Module Locking in Biochemical Synthesis

1. Brian Fett and Marc D. Riedel Module Locking in Biochemical Synthesis Electrical and Computer EngineeringUniversity of Minnesota Brian’s Automated Modular Biochemical Instantiator (BAMBI)

2. Tim Mullins Senior Technical Staff Member, HPC Life Sciences Applications, IBM Systems and Technology Group Acknowledgements students at the University of Minnesota Brian Fett Adam Shea Weikang Qian Matt Cook Institute of Neuroinformatics, ETH Zürich

3. Acknowledgements Who is this guy? • Most of the cells in his body are not his own! • Most of the cells in his body are not even human! • Most of the DNA in his body isalien! “Minnesota Farmer”

4. Who is this guy? He’s a human-bacteria hybrid: • 100 trillion bacterial cells of at least 500 different types inhabit his body. [like all of us] vs. • only 1 trillion human cells of 210 different types. “Minnesota Farmer”

5. What’s in his gut? Who is this guy? He’s a human-bacteria hybrid: • 100 trillion bacterial cells of at least 500 different types inhabit his body. [like all of us] vs. • only 1 trillion human cells of 210 different types. “Minnesota Farmer”

6. What’s in his gut? “E. coli, a self-replicating object only a thousandth of a millimeter in size, can swim 35 diameters a second, taste simple chemicals in its environment, and decide whether life is getting better or worse.” – Howard C. Berg About 3 pounds of bacteria!

7. We should put these critters to work… “Stimulus, response! Stimulus response! Don’t you ever think!”

8. Synthetic Biology • Positioned as an engineering discipline. • “Novel functionality through design”. • Repositories of standardized parts. • Driven by experimental expertise in particular domains of biology. • Gene-regulation, signaling, metabolism, protein structures …

9. Building Bridges • Quantitative modeling. • Mathematical analysis. • Incremental and iterative design changes. "Think of how engineers build bridges. They design quantitative models to help them understand what sorts of pressure and weight the bridge can withstand, and then use these equations to improve the actual physical model. [In our work on memory in yeast cells] we really did the same thing.” – Pam Silver, Harvard2007 Engineering Design

10. Synthetic Biology Feats of synthetic bio-engineering: • Cellulosic ethanol (Nancy Ho, Purdue, ’04) • Anti-malarial drugs (Jay Keasling, UC Berkeley, ‘06) • Tumor detection (Chris Voigt, UCSF ‘06) Strategy: apply experimental expertise; formulate ad-hoc designs; perform extensive simulations.

11. From ad hoc to Systematic… “A Symbolic Analysis of Relay and Switching Circuits,”M.S. Thesis, MIT, 1937 “A Mathematical Theory of Communication,” Bell System Technical Journal,1948. Claude E. Shannon1916 –2001 Basis of all digital computation. Basis of information theory, coding theoryand all communication systems.

12. inputs outputs digital circuit Building Digital Circuits • Design is driven by the input/output specification. • CAD tools are not part of the design process; they are the design process. . . .

13. BiologicalProcess [computational]Synthetic Biology [computational] Analysis “There are known ‘knowns’; and there are unknown ‘unknowns’; but today I’ll speak of the known ‘unknowns’.” – Donald Rumsfeld, 2004 Molecular Inputs Molecular Products Known /Unknown Given Known Unknown Unknown Known

14. Artificial Life Going from reading genetic codes to write them. US Patent 20070122826(pending):“The present invention relates to a minimal set of protein-coding genes which provides the information required for replication of a free-living organism in a rich bacterial culture medium.” – J. Craig Venter Institute

15. Artificial Life Going from reading genetic codes to write them. Moderator: “Some people have accused you of playing God.” J. Craig Venter:“Oh no, we’re not playing.

16. Biochemistry in a Nutshell Nucleotides: DNA: string of n nucleotides (n ≈ 109) ... ACCGTTGAATGACG... Amino acid: coded by a sequence of 3 nucleotides. Proteins: produced from a sequence of m amino acids (m ≈ 103).

17. 0 0 0 0 1 1 1 0 1 1 1 0 + 2a c b + Basic Mechanisms Logic Gates: how digital values are computed. “XOR” gate Biochemical Reactions: how types of molecules combine.

18. + Biochemical Reactions cell species count 9 8 6 5 7 9 Discrete chemical kinetics; spatial homogeneity.

19. + + + Biochemical Reactions Relative rates or (reaction propensities): slow medium fast Discrete chemical kinetics; spatial homogeneity.

20. Biochemical Reactions N M Synthesizing Biological Computation Design a system that computes output quantitiesas functionsof input quantities. given obtain Quantities of Different Types Quantities of Different Types independent specified for us to design

21. Produce of type n. + fast + a n a n 2 obtain 1 of n med a slow m b + v . fast + n b 2 c b M obtain of n 2 M 2 fast b med . c n Example: Exponentiation Start with M of type m. Use working types a,b,c. Start with anynon-zero amount of types aandn. Start with no amountof types bandc.

