Loads in biological circuits: How to engineer modular systems?

Domitilla Del VecchioMechanical Engineering

MIT

Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks, Harvard, Nov 2019

Engineering de novo gene circuits in living cells foruseful functionalities

BiofuelsControl of cell fate Tracking, recognizing, killing cancer cells

Courtesy of Tal Danino

2

s

Synthetic Biology

2000

To systems and LSI

201X

Genetic Engineering

Jacob and MonodArberMullis…

Motifs era

Understanding biologyBio-inspired principles

Programming cells for useful functionalities

From understanding biology to programming biological systems for useful functionalities

In synthetic biology, we miss a way to describe/analyze composition in a way that leads to practical design/verification tools- we have large library of

partsà technology advancing fast

- BUT: when modules are put together, they do not retain their behavior in isolationàcontext-dependentàneed to re-design modules after composition

3

Describing a sophisticated system as the composition of simpler subsystems helps overcoming the complexity of analysis, verification and design:- can “forget” the details

within a subsystem to design the final system

- feedback can maintain I/O properties providing simplified abstractions for layered design

Design abstractions in synthetic biology

Increased scale is becoming possible in synthetic biology by composing simpler gates

[Moon et al. Nature 2012][Hanahan & Weinberg (2000)]

In natural systemscore processes areconserved during evolution and recur in different systems

A promising approach

But for a circuit with 11genes it takes one PhD

thesis of 5-6 years

Some sources of context-dependence

These issues can be viewed as a problem of lack of robustness to perturbations

à This is a problem for the field of “Control Systems”

4

Cellular ‘circuitry’, growth,… Modules often have “off-target” interactionsare subject to noise and growth rate changes

Cellular resourcesLoads applied by downstream modules is onesource of context dependence

Modules apply a load to the cellular resources: creates subtle couplings

Some sources of context-dependence

Cellular resourcesLoads applied by downstream modules is onesource of context dependence

Modules apply a load to the cellular resources: createssubtle couplings

5

Example:

u

B Expected behavior

RNAP, Ribosomes

Actual behavior!

0

20000

40000

60000

80000

100000

120000

-2 0 2 4Fluo

resc

ence

(A.U

.)

u (AHL)

Bu

Activation cascade

A

Sharing a limited amount of resources creates subtle couplings

6

Outline

Predicting and modulating emergent interaction networks

Decentralized (quasi-integral) control for mitigating effects of hidden interactions

re-scaling of existing regulatory links(they are weakened)

“hidden” interactions

Gi(u)

resource demand coefficientsJk / dkkk

xT

k

new interactions emerge(not due to regulatory links)

Network-level effects of limited resources

piHill function

ui

ui

Hi ui activator

ui repressor↵i /x

i

y

ki

uj pj

pi = ↵iFi(ui)� �ipi

Hi(ui)

New model

pi = ↵iFi(ui)

1 + JiFi(ui) +P

j JjFj(uj)� �ipi

effective interaction graph@Gi(u)

@u=

↵i@Fi/@u

(1 +P

j JjFj)2�

↵iFiP

j Jj@Fj/@u

(1 +P

j JjFj)2

standard models assume x (RNAP) and y (Ribo) are constant parameters

xT = x+X

xi, yT = y +X

yibut they are not: resources occupied by node i

x y

7

Qian, Huang et al. ACS Syn Bio, 2017

Effective interaction graphspipj

If pj is an activator, it is an effective repressor for any node not regulatedby it (“lateral repression”)

pj pi

If pj is a repressor, it is an effective activator for any node not regulatedby it (“lateral activation”)

=

pj pi

The overall effect of pj on a node pi regulated by it is undetermined if pi is not the only node regulated by pj

Qian, Huang et al. ACS Syn Bio, 2017

=

The overall effect of pj on a node piregulated by it is not changed if pi

is the only node regulated by pj(but it is weaker)

pj pi

=

8

9

MBP 1.0

MBP-dRFP

MBP-gapA

Gyorgy et al. Biophysical J. 2015

pipj

Experiments confirm “lateral repression”

When only RFP mRNA is produced there is no effect on GFPà The coupling is due to loading translation resources

Competition for gene expressionresources leads to up to 70% inhibition of non-target genes formedium copy number plasmids

BACTERIA!!!

