocity for a range of biological systems as a function of scaling parameter

radickD where D is

the diusion constant of the propagating signal and k is the typical autocatalytic rate of each system The DNA compartment array is denoted in red Exactrange appears in Supplementary Table 1

The diffusion between compartments effective protein lifetimeand nonlinear interactions dictated by the genetic circuit canall be summarized in a discrete one-dimensional reactionndashdiffusion equation

parttpi=1piminuspiτ+ f (pi)

Here f (pi) is the protein synthesis rate in response to the localprotein concentration pi and is determined by the genetic circuitThe array was designed to obtain nearest-neighbour interactionswith a diffusion length smaller than a single compartmentradicDτasymp01mmltL2 (Supplementary Equations 22ndash24) Indeed we

measured an exponentially decaying protein concentration gradientfrom a single DNA source with a decay length of λasymp04mm (onecompartment) along the array (Fig 1b)

To program signal propagation we designed a bistable gene cir-cuit comprising an activator in a self-feedback loop and its inhibitor(Fig 1a inset Supplementary Fig 3)25 The circuit dynamics at-tained one of two steady-state protein expression levels reportedusing green fluorescent protein (GFP) high pHighasymp05microm or pLow ofconcentration lower than detection limit (asymp50 nM SupplementaryFig 4) In the absence of the inhibitor a small leak initiates the pos-itive feedback and the circuit dynamics has a single steady-state so-lution pHigh The circuit is modelled accounting for the competition

over gene expressionmachinery (Supplementary Equations 25ndash40)resulting in a circuit response function f (pi) for the activatordynamics pi (Supplementary Equation 40) The bistable circuit waspatterned in all compartments except for the anterior onewhichwaspatterned with a lsquostarterrsquo gene constantly expressing the activator atconcentration lower than pHigh

During the first 35 h of expression all compartments maintainedpLow (Fig 1cd tlt35h) Signalling was initiated from the anteriorcompartment followed by diffusion of activator to the neighbouringcompartment This triggered the autocatalytic reaction switchingthe neighbouring compartment to pHigh at t = 35 h and creatinga new source of activator The cycle of synthesis and diffusionpropagated along the array at a constant velocity of v=062mmhminus1(155 compartment hminus1 with compartment unit length L2=04mmFig 1d) The expression dynamics in the array exhibited sequentialswitching to a high steady-state level with a delay of 1t asymp 07 hbetween neighbouring compartments (Fig 1c) and a gradualdecrease in protein synthesis due to intrinsic decay in cell extractactivity (Methods) In a moving frame of reference ξ=xminusvt the spatiotemporal levels collapsed to a single step-functionTanh((ξη)) with η= 02mm (half a compartment Fig 1e) Thefront velocity is consistent with the scaling vprop

radickDasymp034mmhminus1

Here kasymp54hminus1 is the growth rate of the autocatalytic reactionestimated experimentally from the initial protein synthesis rate

2 NATURE PHYSICS | ADVANCE ONLINE PUBLICATION | wwwnaturecomnaturephysics

NATURE PHYSICS DOI 101038NPHYS3469 LETTERS

Compartment

i ii iii

5 10 15Compartment

5 10 15

minus06 minus04 minus02 00log( )α

log(p) log(p)

Monostable

pHighpHighpLow pTH

c ( )α τ

Bistable

minus1)

0001 02 03

0 2 4 6

asymp 04 hτ

α8 10

0 2 4 6α

i ii iii = x minus vt (mm)ξ

)η (mm)η

minus1)

Figure 2 | Propagation dynamics regulated by gene circuit a A model-based phase diagram in parameter space of lifetime τ and gene ratio α=GIGAshowing a region of monostability with a single fixed point (left inset) and a region of bistability with two stable (pHigh and pLow) and one unstable (pTH)fixed points (right inset) Error bars are estimated from variation in lifetime and gene ratio (Supplementary Fig 7) Points labelled indashiii are described in bb Spacetime plots of propagator in the DNA array for the three points marked in a in the (i) monostable (ii) close to transition and (iii) bistable regimesBlue (green) colour represents low (high) protein level c Propagation velocity as a function of α Plot shows three dierent experiments Solid line is a fit tov=v0α

minusβ β=04plusmn007 v0=059plusmn002mmhminus1 Each data point is taken from a single experiment with front propagation over a number ofcompartments The velocity is extracted by fitting a linear slope to the expression onset time in each compartment as a function of compartment locationThe error bar is given by the velocity fit error for each experiment d Propagation front width η as a function of α calculated from a fit of the collapsed andnormalized propagating front Solid line is a fit to η=007(1+2αminus04)(mm) Inset velocity as a function of front width black line is a linear fit Each datapoint is taken from a single experiment and the error bar is given by the width fit error for each experiment

parttpi=kpi which fits to an exponential growth with a rate k at lowprotein concentrations (Supplementary Fig 5) This scaling alsoknown as Lutherrsquos formula16 is common to autocatalytic reactionndashdiffusion systems in chemistry and biology and has been observedover many orders of magnitude (Fig 1f and SupplementaryTable 1) including gene expression fronts propagating throughthe anteroposterior axis of developing vertebrates26 mitosis wavesin Xenopus eggs11 cAMP waves spatial organization of amoeba27calcium waves in the heart28 and action potentials in neurons16The gene expression propagation velocity in the array is slower thanin vitro enzymatic front waves101420 v asymp 3mm hminus1 and chemicalreactions such as BelousovndashZhabotinsky16 vasymp140mmhminus1

The theoretical model of the gene circuit f (pi) (SupplementaryEquation 40) revealed a transition from a bistable regime sup-porting front propagation to a monostable regime which occursalong a saddle-node bifurcation line αc(τ ) in the parameter spaceof protein lifetime τ and gene ratio α= (GIGA) of inhibitor andactivator (Fig 2a and Supplementary Fig 6) The inhibitor geneconcentrationwas fixed in theory and experiment A bistable regimerequires a high inhibitor concentration to suppress the autocatalyticleak which corresponds to a long protein lifetime or high generatio A monostable regime is found at a low gene ratio or shortlifetime In the bistable regime αgtα (τ) the activator flow chart

exhibits two stable fixed points corresponding to high and lowprotein levels (Fig 2a right inset) There is an additional unstablefixed point pTH which is the concentration threshold for switchingthe compartment between the two expression states In crossing thesaddle-node bifurcation line the two fixed points pTH and pLow areannihilated and in the monostable regime α ltαc (τ ) there is asingle fixed point of high levels pHigh (Fig 2a left inset) Notablythe competition over gene expression machinery is not necessaryto achieve bistability but expands the bistable region in parameterspace (Supplementary Fig 6)29

We fabricated multiple arrays with identical lifetime τ asymp 04 hand different gene ratios 01lt α lt 10 with 5ndash10 variation inlifetime and gene ratio13 (Supplementary Fig 7) We observedtwo distinct regimes as predicted in the phase diagram At lowinhibitor ratio α lt 07 expression initiated simultaneously in allthe compartments and reached high levels without observablepropagation corresponding to the monostable regime (Fig 2b(i))For 07ltα lt 10 we observed a travelling gene expression front(Fig 2b(iii)) The compartments maintained low expression levels(pLow) until triggered by the propagating activator corresponding tothe bistable regime Near the transition line αasymp 07 we observedsignal propagation for a finite time after which expression initiatedsimultaneously in the entire array (Fig 2b(ii)) This suggests the

log(p)

00 2 4

Time (h)6 8

= 031 hτ = 046 hτ = 062 hτ

0minus10 minus08 minus06 minus04 minus02 00

Bistable

2 4 6 8 2 4 6 8 2 4 6 8

Compartment Compartment Compartment minus c ( )αα τ

( minus c)minus12αα

minus c lt 0αα

minus c asymp minus05αα minus c asymp minus03αα minus c asymp 0αα

minus c asymp 0αα minus c gt 0αα

) (times

Figure 3 | Emergent fluctuations in single compartments near the transition a Overlay image of GFP and DNA in single compartments after 10 h ofexpression The nine compartments were patterned with the bistable gene circuit at the same gene ratio α Scale bar 100 microm b Kinetics of the circuit insingle compartments with τ= 1h for three dierent gene ratios c Reaction onset time in the compartments as a function of αminusαc(τ ) for three dierentlifetimes Each lifetime exhibited a dierent αc and the function was subtracted accordingly (Supplementary Information) Errors are taken from ninemeasurements for each point Standard deviation increased up to 35 as the DNA ratio approached the transition to the bistable region αrarrαcd Spacetime plots showing nine repeats of single-compartment circuit kinetics with τ=062h for three dierent gene ratios as denoted Blue (green)colour represents low (high) protein level

system is in the monostable regime but exhibits long onset timesOur model implies a third regime for α gt 10 in which thesystem supports front propagation of pLow into pHigh This is notobservable because the initial state of the array is pLow and there isa constant flux of activator proteins from the starter compartment(Supplementary Fig 6)

We next explored the propagation velocity and front width asa function of gene ratio α in the bistable regime (Fig 2cd andSupplementary Fig 8 αgt07) At high inhibitor to activator generatio ααc the propagation was slow v (α=10)=02mmhminus1 Aswe approached the bifurcation line gene ratio in the compartmentdecreasedαrarrαc positive feedbackwas triggered at lower activatorconcentration and the velocity increased by a factor of three atα=075 Our model shows the threshold concentration is low nearthe bifurcation point pTH (αc)rarr pLow hence compartments areeasily excited to high activator levels which is consistent with theobserved faster propagation The velocity is fitted with a power lawv = v0αminusβ with β = 04plusmn 007 v0 = 059plusmn 002mmhminus1 (Fig 2c)which is close to the classical Luther scaling v=(Dk)

12 propαminus

12 where

the autocatalytic growth rate is proportional to the activator geneconcentration and inversely proportional to the gene ratio The frontwidth broadenedwith decreasing gene ratioα but remained sharperthan a compartment 0125ltηlt025mm (Fig 2d) The front widthexhibited a linear dependence on the front velocity η=η0+ (vk0)(Fig 2d) and k0 = 42 hminus1 is close to the measured autocatalyticreaction rate 54 hminus1 This is consistent with the observed lineardependence ηpropv in other bistable models18

We next investigated the behaviour of the gene circuit in isolatedcompartments for varying lifetime τ and gene ratio α (Fig 3a)We observed a transition between a monostable regime αltαc inwhich the compartments spontaneously switched to high activatorlevels and a bistable regime α gtαc in which the compartmentsremained at low levels (Fig 3b) consistent with the propagationbehaviour The expression onset time in the monostable regimediverged near the bifurcation αc (τ ) where the inhibition is suffi-ciently strong to prevent the onset of the positive feedback beyondthe duration of the experiment (sim13 h Fig 3bc) The transitionpoint αc(τ ) decreased with increasing lifetime τ consistent withthe phase diagram (Fig 2a and Supplementary Figs 9 and 10)

The divergence was consistent with a universal power-law scalingτonsim (αminusαc (τ ))

minus12 as expected near a saddle-node bifurcation30Furthermore we found a large variation in the expression onsettime near the bifurcation (Fig 3ad and Supplementary Fig 10)At α minus αc =minus05 the expression onset time was τon = 2 h withless than 5 variation between compartments Near the transitionαasympαc the variation was greater than 35 with only 40 of thecompartments initiating expression in 13 h (Supplementary Fig 11)The observed variation is surprising because the number of DNAcopies in each compartment is large13sim107 and therefore stochasticeffects should be negligible However the proximity to a transi-tion point with diverging onset times amplifies small differencesin gene ratio between compartments This mechanism can play acrucial role in biological processes such as development whichrelies on spontaneous symmetry breaking31 To summarize we havedemonstrated front propagation of gene expression along an arrayof artificial cells using programmable integrated gene circuits Thespatial organization of DNA circuits together with short interactionlength set by the array geometry will allow integrating long-rangesignallingwith local information processing reactions based on geneexpression in analogy to multicellular systems electronic circuitsand neuronal networks

