Feedback and Control in Biological Circuit Design

Richard M. MurrayControl & Dynamical Systems / Bioengineering

California Institute of Technology

GloverFest 2013

Emzo de los Santos (BE) Marcella Gomez (ME) Shaobin Guo (BMB) Victoria Hsiao (BE) Jongmin Kim (BE) Joe Meyerowitz (BMB)

Dan Siegal-Gaskins (BE) Vipul Singhal (CNS) Zachary Sun (Bio)Anu Thubagere (BE) Zoltan Tuza (PPCU) Yong Wu (ChE) Enoch Yeung (CDS)

Ophelia Venturelli (BMB) / Somayeh Sojoudi (CDS) Elisa Franco (UC Riverside) / Javad Lavaei (Columbia) / Shaunak Sen (IIT Dehli)

Domitilla Del Vecchio (MIT) / Mary Dunlop (U. Vermont)

Richard M. Murray, Caltech CDS/BEUCSB, May 2013

Biological Circuit Design (Synthetic Biology)

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Repressilator (Elowitz & Leibler; 2000)• Ring oscillator with three repressors

in a cycle• Provides oscillations at frequency

comparable to cell cycle

Synchronized oscillators (Danino, Mondragon-Palomino et al, 2010)• Coupled oscillators by using cell-cell

signaling• Used relaxation style oscilator built on

coupled +/- feedback loops + delay

Richard M. Murray, Caltech CDS/BEGloverFest, 23 Sep 2013

Synthetic Biology ApplicationsLiving Foundries

• Conversion of input resources to output products in modular way• Control systems to regu-

late metabolic pathways and stress response• Provide modularity and

robustness, with ability to rapidly redesign pathway for new input/output pairs

Event Detectors

• Component technologies: signal detection, event memory, species com-parison, logic functions• Event detectors: A > B, A

followed by B, A > thresh• Interconnection framework:

modular techniques for interconnecting compo-nents and detectors

Artificial Cells

• Self-contained nanoscale biomolecular machines • Subsystems: chassis,

power supply, sensing (internal and external), actuation, regulation• All components should

be synthetic and pro-grammed (compiled)

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Living Foundries: The Vision

Chemicals

Fuels

Pharma

DNA instruction set

PolymersCatalysts Electronic/ optical materials

Multi-cellular constructsSelf-repairing systems“cell-free” systems

Approved for Public Release, Distribution Unlimited 7

AAGCAGTATCATCGACCCAGTAATATAGCAGACCGTTAGATAC…

Genome design Synthesis

Sugar

Cellulose

PET

Coal

Molecules

Custom, distributed, on-demand manufacturing

Natural gas

“cell-like”factory

Richard M. Murray, Caltech CDS/BEGloverFest, 23 Sep 2013

The Hype• The ‘parts’ work like Lego• Cells can simply be rewired• A promise of unprecedented power

Hard Truths• Many of the parts are undefined• The circuitry is unpredictable• The complexity is unwieldy• Many parts are incompatible• Variability crashes the system

Analysis & Design of Biomolecular Feedback Systems

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“Circuit Theory”• Role of feedback• System identification• Resource limits,

effects of crosstalk

In Vitro Testbeds• RNA-based genelets

• Biomolecular breadboards

• Droplet-based automation

Feedback Control Design• (Fast) Feedback devices

• Modularity, programmability

• Uncertainty management

• Design of dynamics

SH3

PTaz

LZB

RFP

LZb

CpxR LZbSH3GFP

Pcon HK Pcon RR PCpxR Anti-sca!old

PReference Sca!old

Richard M. Murray, Caltech CDS/BEUCSB, May 2013

Bimodality, Bistability and FeedbackGalactose metabolism in yeast shows biomodality• Instead of “graded”

response, some fraction of cells are on, some are off• Q1: which (combination of)

feedback is responsible?• Q2: why is this beneficial?

