Toward in vivo Digital Circuits Ron Weiss, George Homsy, Tom Knight MIT Artificial Intelligence Laboratory

? Goal: program biological cells ? Characteristics  small ( E.coli : 1x2  m, 10 9 /ml)  self replicating  energy efficient ? Potential applications  “smart” drugs / medicine  agriculture  embedded systems Motivation

Approach logic circuit microbial circuit compiler genome high-level program in vivo chemical activity of genome implements computation specified by logic circuit

Key: Biological Inverters ? Propose to build inverters in individual cells Deach cell has a (complex) digital circuit built from inverters ? In digital circuit:  signal = protein synthesis rate  computation = protein production + decay

Digital Circuits ? With these inverters, any (finite) digital circuit can be built! A B CD C C A B D = gene ? proteins are the wires, genes are the gates ? NAND gate = “wire-OR” of two genes

Outline ? Compute using Inversion ? Model and Simulations ? Measuring signals and circuits ? Microbial Circuit Design ? Related work ? Conclusions & Future Work

Components of Inversion Use existing in vivo biochemical mechanisms ? stage I: cooperative binding  found in many genetic regulatory networks ? stage II: transcription ? stage III: translation ? decay of proteins (stage I) & mRNA (stage III) D examine the steady-state characteristics of each stage to understand how to design gates

    input protein synthesis rate     repression activity (concentration of bound operator)  steady-state relation C is sigmoidal Stage I: Cooperative Binding input protein repression cooperative binding input protein    “clean” digital signal   C C 01

Stage II: Transcription     repression activity     mRNA synthesis rate  steady-state relation T is inverse  invert signal repression mRNA synthesis transcription     T T

Stage III: Translation     output signal of gate  steady-state relation L is mostly linear  scale output output protein mRNA synthesis mRNA translation     L L

 inversion relation I “ideal” transfer curve:  gain (flat,steep,flat)  adequate noise margins Putting it together    I     L ∘ T ∘ C (   ) input protein output protein repression cooperative binding mRNA synthesis transcription input protein mRNA translation signal     LTC  I  “gain” 01

Outline ? Compute using Inversion ? Model and Simulations  model based on phage  steady-state and dynamic behavior of an inverter  simulations of gate connectivity, storage ? Measuring signals and circuits ? Microbial Circuit Design ? Related work ? Conclusions & Future Work

Model ? Understand general characteristics of inversion  Model phage elements [Hendrix83, Ptashne92]  repressor (CI)  operator (O R 1:O R 2)  promoter (P R )  output protein (dimerize/decay like CI) [Ptashne92] OR1OR1OR2OR2 structural gene

Steady-State Behavior ? Simulated transfer curves:   CC BB  BB  BB CC ? asymmetric (hypersensitive to LOW inputs)  later in talk: ways to fix asymmetry, measure noise margins

active gene Inverter’s Dynamic Behavior ? Dynamic behavior shows switching times [A][A] [Z][Z] [ ] time (x100 sec)

Connect: Ring Oscillator ? Connected gates show oscillation, phase shift time (x100 sec) [A][A] [C][C] [B][B]

B _S_S _R_R Memory: RS Latch time (x100 sec) _[R]_[R] [B][B] _[S]_[S] [A][A] = A

Outline ? Compute using Inversion ? Model and Simulations ? Measuring signals and circuits  measure a signal  approximate a transfer curve (with points)  the transfer band for measuring fluctuations ? Microbial Circuit Design ? Related work ? Conclusions & Future Work

Measuring a Signal ? Attach a reporter to structural gene  Translation phase reveals signal: w n copies of output protein Z w m copies of reporter protein RP (e.g. GFP) l Signal: l Time derivative: l Measured signal: [in equlibrium]

Measuring a Transfer Curve ? To measure a point on the transfer curve of an inverter I (input A, output Z) :  Construct a “fixed drive” (with reporter) w a constitutive promoter with output protein A  measure reporter signal    · Construct “fixed drive” + I (with reporter)  measure reporter signal     Result: point (     )  on transfer curve of I A “drive” gene inverter Z A RP

Measuring a Transfer Curve II Approximate the transfer curve with many points Example: 3 different drives each with cistron counts 1 to 10 > mechanism also useful for more complex circuits  

Models vs. Reality ? Need to measure fluctuations in signals ? Use flow cytometry  get distribution of fluoresence values for many cells typical histogram of scaled luminosities for “identical” cells cell suspension single-cell luminosity readout

The Transfer Band ? The transfer band:  captures systematic fluctuations in signals  constructed from dominant peaks in histograms ? For histogram peak:  min/max =   /   ? Each pair of drive + inverter signals yield a rectangular region input output    

Outline ? Compute using Inversion ? Model and Simulations ? Measuring signals and circuits ? Microbial Circuit Design  issues in building a circuit  matching gates  modifying gates to assemble a library of gates  BioSpice ? Related work ? Conclusions & Future Work

Microbial Circuit Design ? Problem: gates have varying characteristics ? Need to (1)measure gates and construct database (2)attempt to match gates (3)modify behavior of gates (4)measure, add to database, try matching again ? Simulate & verify circuits before implementing

Matching Gates ? Need to match gates according to thresholds input output I il I ih I max (I ih ) I min (I il ) I max I min LOW HIGH

Modifications to Gates modificationstage  Modify repressor/operator affinity C  Modify the promoter strength T  Alter degradation rate of a protein C  Modify RBS strength L  Increase cistron count T  Add autorepression C  Each modification adds an element to the database

Modifying Repression ? Reduce repressor/operator binding affinity  use base-pair substitutions   C Schematic effect on cooperative-binding stage: Simulated effect on entire transfer curve:  

Modifying Promoter ? Reduce RNAp affinity to promoter Schematic effect on transcription stage: Simulated effect on entire transfer curve:   T  

BioSpice ? Prototype simulation & verification tool  intracellular circuits, intercellular communication ? Given a circuit (with proteins specified)  simulate concentrations/synthesis rates ? Example circuit to simulate:  messaging + setting state

BioSpice Simulation ? Small colony: 4x4 grid, 2 cells (outlined) (1) original I = 0 (2) introduce D send msg M (3) recv msg set I (4) msg decays I latched

Limits to Circuit Complexity ? amount of extracellular DNA that can be inserted into cells ? reduction in cell viability due to extra metabolic requirements ? selective pressures against cells performing computation ? probably not: different suitable proteins

Related Work ? Universal automata with bistable chemical reactions [Roessler74,Hjelmfelt91] ? Mathematical models of genetic regulatory systems [Arkin94,McAdams97,Neidhart92] ? Boolean networks to describe genetic regulatory systems [Monod61,Sugita63,Kauffman71,Thomas92] ? Modifications to genetic systems [Draper92, vonHippel92,Pakula89]

Conclusions + Future Work ? in vivo digital gates are plausible ? Now:  Implement and measure digital gates in E. coli ? Also:  Analyze robustness/sensitivity of gates  Construct a reaction kinetics database ? Later:  Study protein  protein interactions for faster circuits

Inverter: Chemical Reactions