1 / 141

Simulating Biological Systems in the Stochastic Pi-calculus

Simulating Biological Systems in the Stochastic Pi-calculus. Andrew Phillips with Luca Cardelli Microsoft Research, Cambridge UK. Biological Computing. Modelling Biology. The Human Genome project: Map out the complete genetic code in humans

mikkel
Download Presentation

Simulating Biological Systems in the Stochastic Pi-calculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Simulating Biological Systems in the Stochastic Pi-calculus Andrew Phillips with Luca Cardelli Microsoft Research, Cambridge UK

  2. Biological Computing

  3. Modelling Biology • The Human Genome project: • Map out the complete genetic code in humans • To understand and predict gene and protein behaviour • Like reading the source code of a computer program... • But functional meaning of the code is still a mystery! • Systems Biology: • Understand and precisely describe the behaviour of biological systems • Two complementary approaches: • Look at experimental results and infer general system properties • Build detailed models of systems and test these in the lab • Biological Modelling: • Conduct virtual experiments, saving time and money. • Need tools for modelling complex parallel systems. • Should also scale up to very large systems. • The beginnings of a biological programming language...

  4. Languages for complex, parallel computer systems: Languages for complex, parallel biological systems: Programming Biology stochasticp-calculus

  5. Traditional modelling: model individual reactions Reactions vs. Components

  6. Traditional modelling: model individual reactions Reactions vs. Components

  7. Large, Connected Reaction Graphs http://www.celldesigner.org/

  8. Traditional modelling: model the individual reactions Stochastic p-calculus: model the components Reactions vs. Components

  9. Compositional Modelling Build complex models incrementally, by direct composition of simpler components:

  10. Model Analysis • A formal programming language • Analysis techniques (types,equivalences,model-checking) • Could help provide insight into fundamental properties of biological systems

  11. Equivalent Models • Can we replace one model with another?

  12. Related Work • Stochastic p-calculus proposed by [Priami, 1995] • Used to simulate a range of biological systems: • RTK MAPK pathway [Regev et al., 2001] • Gene Regulation by positive Feedback [Priami et al., 2001] • Cell Cycle Control in Eukaryotes [Lecca and Priami, 2003] • First simulator for stochastic p-calculus [BioSPI] • A subset of p-calculus with limited choice • Compiles a calculus process to an FCP procedure • Executed by the FCP Logix platform [Silverman et al., 1987]

  13. Graphical Stochastic p-calculus • Display stochastic p-calculus models as graphs • [Phillips and Cardelli, 2005] • Helps make the stochastic p-calculus more accessible • Defined a graphical calculus and graphical execution model • Proved equivalent to the stochastic p-calculus • [Phillips, Cardelli and Castagna, 2006] PROVED EQUIVALENT

  14. The Stochastic PiMachine • A simulation algorithm for stochastic p-calculus • [Phillips and Cardelli, 2004] • Based on standard theory of chemical kinetics [Gillespie, 1977] • The probability of a reaction is proportional to its rate • Proved correct with respect to the stochastic p-calculus. PROVED CORRECT

  15. The SPiM Simulator • Simulation algorithm mapped to functional code (F#) • Used as the basis for implementing the SPiM simulator. • [Phillips, 2006] GUI by James Margetson, MSRC • Close correspondence between formal algorithm and functional code • Correct specification improves confidence in simulation results • Used in various research centres (UK, France, Italy, Sweden...) http://research.microsoft.com/~aphillip/spim

  16. Visualising Simulations in 3D • Generate a 3D view of the interactions Software by Rich Williams, MSRC

  17. Course Outline • The Stochastic Pi-calculus • Gene Networks • Signalling Networks • Immune System Pathway

  18. The Stochastic Pi-calculus Introductory Tutorial

  19. Calculus Syntax p::= ?x(m) Input value m on channel x !x(n)   Output value n on channel x trDelay at rate r P::= p1.P1 + ... + pN.PNChoice between actions P1 | ... | PMParallel composition of processes X(n)   Instance of X with arguments n new x1,...,xNP Restriction of names x1,...,xN to P E::= X(m) = P Definition of X, where fn(P) Ím E1, ... ,ENUnion of definitions

  20. Graphical Syntax

  21. Execution: Stochastic Delay tr.P1 + ... + pN.PN

  22. Execution: Stochastic Delay tr.P1 + ... + pN.PN ¾®P1

  23. Execution: Interaction !x(n).P1 + ... + pN.PN | ?x(m).Q1 + ... + pM.QM

  24. Execution: Interaction !x(n).P1 + ... + pN.PN | ?x(m).Q1 + ... + pM.QM ¾®P1 |Q1{n/m} {n/m}

  25. Execution: Binding Interaction new n (!x(n).P1 + ... + pN.PN ) | ?x(m).Q1 + ... + pM.QM

  26. Execution: Binding Interaction new n (!x(n).P1 + ... + pN.PN ) | ?x(m).Q1 + ... + pM.QM ¾® new n ( P1 | Q1{n/m} ) n {n/m}