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O. S Venturelli, H. El-Samad, R. M Murray, PNAS 2013

Richard M. Murray, Caltech CDS/BBESB 6.0, 9 Jul 2013

Event detector

• Add’l proteases, RNAses, etc

• Modulate pH, ATP, etc

• Vary component concentrat’n

• Extract: cytoplasmic proteins

• Amino acid mix

• Buffer + NTP, RNAP, etc

TXTL

TXTL

vesi

cle

orig

ami

Implementation iterations (slow)

Cell-Free Biomolecular Breadboards

Key characteristics of the cell-free (TX-TL) breadboard (Shin & Noireaux, ACS Syn Bio, 2011)

• Inexpensive and fast: ~$0.03/ul for reactions; typical reactions run for 4-6 hours• Easy to use: works with many plasmids or linear DNA (PCR products!)- Can adjust concentration to explore copy number/expression strength quickly

• Flexible environment: adjust energy level, pH, temperature, degradationTX-TL breadboard components• Bulk reactions: 10 ul, 10-25 variations ([DNA], [inducers], etc) in a plate reader• Droplet-based microfluidics: 0.3 ul, 50-100 variations + merge/split/etc • Vesicle-based reactions (“artificial cells”): 1-100 fl, 100-1000 phospholipid vesicles• Spatial localization using DNA origami: 1000 copies w/ 10-100 nm spatial ctrl• Reaction-based modeling: MATLAB/Simbiology toolbox, with resource limits

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Model

PrototypingDebugging

SystemModel

Model

Design iterations (fast)

Model

http://www.openwetware.org/wiki/breadboards

Sun et al, JoVE 2013Sun et al, ACS Syn Bio, 2013 (s)

Richard M. Murray, Caltech CDS/BEONR Program Review, 23 Jul 2013

TX-TL Testing of MIT Phospho-Insulator CircuitGoals of TX-TL based characterization• Compare in vitro to in vivo to in silico• Provide platform for rapid exploration of

dynamics, performance, robustness

Results to date• Circuit implemented and working in TX-TL• Control: low NRI (resp. reg.) concentration• Loading: 0X versus 2X add’l promoter sites• Similar insulation properties: insulator

buffers effects of downstream loading

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In vivo (MIT) TX-TL (Caltech)

low gain high gain

kinase [DNA]

outp

ut fl

uore

scen

se

Guo, Nilgiriwala, Del Vecchio and M, 2013 (in prep)

Richard M. Murray, Caltech CDS/BEGloverFest, 23 Sep 2013

Concentration Regulation via Scaffold Proteins (Hsiao)

Circuit operation• Use scaffold domains to

modulate activity of histidine kinase and response regulator proteins• Use anti-scaffold feedback to

modulate activity level and regulate con-centration of output to match input

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Del los Santos, Hsiao and M, ACC 2013

Output

Input

0.5 1 1.5 2 2.5 3 3.5x 104

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2 x 104

Ara0Ara0.0001Ara0.001Ara0.01

0.5 1 1.5 2 2.5 3 3.5x 104

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2 x 104

Ara0Ara0.0001Ara0.001Ara0.01

Sca!old Expression (RFP/OD, a.u)

Anti-

sca!

old

Expr

essi

on (G

FP/O

D, a

.u)

Sca!old Expression (RFP/OD, a.u)

Anti-

sca!

old

Expr

essi

on (G

FP/O

D, a

.u)

WW62 Closed Loop ( - CusS phosphatase)

BW27783 Closed Loop ( + CusS phosphatase)

Richard M. Murray, Caltech CDS/BEGloverFest, 23 Sep 2013

Design of Biomolecular Feedback SystemsDesign the easy parts• Interconnection matrix • Time delay matrix

Design tools exist for pairwise combinations• Linear + uncertain =

robust control theory• Linear + nonlinear =

describing functions• Linear + network =

formation stabilization• Linear + delay = delay

differential equations

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Open questions• What is the class of feedback compensators we can obtain using L and τ ?• How do we specify robustness and performance in highly stochastic settings?• Can feedback be used to design robust dynamics that implements useful functionality?

Richard M. Murray, Caltech CDS/BEGloverFest, 23 Sep 2013

Some Challenges and Research Directions (BFS)Better understanding of uncertainty• How do we capture observed behavior using

structured models for (dynamic) uncertainty

Stochastic specifications and design tools• How do we describe stochastic behavior in a

systematic and useful way?• How do we design stochastic behavior?• What are the right design “knobs”?

Higher level design abstractions• What are the right “device-level” design

abstractions (and corresponding diagrams)?

Redundant design strategies• Start implementing non-minimal designs• Analogy: stochastic memory storage

Scaling up: components → devices → systems• How can we use in vitro “breadboarding” to

design and implement complex systems

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