Synthesis of Biological Models from Mutation Experiments

Transcription

1 Synthesis of Biological Models from Mutation Experiments Ali Sinan Köksal, Saurabh Srivastava, Rastislav Bodík, UC Berkeley Evan Pu, MIT Jasmin Fisher, Microsoft Research Cambridge Nir Piterman, University of Leicester

2 Overview Concurrent program synthesis from examples Programs biological explanations Examples biological experiments We assist natural sciences with formal methods Given experiments, are there other explanations? If so, compute a new, disambiguating experiment This avoids conducting superfluous experiments This talk: how stem cells coordinate their fates 2

3 Understanding Diseases Cancer is fundamentally a disease of failure of regulation of tissue growth. In order for a normal cell to transform into a cancer cell, the genes which regulate cell growth and differentiation must be altered. from Wikipedia Research on cell differentiation helps understanding diseases such as cancer. 3

4 C. elegans: A Model Organism Earthworm used in developmental biology. 959 cells; its organs found in other animals. Differentiation studied on vulval development. 4

5 Initial division of embryo Identical precursor cells collaborate to decide their fate Differentiation and then development into organ parts 5

6 Research Goal of Biologists What is the mechanism (program) within each cell for deciding fates through communication? 6

7 Building Blocks of these Programs Cells contain communicating proteins. Protein interaction: a protein senses the concentration of other proteins. Interaction is either activation or inhibition. A B A B 7

8 How the Vulval Cells Differentiate Anchor Cell If cells sense the same signal strength, data races occur. high med low let-23 let-23 let lin-12 lst sem-5 let-60 lin-12 lst sem-5 let-60 lin-12 lst sem-5 let-60 mpk-1 mpk-1 mpk-1 1º 2º 3º 8

9 How Biologists Discover Interactions Measuring protein levels over time is infeasible. If such cell tracing is infeasible, infer protein interaction from end-to-end experiments. That is, mutate cells observe resulting fates. Mutation experiments change protein behavior in a controlled way: Enable a protein via gene overexpression. Disable a protein via gene suppression. 9

10 A Mutation Experiment Anchor Cell high med low let-23 let-23 let lin-12 lin-12 lin-12 1º 2º 1º 3º 10

11 Putting Experiments Together No protein is mutated. Fate of six neighboring cells Experiment AC lin-12 lin-15 let-23 lst Fate decisions 1 ON ON ON ON ON {332123} 2 ON OFF ON ON ON {331113} 3 ON ON OFF ON ON {112121,122121, } lin-12 is turned off. Multiple outcomes observed Experiments over 35 years by 11 groups 11

12 How to Build Accurate Models? Anchor Cell Inhibition discovered by predictive modeling [Fisher et al. 2007] high med low let-23 let-23 let lin-12 lst sem-5 let-60 lin-12 lst sem-5 let-60 lin-12 lst sem-5 let-60 mpk-1 mpk-1 mpk-1 1º 2º 3º 12

13 Semantics of the Modeling Language Program has cells Non-deterministic outcomes via schedule interleaving Cell 1 Cell 2 let-23 Cell has proteins All proteins advance synchronously lin-12 lst sem-5 let-60 mpk-1 input = med true Proteins have discrete state and update functions. low med high input = high input apple low true 13

14 Synthesizing Cellular Programs 14

15 Synthesis of Programs biological insight Given as a partial program synthesizer completed program specification Experiment AC lin-12 lin-15 let-23 lst Fate decisions 1 ON ON ON ON ON {332123} 2 ON OFF ON ON ON {331113} 3 ON ON OFF ON ON {112121,122121, }... 15

16 Partial Programs Partial programs express biological insight: Which proteins are in the cell Which proteins may interact Update functions can be unknown. let-23 sem-5?? low med high input apple low input = med input = high true true lin-12 lst let-60 mpk-1 16

17 Synthesis Algorithm 17

18 Correctness Condition Experiment AC lin-12 lin-15 let-23 lst Fate decisions 1 ON ON ON ON ON {332123} 2 ON OFF ON ON ON {331113} 3 ON ON OFF ON ON {112121, , }... Safety: all schedules must lead the program to produce experiment outcomes observed in the wet lab. mutation m. schedule s. P(m, s) E(m) Completeness: each observed experiment outcome must be reproducible by the program for some schedule. mutation m. fate f E(m). schedule s. P(m, s) = f 18

19 Counterexample-Guided Inductive Synthesis counterexample: execution P(m, s) with bad outcome initial set of input/output examples inductive synthesizer candidate completion no candidate completion counterexample: observation (m, f) not reproducible safety verifier ok completeness verifier 19

20 Synthesized Models We synthesized two models of VPCs. Input: Partial model that specifies known, simple protein behaviors. Output: Synthesized update functions for two key proteins. ac = 0 (ac [0,1] hyp = 0) (ac = 2 hyp = 0) (ac [1,2] hyp = 1) S0 / 0 S1 / 0 (ac = 1 hyp = 1) ac [2,3] (lin12 = 0 ls ac = 0 = 3 let23 = 0) (ls = 0 let23 = 1) (ls = 1 let23 = 1) (lin12 = 0 ls = 1) S1 / 0 (lin12 = 0 ls = 1) (lin12 [1,3] ls = 0 let23 = 0) S0 / 0 model 1 S2 / 1 lin12 [1,3] ls = 1 lin12 = 0 ls = 1 ac [2,3] (ac [1,2] hyp = 1) ls = 0 lin12 [1,3] ls = 1 let23 = 0 S2 / 1 lin12 = 3 (lin12 [1,2] ls = 1) ac = 0 (ac [0,1] hyp = 0) (ac = 2 hyp = 0) (ac [1,2] hyp = 1) S0 / 0 S1 / 0 ac = 3 lin12 = 0 ls = 0 (ac = 1 hyp = 1) ac [2,3] S2 / 1 ac [2,3] (ac [1,2] hyp = 1) lin12 = 0 sem5 = 1 S0 / 0 S1 / 1 lin12 [1,3] ls = 1 model 2 (lin12 = 0 ls = 1 sem5 = 0) (lin12 [1,3] ls = 1) 20

21 Additional Algorithms for Going Beyond Synthesis to Assist Scientists 21

22 Querying Spaces of Models Assume a scientist obtains a formal model that agrees with all performed experiments. How can he make sure that a future mutation experiment won t invalidate this model? We can search for an alternative model that differs on a future experiment. Performing the new experiment will disambiguate between the two models. 22

23 Finding Disambiguating Experiments Simulation of future experiments using partial data: Assuming we didn t have the experiments from Sternberg and Horvitz 1989, we can synthesize four hypothesis models. Our tool suggests experiments from this paper to invalidate two of them. 23

24 Differentiating Plausible Models Can we differentiate the two plausible models that we synthesized? let-23 sem-5 let-23 sem-5 lin-12 lst let-60 lin-12 lst let-60 mpk-1 mpk-1 Mutating the modeled proteins will not suffice to disambiguate them, which suggests other methods (e.g. gene marking). 24

25 Avoiding Superfluous Experiments Can the scientist avoid performing superfluous experiments when revalidating results? We can search for a minimal, non-ambiguous subset of a set of experiments. Out of 48 VPC experiments, 4 suffice to yield a unique model from a given partial program. 25

26 Conclusion Biological experiments as specification for synthesis A synthesis algorithm with three solvers Explore spaces of alternative models Avoid conducting superfluous experiments 26