MethodsMethods and any associated references are available in the onlineversion of the paper

Received 7 April 2015 accepted 10 August 2015published online 21 September 2015

References1 Gregor T Fujimoto K Masaki N amp Sawai S The onset of collective behavior

in social amoebae Science 328 1021ndash1025 (2010)2 Bassler B L amp Losick R Bacterially speaking Cell 125 237ndash246 (2006)3 Hubaud A amp Pourquieacute O Signalling dynamics in vertebrate segmentation

Nature Rev Mol Cell Biol 15 709ndash721 (2014)4 Kandel E Schwartz J Jessell T M Seigelbaum S A amp Hudspeth A J

Principles of Neural Science (McGraw-Hill Professional 2012)5 Bulter T et al Design of artificial cellndashcell communication using gene and

metabolic networks Proc Natl Acad Sci USA 101 2299ndash2304 (2004)

NATURE PHYSICS DOI 101038NPHYS3469 LETTERS6 Basu S Gerchman Y Collins C H Arnold F H ampWeiss R A synthetic

multicellular system for programmed pattern formation Nature 4341130ndash1134 (2005)

7 Matsuda M Koga M Nishida E amp Ebisuya M Synthetic signal propagationthrough direct cellndashcell interaction Sci Signal 5 ra31 (2012)

8 Danino T Mondragoacuten-Palomino O Tsimring L amp Hasty J A synchronizedquorum of genetic clocks Nature 463 326ndash330 (2010)

9 Isalan M Lemerle C amp Serrano L Engineering gene networks to emulateDrosophila embryonic pattern formation PLoS Biol 3 e64 (2005)

10 Loose M Fischer-Friedrich E Ries J Kruse K amp Schwille P Spatialregulators for bacterial cell division self-organize into surface waves in vitroScience 320 789ndash792 (2008)

11 Chang J B amp Ferrell J E Mitotic trigger waves and the spatial coordination ofthe Xenopus cell cycle Nature 500 603ndash607 (2013)

12 Keber F C et al Topology and dynamics of active nematic vesicles Science345 1135ndash1139 (2014)

13 Karzbrun E Tayar A M Noireaux V amp Bar-Ziv R H Programmableon-chip DNA compartments as artificial cells Science 345 829ndash832 (2014)

14 Zadorin A S Rondelez Y Galas J-C amp Estevez-Torres A Synthesis ofprogrammable reactionndashdiffusion fronts using DNA catalyzers Phys Rev Lett114 068301 (2015)

15 Cross M amp Hohenberg P Pattern formation outside of equilibrium Rev ModPhys 65 851ndash1112 (1993)

16 Tyson J J amp Keener J P Singular perturbation theory of traveling waves inexcitable media (a review) Physica D 32 327ndash361 (1988)

17 Fisher R A The wave of advance of advantageous genes Ann Eugen 7355ndash369 (1937)

18 Keener J P amp Sneyd JMathematical Physiology I (Springer 1998)19 Winfree A T Spiral waves of chemical activity Science 175 634ndash636 (1972)20 Bauer G J McCaskill J S amp Otten H Traveling waves of in vitro evolving

RNA Proc Natl Acad Sci USA 86 7937ndash7941 (1989)21 Noireaux V Bar-Ziv R amp Libchaber A Principles of cell-free genetic circuit

assembly Proc Natl Acad Sci USA 100 12672ndash12677 (2003)22 Noireaux V amp Libchaber A A vesicle bioreactor as a step toward an artificial

cell assembly Proc Natl Acad Sci USA 101 17669ndash17674 (2004)23 Weitz M et al Diversity in the dynamical behaviour of a compartmentalized

programmable biochemical oscillator Nature Chem 6 295ndash302 (2014)

24 Niederholtmeyer H Stepanova V amp Maerkl S J Implementation of cell-freebiological networks at steady state Proc Natl Acad Sci USA 11015985ndash15990 (2013)

25 Kim J White K S amp Winfree E Construction of an in vitro bistable circuitfrom synthetic transcriptional switchesMol Syst Biol 2 68 (2006)

26 Bajard L et alWnt-regulated dynamics of positional information in zebrafishsomitogenesis Development 141 1381ndash1391 (2014)

27 Kessler D amp Levine H Pattern formation in dictyostelium via the dynamics ofcooperative biological entities Phys Rev E 48 4801ndash4804 (1993)

28 Meyer T Cell signalling by second messenger waves Cell 64 675ndash678 (1991)29 Rondelez Y Competition for catalytic resources alters biological network

dynamics Phys Rev Lett 108 018102 (2012)30 Strogatz S H International Edition Nonlinear Dynamics and Chaos With

Applications to Physics Biology Chemestry and Engeneering (WestviewPress 2001)

31 Artavanis-Tsakonas S Rand M D amp Lake R J Notch signalingCell fate control and signal integration in development Science 284770ndash776 (1999)

AcknowledgementsWe thank S S Daube for helpful discussions VN thanks J Garamella R Marshall andM Rustad for technical help This work was supported by the Israel Science Foundationthe Minerva Foundation and the Volkswagen Foundation (RHB-Z) the USndashIsraelBinational Science Foundation (RHB-Z and VN)

Author contributionsAll authors contributed to all aspects of this work

Additional informationSupplementary information is available in the online version of the paper Reprints andpermissions information is available online at wwwnaturecomreprintsCorrespondence and requests for materials should be addressed to RHB-Z

Competing financial interestsThe authors declare no competing financial interests

MethodsBiochip fabrication The fabrication and assembly protocol of the DNAcompartments is similar to previous work13 Each array was composed of15 interconnected circular compartments etched 25ndash3microm deep into a siliconwafer and connected to a main flow channel (Supplementary Fig 1A) Siliconwafers (5primeprime 0525mm thickness test grade 〈100〉 p-type University Wafers)were used as substrates The compartments had a radius of 50 microm and wereconnected through a capillary channel 10ndash15 microm in width to each other and to aperpendicular flow channel 50 microm deep and 900 microm wide (Fig 1a andSupplementary Fig 1B) The flow channel had an inlet at one side and a50-microm-wide serpentine ending with an outlet at the other side The silicon waferwas patterned using standard lithography techniques (Photoresists S1818 AZ4562MicroChem) and etched using reactive ion etching in an ICP-RIE (SurfaceTechnology Systems) using the Bosch process32 for deep features (gt5microm) Thecompartment and flow channel were etched in two separate steps The inlets andoutlets of each device were drilled using a drill machine (Proxxon TBM 220)The device was cleaned using a base piranha solution followed by shortincubation in hydrofluoric acid The device was coated with asim50 nm SiO2

layer deposited by low-temperature ALD (atomic layer deposition FIJI F200Cambridge Nanotech)

Biocompatible photoactivable monolayer assembly The SiO2-coated device wasincubated with a biocompatible photoactivable polymer solution thatself-assembled into a monolayer on the SiO2 surface for subsequent activation byultraviolet light and binding of biomolecules33 The polymer is composed of apolyethylene glycol backbone with a Nvoc-protected amine at one end and atrialkoxysilane function at the other end33 Incubation was carried for 20min at02mgmlminus1 in toluene followed by rinsing in toluene and drying

Lithography patterning for DNA assembly The device was mounted on thetranslation stage of an inverted microscope (Zeiss Axiovert 200) Ultraviolet lightfrom a fluorescent light source (EXFO X-Cite 120Q) was illuminated through arectangular pinhole and a 365 nm band-pass filter (Chroma) and focused on thesubstrate using atimes60 objective The exposure time was set to yield a total25 J cmminus2 Reactive amine groups on the biocompatible photoactivable monolayerwere exposed in surface patterns illuminated by ultraviolet light33 BiotinN -hydroxysuccinimidyl ester (biotin-NHS) dissolved in a borate buffered saline(05mgmlminus1) was incubated on the chip for 15min The biotin-NHS covalentlybound to the exposed amine groups on the exposed monolayer33 We thus attaineda surface patterned with biotin

DNA deposition and brush assembly Linear DNA fragments were produced bypolymerase chain reaction (PCR) with KAPA HiFi HotStart ReadyMix (KK2601KAPA BIOSYSTEMS) using one primer with biotin and another with Alexa Fluor647 both attached at the 5prime-end (IDT) The biotin primer was located downstreamof the transcription terminator PCR products were cleaned using Promega WizardSV-Gel and PCR Clean-Up DNA was conjugated to streptavidin (SA) by mixing insolution in a molar ratio of 115 DNASA The final DNA solution containedSA-conjugated DNA at a concentration of 100ndash300 nM in phosphate bufferedsaline (PBS)

Nanolitre DNAndashSA droplets were individually deposited onto the reactorchambers using the GIX Microplotter II (Sonoplot) and 60-microm-diametermicropipettes The DNAndashSA solutions were incubated on the device for 1ndash2 h inPBS During incubation the DNA formed a dense brush on the surface The brushdensity was of the order of 103 DNA micromminus2 (refs 3334) The promoter orientation ofthe DNA was towards the surface of the DNA brush35 The gene size varied in therange 700ndash1500 bp The distance between the DNA top and the promoter is about100ndash200 bp and a similar distance between the terminator and the DNA endattached to the surface Finally DNA brushes were localized to the lithographicallypatterned areas inside the etched compartments (Fig 1a and SupplementaryFig 1) The device was then bathed in PBS and then in water to remove excessadsorbed DNA The device was then gently dried with nitrogen

All E coli cell-free transcriptionndashtranslation reaction (CFE) In this study weused a CFE that is a cytoplasmic extract from E coli strain BL21 Rosetta2(Novagen) according to a procedure described previously36 The cell-free reactionswere composed of 33 (volume) crude extract and 66 (volume) of water DNAand buffer with the following final composition 50mMHEPES pH 8 15mM ATP15mM GTP 09mM CTP 09mM UTP 02mgmlminus1 tRNA 026mM coenzyme A033mM NAD 075mM cAMP 0068mM folinic acid 1mM spermidine 30mM3-phosphoglyceric acid 2mM DTT 15mM amino acids 65mMMg-glutamate100mM K-glutamate and 2 PEG 8000 During extract preparation theendogenous DNA and mRNA were degraded The cell extract provided thetranscription and the translation machineries necessary for gene expressionTranscription was driven by the endogenous E coli RNA polymerase and thusallowed us to use the entire repertoire of the E coli regulation toolbox3738 The CFEcontained active proteases and ribonucleases Previously we studied the stability of

proteins and mRNA in our cell-free system133639 Proteins without a degradationtag were stable with no observed degradation The protein GamS was added to allof the reactions at a concentration of 3 microM to minimize the degradation of linearDNA by the 3prime exonuclease activity of the RecBCD complex40 which was present inthe CFE The CFE was supplemented with 3-phosphoglyceric acid (3-PGA) forATP regeneration36 The 3-PGA is a natural substrate to E coli and therefore noenzyme was added to the extract