10

price increases as RBS strength decreases

Experimental data

Any pair of protein products is constrained on isocost lines

price of p1 price of p2

allowed ribosome

budget

↵p1 + �p2 = yT

x ⌧ i, y ⌧ ki linear binding assumptionp2p1

Gyorgy et al. Biophysical J. 2015

Realizable region is the intersection of simplexes

11

p1

p2

Theorem: The set of realizable protein concentrations is the intersection of the simplexesS =

\

i

Si

realizableregion

S

Gyorgy and Del Vecchio, Proc. IEEE CDC, 2014

p1 p2

pmax2

p11pmax1

p12ideal realizable regionwithout considering

resource sharing

Qian, Huang et al. ACS Syn Bio, 2017

12

with hidden interactions

p1 p2

10 20 30 40 50 60 70 80-1

0

101

Larger J 2

10

10

RB

S st

reng

th

J decre

asesJ / DNA copy #

RBS strengthof target

can use J to tunestrength of hidden interactions

The effective interaction graph of an activation cascade is an IFFL

u

p2Expected behavior

p2u p1

DNA copy #

13

Outline

Predicting and modulating emergent interaction networks

Decentralized (quasi-integral) control for mitigating effects of hidden interactions

System withouthidden interactions

Decentralized feedback control problem

14

System withhidden interactions

wi di

resource demand at node i

di / Ji

wi

di

yigenetic

module i

vi

vi

yi

i

wi =X

j 6=i

di

rest of net

Problem: Design a local feedback controllersuch that yi depends only on vi and it isindependent of wi

Decentralized feedback control problem

15

i vi

yi

biomolecularcontroller

wi

yigenetic

module i

vi

di

resource demand at node i

di / Ji

wi =X

j 6=i

di

System withhidden interactions

wi

di

System withouthidden interactions

rest of net

Disturbance rejection via quasi-integral controlbiomolecular

controller

genetic module

Problem: Determine a biomolecular controller such that the steady state input/output response v to y is independent of w

v

y

w x

z

Challenge: molecular decay is unavoidable in vivo due to cell growth à integrator leakiness

z = k(v � y)� �z

y = g(x)x = f(x, z, w),

Qian and Del Vecchio. J. Royal Society Interface, 2018

Approach: For v and w constants, use integral control, e.g.

y = g(x)

z = k(v � y)

x = f(x, v, z, w),

under stability, y is independent of w at steady state

y = g(x)cannot send growth to zeroà increase speed of

all controller’s reactions

x = f(x, z, w),

z =1

✏(v � y)� �z

z

quasi-integral controlstructure

16

Examples:

y = x<latexit sha1_base64="5IcvhTxSge5jXDRRGh40dr4bw5k=">AAAB63icbVBNS8NAEJ34WetX1aOXxSJ4KkkV9CIUvXisYD+gDWWz3bRLdzdhdyOG0L/gxYMiXv1D3vw3btoctPXBwOO9GWbmBTFn2rjut7Oyura+sVnaKm/v7O7tVw4O2zpKFKEtEvFIdQOsKWeStgwznHZjRbEIOO0Ek9vc7zxSpVkkH0waU1/gkWQhI9jkUnr9VB5Uqm7NnQEtE68gVSjQHFS++sOIJIJKQzjWuue5sfEzrAwjnE7L/UTTGJMJHtGepRILqv1sdusUnVpliMJI2ZIGzdTfExkWWqcisJ0Cm7Fe9HLxP6+XmPDKz5iME0MlmS8KE45MhPLH0ZApSgxPLcFEMXsrImOsMDE2njwEb/HlZdKu17zzWv3+otq4KeIowTGcwBl4cAkNuIMmtIDAGJ7hFd4c4bw4787HvHXFKWaO4A+czx97tI3e</latexit>

