Biological Logic and Computation
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The document discusses biological computation and gene regulation in cells. It describes how (1) cells perform biochemical information processing to transform cues into biological functions, (2) embryonic stem cells can adopt different states through gene regulation, and (3) techniques like Boolean networks and satisfiability modulo theories can be used to model and analyze gene interaction networks inferred from experimental data. The techniques allow predicting cell behaviors and identifying gene interaction programs governing processes like stem cell differentiation.
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Biological Logic and Computation
- 11. Biological Computation /bΚΙͺΙ(Κ)ΛlΙdΚΙͺk(Ι)l/ /kΙmpjΚΛteΙͺΚ(Ι)n/ noun The biochemical information-processing carried out by cells in order to transform chemical, electrical and mechanical cues into biological function.
- 12. What are the biological programs that govern Development?
- 13. βNaΓ―veβ embryonic stem cells (ESCs)Blastocyst: structure formed just days into development
- 15. Adult Cell Insert key genes Transform to stem cell Shinya Yamanaka
- 20. Modelling Dynamic Gene Interactions DecisionSignal Input Layer Output LayerComputation Layer Gene Gene Gene Gene Gene Gene
- 21. Modelling Dynamic Gene Interactions Boolean Network State transition system 111 110 011 010 101 001 100000 0 1 1 A B C Bit-vector Kauffman, 1969 AND OR
- 22. Inferring Interactions Between Genes Perturbations Expression correlation Chip Seq
- 23. Challenge: In reality, experimental data only indicates the possibility of an interaction Abstract Boolean Network (ABN) Classifying π interactions as possible defines 2 π unique topologies
- 24. Challenge: Unique networks can produce the same behaviour 111 110 011 010 100001 101 000 110 111 011 001101 010 100 000 We need to consider the set of potential models
- 25. Examining Dynamic Behaviour State Transition System Time Concentration Simulation
- 26. Formal verification techniques allow us to specify and analyse the behaviour of software and hardware
- 27. βIf gene A is active, then gene B is active or gene C is active.β π΄ β (π΅ β¨ πΆ) βIn Experiment 1, initially A is inactive and at step 6 it is active.β πΈ0 1 . π΄ = 0 β§ πΈ6 1 . π΄ = 1 Gene A Gene B Gene C
- 28. Boolean Satisfiability (SAT) 1. Given a propositional formula π, determine if there is a variable assignment such that π evaluates to TRUE. 2. Generate a model that satisfies π. π β π΄ β (π΅ β¨ πΆ) βIf gene A is active, then gene B is active or gene C is active.β {π΄, π΅, πΆ} {Β¬π΄, Β¬π΅, Β¬πΆ} {π΄, Β¬π΅, πΆ} Assignments under which π is TRUE {π΄, π΅, Β¬πΆ} π is SATISFIABLE
- 29. Satisfiability Modulo Theories (SMT) β’ Decision procedures for pre-defined theories β’ Boolean β’ Uninterpreted functions β’ Integers β’ Bit-vectors β’ Floating point numbers β’ Data types (Strings, Arrays, Lists, etc.) β’ Theory combination strategy β’ Standardisation
- 30. SAT/SMT problems are hard (or undecidable) de Moura and BjΓΈrner, TACAS, 2008
- 31. πΈ0 1 . π1 πΈ0 1 . π2 πΈ0 1 . π΄ πΈ0 1 . π΅ πΈ0 1 . πΆ πΈ1 1 . π1 πΈ1 1 . π2 πΈ1 1 . π΄ πΈ1 1 . π΅ πΈ1 1 . πΆ πΈ πΎ 1 . π1 πΈ πΎ 1 . π2 πΈ πΎ 1 . π΄ πΈ πΎ 1 . π΅ πΈ πΎ 1 . πΆ β¦ πΈ0 2 . π1 πΈ0 2 . π2 πΈ0 2 . π΄ πΈ0 2 . π΅ πΈ0 2 . πΆ πΈ1 2 . π1 πΈ1 2 . π2 πΈ1 2 . π΄ πΈ1 2 . π΅ πΈ1 2 . πΆ πΈ πΎ 2 . π1 πΈ πΎ 2 . π2 πΈ πΎ 2 . π΄ πΈ πΎ 2 . π΅ πΈ πΎ 2 . πΆ β¦ System variables Statevariables (Experiment1) Statevariables (Experiment2) πΌπ΄,π΅ + πΌπ΄,π΅ β πΌ π΅,π΄ + πΌπ΄,πΆ + πΌπ΄,πΆ β πΌ π΅,πΆ + πΌ πΆ,π΅ β β¦ π π΄ π π΅ π πΆ π π1 π π2 Cell network Update functions βIn Experiment 1, initially S1 is inactive and S2 is active.βπΈ0 1 . π1 = 0 β§ πΈ0 1 . π2 = 1 Encoding an ABN as an SMT Problem
- 32. 101 000 . . .