Sealing the device and flow of CFE The carved side of the device was sealedwith a PDMS-coated glass coverslip and magnets Magnets embedded in apunched PDMS were attached to the backside of the device (the untreated sideof the device) aligned to the drilled inlet and outlet The device inlet wasconnected using elastic tubing to a reservoir of PBS cooled to 2ndash4 C with acooling circulator (Huber ministat) The outlet was connected to a syringe pump(Harvard Apparatus Pico Plus) The device was placed on a microscope in anincubating chamber (30 C) Once the syringe pump was turned on vacuumwas applied and PBS flowed into the main flow channel and entered bycapillarity into the compartments within a minute pushing out air through thePDMS The experiment began by exchanging PBS with CFE flowing in the mainchannel at a rate ofsim02 microlminminus1 and diffusing through the thin capillaries intoDNA compartments Constant flow was maintained during the experimentwhich was carried on for 12ndash15 h During this long period there is a slow loss ofextract activity which is observed in a decaying expression envelope for all ofthe compartments

Imaging Cell-free expressed GFP in the compartments was imaged on an invertedmicroscope (Zeiss Axiovert 200) equipped with an automated translation stage asensitive wide view camera (ANDOR Neo sCMOS Andor Technology) through atimes10 objective (Zeiss) and fluorescent excitation (Hg-illumination lamp (X-Cite120) through a GFP filter set (488 nM)

Gene circuit design and assemblyDNA constructs used in this work are describedin Supplementary Table 2 Their assembly into single gene constructs and genenetworks is described in Supplementary Table 3 as well as in Supplementary Fig 3All the plasmids were constructed from the pBEST-Luc plasmid (Promega) withthe UTR1 (untranslated region) DNA constructs (promoter gene) were assembledin vitro by PCR using a primer coding for the promoter and a plasmid templatecoding for the gene This was followed by a second PCR with biotinylated primersand primers with Alexa Fluor 647 as previously described

The bistable gene circuit (Fig 1a inset Supplementary Fig 3 andSupplementary Tables 2ndash3) was constructed using an autocatalytic element andits inhibitor2541ndash44

Activator (P) P28minusσ28 autocatalytic construct expressing the sigma-28

transcription factor37 under its own promoter P28 thereby forming a positivefeedback loop

Inhibitor (I) P70minusAσ 28 constitutively expressing the anti-sigma factor 28(FlgM ref 45) under a σ 70 promoter37 The anti-sigma protein binds the sigmatranscription factor with high affinity and forms a complex (C) and thus sequestersthe binding of sigma-28 to its prompter inhibiting the positive feedback

In the experiment the gene ratio α=(GIGp) of inhibitor GI and autocatalyticGp elements of the circuit were varied (Supplementary Fig 3) The inhibitor andreporter constructs were kept at a constant concentration while the activatorconcentration was changed To maintain the total DNA of each brush constant weused a non-coding lsquodummyrsquo DNA of the same length and concentration as theactivator construct

References32 Wang X Zeng W Lu G Russo O L amp Eisenbraun E High aspect ratio

Bosch etching of sub-025 microm trenches for hyperintegration applications J VacSci Technol B 25 1376ndash1381 (2007)

33 Buxboim A et al A single-step photolithographic interface for cell-free geneexpression and active biochips Small 3 500ndash510 (2007)

34 Bracha D Karzbrun E Shemer G Pincus P A amp Bar-Ziv R HEntropy-driven collective interactions in DNA brushes on a biochip Proc NatlAcad Sci USA 110 4534ndash4538 (2013)

35 Daube S S Bracha D Buxboim A amp Bar-Ziv R H Compartmentalizationby directional gene expression Proc Natl Acad Sci USA 1072836ndash2841 (2010)

36 Shin J amp Noireaux V Efficient cell-free expression with the endogenousE coli RNA polymerase and sigma factor 70 J Biol Eng 4 8 (2010)

37 Shin J amp Noireaux V An E coli cell-free expression toolbox Applicationto synthetic gene circuits and artificial cells ACS Synth Biol 129ndash41 (2012)

38 Caschera F amp Noireaux V Synthesis of 23mgml of protein with an allEscherichia coli cell-free transcriptionndashtranslation system Biochimie 99162ndash168 (2014)

NATURE PHYSICS | wwwnaturecomnaturephysics

NATURE PHYSICS DOI 101038NPHYS3469 LETTERS39 Karzbrun E Shin J Bar-Ziv R H amp Noireaux V Coarse-grained

dynamics of protein synthesis in a cell-free system Phys Rev Lett 106048104 (2011)

40 Karu A E Sakaki Y Echols H amp Linn S The γ protein specified bybacteriophage γ Structure and inhibitory activity for the recBC enzyme ofEscherichia coli J Biol Chem 250 7377ndash7387 (1975)

41 Ferrell J E Tripping the switch fantastic How a protein kinase cascade canconvert graded inputs into switch-like outputs Trends Biochem Sci 21460ndash466 (1996)

42 Gardner T S Cantor C R amp Collins J J Construction of a genetic toggleswitch in Escherichia coli Nature 403 339ndash342 (2000)

43 Chang D-E et al Building biological memory by linkingpositive feedback loops Proc Natl Acad Sci USA 107175ndash180 (2010)

44 Huang D Holtz W J amp Maharbiz M M A genetic bistable switch utilizingnonlinear protein degradation J Biol Eng 6 9 (2012)

45 Hughes K T amp Mathee K The anti-sigma factors Annu Rev Microbiol 52231ndash286 (1998)

13 113

Supplementary13 Information13 for13

Propagating gene expression fronts in a 1D coupled system of

artificial cells

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

Propagating gene expression fronts in a one-dimensional coupled system of artificial cells

SUPPLEMENTARY INFORMATIONDOI 101038NPHYS3469

NATURE PHYSICS | wwwnaturecomnaturephysics 1

13 213

Table13 of13 Contents13

Supplementary13 Text13 13 413 DNA13 Compartment13 theory13 13 413

Single13 Compartment13 Lifetime13 13 413 One13 Dimensional13 array13 of13 compartments13 effective13 lifetime13 and13 diffusion13 13 513

Inhibitor-shy‐Autocatalytic13 Bistable13 Network13 Analysis13 13 813 Network13 dynamics13 13 813 Network13 dynamics13 with13 competition13 over13 RNA13 polymerase13 13 1013

The13 propagator13 velocity13 13 1113 Flow13 in13 the13 compartment13 array13 13 1213 Variation13 in13 DNA13 Ratio13 and13 compartment13 lifetime13 13 1313 Analysis13 of13 the13 propagation13 velocity13 13 1313

Bibliography13 13 1413 Figures13 13 1513

Main13 Text13 13 1513

Fig13 S113 Microfluidic13 device13 and13 DNA13 compartment13 array13 13 1513 Fig13 S213 Linear13 concentration13 profile13 along13 the13 capillary13 in13 a13 single13 compartment13 13 1613

Fig13 S313 Bistable13 gene13 circuit13 network13 scheme13 13 1713 Fig13 S413 The13 bistable13 protein13 kinetics13 13 1813

Fig13 S513 Growth13 rate13 of13 the13 autocatalytic13 process13 k13 13 1913 Fig13 S613 Phase13 diagram13 with13 and13 without13 competition13 over13 RNAP13 13 2013

Fig13 S713 Variation13 in13 DNA13 ratio13 α13 and13 compartment13 lifetime13 τ13 13 2113

Fig13 S813 Propagation13 velocity13 for13 different13 experiments13 13 2213 Fig13 S913 Divergence13 of13 onset13 times13 near13 the13 transition13 13 2313

Fig13 S1013 Onset13 time13 in13 single13 compartments13 for13 different13 gene13 ratios13 and13 lifetimes13 approaching13 the13 transition13 to13 the13 bistable13 regime13 13 2413

Fig13 S1113 Probability13 to13 switch13 into13 an13 active13 state13 near13 the13 transition13 13 2513

SI13 Figures13 13 2613 Fig13 S1213 DNA13 compartment13 scheme13 13 2613

Fig13 S1313 Single-shy‐compartment13 exponentially13 decaying13 profile13 and13 propagating13 front13 in13 array13 13 2713 Fig13 S1413 Time13 derivative13 of13 protein13 concentration13 and13 velocity13 measurements13 13 2813 Table13 S113 Luther13 scaling13 ndash13 propagation13 velocities13 diffusion13 coefficients13 and13 reaction13 rates13 in13 different13 systems13 13 2913

Table13 S213 DNA13 Modules13 13 3013 Table13 S313 DNA13 Constructs13 ndash13 Bistable13 network13 and13 starter13 13 3013

Table13 S413 Values13 taken13 for13 the13 rate13 balance13 plots13 and13 the13 phase13 diagram13 13 3113

2 NATURE PHYSICS | wwwnaturecomnaturephysics

SUPPLEMENTARY INFORMATION DOI 101038NPHYS3469

13 313

Video13 13 3213 13 13 13

13 413

Supplementary13 Text13

DNA13 Compartment13 theory13 13 Single13 Compartment13 Lifetime13 13 The13 derivation13 of13 the13 gene13 expression13 dynamics13 in13 a13 single13 compartment13 was13 previously13 published13 and13 is13 summarized13 here13 for13 clarity1313 The13 synthesis13 of13 protein13 in13 the13 circular13 compartment13 is13 a13 slower13 process13 than13 diffusion13 across13 the13 compartment13 and13 capillary13 With13 119871119871 = 150microμm13 119863119863 = 35microμms 13 T = L2119863119863 =5min13 whereas13 the13 time13 scale13 to13 reach13 steady-shy‐state13 protein13 synthesis13 T asymp 1hr 13 (Fig13 S2)13 This13 separation13 of13 time13 scales13 allows13 us13 to13 use13 a13 steady-shy‐state13 approximation13 in13 which13 the13 concentration13 of13 protein13 is13 homogenous13 in13 the13 compartment13 and13 the13 diffusion13 along13 the13 capillary13 is13 at13 steady-shy‐state13 The13 protein13 concentration13 119901119901(119905119905119910119910)13 follows13 a13 1D13 diffusion13 equation13 along13 the13 capillary 0 lt 119910119910 lt11987111987113 13 120597120597119901119901 = 119863119863120597120597119901119901 (1) 13 13 13 with13 a13 boundary13 condition13 at13 the13 main13 flow13 channel13 119901119901 119910119910 = 119871119871 = 0 13 At13 the13 compartment13 opening13 119910119910 = 013 the13 protein13 concentration13 is13 equal13 to13 that13 within13 the13 compartment13 119901119901 119910119910 = 0 = 119901119901(119905119905)13 which13 is13 the13 slow13 variable13 of13 interest13 Thus13 the13 concentration13 drop13 is13 linear13 along13 the13 capillary13 We13 have13 previously13 shown1313 that13 the13 diffusion13 dynamics13 along13 the13 capillary13 is13 13 119901119901 = 119901119901(t) sdot 1minus

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

13 as13 measured13 (Fig13 S2)13 Within13 the13 compartment protein13 is13 synthesized13 at13 rate13 11988611988613 and13 diffuses13 out13 of13 the13 compartment13 at13 a13 flux13 119869119869 13 The13 protein13 dynamics13 in13 the13 compartment13 is13 thus13 13 120597120597119901119901 = 119886119886 + J13 (4) 13 From13 Fickrsquos13 law13 the13 diffusion13 flux13 out13 of13 the13 compartment13 is13 13 119869119869 =

119863119863119860119860119881119881 120597120597119901119901

13 (5)

13 Here13 we13 used13 the13 compartment13 volume13 119881119881 = 120587120587119877119877ℎ13 and13 compartment13 opening13 area13 119860119860 = ℎ11988211988213 The13 channel13 and13 compartment13 height13 is13 ℎ13 the13 compartment13 radius13 is13 119877119877 13 and13 the13 opening13 width13 is13 119882119882 13 We13 thus13 obtain13 a13 first-shy‐order13 differential13 equation13 for13 the13 protein13 dynamics13 in13 the13 compartment13 13 13 120597120597119901119901 = 119886119886 minus