y

w<latexit sha1_base64="QTJW+ZXlGFskIVTQXzavcle4NeE=">AAAB+3icbVC7TsMwFHXKq4RXKCOLRYXEVCUFCcYKFsYi0YfURJXjOK1Vx4lsB6ii/AoLAwix8iNs/A1OmgFajnSlo3Pu9fU9fsKoVLb9bdTW1jc2t+rb5s7u3v6BddjoyzgVmPRwzGIx9JEkjHLSU1QxMkwEQZHPyMCf3RT+4IEISWN+r+YJ8SI04TSkGCktja2GmbnlK5kgQf6Yu645tpp2yy4BV4lTkSao0B1bX24Q4zQiXGGGpBw5dqK8DAlFMSO56aaSJAjP0ISMNOUoItLLyq05PNVKAMNY6OIKlurviQxFUs4jX3dGSE3lsleI/3mjVIVXXkZ5kirC8WJRmDKoYlgEAQMqCFZsrgnCguq/QjxFAmGl4ypCcJZPXiX9dss5b7XvLpqd6yqOOjgGJ+AMOOASdMAt6IIewOAJPINX8GbkxovxbnwsWmtGNXME/sD4/AHSvpRM</latexit> no leakiness

2D controller: sequestration-basedx = z1 � x+ w

z1 =1

✏(v � z1z2)� z1

z2 =1

✏(x� z1z2)� z2

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z = z1 � z2

z =1

✏(v � x)� z

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note the memory variable:

w. leakinessw. leakiness/fast controller

biomolecularcontroller

genetic module

Problem: Determine a biomolecular controller such that the steady state input/output response v to y is independent of w

v

y

w x

z

Challenge: molecular decay is unavoidable in vivo due to cell growth à integrator leakiness

z = k(v � y)� �z

y = g(x)x = f(x, z, w),

Qian and Del Vecchio. J. Royal Society Interface, 2018

Approach: For v and w constants, use integral control, e.g.

y = g(x)

z = k(v � y)

x = f(x, v, z, w),

under stability, y is independent of w at steady state

y = g(x)cannot send growth to zeroà increase speed of

all controller’s reactions

x = f(x, z, w),

z =1

✏(v � y)� �z

z

quasi-integral controlstructure

Theorem: x = f(x, z, w)

z1 =1

✏h(v, z, x)� �z1

z2 =k

✏(v � y)� �z2

y = g(x)<latexit sha1_base64="MVekuLLkJa4SJItdkR3oZtY9VrI=">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</latexit>

If this closed loop system with is LES,� = 0<latexit sha1_base64="ReEE4Spm8VtgQNe2J67PQh1D1rw=">AAAB8XicbVBNS8NAEJ34WeNX1aOXxSJ4KkkV9CIUvXisYD+wDWWz3bRLdzdhdyOU0H/hxYMiXv033vw3btoctPXBwOO9GWbmhQln2njet7Oyura+sVnacrd3dvf2yweHLR2nitAmiXmsOiHWlDNJm4YZTjuJoliEnLbD8W3ut5+o0iyWD2aS0EDgoWQRI9hY6dHtDbEQ+Npz++WKV/VmQMvEL0gFCjT65a/eICapoNIQjrXu+l5iggwrwwinU7eXappgMsZD2rVUYkF1kM0unqJTqwxQFCtb0qCZ+nsiw0LriQhtp8BmpBe9XPzP66YmugoyJpPUUEnmi6KUIxOj/H00YIoSwyeWYKKYvRWREVaYGBtSHoK/+PIyadWq/nm1dn9Rqd8UcZTgGE7gDHy4hDrcQQOaQEDCM7zCm6OdF+fd+Zi3rjjFzBH8gfP5A+exj8I=</latexit>

y(✏) ! v as ✏ ! 0 independent of wThen: all fast controller reactions compute the difference and integrate

Biomolecular implementation:

17

Disturbance rejection via quasi-integral control

Tracking performance of quasi-integral controlProblem: Analytically determine tracking performance of the quasi-integral controller for time-varying inputs as timescale separation between controller reactions and molecular decay increases (i.e., smaller )✏