  27. Ionization: Na + Cl  Na+ + Cl- let Na() = !ionize; Na_plus() and Na_plus() = ?deionize; Na() run Na() let Cl() = ?ionize; Cl_minus() and Cl_minus() = !deionize; Cl() run Cl() • Na can ionize Cl at rate(ionize) = 100s-1 • Cl-can deionize Na+ at rate(deionize) = 10s-1

  28. Ionization: Na + Cl  Na+ + Cl- let Na() = !ionize; Na_plus() and Na_plus() = ?deionize; Na() run Na() let Cl() = ?ionize; Cl_minus() and Cl_minus() = !deionize; Cl() run Cl() • Na can ionize Cl by an output on the ionize channel

  29. Ionization: Na + Cl  Na+ + Cl- let Na() = !ionize; Na_plus() and Na_plus() = ?deionize; Na() run Na_plus() let Cl() = ?ionize; Cl_minus() and Cl_minus() = !deionize; Cl() run Cl_minus() • Cl-can deionize Na+ by an output on the deionize channel

  30. Ionization: Na + Cl  Na+ + Cl- let Na() = !ionize; Na_plus() and Na_plus() = ?deionize; Na() run Na() let Cl() = ?ionize; Cl_minus() and Cl_minus() = !deionize; Cl() run Cl() • Na and Cl are no longer charged

  31. Ionization: Na + Cl  Na+ + Cl- • A number of Na and Cl atoms can be composed in parallel.

  32. Ionization: Na + Cl  Na+ + Cl- • One of the Na atoms can ionize one of the Cl atoms.

  33. Ionization: Na + Cl  Na+ + Cl- • Additional Na and Cl atoms can interact in parallel.

  34. Ionization: Na + Cl  Na+ + Cl- • A Cl-ion can deionize any of the Na+ ions.

  35. Ionization: Na + Cl  Na+ + Cl- • These reactions can continue indefinitely...

  36. Virtual Experiment: Na + Cl  Na+ + Cl- • What happens if we mix 100×Na and 100×Cl ? • Use a more compact representation to count populations. • The colour is proportional to the number of atoms:

  37. Virtual Experiment: Na + Cl  Na+ + Cl- • One of the Na atoms can ionize one of the Cl atoms.

  38. Virtual Experiment: Na + Cl  Na+ + Cl- • Additional Na and Cl atoms can interact in parallel.

  39. Virtual Experiment: Na + Cl  Na+ + Cl- • A Cl-ion can deionize any of the Na+ ions.

  40. Virtual Experiment: Na + Cl  Na+ + Cl- • Eventually an Equilibrium is reached...

  41. Virtual Experiment: Na + Cl  Na+ + Cl- • At equilibrium: 100×[Na][Cl] = 10×[Na+][Cl-] • Approximately 76×Na and 24×Na+

  42. Binding: H + Cl  HCl let H() = new e@10.0 ( !share(e); H_Bound(e)) and H_Bound(e) = !e; H() let Cl() = ?share(e); Cl_Bound(e) and Cl_Bound(e) = ?e; Cl() run ( H() | Cl() ) • H has a private electron e. • H can share its electron with Cl at rate(share) = 100s-1 • HCl can break its private bond at rate(e) = 10s-1

  43. Binding: H + Cl  HCl let H() = new e@10.0 ( !share(e); H_Bound(e)) and H_Bound(e) = !e; H() let Cl() = ?share(e); Cl_Bound(e) and Cl_Bound(e) = ?e; Cl() run ( H() | Cl() ) • H can share its electron with Cl on the share channel.

  44. Binding: H + Cl  HCl let H() = new e@10.0 ( !share(e); H_Bound(e)) and H_Bound(e) = !e; H() let Cl() = ?share(e); Cl_Bound(e) and Cl_Bound(e) = ?e; Cl() run new e (H_Bound(e) |Cl_Bound(e)) • HCl can break its private bond by synchronising on e. e

  45. Binding: H + Cl  HCl let H() = new e@10.0 ( !share(e); H_Bound(e)) and H_Bound(e) = !e; H() let Cl() = ?share(e); Cl_Bound(e) and Cl_Bound(e) = ?e; Cl() run (H() | Cl() ) • H and Cl are no longer bound

  46. Binding: H + Cl  HCl • A number of H and Cl atoms can be composed in parallel.

  47. Binding: H + Cl  HCl • One of the H atoms can bind with one of the Cl atoms

  48. Binding: H + Cl  HCl e • Additional H and Cl atoms can bind in parallel.

  49. Binding: H + Cl  HCl e • A single HCl molecule can split into H and Cl atoms. e

  50. Binding: H + Cl  HCl e • These reactions can continue indefinitely...

More Related