119901119901120591120591 13

13 513

with13 effective13 protein13 lifetime13 in13 the13 compartment13 13

τ =120587120587119877119877

11986311986311988211988211987111987113

13 For13 a13 compartment13 with13 the13 parameters13 119871119871 = 150microμm13 119882119882 = 10microμm13 119877119877 = 50microμm13 the13 lifetime13 is13 120591120591 = 09hr consistent13 with13 the13 kinetics13 of13 the13 protein13 in13 the13 compartment13 (Fig13 S2)13 and13 longer13 than13 the13 diffusion13 time13 scale13 120591120591 = 5min13 thus13 proving13 the13 validity13 of13 the13 steady-shy‐state13 approximation13 above13 13

One13 Dimensional13 array13 of13 compartments13 effective13 lifetime13 and13 diffusion13 Next13 we13 consider13 an13 array13 of13 circular13 compartments13 interconnected13 through13 small13 capillaries13 (Fig13 1A13 S1A13 S12)13 Proteins13 synthesized13 in13 the13 compartments13 diffuse13 to13 the13 main13 flow13 channel13 through13 capillaries13 with13 width13 11988211988213 and13 length13 11987111987113 (red13 lines13 Fig13 S12)13 setting13 the13 turnover13 mechanism13 described13 in13 the13 previous13 section13 Proteins13 diffuse13 between13 compartments13 along13 capillaries13 of13 width13 11988211988213 and13 length13 11987111987113 (blue13 lines13 Fig13 S12)13 These13 capillaries13 are13 also13 connected13 to13 the13 main13 channel13 through13 shunts13 of13 width13 11988211988213 and13 length13 119871119871(black13 lines13 Fig13 S12)13 13 In13 this13 section13 we13 show13 how13 the13 protein13 dynamics13 in13 the13 array13 can13 be13 described13 as13 an13 effective13 one-shy‐dimensional13 diffusion-shy‐reaction13 equation13 13 The13 protein13 dynamics13 in13 the13 11989411989411990411990413 compartment13 is13 composed13 of13 diffusion13 flux13 of13 proteins13 from13 and13 to13 shunts13 13 119895119895 minus 1 and13 13 119895119895 13 and13 to13 the13 main13 channel13 (Fig13 S12)13 13 120597120597119901119901 = 119869119869 + 119869119869 minus

119901119901 13 13 (8)

As13 in13 previous13 section13 we13 assume13 the13 dynamics13 along13 all13 capillaries13 is13 faster13 than13 in13 the13 compartment13 hence13 we13 use13 the13 steady-shy‐state13 linear13 concentration13 gradients13 and13 Fickrsquos13 law13 to13 derive13 the13 protein13 diffusion13 flux13 13 120597120597119901119901 =

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

13 To13 determine13 11990111990113 we13 use13 Kirchhoff13 current13 conservation13 law13 at13 junction13 j-shy‐113 13

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

13 We13 now13 define13 the13 geometrical13 ratio13 120579120579 =

13 13 which13 determines13 the13 diffusion13 flux13 through13 the13 shunt13 13

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

13 At13 the13 limit13 of13 very13 long13 and13 thin13 shunt13 120579120579 ≪ 1 the13 flux13 through13 the13 shunt13 is13 negligible13 and13 the13 concentration13 at13 the13 junction13 119895119895 minus 1 is13 the13 average13 of13 the13 two13 adjacent13 compartments13 At13 the13 limit13 of13 very13 short13 and13 wide13 shunt13 120579120579 ≫ 113 the13 diffusion13 between13 compartments13 is13 negligible13 compared13 with13 diffusion13 out13 to13 the13 main13 channel13 through13 the13 shunt13 and13 119901119901 rarr 013 13 13 Using13 eq13 (10)13 and13 13 (13)13 we13 find13 13

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 We13 define13 two13 time13 scales13 120591120591 =

13 120591120591 =

13 The13 effective13 lifetime13 13 120591120591 as13 in13 an13 isolated13 compartment13 and13 120591120591 13 is13 the13 diffusion13 time13 between13 two13 compartments13 in13 a13 system13 with13 no13 shunt13 13 120597120597119901119901 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

13 We13 obtained13 a13 discrete13 1D13 diffusion13 equation13 with13 an13 effective13 diffusion13 constant13 119863119863 and13 an13 effective13 lifetime13 12059112059113 13

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

13 with13 a13 geometrical13 ratio13 120579120579 =

13 13 At13 the13 limit13 of13 a13 system13 with13 no13

shunt 120579120579 rarr 0 13 we13 find13 119863119863 = 119889119889120591120591 13 and13 120591120591 = 120591120591 13 as13 previously13 published1313 In13 the13 opposite13 limit13 120579120579 ≫ 113 the13 diffusion13 between13 compartments13 is13 small13 119863119863~

rarr 013

and13 the13 lifetime13 in13 the13 compartment13 has13 a13 finite13 correction13 120591120591 = 120591120591(1+ 4120579120579)13 We13 conclude13 that13 the13 shunt13 enables13 control13 over13 effective13 diffusion13 in13 the13 system13 with13 small13 effects13 over13 protein13 lifetime13 13 13 For13 example13 we13 calculate13 the13 effect13 of13 the13 shunt13 on13 the13 lifetime13 of13 the13 array13 shown13 in13 Fig13 113 13

No13 shunt13 With13 shunt13 119871119871 = 150microμm13 119871119871 = 400microμm13

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119871119871 = 150microμm13 119871119871 = 400microμm13 119871119871 = 40microμm13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120591120591 asymp 08 hr13 120591120591 asymp 04 hr13 119863119863 = 0075mmhr13 119863119863 = 0021mmhr13

13 Note13 that13 in13 the13 main13 text13 we13 refer13 to13 the13 lifetime13 and13 effective13 diffusion13 using13 functions13 of13 the13 geometry13 12056712056713 and13 12056712056713 which13 are13 defined13 here13 13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

In13 the13 continuum13 limit13 119909119909 = 119871119871 sdot 11989411989413 119901119901 rarr 119901119901(119909119909)13 we13 obtain13 a13 1D13 reaction-shy‐diffusion13 equation13 13 120597120597119901119901 = 119863119863120597120597119901119901 minus

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 13 Here13 119891119891(119901119901)13 is13 a13 programmable13 cellular13 response13 function13 13

13 813

For13 an13 array13 with13 a13 localized13 single13 DNA13 source13 the13 steady13 state13 protein13 concentration13 is13 an13 exponential13 decaying13 profile13 13 119901119901 119909119909 = 119901119901119890119890

13 (23) 120582120582 = 119863119863119863119863 (24) 13 The13 theoretical13 decay13 length13 for13 our13 system13 (119863119863 = 0021mmhr13 13 120591120591 = 04hr)13 is13 120582120582 asymp 01mm = 119871119871413 and13 the13 measured13 decay13 length13 (Fig13 1BS13)13 is13 120582120582 asymp 04mm =11987111987113 The13 discrepancy13 results13 from13 (i)13 The13 exponential13 solution13 only13 holds13 for13 120582120582 ≫ 11987111987113 since13 the13 concentration13 profile13 between13 compartments13 is13 linear13 (ii)13 The13 measurement13 was13 obtained13 for13 a13 DNA13 source13 in13 the13 first13 compartment13 with13 only13 one13 shunt13 connection13 and13 the13 theory13 is13 derived13 for13 an13 infinite13 array13 13

Inhibitor-shy‐Autocatalytic13 Bistable13 Network13 Analysis13 13 Network13 dynamics13 13 The13 bistable13 gene13 circuit13 (Fig13 1A13 inset13 Fig13 S313 Table13 S2-shy‐S3)13 was13 constructed13 using13 an13 autocatalytic13 element 119875119875 minus 120590120590 13 119953119953 13 and13 its13 inhibitor13 119875119875 minus 11986011986012059012059013 119920119920 2541ndash4413 The13 anti-shy‐sigma13 protein13 binds13 the13 sigma13 transcription13 factor13 with13 high13

affinity13 and13 forms13 a13 complex13 119914119914 13 and13 thus13 sequesters13 the13 binding13 of13 sigma-shy‐2813 to13 its13 prompter13 inhibiting13 the13 positive13 feedback13 The13 sigma13 factor13 120590120590 13 was13 endogenously13 present13 in13 the13 cell-shy‐free13 extract13 (CFE)36373913 leading13 to13 constitutive13 expression13 of13 the13 inhibitor13 as13 well13 as13 a13 leak13 from13 the13 activator13 promoter13 11987511987513 We13 model13 the13 network13 dynamics13 in13 the13 following13 equations13 13

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 The13 parameters13 are13 11989611989613 synthesis13 rate13 of13 activator 119896119896 13 Synthesis13 rates13 of13 inhibitor13 120598120598 13 synthesis13 leak13 of13 the13 autocatalytic13 construct13 119896119896 Michaelis-shy‐Menten13 (MM)13 constant13 for13 binding13 of13 the13 activator13 to13 its13 promoter13 11987511987513 12059112059113 Lifetime13 of13 proteins13 in13 the13 compartment13 11989611989613 binding13 rate13 of13 activator13 and13 inhibitor13 11989611989613 disassociation13 rate13 of13 activator13 and13 inhibitor13 In13 eq13 (25)13 the13 first13 term13 is13 the13 autocatalytic13 expression13 and13 leak13 the13 second13 term13 is13 protein13 turnover13 and13 last13 two13 terms13 are13 binding13 and13 unbinding13 to13 inhibitor13 I13 In13 eq13 (26)13 the13 first13 term13 is13 the13 constitutive13 expression13 of13 the13 inhibitor13 the13 second13 term13 is13 inhibitor13 turnover13 and13 the13 last13 two13 terms13 as13 in13 eq13 (25)13 In13 eq13 (27)13 the13 first13 term13 is13 the13 complex13 turnover13 and13 the13 last13 two13 terms13 as13 in13 eq13 (25)13 13 13

13 913

In13 our13 analysis13 we13 neglect13 mRNA13 dynamics13 and13 assume13 mRNA13 is13 localized13 in13 the13 DNA13 compartment13 The13 mRNA13 is13 biochemically13 degraded13 in13 the13 CFE13 within13 120591120591 asymp 5min 13 and13 diffuses13 slowly13 compared13 to13 the13 protein13 119863119863 lt 10microμms (0036mmhr) 13 Thus13 we13 estimate13 mRNA13 must13 be13 localized13 to13 a13 distance13 119897119897 = 119863119863120591120591 asymp 50microμm13 of13 the13 DNA13 which13 is13 smaller13 than13 compartment13 size13 The13 mRNA13 transcription13 time13 provides13 an13 additional13 delay13 in13 the13 synthesis13 kinetics13 that13 may13 be13 important13 for13 understanding13 oscillatory13 dynamics13 13 13 We13 consider13 the13 scenario13 of13 front13 propagation13 in13 the13 array13 and13 make13 two13 simplifying13 assumptions13 113 The13 Inhibitor13 construct13 is13 constitutively13 expressing13 119868119868 13 in13 all13 of13 the13 compartments13 and13 reaches13 a13 steady-shy‐state13 concentration13 119868119868 = 119896119896120591120591 asymp 1microμM 13 at13 about13 1hr13 before13 the13 activator13 119901119901 front13 wave13 initiates13 at13 119905119905 gt 3hr13 this13 is13 for13 120591120591 asymp 04hr and13 119896119896 = 2minus 25microμMhr 13 (Table13 S4)13 Thus13 we13 assume13 the13 total13 concentration13 of13 inhibitor13 is13 constant13 during13 the13 experiment13 13 120597120597119868119868 = 120597120597(119868119868 + 119862119862) = 013 (28) 13 Removing13 this13 assumption13 will13 not13 affect13 the13 phase13 diagram13 but13 the13 propagation13 kinetics13 will13 have13 two13 coupled13 equations13 for13 the13 activator13 and13 inhibitor13 13 13 13 13 213 The13 kinetics13 of13 the13 complex13 concentration13 11986211986213 is13 dominated13 by13 binding13 and13 unbinding13 of13 inhibitor13 and13 activator13 which13 occurs13 at13 fast13 time13 scales13 (119896119896119868119868) asymp2min13 (119896119896 = 7 nMsTable13 S4)13 compared13 with13 the13 accumulation13 of13 activator13 levels13 in13 the13 compartment13 which13 occurs13 over13 120591120591 asymp 04hr13 We13 thus13 assume13 that13 the13 complex13 119862119862 13 is13 always13 at13 steady-shy‐state13 with13 respect13 to13 the13 free13 activator13 concentration13 13 120597120597119862119862 = 013 (29) 13 and13 using13 eq13 (27)13 13 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 minus