22. Functional Dependencies Exponentiation Logarithm Linear Raising-to-a-Power

23. Biochemical Reactions Synthesizing Biological Computation inputs computation outputs Molecular Triggers Molecular Products

24. Biological Computation at the Populational Level How can we control the quantity of molecular product at the populational level?

25. Synthesizing Stochasticity Engineer a probabilistic response in each cell. product with Prob.0.3 trigger product with Prob.0.7

26. Biological Computation at the Populational Level Obtain a fractional response.

27. k1 + k2 + k3 + Stochastic Kinetics • Its rate. • The quantities of its reactants. The probability that a given reaction is the next to fire is proportional to: See D. Gillespie, “Stochastic Chemical Kinetics”, 2006.

28. Jargon vs.Terminology “Now this end is called the thagomizer, after the late Thag Simmons.”

29. Biochemical Reactions Synthesizing Stochasticity Design a system that produces a probability distribution on the production of output types as a functionof input quantities. given obtain Quantities of Different Types Probability Distribution on Different Types Quantities of Different Types independent specified for us to design

30. Synthesizing Stochasticity Design a system that produces a probability distribution on the production of output types as a functionof input quantities. A with Prob.0.3 B with Prob.0.2 cell C with Prob.0.5

31. A and B with Prob.0.3 B and C with Prob.0.7 Synthesizing Stochasticity Design a system that produces a probability distribution on the production of output types as a functionof input quantities. Generalization: engineer a probability distribution on logical combinations of different outcomes. X Y cell Further: program probability distribution with (relative) quantity of input compounds.

32. x n e m StochasticModule y Synthesizing Stochasticity Generalization: engineer a probability distribution with a functional dependence on input quantities.

33. Synthesizing Stochasticity Strategy: • Structure computation to obtain initial choice probabilistically. • Thenamplify this choice and inhibitother choices. Method is: • Precise. • Robust. • Programmable. With “locking”, produces designs that areindependentof rates.

34. + + + Timing Synthesis schemes dependent on relative reaction rates. slow medium fast

35. Composition Module 1 Module 2 . . . . . . . . . < fast1 slow2 ? Rate separation increases with composition/modularity. fast2 slow2 fast1 slow1

36. Mario Luigi Timing Biochemical rules are inherently parallel. Sequentialize? Step 1: then Step 2:

37. Module Locking slow slow slow + slow slow + + fast + Sequentialize computation with only two rates: “fast” and “slow”.

38. Module Locking Sequentialize computation with only two rates: “fast” and “slow”.

39. A Comparison of the Accuracy of the Locked and Unlocked Versions of Three Modules: Multiplication, Exponentiation, and Logarithm. Unlocked Locked “Accuracy”:

40. Locking the Linear Stochastic Module

41. CAD Tool Brian’s Automated Modular Biochemical Instantiator (BAMBI) • Library of biochemical models. • Designated input and output types. • Specific quantities (or ranges) of input types. • Target functional dependencies. • Target probability distribution. Given: Outputs: • Reactions/parameters implementing specification. • Detailed measures of accuracy and robustness. Targets can be nearly any analytic function or data set.

42. Computational Infrastructure • Implementing a “front-end” database of biochemical models in Structured Query Language (SQL) from online repositories: BioBricks, SBML.org, … • Implementing “back-end” number crunching algorithms for analysis and synthesis on a high performance computing platform. IBM System Z Mainframe IBM’s Blue Gene/L

43. Computational Synthetic Biology vis-a-vis Technology-Independent Logic Synthesis Experimental Design vis-a-vis Technology Mapping in Circuit Design Discussion • Synthesize a design for a precise, robust, programmable probability distribution on outcomes – for arbitrary types and reactions. • Implement design by selecting specific types and reactions – say from “toolkit”.

44. Stochastic Logic inputs computation outputs Probability Distributions on Boolean output streams circuit Probability Distributions on Boolean input streams DAC 08, “The Synthesis of Robust Polynomial Arithmetic with Stochastic Logic”

45. inputs outputs p1 = Prob(one) circuit p2 = Prob(one) Stochastic Logic Consider a probabilistic interpretation: 0,1,1,0,1,0,1,1,0,1,… 1,0,0,0,1,0,0,0,0,0,…

46. inputs outputs circuit Stochastic Logic Consider a probabilistic interpretation:

47. inputs outputs circuit Stochastic Logic Consider a probabilistic interpretation: 0 1 p1 = Prob(one) 0 0 circuit 1 0 1 p2 = Prob(one) 0 0 0 parallel bit streams

48. Stochastic Logic Consider a probabilistic interpretation: 0 1 p1 = Prob(one) 0 0 circuit 1 0 1 p2 = Prob(one) 0 0 0 parallel bit streams

49. Probabilistic Bundles 0 1 x 0 X 0 1 A real value x in [0, 1] is encoded as a stream of bits X.For each bit, the probability that it is one is: P(X=1) = x.

50. Communicating Ideas