- 33. Bounded model checking (BMC) 1. Encode state space, π = β¬ 2. Encode transition relation, π π, πβ² 3. βUnrollβ the transition relation (πΎ steps) to identify reachable states Biere, Cimatti, Clarke, Zhu, TACAS, 1999 Type equation here. Q Reachable states K q0 q1 q2 qK πΆβ² πΌπΉπΉ π΄ ππ [π΅ πΌπΉ π΅ β πΆ] π π, πβ² BMC checks if there is a path that satisfies the properties: πΈ0 1 . π΄ = 0 β§ πΈ6 1 . π΄ = 1
- 34. Bounded model checking (BMC) Biere, Cimatti, Clarke, Zhu, TACAS, 1999 Type equation here. Q Reachable states K q0 q1 q2 qK βπ0, π1, β¦ , π πΎ β π (variables) (system dynamics) (properties) π π0, π1 β§ π π1, π2 β§ β― β§ π π πΎβ1, π πΎ β§ π0(π0) β§ π1(π1) β¦ β§ π πΎ(π πΎ) βπ. πππ‘β(π) β§ Ξ (π) There exists a path that satisfies the properties βπ, π. πππ‘β(π, π) β§ Ξ (π) β§ Ξ¨(π) BMC-based synthesis
- 35. Analysis Strategies β’ Synthesis β’ SAT: a system design (network, π) and executions (trajectories, π) that satisfy the properties (observations, Ξ ) β’ UNSAT: proof that no valid designs exist (up to πΎ) β’ Enumeration β’ Additional constraints: πβ² β π β’ Optimisation β’ Define a property π π β β, find a solution, assert π πβ² < π π βπ, π. πππ‘β(π, π) β§ Ξ (π) β§ Ξ¨(π)
- 36. Reasoning Engine for Interaction Networks (RE:IN) Concrete networks consistent with experimental observations research.microsoft.com/rein http://rein.cloudapp.net/ Dunn, Yordanov & Martello et al., Science (2014) Abstract Boolean Network Experimental observations
- 37. What is the biological program governing stem cell pluripotency?
- 39. Identifying Possible Gene Interactions Pearson coefficient: -0.98 Pearson coefficient: 0.98 Experimental data describing the expression of key genes under different inputs
- 40. Gene expression correlation does not indicate which gene behaves as the regulator Abstract Network Topology Four unique possibilities
- 41. ES cells can efficiently convert between culture conditions Experimental Constraints Transform into constraints on network trajectories
- 42. Synthesis
- 43. Required and Disallowed Interactions Abstract Boolean Network (ABN) Constrained ABN RE:IN
- 44. The models accurately predict the response to network perturbations Dunn, Martello, Yordanov et al., Science 2014 Remain pluripotent Differentiate
- 46. Network Dynamics as a Proxy for Efficiency EpiSC Step 1 Step 10 NaΓ―ve state
- 47. Enhanced Reprogramming Efficiency EpiSC, Klf2 OE Step 1 Step 4, NaΓ―ve state
- 50. β’ Uncovered the biological program governing stem cell decision-making β’ Consistent with 149 different experiments β’ Predictive accuracy of 80% β’ Used to inform biological experiments β’ Increased reprogramming efficiency to 100%, and reduced time to just 24hrs β’ Predicted gene activation trajectories substantiated even at single cell resolution Dunn & Li et al., EMBO J (2019)
- 54. Acknowledgements β’ Amy Li, Graziano Martello and Austin Smith β’ Boyan Yordanov, Hillel Kugler, Christoph Wintersteiger β’ www.research.microsoft.com/rein
- 55. Paul Grant Neil Dalchau Boyan Yordanov Carlo Spaccasassi Collaborators Programming Stem Cells University of Cambridge Stem Cell Institute: Austin Smith University of Cambridge Metabolic Research Laboratories: Davide Chiarugi, Anne-Claire Guenantin, Antonio Vidal-Puig University of Padova: Graziano Martello Programming DNA Princeton University: Bonnie Bassler University of Washington: Georg Seelig, Gourab Chatterjee, Suzie Pun University of New Mexico: Matthew Lakin Rice University: Dave Zhang University of Cambridge: Ulrich Keyser, Elisa Hemmig Microsoft Research: Karin Strauss, Yuan Chen Caltech: Frits Dannenberg Programming Genetic Devices University of Cambridge: Jim Ajioka, Jim Haseloff, Om Patange, Eugene Nadezhdin UCL: Chris Barnes, Luca Rosa Luca Cardelli Filippo Polo Colin Gravill Sara-Jane Dunn James Locke Andrew Phillips Jacob Halatek Prashant Vaidyanathan