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

where13 we13 defined13 the13 effective13 complex13 disassociation13 constant13 119896119896 =

13 Use13 equations13 (31)13 and13 13 (28)13 in13 (26)13 13 120597120597119868119868 = 013 (32) 119896119896 minus

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

13 Using13 equations13 (34)13 and13 (31)13 back13 in13 (25)13 we13 find13 an13 effective13 equation13 for13 the13 activator13 dynamics13 13 120597120597119901119901 = 119896119896 sdot [120598120598 +

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

13 The13 first13 term13 is13 the13 synthesis13 leak13 the13 second13 term13 is13 the13 positive13 feedback13 the13 third13 term13 is13 the13 protein13 turn13 over13 and13 the13 last13 term13 is13 inhibition13 The13 synthesis13 rate13 ratio13 120572120572 =

13 is13 proportional13 to13 the13 DNA13 ratio13 in13 each13 compartment13 120572120572 prop

13 Network13 dynamics13 with13 competition13 over13 RNA13 polymerase13 Previous13 work13 have13 shown13 that13 for13 a13 network13 of13 reactions13 where13 an13 enzyme13 (RNA13 polymerase13 119877119877)13 is13 shared13 by13 more13 than13 one13 substrate13 (sigma13 factors13 120590120590)13 the13 different13 substrates13 competitively13 inhibit13 each13 other293713 The13 Michaelis-shy‐Menten13 binding13 equilibrium13 then13 becomes13 13

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 with13 119896119896 13 the13 Michaelis-shy‐Menten13 constant13 for13 binding13 to13 the13 enzyme13 The13 corresponding13 synthesis13 rates13 of13 protein13 119909119909 13 under13 control13 of13 sigma13 factor13 120590120590 13 is13 13 13 120597120597119909119909 = 119881119881[119877119877120590120590]13 (37) 13 Here13 119881119881 13 is13 the13 synthesis13 rate13 constant13 In13 the13 cell-shy‐free13 system13 used13 in13 this13 work13 the13 transcription13 factor13 concentrations13 can13 exceed13 the13 RNA13 Polymerase13 concentration13 119877119877 asymp 100nM3913 and13 therefore13 different13 transcription13 factors13 can13 competitively13 inhibit13 each13 other13 The13 endogenous13 concentration13 transcription13 factor13 12059012059013 in13 the13 reaction13 is13 constant13 120590120590 asymp 30nM3713 while13 12059012059013 is13 expressed13 from13 the13 autocatalytic13 construct13 We13 thus13 use13 eq13 (37)13 to13 write13 MM13 equations13 for13 competitive13 binding13 of13 12059012059013 (activator13 -shy‐A)13 and13 12059012059013 to13 the13 11987711987713 13 13 13 Without13 competition13 With13 competition13 13

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

Here13 we13 defined13 119896119896 = 11988111988111987711987713 and13 119896119896 =

+ 11989611989613 119896119896$ =()

We13 thus13 get13 a13 modified13 equation13 for13 the13 activator13 p13 13

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

13 with13 the13 main13 difference13 from13 eq13 (35)13 being13 the13 inhibition13 term13 which13 vanishes13 for13 high13 activator13 concentration13 due13 to13 competition13 over13 RNA13 polymerase13 13 The13 effective13 reaction-shy‐diffusion13 equation13 for13 the13 activator13 is13 thus13 13

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 The13 resulting13 response13 function13 119891119891(119901119901)13 is13 a13 minimal13 model13 for13 the13 gene13 network13 dynamics13 and13 shows13 both13 monostable13 and13 bistable13 regimes13 in13 the13 phase13 plane13 of13 gene13 ratio13 12057212057213 and13 lifetime13 13 12059112059113 which13 are13 consistent13 with13 the13 experiment13 (Fig13 2A13 S6)13 13

The13 propagator13 velocity13 13 Traveling13 fronts13 and13 waves13 emerge13 in13 excitable13 non-shy‐linear13 systems13 and13 are13 thus13 expected13 in13 the13 DNA13 compartment13 array13 with13 a13 reaction13 diffusion13 equation13 120597120597119901119901 = 119863119863120571120571119901119901 + 119892119892 119901119901 13 and13 an13 autocatalytic13 nonlinear13 function13 119892119892(119901119901) 13 Traveling13 fronts13 change13 the13 state13 of13 the13 system13 from13 its13 initial13 state13 119901119901 13 to13 a13 state13 119901119901 13 An13 analytically13 solvable13 model13 is13 the13 Fisher-shy‐KPP13 equation174613 13 in13 which13 the13 state13 119901119901 13 is13 an13 unstable13 fixed13 point13 and13 state13 11990111990113 is13 stable13 fixed13 point13 13 13 119892119892 119901119901 asymp 119896119896(119901119901 minus 119901119901)+ 119900119900(119901119901)13 (41) 119892119892 119901119901 = 119892119892 119901119901 = 0 119896119896 = 120597120597119892119892 119901119901 gt 0120597120597119892119892 119901119901 lt 0 13 In13 this13 model13 a13 linear13 analysis13 is13 sufficient13 to13 deduce13 a13 constraint13 on13 the13 front13 velocity174613 13 13 119907119907 ge 2 119896119896119896119896 (42) 13 where13 119896119896 = 120597120597119892119892(119901119901)13 is13 the13 rate13 constant13 of13 the13 autocatalytic13 process13 and13 11986311986313 is13 the13 diffusion13 coefficient13 Indeed13 this13 condition13 was13 experimentally13 observed13 in13 BZ13 reactions1613 13 as13 well13 as13 in13 more13 recent13 DNA13 autocatalytic13 reactions1413 13 Another13 class13 of13 models13 which13 exhibit13 front13 propagation13 are13 bistable13 systems18474813 in13 which13 both13 the13 initial13 and13 final13 states13 of13 the13 system13 are13 stable13 fixed13 points13 and13 an13 additional13 unstable13 fixed13 point13 119901119901 lt 119901119901 lt 119901119901 13 13 13 119892119892 119901119901 = 119892119892 119901119901 = 119892119892 119901119901 = 0 (43) 120597120597119892119892 119901119901 120597120597119892119892 119901119901 lt 0

13 1213

13 A13 bistable13 system13 is13 more13 robust13 to13 external13 perturbations13 and13 thus13 offers13 an13 experimental13 advantage13 for13 studying13 front13 propagation13 At13 a13 higher13 level13 of13 complexity13 appear13 the13 FitzHugh-shy‐Nagumo13 (FN)13 and13 Hodgkin-shy‐Huxley13 (HH)13 type13 models13 which13 are13 characterized13 with13 traveling13 pulses13 solutions13 In13 bistable13 systems13 FN13 and13 HH13 systems13 linear13 analysis13 around13 the13 initial13 state13 11990111990113 does13 not13 provide13 information13 about13 the13 front13 velocity13 but13 there13 are13 other13 velocity13 constraints13 that13 include13 integration13 over13 the13 entire13 function13 119892119892(119901119901)4913 13 13 In13 addition13 we13 expect13 a13 scaling13 relation13 based13 on13 dimensional13 analysis5013 13 119907119907 prop 119896119896119896119896 (44) 13 Here13 11989611989613 is13 a13 suprathreshold13 excitation13 rate13 which13 may13 be13 a13 complex13 function13 of13 the13 systemrsquos13 kinetic13 parameters13 and13 can13 be13 extracted13 experimentally1613 In13 our13 system13 the13 effective13 diffusion13 coefficient13 is13 119863119863 = 0021mmhr 13 and13 the13 measured13 growth13 rate13 of13 the13 autocatalytic13 process13 is13 119896119896 = 54ℎ119903119903(Fig13 S5)13 Thus13 the13 predicted13 velocity13 is13 033mmhr 13 close13 to13 measured13 velocities13 119907119907 = 02minus062mmhr13 13

Flow13 in13 the13 compartment13 array13 The13 capillaries13 connecting13 the13 1D13 array13 were13 parallel13 to13 the13 flow13 channel13 hence13 a13 pressure13 drop13 was13 maintained13 along13 the13 array13 But13 flow13 in13 the13 array13 was13 minimized13 because13 of13 its13 high13 hydrodynamic13 resistivity13 compared13 to13 that13 of13 the13 flow13 channel13 The13 shallow13 ℎ asymp 2microμm 13 and13 thin13 119882119882 = 10microμm 13 capillaries13 were13 whereas13 the13 main13 flow13 channel13 was13 deep13 Hasymp 50microμm13 and13 wide13 119882119882 = 900microμm13 The13 flow13 rate13 in13 the13 main13 flow13 channel13 was13 set13 to13 119876119876 = 02microμlmin13 yielding13 a13 mean13 velocity13 in13 the13 main13 channel13 of13 119907119907 = 180mmhr13 The13 ratio13 between13 the13 flow13 velocity13 in13 the13 capillaries13 and13 the13 main13 channel13 is13 estimated13 by13 13 119907119907$amp

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

13 Here13 we13 used13 the13 Poiseuille13 equation13 for13 hydrodynamic13 resistance13 in13 a13 rectangular13 cross13 section 119877119877 =

13 with13 CFE13 viscosity13 is13 12057812057813 We13 neglected13 the13

dimensions13 of13 the13 compartment13 and13 treated13 it13 as13 a13 point13 along13 the13 capillary13 array13 Thus13 the13 velocity13 in13 the13 capillary13 connecting13 the13 compartments13 was 119907119907$amp = 0036mmhr13 Finally13 we13 compare13 the13 protein13 diffusion13 time13 120591120591 13 between13 compartments13 of13 length13 119871119871 = 04mm13 to13 the13 flow13 time13 120591120591$ 13 13 13 120591120591$ =

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 concluding13 that13 indeed13 transport13 by13 diffusion13 was13 dominant13 120591120591 ≪ 120591120591$ 13 13

13 1313

Variation13 in13 DNA13 Ratio13 and13 compartment13 lifetime13 13 To13 determine13 the13 variation13 in13 gene13 ratio13 between13 compartments13 we13 analyzed13 the13 variation13 in13 total13 DNA13 density13 We13 measured13 the13 fluorescent13 intensity13 of13 the13 end13 labeled13 DNA13 in13 a13 series13 of13 compartments13 All13 three13 DNA13 segments13 were13 end-shy‐labeled13 with13 a13 red13 fluorophore13 (647nm)13 the13 inhibitor13 the13 autocatalytic13 constructs13 and13 the13 reporter13 The13 variation13 was13 measured13 for13 19613 DNA13 compartments13 in13 1413 sets13 of13 1413 different13 concentrations13 normalized13 to13 their13 mean13 fluorescence13 the13 mean13 variation13 was13 found13 to13 be13 120549120549120549120549 = 12plusmn 313 (Fig13 S7a)13 13 13 13 The13 lifetime13 in13 the13 compartment13 is13 set13 by13 the13 geometrical13 parameters13 which13 are13 patterned13 by13 lithography13 120591120591 prop 11987711987711987111987111988211988213 where13 119877119877 is13 the13 compartment13 radius13 119871119871 is13 the13 capillary13 length13 and13 11988211988213 is13 the13 capillary13 width13 The13 variation13 13 due13 to13 local13 differences13 in13 fabrication13 is13 estimated13 from13 image13 analysis13 of13 geometrical13 parameters13 The13 ratio13 119877119877119871119871119882119882 13 was13 measured13 for13 21413 compartments13 in13 two13 separate13 devices13 The13 variation13 in13 lifetime13 was13 found13 to13 be13 120549120549120549120549 = 8(13 Fig13 S713 b)13 13 13 13