<latexit sha1_base64="IADNbfSLzf03DbPLELFcTrsJATM=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexKQI8BLx4jmAckS5id9CZDZmfWmVkhhPyEFw+KePV3vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMirTDJtMCaU7ETUouMSm5VZgJ9VIk0hgOxrfzv32E2rDlXywkxTDhA4ljzmj1kmdHqaGCyX75Ypf9Rcg6yTISQVyNPrlr95AsSxBaZmgxnQDP7XhlGrLmcBZqZcZTCkb0yF2HZU0QRNOF/fOyIVTBiRW2pW0ZKH+npjSxJhJErnOhNqRWfXm4n9eN7PxTTjlMs0sSrZcFGeCWEXmz5MB18ismDhCmebuVsJGVFNmXUQlF0Kw+vI6aV1VA78a3Ncq9VoeRxHO4BwuIYBrqMMdNKAJDAQ8wyu8eY/ei/fufSxbC14+cwp/4H3+AEibkBI=</latexit><latexit sha1_base64="IADNbfSLzf03DbPLELFcTrsJATM=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexKQI8BLx4jmAckS5id9CZDZmfWmVkhhPyEFw+KePV3vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMirTDJtMCaU7ETUouMSm5VZgJ9VIk0hgOxrfzv32E2rDlXywkxTDhA4ljzmj1kmdHqaGCyX75Ypf9Rcg6yTISQVyNPrlr95AsSxBaZmgxnQDP7XhlGrLmcBZqZcZTCkb0yF2HZU0QRNOF/fOyIVTBiRW2pW0ZKH+npjSxJhJErnOhNqRWfXm4n9eN7PxTTjlMs0sSrZcFGeCWEXmz5MB18ismDhCmebuVsJGVFNmXUQlF0Kw+vI6aV1VA78a3Ncq9VoeRxHO4BwuIYBrqMMdNKAJDAQ8wyu8eY/ei/fufSxbC14+cwp/4H3+AEibkBI=</latexit><latexit sha1_base64="IADNbfSLzf03DbPLELFcTrsJATM=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexKQI8BLx4jmAckS5id9CZDZmfWmVkhhPyEFw+KePV3vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMirTDJtMCaU7ETUouMSm5VZgJ9VIk0hgOxrfzv32E2rDlXywkxTDhA4ljzmj1kmdHqaGCyX75Ypf9Rcg6yTISQVyNPrlr95AsSxBaZmgxnQDP7XhlGrLmcBZqZcZTCkb0yF2HZU0QRNOF/fOyIVTBiRW2pW0ZKH+npjSxJhJErnOhNqRWfXm4n9eN7PxTTjlMs0sSrZcFGeCWEXmz5MB18ismDhCmebuVsJGVFNmXUQlF0Kw+vI6aV1VA78a3Ncq9VoeRxHO4BwuIYBrqMMdNKAJDAQ8wyu8eY/ei/fufSxbC14+cwp/4H3+AEibkBI=</latexit><latexit sha1_base64="IADNbfSLzf03DbPLELFcTrsJATM=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexKQI8BLx4jmAckS5id9CZDZmfWmVkhhPyEFw+KePV3vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMirTDJtMCaU7ETUouMSm5VZgJ9VIk0hgOxrfzv32E2rDlXywkxTDhA4ljzmj1kmdHqaGCyX75Ypf9Rcg6yTISQVyNPrlr95AsSxBaZmgxnQDP7XhlGrLmcBZqZcZTCkb0yF2HZU0QRNOF/fOyIVTBiRW2pW0ZKH+npjSxJhJErnOhNqRWfXm4n9eN7PxTTjlMs0sSrZcFGeCWEXmz5MB18ismDhCmebuVsJGVFNmXUQlF0Kw+vI6aV1VA78a3Ncq9VoeRxHO4BwuIYBrqMMdNKAJDAQ8wyu8eY/ei/fufSxbC14+cwp/4H3+AEibkBI=</latexit>

Qian and Del Vecchio, IEEE Control Systems Letters, 2018

Real-10 4 -10 2 -10 0 -10 -2

Imag

-50

-40

-30

-20

-10

0

10

20

30

40

50 Poles of the full system

Real-10 4 -10 2 -10 0 -10 -2

Imag

-50

-40

-30

-20

-10

0

10

20

30

40

50 Poles of the reduced systemLinearized model pole map

Challenge: the quasi-integral control structure is a singular singularly perturbed (SSP) system:

Boundary layer dynamics: • Does not have an equilibrium unless

• Tikhonov theorem inapplicable

18

✏m = u(t)� ✓ms� ✏�m

✏s = y � ✓ms� ✏�s

y = R(w)m� �y<latexit sha1_base64="8fDSM365ZFxqxsRzwPBDElDZ2pc=">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</latexit>

m0 = u� ✓ms

s0 = y � ✓ms<latexit sha1_base64="W0KdoQzAnnkn0CQri6BVoUxql0U=">AAACDXicbZDLSgMxFIYz9VbHW9Wlm2C9bSwzWrwshIIblxXsBTqlZNJMG5rMDMkZoZS+gBtfxY0LRdy6d+fbmGmLVOsPgZ/vnMPJ+f1YcA2O82Vl5uYXFpeyy/bK6tr6Rm5zq6qjRFFWoZGIVN0nmgkesgpwEKweK0akL1jN712n9do9U5pH4R30Y9aUpBPygFMCBrVye/Lw4Co59qDLgGCJtefZ2iDcn2KtXN4pOCPhWeNOTB5NVG7lPr12RBPJQqCCaN1wnRiaA6KAU8GGtpdoFhPaIx3WMDYkkunmYHTNEO8b0sZBpMwLAY/o9MSASK370jedkkBX/62l8L9aI4HgojngYZwAC+l4UZAIDBFOo8FtrhgF0TeGUMXNXzHtEkUomADtUQiXqc5+Tp411ZOCe1oo3hbzpeIkjizaQbvoCLnoHJXQDSqjCqLoAT2hF/RqPVrP1pv1Pm7NWJOZbfRL1sc3o52Zfw==</latexit>

u = y<latexit sha1_base64="oGHP3bffzbuopYYSBo9QT163NOk=">AAAB6nicbVDLSsNAFL2pr1pfVZduBovgqiRafCyEghuXFe0D2lAm00k7dDIJMxMhhH6CGxeKuPWL3Pk3TtIgaj1w4XDOvdx7jxdxprRtf1qlpeWV1bXyemVjc2t7p7q711FhLAltk5CHsudhRTkTtK2Z5rQXSYoDj9OuN73O/O4DlYqF4l4nEXUDPBbMZwRrI93FV8mwWrPrdg60SJyC1KBAa1j9GIxCEgdUaMKxUn3HjrSbYqkZ4XRWGcSKRphM8Zj2DRU4oMpN81Nn6MgoI+SH0pTQKFd/TqQ4UCoJPNMZYD1Rf71M/M/rx9q/cFMmolhTQeaL/JgjHaLsbzRikhLNE0MwkczcisgES0y0SaeSh3CZ4ez75UXSOak7p/XGbaPWbBRxlOEADuEYHDiHJtxAC9pAYAyP8AwvFreerFfrbd5asoqZffgF6/0LVXiN7Q==</latexit>

A1. There exists a coordinate transformation to isolate the true fast variables

A2. The reduced system, obtained by setting the true fast variablesto QSS, is a high gain (1/𝛜) feedback interconnection of SPR systems

then:

Tikhonov-like theorem for general linear SSP systems:

lim supt!1

|y(t)� u(t)| = O(p✏)

<latexit sha1_base64="70iQP5a8rfKWJe3SMi9IIjWwCDY=">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</latexit>

