Toward in vivo Digital Circuits

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

2. Motivation • Goal: program biological cells • Characteristics • small (E.coli: 1x2m , 109/ml) • self replicating • energy efficient • Potential applications • “smart” drugs / medicine • agriculture • embedded systems

3. Approach in vivo chemical activity of genomeimplementscomputation specified by logic circuit logic circuit high-level program genome microbial circuit compiler

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

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

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

7. 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) • examine the steady-state characteristics of each stage to understand how to design gates

8. fA rA cooperative binding repression input protein input protein 0 1  “clean” digital signal Stage I: Cooperative Binding C • fA = input protein synthesis rate • rA = repression activity (concentration of bound operator) • steady-state relation C is sigmoidal C rA fA

9.  invert signal Stage II: Transcription • rA = repression activity • yZ = mRNA synthesis rate • steady-state relation T is inverse T rA yZ transcription repression mRNA synthesis T yZ rA

10.  scale output Stage III: Translation L • fZ = output signal of gate • steady-state relation L is mostly linear yZ fZ translation mRNA synthesis output protein mRNA L fZ yZ

11. Putting it together signal C T L fA rA yZ fZ cooperative binding transcription translation repression input protein mRNA synthesis output protein input protein mRNA • inversion relation I : • “ideal” transfer curve: • gain (flat,steep,flat) • adequate noise margins I fZ = I (fA) = L∘ T∘ C(fA) “gain” fZ 0 1 fA

12. 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

13. Model • Understand general characteristics of inversion • Model phage  elements [Hendrix83, Ptashne92] • repressor (CI) • operator (OR1:OR2) • promoter (PR) • output protein (dimerize/decay like CI) OR2 OR1 structural gene [Ptashne92]

14. fA fB fC fA fB fB fC fA fA Steady-State Behavior • Simulated transfer curves: • asymmetric (hypersensitive to LOW inputs) • later in talk: ways to fix asymmetry, measure noise margins

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

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

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

18. 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

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

20. A “drive” gene 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) • a constitutive promoter with output protein A • measure reporter signal  fA • Construct “fixed drive” + I (with reporter) • measure reporter signal  fZ • Result: point (fA, fZ)on transfer curve of I A RP “drive” gene Z RP inverter

21. Measuring a Transfer Curve II Approximate the transfer curve with many points • Example: • 3 different drives • each with cistron counts 1 to 10 fZ fA • mechanism also useful for more complex circuits

22. cell suspension single-cell luminosity readout 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

23. output fZ fZ fA fA input The Transfer Band • The transfer band: • captures systematic fluctuations in signals • constructed from dominant peaks in histograms • For histogram peak: • min/max = fA/fA • Each pair of drive + invertersignals yield a rectangularregion

24. 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

25. 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

26. I I il ih Matching Gates • Need to match gates according to thresholds output HIGH Imax Imin Imin(Iil) Imax(Iih) LOW input LOW HIGH

27. Modifications to Gates modification stage • 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

28. C rA fA Modifying Repression • Reduce repressor/operator binding affinity • use base-pair substitutions Schematic effect on cooperative-binding stage: Simulated effect on entire transfer curve: fZ fA

29. T yZ rA Modifying Promoter • Reduce RNAp affinity to promoter Schematic effect on transcription stage: Simulated effect on entire transfer curve: fZ fA

30. 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

31. 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

32. 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

33. 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]

34. 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

35. Inverter: Chemical Reactions