Analysis13 of13 the13 propagation13 velocity13 For13 each13 compartment13 in13 an13 array13 with13 a13 given13 gene13 ratio13 12057212057213 a13 time13 derivative13 of13 the13 protein13 concentration13 was13 calculated13 13

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 where13 119901119901 13 is13 the13 protein13 level13 at13 frame13 11989411989413 and13 12057512057512057512057513 is13 the13 time13 difference13 between13 measurements13 (Fig13 S14)13 The13 time13 derivative13 dynamics13 at13 each13 compartment13 is13 characterized13 by13 a13 peak13 at13 the13 time13 of13 arrival13 of13 the13 propagating13 front13 Thus13 we13 set13 the13 compartment13 onset13 time13 as13 the13 time13 at13 which13 the13 derivative13 reached13 its13 maximal13 value13 The13 velocity13 and13 its13 error13 were13 calculated13 from13 the13 slope13 of13 the13 compartment13 as13 a13 function13 of13 its13 onset13 time13 119909119909(120591120591)13 (Fig13 S14b)13 13 13

13 1413

Bibliography13

4613 Kolmogorov13 A13 Petrovsky13 L13 amp13 Piskunov13 N13 An13 investigation13 of13 the13 diffusion13 equation13 combined13 with13 an13 increase13 in13 mass13 and13 its13 application13 to13 a13 biological13 problem13 Bull13 Uni13 Moscow13 Ser13 Int13 A13 113 1ndash2613 (1937)13

4713 Marsden13 S13 Wiggins13 L13 amp13 Glass13 L13 Interdisciplinary13 Applied13 Mathematics13 Mathematical13 physiology13 (1993)13

4813 Volpert13 V13 amp13 Petrovskii13 S13 Reaction-shy‐diffusion13 waves13 in13 biology13 Phys13 Life13 Rev13 613 267ndash31013 (2009)13

4913 Benguria13 R13 D13 amp13 Depassier13 M13 C13 Speed13 of13 Fronts13 of13 the13 Reaction-shy‐Diffusion13 Equation13 Phys13 Rev13 Lett13 7713 1171ndash117313 (1996)13

5013 LutherRZ13 Investigation13 and13 analysis13 of13 chemical13 waves13 Elektrochem13 1213 59613 (1906)13

5113 Showalter13 K13 amp13 Tyson13 J13 J13 Lutherrsquos13 190613 discovery13 and13 analysis13 of13 chemical13 waves13 J13 Chem13 Educ13 6413 74213 (1987)13

5213 Tomchik13 K13 J13 amp13 Devreotes13 P13 N13 Adenosine13 3rsquo5-shy‐monophosphate13 waves13 in13 Dictyostelium13 discoideum13 a13 demonstration13 by13 isotope13 dilution-shy‐-shy‐fluorography13 Science13 21213 443ndash613 (1981)13

5313 Jaffe13 L13 F13 Organization13 of13 early13 development13 by13 calcium13 patterns13 Bioessays13 2113 657ndash6713 (1999)13

5413 Yu13 S13 R13 et13 al13 Fgf813 morphogen13 gradient13 forms13 by13 a13 source-shy‐sink13 mechanism13 with13 freely13 diffusing13 molecules13 Nature13 46113 533ndash613 (2009)13

5513 Muumlller13 P13 Rogers13 K13 W13 Yu13 S13 R13 Brand13 M13 amp13 Schier13 A13 F13 Morphogen13 transport13 Development13 14013 1621ndash3813 (2013)13

5613 Maeda13 H13 Fujita13 N13 amp13 Ishihama13 A13 Competition13 among13 seven13 Escherichia13 coli13 sigma13 subunits13 relative13 binding13 affinities13 to13 the13 core13 RNA13 polymerase13 Nucleic13 Acids13 Res13 2813 3497ndash50313 (2000)13

5713 Chadsey13 M13 S13 Karlinsey13 J13 E13 amp13 Hughes13 K13 T13 The13 flagellar13 anti-shy‐sigma13 factor13 FlgM13 actively13 dissociates13 Salmonella13 typhimurium13 sigma2813 RNA13 polymerase13 holoenzyme13 Genes13 Dev13 1213 3123ndash3613 (1998)13 13

13 1513

Figures13

Main13 Text13

Fig13 S113 Microfluidic13 device13 and13 DNA13 compartment13 array13 13 (a)13 An13 array13 of13 circular13 compartments13 carved13 in13 silicon13 (ℎ~2microμm)13 and13 connected13 through13 small13 capillaries13 to13 a13 flow13 channel13 (119867119867~50microμm)13 Each13 compartment13 is13 patterned13 with13 a13 DNA13 brush13 The13 transcriptiontranslation13 cell13 extract13 enters13 by13 diffusion13 into13 the13 thin13 capillaries13 from13 the13 flow13 channel13 (b)13 Image13 of13 end13 labeled13 DNA13 brush13 (white13 square13 red13 fluorophore13 647nm)13 Compartment13 dimensions13 119877119877 = 50microμm 119871119871 = 150microμm 119871119871 = 400microμm 119871119871 = 40microμm 13 and13 119882119882 = 12microμm 13 In13 the13 compartments13 proteins13 are13 expressed13 from13 the13 brush13 and13 diffuse13 through13 the13 capillaries13 13

13 1613

Fig13 S213 Linear13 concentration13 profile13 along13 the13 capillary13 in13 a13 single13 compartment13 (a)13 Fluorescent13 image13 of13 a13 single13 compartment13 patterned13 with13 an13 unregulated13 gene13 constitutively13 expressing13 GFP13 Compartment13 dimensions13 radius13 119877119877 = 50microμm13 capillary13 length13 119871119871 = 150microμm13 capillary13 width13 119882119882 = 12microμm13 and13 height13 ℎ = 25microμm13 Scale13 bar13 50microμm13 (b)13 GFP13 concentration13 profile13 for13 an13 unregulated13 construct13 along13 the13 compartment13 and13 capillary13 13 The13 profile13 is13 homogenous13 in13 the13 compartment13 and13 decays13 linearly13 from13 a13 maximal13 value13 in13 the13 compartment13 to13 zero13 value13 at13 the13 flow13 channel13 (c)13 Protein13 expression13 kinetics13 in13 the13 compartment13 reaching13 a13 steady-shy‐state13 level13 and13 running13 for13 813 hours13 13 13

13 1713

13 13 13 13 13

Fig13 S313 Bistable13 gene13 circuit13 network13 scheme13 13 (a)13 Network13 scheme13 of13 an13 Inhibitor-shy‐Autocatalytic13 construct13 with13 a13 GFP13 reporter13 (b)13 An13 autocatalytic13 construct13 with13 transcription13 factor13 12059012059013 activating13 its13 own13 promoter13 and13 activating13 a13 reporter13 construct13 synthesizing13 GFP13 The13 positive13 feedback13 of13 the13 autocatalytic13 construct13 is13 inhibited13 by13 11986011986012059012059013 protein13 binding13 to13 the13 13 12059012059013 preventing13 it13 from13 binding13 to13 the13 11987511987513 promoter13

13 1813

Fig13 S413 The13 bistable13 protein13 kinetics13 (a)13 A13 reporter13 gene13 with13 inhibitor13 concentration13 of13 100nM13 without13 an13 autocatalytic13 element13 responding13 to13 an13 external13 addition13 of13 12059012059013 transcription13 factor13 (tlt35hr)13 and13 shutting13 down13 expression13 when13 external13 signal13 is13 washed13 out13 of13 the13 system13 (tgt35hr)13 13 (green)13 reporter13 gene13 with13 no13 external13 addition13 of13 13 120590120590 13 transcription13 factor(Red)13 Measurements13 conducted13 in13 two13 different13 experiments13 (b)13 A13 bistable13 construct13 in13 a13 single13 compartment13 responding13 to13 the13 external13 perturbation13 of13 12059012059013 transcription13 factor13 13 The13 compartment13 switches13 to13 high13 expression13 levels13 119901119901 13 as13 a13 result13 of13 the13 perturbation13 In13 the13 absence13 of13 the13 perturbation13 low13 expression13 levels13 11990111990113 is13 maintained13 The13 bistable13 construct13 was13 taken13 with13 120572120572 = 1613 120591120591 = 09hr13 13 13 13

13 1913

Fig13 S513 Growth13 rate13 of13 the13 autocatalytic13 process13 11994811994813 Protein13 derivative13 in13 [AU sdot hr]13 as13 a13 function13 of13 protein13 concentration13 in13 11986011986011986011986013 13 Black13 line13 is13 a13 linear13 fit13 with13 a13 slope13 of13 119896119896 = (54plusmn 1)hr13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2013

Fig13 S613 Phase13 diagram13 with13 and13 without13 competition13 over13 RNAP13 (a)13 Network13 scheme13 without13 competition13 over13 RNAP13 and13 with13 competition13 (b)13 Phase13 diagram13 of13 the13 monostable13 (White)13 and13 bistable13 regions13 without13 competition13 (Dark13 Gray)13 with13 competition13 (Bright13 gray)13 and13 a13 region13 corresponding13 to13 theoretical13 negative13 velocity13 (Blue)13

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

Fig13 S713 Variation13 in13 DNA13 ratio13 12063012063013 and13 compartment13 lifetime13 12064912064913 (a)13 Distribution13 of13 19613 measurements13 of13 fluorescence13 end13 labeled13 DNA13 (647nm)13 1413 different13 gene13 ratios13 normalized13 to13 their13 mean13 fluorescent13 value13 in13 1413 different13 compartments13 Red13 line13 is13 a13 fit13 to13 a13 Gaussian13 with13 an13 expected13 value13 120583120583 = 099 13 of normalized fluorescent DNA and13 variance13 120590120590 = 001613 normalized fluorescent DNA13 compatible13 to13 a13 variation13 of13 12plusmn 3 13 (b)13 Distribution13 of13 21413 normalized13 geometrically13 calculated13 lifetimes 120591120591 prop

calculated13 from13 image13 analysis13 of13 dimensions13 of13 compartments13 Variation13 is13 due13 fabrication13 differences13 Data13 is13 taken13 for13 two13 separate13 chips13 Variation13 in13 data13 is13 120549120549120549120549 = 1013 13 13

13 2213

Fig13 S813 Propagation13 velocity13 for13 different13 experiments13 13 (a)13 DNA13 brush13 patterned13 in13 two13 array13 geometries13 Both13 have13 effective13 lifetime13 of13 120591120591~04hr 13 (b)13 Propagation13 velocity13 in13 [compartmenthr]13 as13 measured13 as13 a13 function13 of13 gene13 ratio13 Different13 colors13 indicate13 different13 experiments13 Measurements13 are13 taken13 both13 from13 device13 113 (circles)13 and13 device13 213 (triangles)13 13