Quasi-integral control implementation via sRNA silencing

19

Qian and Del Vecchio. IEEE CDC, 2016

high RNA transcription rates

fast RNAinteractions

biomolecularcontroller

genetic module

v

y

wx

z

regulatedgene sRNA

Ø

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m<latexit sha1_base64="Dwj5TRChP0z4GP299Yoc+Cu/nW0=">AAAB53icbVBNS8NAEJ3Ur1q/qh69BIvgqSQiqLeCF48tGFtoQ9lsJ+3a3U3Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZelHKmjed9O6W19Y3NrfJ2ZWd3b/+genj0oJNMUQxowhPViYhGziQGhhmOnVQhERHHdjS+nfntJ1SaJfLeTFIMBRlKFjNKjJVaol+teXVvDneV+AWpQYFmv/rVGyQ0EygN5UTrru+lJsyJMoxynFZ6mcaU0DEZYtdSSQTqMJ8fOnXPrDJw40TZksadq78nciK0nojIdgpiRnrZm4n/ed3MxNdhzmSaGZR0sSjOuGsSd/a1O2AKqeETSwhVzN7q0hFRhBqbTcWG4C+/vEqCi/pN3Wtd1hqXRRplOIFTOAcfrqABd9CEACggPMMrvDmPzovz7nwsWktOMXMMf+B8/gA/doy2</latexit><latexit sha1_base64="Dwj5TRChP0z4GP299Yoc+Cu/nW0=">AAAB53icbVBNS8NAEJ3Ur1q/qh69BIvgqSQiqLeCF48tGFtoQ9lsJ+3a3U3Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZelHKmjed9O6W19Y3NrfJ2ZWd3b/+genj0oJNMUQxowhPViYhGziQGhhmOnVQhERHHdjS+nfntJ1SaJfLeTFIMBRlKFjNKjJVaol+teXVvDneV+AWpQYFmv/rVGyQ0EygN5UTrru+lJsyJMoxynFZ6mcaU0DEZYtdSSQTqMJ8fOnXPrDJw40TZksadq78nciK0nojIdgpiRnrZm4n/ed3MxNdhzmSaGZR0sSjOuGsSd/a1O2AKqeETSwhVzN7q0hFRhBqbTcWG4C+/vEqCi/pN3Wtd1hqXRRplOIFTOAcfrqABd9CEACggPMMrvDmPzovz7nwsWktOMXMMf+B8/gA/doy2</latexit><latexit sha1_base64="Dwj5TRChP0z4GP299Yoc+Cu/nW0=">AAAB53icbVBNS8NAEJ3Ur1q/qh69BIvgqSQiqLeCF48tGFtoQ9lsJ+3a3U3Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZelHKmjed9O6W19Y3NrfJ2ZWd3b/+genj0oJNMUQxowhPViYhGziQGhhmOnVQhERHHdjS+nfntJ1SaJfLeTFIMBRlKFjNKjJVaol+teXVvDneV+AWpQYFmv/rVGyQ0EygN5UTrru+lJsyJMoxynFZ6mcaU0DEZYtdSSQTqMJ8fOnXPrDJw40TZksadq78nciK0nojIdgpiRnrZm4n/ed3MxNdhzmSaGZR0sSjOuGsSd/a1O2AKqeETSwhVzN7q0hFRhBqbTcWG4C+/vEqCi/pN3Wtd1hqXRRplOIFTOAcfrqABd9CEACggPMMrvDmPzovz7nwsWktOMXMMf+B8/gA/doy2</latexit> s

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ribosomeavailability change

w

v

y = R(w)m� �y

m =v

✏� ✓

✏ms� �m

s =y

✏� ✓

✏ms� �s

z = m� smemory variable

LES of closed loop system when Is satisfied

then

independent of disturbance (ribosome availability)

✏z = (v � y)� ✏�z

y(✏) ! v as ✏ ! 0

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note: need both fast RNA interactions and high RNA transcription rate

(for “free”)

(we can tune)

20

unregulated device regulated deviceAHL = 0 AHL = 1000 nM

normalized fluorescence histograms from single-cell measurements by cytometery

GFP fluorescence GFP fluorescence

biological replicate #1

biologicalreplicate #2

biological replicate #3

OL CL

0

2

4

6× 104

0.4

1

0

2

4

6× 104

unregulated device regulated device

Nor

mal

ized

GF

P/O

DR

FP

/OD

(A

.U.)

time (hr)time (hr)

ln (

OD

600)

ln (

OD

600)

-0.5 1.5 3.5 5.5 7.5-2.5 -0.5 1.5 3.5 5.5 7.5-2.5

AHL induction AHL induction

population-level measurements by mircoplate photometerN

orm

aliz

edG

FP

/OD

RF

P/O

D (

A.U

.)

0 0

-4

-3

-4

-3

AHL = 0AHL = 1000 nM

0.4

1

0 7.5 0 7.5time (hr)time (hr)

(OL) (CL)

output interfaceunaltered by controller

input interfaceunaltered by controller

Huang, Qian, and Del Vecchio. Nat. Comm., December 2018

QIC control for resource decoupling via sRNA silencing

Summary

Cellular resourcesModules apply a load to the “cellular system”: creates subtle couplings

= =

We have uncovered andmodeled hidden interactionsà resource-aware circuit design

Resource decoupling for adaptation of

genetic modules to resource variability

through quasi-integral control (QIC) Implementing QIC withsRNA interference allows forhighly scalable and tunabledesign of post-TX controllersthat leave input and outputInterfaces of genetic modulesunchanged

21

Ross Jones Hussein Abdallah

Bose Research Award

Thanks to

Yili QianHsin-Ho Huang

Ross Jones

Former Students/Post-docs:

Andras Gyorgy(NYU, Abu Dhabi)

Hattie Chang(Harvard)

Jose Jimenez(U. of Surrey)

John Yazbek

22