13 2313

Fig13 S913 Divergence13 of13 onset13 times13 near13 the13 transition13 13 Onset13 time13 120591120591 of13 the13 bistable13 gene13 circuit13 in13 single13 compartments13 as13 a13 function13 of13 (a)13 gene13 ratio13 120572120572 =

13 at13 four13 different13 lifetime13 values13 12059112059113 each13 corresponding13 to13

a13 different13 critical13 value13 of13 gene13 ratio13 120572120572 13 Dashed13 lines13 are13 fits13 to13 power13 laws13 120591120591 = 120591120591 120572120572 minus 120572120572

(b)13 Protein13 lifetime13 in13 the13 compartment13 12059112059113 at13 four13 different13 gene13 ratios13 Data13 points13 that13 do13 not13 fit13 the13 line13 include13 onset13 times13 that13 are13 larger13 than13 the13 measurement13 time13 and13 therefore13 relate13 only13 to13 the13 lower13 limit13 of13 the13 measurement13 Each13 point13 is13 an13 average13 over13 913 measurements13 Solid13 lines13 are13 fits13 to13 power13 law13 120591120591 = 120591120591 120591120591 minus 120591120591

(c)13 Three13 13 points13 120572120572 120591120591 13 from13 the13 fit13 to13 the13 lines13 in13 (a)13 plotted13 on13 the13 phase13 diagram13 13

13 13 13

13 2413

Fig13 S1013 Onset13 time13 in13 single13 compartments13 for13 different13 gene13 ratios13 and13 lifetimes13 approaching13 the13 transition13 to13 the13 bistable13 regime13 13 (a)13 Space13 time13 plots13 of13 single13 compartments13 patterned13 with13 the13 bistable13 gene13 circuit13 at13 different13 gene13 ratios13 120572120572 = 03minus 078 13 and13 lifetimes13 120591120591 = 03minus 093hr 13 Experiment13 was13 conducted13 by13 varying13 the13 length13 of13 the13 capillaries13 119871119871 = 100minus300microμm 13 Each13 plot13 consists13 of13 913 identical13 single13 compartments13 High13 (Low)13 expression13 state13 119901119901 13 ( 119901119901) 13 marked13 in13 green13 (blue)13 13 Shades13 of13 green13 correspond13 to13 different13 levels13 of13 expression13 for13 by13 different13 concentration13 of13 sigma-shy‐2813 as13 noted13 in13 the13 color13 bar13 (b)13 Space13 time13 plot13 for13 an13 unregulated13 construct13 expressing13 GFP13 under13 a13 119875119875 13 promoter13 at13 lifetime13 120591120591 = 093hr 13 Plot13 consists13 of13 713 identical13 single13 compartments13 Variation13 between13 expression13 times13 is13 about13 513

13 2513

Fig13 S1113 Probability13 to13 switch13 into13 an13 active13 state13 near13 the13 transition13 Number13 of13 compartments13 with13 high13 expression13 levels13 divided13 by13 number13 of13 compartment13 in13 the13 experiment13 at13 a13 given13 lifetime13 12059112059113 Nine13 measurements13 were13 conducted13 for13 every13 12059112059113 All13 measurements13 are13 for13 gene13 ratio13 120572120572 = 07813 13 13

13 2613

SI13 Figures13

Fig13 S1213 DNA13 compartment13 scheme13 Illustration13 of13 compartments13 array13 interconnected13 by13 capillaries13 with13 a13 short13 shunt13 to13 the13 main13 flow13 channel13 Synthesized13 protein13 diffuses13 along13 the13 x-shy‐axis13 to13 adjacent13 compartments13 and13 along13 the13 y-shy‐axis13 to13 the13 main13 channel13 to13 be13 evacuated13 from13 the13 array13 13

13 2713

Fig13 S1313 Single-shy‐compartment13 exponentially13 decaying13 profile13 and13 propagating13 front13 in13 array13 (a)13 Image13 of13 GFP13 expression13 profile13 along13 the13 DNA13 array13 generated13 from13 a13 source13 is13 located13 in13 the13 leftmost13 compartment13 The13 GFP13 intensity13 is13 homogenous13 within13 a13 compartment13 decays13 between13 two13 neighboring13 compartments13 image13 taken13 at13 119905119905 = 4hr13 Second13 image13 GFP13 expression13 profile13 propagating13 along13 the13 array13 at13 119905119905 = 6hr13 (b)13 Protein13 profile13 along13 the13 array13 for13 a13 single13 DNA13 source13 (Blue)13 and13 propagator13 network13 (Red)13 13 13 13

13 2813

Fig13 S1413 Time13 derivative13 of13 protein13 concentration13 and13 velocity13 measurements13 (a)13 DNA13 Brushes13 in13 an13 array13 of13 1513 connected13 compartments13 the13 leftmost13 compartment13 patterned13 with13 a13 low-shy‐density13 starter13 amount13 of13 activator13 and13 compartments13 2-shy‐1513 patterned13 with13 the13 bistable13 gene13 circuit13 Measurement13 are13 plotted13 for13 lifetime13 120591120591 = 04ℎ11990311990313 and13 varying13 gene13 ratio13 120572120572 = 11625513 (b)13 Plots13 of13 time13 derivatives13 of13 protein13 synthesis13 kinetics13 in13 compartments13 (c)13 Distance13 from13 origin13 as13 a13 function13 of13 compartment13 onset13 time13 with13 propagation13 velocity13 evaluated13 from13 the13 slope13 (d)13 Space-shy‐Time13 plot13 of13 propagator13 Low13 (High)13 expression13 levels13 are13 marked13 in13 Blue13 (Green)13 13 13 13 13

13 2913

13 13 13

Table13 S113 Luther13 scaling13 ndash13 propagation13 velocities13 diffusion13 coefficients13 and13 reaction13 rates13 in13 different13 systems13 13 13 13 13

Model13 System13 Signal13 Velocity13 [mmhr]13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

Neurons13 (Squid13 Giant13 Axon)5113

Action13 Potentials13 13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Heart13 (Myocytes13 guinea13 pig)2813

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

Belousov13 Zhabotinsky13 reaction1613

Chemical13 weves13 13

14413 13

72013 13

7213 13

Dictyestilum28525

313 cAMP13 Waves13 18

2113 13 13

413 13 13

Xenophus13 1113 Mitosis13 Waves13 3613 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

In13 vitro13 enzymatic13 catalytic13 reaction1413

DNA13 3613 13 46813 0313 1113 13

DNA13 compartments13 (present13 work)13

Gene13 expression13

06213 5413 02113 03313

Somitogenesis13 (Zebra13 fish13 values13 taken13 from13 FGF8)26545513

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 13 13 Promoter13 13 Description13 Reference13 P7013 Lambda13 phage13 promoter13 OR2-shy‐OR1-shy‐Pr13 specific13 to13 E13 coli13

σ7013 13 3613 P2813 Promoter13 of13 the13 tar13 gene13 (E13 coli)13 specific13 to13 σ13 2813 3713 Untranslated13 region13

13 13 UTR113 The13 untranslated13 region13 containing13 the13 T713 g1013 leader13 sequence13 for13 highly13 efficient13 translation13 initiation13 3713

Transcription13 terminator13

13 13 T50013 Transcription13 terminator13 for13 E13 coli13 RNA13 polymerase13 13 3713 Gene13

13 13 GFP13 The13 enhanced13 green13 fluorescent13 protein13 truncated13 and13 modified13 in13 N-shy‐13 and13 C-shy‐13 termini13 3713

σ13 2813 rpoF13 (E13 coli13 σ13 28)13 3713 11986011986012059012059013 Anti-shy‐sigma13 factor13 FlgM13 (E13 coli13 Aσ13 28)13

13 4513

Table13 S213 DNA13 Modules13

13 13 Description13 Network13 113 Autocatalytic13 119875119875 minus σ13

Inhibitor13 13 119875119875 minus 11986011986012059012059013

Reporter13 13 119875119875 minus 11988911988911988911988911988911988911988911988911988911988913 Starter13 13 119875119875 minus 12059012059013

Table13 S313 DNA13 Constructs13 ndash13 Bistable13 network13 and13 starter13 13 13

13 3113

13 13 REF13 Parameter13 Value13 13 12059012059013 Synthesis13 rate13 13 119896119896 13 1minus 2microμMhr13

13 Leak13 of13 the13 11990111990113 promoter13 12059812059813 1-shy‐1013

13 Michaelis-shy‐Menten13 constant13 binding13 of13 12059012059013 to13 the13 promoter13 11987511987513

5613 11989611989613 074minus 296nM13 13

Effective13 binding13 affinity13 of13 the13 sigma13 ndash13 anti-shy‐sigma13

13 119896119896 =

119896119896 + 1120591120591119896119896

On13 and13 off13 rates13 of13 binding13 of13 119860119860119860119860 minus 12059012059013 proteins13

5713 119896119896119896119896

13 01minus 02nM13

The13 affinity13 constant13 11989911989911989911989913 is13 proportional13 to13 the13 12059012059013 concentration13 in13 the13 extract13

293713 119896119896$13 08nM13 13

Table13 S413 Values13 taken13 for13 the13 rate13 balance13 plots13 and13 the13 phase13 diagram13 13 13 number13 taken13 lower13 than13 the13 value13 in13 literature13 13 13

13 3213

Video13 Propagating13 gene13 expression13 front13 Bistable13 circuit13 dynamics13 imaged13 by13 GFP13 propagating13 along13 a13 1D13 array13 of13 DNA13 compartments13 One13 sec13 in13 the13 video13 corresponds13 to13 66min13 in13 the13 experiment13

Methods

Figure 1 Travelling gene expression front in an array of coupled DNA compartments

Figure 2 Propagation dynamics regulated by gene circuit

Figure 3 Emergent fluctuations in single compartments near the transition

References

Acknowledgements

Author contributions

Additional information

Competing financial interests

Methods

Biochip fabrication

Biocompatible photoactivable monolayer assembly

Lithography patterning for DNA assembly

DNA deposition and brush assembly

All E coli cell-free transcriptionndashtranslation reaction (CFE)

Sealing the device and flow of CFE

Imaging

Gene circuit design and assembly

References

Bistable DNA compartmenta

WDiffusion

Flow channel

001 2 3 4 5 6

Single DNA sourceeminusxλ

minus1)

10minus2

10minus22

4 6 100 102

SomitogenesisDNA compartments

Calciumwaves

Actionpotentials

Mitosiswaves

DNAcatalysers

cAMPwaves

104 106 108

minus16 minus08 00 = x minus vt (mm)ξ

08 162 4 6Time (h)

(times10

) (times

Tanh( )ξ η

v prop radickD

radickD (mm hminus1)x (mm)x (mm)

v = 062 mm hminus1

DNAstarter

Figure 1 | Travelling gene expression front in an array of coupled DNA compartments a Overlay image of expressed GFP and fluorescently labelled DNApatterns (white squares) Compartments 2ndash15 (from left) were patterned with a bistable gene circuit the first one patterned with a small amount of starterconstruct to initiate propagation Scale bar 100 microm Inset single compartment overlaid with the self-activatorinhibitor (AI) scheme using activator σ 28

and inhibitor Aσ 28 b GFP concentration profile in arbitrary units (au) along 15 compartments formed from a single DNA source in the first compartmentSolid line is an exponential fit eminusxλ with λ=0416plusmn0016mm (104plusmn 004 compartments) averaged over 4 h of expression c Expression dynamics ofthe propagator during 9 h of experiment Each graph represents the profile in a compartment according to their order in the array d A spacetime image ofGFP in the array propagating at a constant velocity of v=062 mm hminus1 (155 compartment hminus1) e Collapse of fronts in the travelling frame of referenceξ=xminusvt Protein levels are normalized to the maximal protein value in the array for each time point (Supplementary Information) Red line is a fit toTanh(ξη) with ηasymp02 mm (05 compartment) f Propagation velocity for a range of biological systems as a function of scaling parameter

radickD where D is

the diusion constant of the propagating signal and k is the typical autocatalytic rate of each system The DNA compartment array is denoted in red Exactrange appears in Supplementary Table 1

The diffusion between compartments effective protein lifetimeand nonlinear interactions dictated by the genetic circuit canall be summarized in a discrete one-dimensional reactionndashdiffusion equation

parttpi=1piminuspiτ+ f (pi)

Here f (pi) is the protein synthesis rate in response to the localprotein concentration pi and is determined by the genetic circuitThe array was designed to obtain nearest-neighbour interactionswith a diffusion length smaller than a single compartmentradicDτasymp01mmltL2 (Supplementary Equations 22ndash24) Indeed we

measured an exponentially decaying protein concentration gradientfrom a single DNA source with a decay length of λasymp04mm (onecompartment) along the array (Fig 1b)

To program signal propagation we designed a bistable gene cir-cuit comprising an activator in a self-feedback loop and its inhibitor(Fig 1a inset Supplementary Fig 3)25 The circuit dynamics at-tained one of two steady-state protein expression levels reportedusing green fluorescent protein (GFP) high pHighasymp05microm or pLow ofconcentration lower than detection limit (asymp50 nM SupplementaryFig 4) In the absence of the inhibitor a small leak initiates the pos-itive feedback and the circuit dynamics has a single steady-state so-lution pHigh The circuit is modelled accounting for the competition

over gene expressionmachinery (Supplementary Equations 25ndash40)resulting in a circuit response function f (pi) for the activatordynamics pi (Supplementary Equation 40) The bistable circuit waspatterned in all compartments except for the anterior onewhichwaspatterned with a lsquostarterrsquo gene constantly expressing the activator atconcentration lower than pHigh

During the first 35 h of expression all compartments maintainedpLow (Fig 1cd tlt35h) Signalling was initiated from the anteriorcompartment followed by diffusion of activator to the neighbouringcompartment This triggered the autocatalytic reaction switchingthe neighbouring compartment to pHigh at t = 35 h and creatinga new source of activator The cycle of synthesis and diffusionpropagated along the array at a constant velocity of v=062mmhminus1(155 compartment hminus1 with compartment unit length L2=04mmFig 1d) The expression dynamics in the array exhibited sequentialswitching to a high steady-state level with a delay of 1t asymp 07 hbetween neighbouring compartments (Fig 1c) and a gradualdecrease in protein synthesis due to intrinsic decay in cell extractactivity (Methods) In a moving frame of reference ξ=xminusvt the spatiotemporal levels collapsed to a single step-functionTanh((ξη)) with η= 02mm (half a compartment Fig 1e) Thefront velocity is consistent with the scaling vprop

radickDasymp034mmhminus1

Here kasymp54hminus1 is the growth rate of the autocatalytic reactionestimated experimentally from the initial protein synthesis rate

Compartment

i ii iii

5 10 15Compartment

5 10 15

log(p) log(p)

Monostable

pHighpHighpLow pTH

c ( )α τ

Bistable

minus1)

0001 02 03

0 2 4 6

asymp 04 hτ

α8 10

0 2 4 6α

)η (mm)η

minus1)

log(p)

00 2 4

Time (h)6 8

= 031 hτ = 046 hτ = 062 hτ

Bistable

2 4 6 8 2 4 6 8 2 4 6 8

minus c lt 0αα

) (times

12 propαminus

12 where

13 113

artificial cells

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 213

Main13 Text13 13 1513

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

Compartment

i ii iii

5 10 15Compartment

5 10 15

log(p) log(p)

Monostable

pHighpHighpLow pTH

c ( )α τ

Bistable

minus1)

0001 02 03

0 2 4 6

asymp 04 hτ

α8 10

0 2 4 6α

)η (mm)η

minus1)

log(p)

00 2 4

Time (h)6 8

= 031 hτ = 046 hτ = 062 hτ

Bistable

2 4 6 8 2 4 6 8 2 4 6 8

minus c lt 0αα

) (times

12 propαminus

12 where

13 113

artificial cells

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 213

Main13 Text13 13 1513

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

log(p)

00 2 4

Time (h)6 8

= 031 hτ = 046 hτ = 062 hτ

Bistable

2 4 6 8 2 4 6 8 2 4 6 8

minus c lt 0αα

) (times

12 propαminus

12 where

13 113

artificial cells

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 213

Main13 Text13 13 1513

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 113

artificial cells

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 213

Main13 Text13 13 1513

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 113

artificial cells

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 213

Main13 Text13 13 1513

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 113

artificial cells

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 213

Main13 Text13 13 1513

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 113

artificial cells

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 213

Main13 Text13 13 1513

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 213

Main13 Text13 13 1513

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 313

Video13 13 3213 13 13 13

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 413

119910119910119871119871 (2)

120597120597119901119901 = minus

119901119901 119905119905119871119871

119863119863119860119860119881119881 120597120597119901119901

13 (5)

119901119901120591120591 13

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 513

τ =120587120587119877119877

11986311986311988211988211987111987113

119901119901 13 13 (8)

119901119901 minus 119901119901 + ()

119901119901 minus 119901119901 minus

119901119901 13 13 (9)

120597120597119901119901 =2119863119863119882119882

120587120587119877119877119871119871119901119901 + 119901119901 minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901

0 = 119863119863119882119882ℎ119901119901 minus 119901119901

1198711198712

+119901119901 minus 119901119901

1198711198712

+0minus 119901119901119871119871119882119882119882119882

13 (11)

13 13 13

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 613

We13 find13 13 119901119901 =

12119901119901 + 119901119901

1+ 1198711198711198821198824119871119871119882119882

13 (12)

119901119901 =12119901119901 + 119901119901

1+ 1205791205794=

12(119901119901 + 119901119901) 120579120579 ≪ 1

2120579120579(119901119901 + 119901119901) 120579120579 ≫ 1

120597120597119901119901 =2119863119863119882119882

12058712058711987711987711987111987112119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901 minus

119863119863119882119882

120587120587119877119877119871119871119901119901 13

13 120591120591 =

2120591120591(12119901119901 + 119901119901

1+ 1205791205794+12119901119901 + 119901119901

1+ 1205791205794minus 2119901119901)minus

119901119901120591120591

13 (15)

120597120597119901119901 =

1120591120591

11+ 1205791205794

119901119901 + 119901119901 minus 2119901119901 minus [4120591120591

1minus1

1+ 1205791205794+1120591120591]119901119901

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 13

119863119863 =

119871119871

1205911205911

1+ 1205791205794

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 713

120591120591 = 120591120591 1+ 4120579120579(1minus

1+ 1205791205794)

rarr 013

119882119882 =119882119882 = 12microμm13 119882119882 = 013

119863119863 = 0126mmhr (35microμms)13 13

119882119882 =119882119882 = 12microμm13 119882119882 = 12microμm13

119863119863 = 0126mmhr13 13

120567120567 equiv 1+ 4120579120579(1minus1

1+ 1205791205794)

120567120567 equiv1

1+ 120579120579413

119901119901120591120591 + 119891119891 119901119901 13 (22)

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 813

119901119901 + 119868119868119896119896119896119896

11986211986213

13 120597120597119901119901 = 119896119896 sdot 120598120598 +

119901119901119901119901 + 119896119896

minus119901119901120591120591 minus 119896119896119901119901 sdot 119868119868 + 11989611989611986211986213 (25)

120597120597119868119868 = 119896119896 minus119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896119862119862 (26)

120597120597119862119862 = minus119862119862120591120591 + 119896119896119901119901 sdot 119868119868 minus 119896119896119862119862 (27)

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 913

119862119862120591120591 = 0 (30)

119862119862 =119868119868 sdot 119901119901119896119896

119868119868120591120591 minus 119896119896119901119901 sdot 119868119868 + 119896119896 sdot

119868119868 sdot 119901119901119896119896

= 0 (33)

119868119868 =

119896119896

120591120591 + (119896119896 minus119896119896119896119896

)119901119901=

119896119896120591120591

1+ 119901119901119896119896

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1013

119901119901119896119896 + 119901119901

minus119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901] (35)

[119877119877120590120590] = 119877119877120590120590

119896119896(1+ 120590120590119896119896 ) 13 (36)

13 120597120597119901119901|$= 119881119881 119877119877119901119901 13

119881119881119901119901119877119877

119896119896 + 119901119901= 119896119896

119901119901119896119896 + 119901119901

13 119881119881119901119901119877119877

119896119896 + 119901119901 + 119896119896120590120590119896119896

= 119896119896119901119901

119896119896prime+ 11990111990113

120597120597119868119868|$= 119881119881 119877119877120590120590 13 119881119881

119877119877120590120590

119896119896 + 120590120590= 119896119896 13 119881119881

119877119877120590120590

119896119896 + 120590120590 +119901119901119896119896119896119896

=119896119896

1+ 119901119901119896119896$13

+ 11989611989613 119896119896$ =()

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1113

120597120597119901119901 = 119896119896 sdot [120598120598 +119901119901

119901119901 + 119896119896primeminus

119901119901119896119896120591120591

minus 120572120572119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

] 13 (38)

120597120597119901119901 = 119863119863119901119901 + 119901119901 minus 2119901119901

119871119871minus119901119901120591120591 + 119891119891 119901119901 13

119891119891(119901119901) =1120572120572 sdot 120598120598 +

119901119901119901119901 + 119896119896prime

minus 119896119896119901119901

119896119896 + 119901119901sdot

1+ 119901119901119896119896$

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1213

119907119907$=RA119877119877119860119860

=119871119871119871119871

ℎℎ

asymp 2 sdot 10 13 (45)

119871119871119907119907$

asymp 11hr13 (46)

120591120591 =

119871119871

2119863119863asymp 06 hr

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1313

119889119889119889119889119889119889119889119889 =

119901119901 minus 119901119901120575120575120575120575 13

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1413

Bibliography13

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1513

Figures13

Main13 Text13

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1613

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1713

13 13 13 13 13

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1813

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 1913

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2013

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2113

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2213

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2313

13 13 13

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2413

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2513

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2613

SI13 Figures13

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2713

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2813

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 2913

13 13 13

119896119896[hr ]13 D13 [mmhr]13

11986311986312059112059113 [mmhr]13

4 sdot 10 13

36 sdot 10 13

36 sdot 1013 13 13

Calcium13 Waves13

36013 13

2232013 13 13

25213 13 13

14413 13

72013 13

7213 13

Dictyestilum28525

2113 13 13

413 13 13

36-shy‐36013 13 13

003613 13 13

1-shy‐3613

DNA13 3613 13 46813 0313 1113 13

Gene13 expression13

06213 5413 02113 03313

Gene13 expression13

007213 13 13

5713 13 13

00057plusmn0007213 13

001813

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 3013

13 4513

Inhibitor13 13 119875119875 minus 11986011986012059012059013

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 3113

5613 11989611989613 074minus 296nM13 13

13 119896119896 =

119896119896 + 1120591120591119896119896

5713 119896119896119896119896

13 01minus 02nM13

293713 119896119896$13 08nM13 13

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

13 3213

Methods

References

Acknowledgements

Methods

Biochip fabrication






Imaging


References

Documents

pages/docs website/publications...LETTERS PUBLISHEDONLINE:21SEPTEMBER2015|DOI:10.1038/NPHYS3469 Propagatinggeneexpressionfrontsina one-dimensionalcoupledsystemofartiﬁcialcells AlexandraM.Tayar