Models and methods in systems biology

1. Models and methods in systems biology Daniel Kluesing Algorithms in Biology Spring 2009

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4. Engineering Principles • Simple primitives • Abstraction layers • Composable Systems • Robust and well characterized • Manage complexity Should also work in biology

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8. Executable Cell Biology Jasmin Fisher, Thomas Henzinger Nature Biotechnology, November 2007

9. Mathematical v Computational • Mathematical • Describe relationships between quantities • Differential equations, probability models • Composition of transfer functions • Simulated, quantitative • Computational • Sequence of steps • State machines • Transitions between states • Executed, qualitative, abstractions

10. Mathematical model • Describe changes in quantities over time • Need an algorithm for simulating and solving • Differential equations

11. Computational Models • Large number of states • Non-linear, non-deterministic • Hard to model mathematically • Executes itself • Abstraction layers

12. Abstraction layers Populations Organism Organ Tissue Cell Signaling networks Metabolic pathways Protien-protien interaction Genes DNA segment Base pairs Molecules Network Program Class Function Variable Bits Logic gates Transistors Atoms

13. Model Checking • Given a model • Test if model meets specification • Systematically analyze the outcomes of a computational model without executing them individually • Explore states rather than all executions • Efficient

14. Model Checking • Computational models can be analyzed by model checking • Yields a proof • Mathematical models can often only be simulated • Only as good as your data, edge cases

15. Formal Verification We know exactly what this chip does, for all input We can prove that it works correctly for all conditions Can make guarantees about its operation No data mining required Fsu.edu

16. Executable cell biology • Many of the algorithms covered in class • Gather a bunch of data • Train a model • Model explains data • May not reflect biology • Looking inside an SVM isn’t useful • Would like to have a model of the underlying system • Algorithms that mimic biological phenomena

17. Executable Biology Fisher et al

18. Boolean Models • Each gene or protein is either on or off • Activation level determines state at next time step • Gene regulatory networks www.ra.cs.uni-tuebingen.de www.zaik.uni-koeln.de

19. Boolean Models • Easy to build, efficient to analyze • Show causal and temporal relationships • Deterministic • But • Difficult to compose • Cannot build larger models from several small ones

20. Petri Nets • Used to model distributed systems • Two types of nodes • Places (resources) • Transitions (events) • Edges connection places to transitions and transitions to places • Multiple tokens on the graph • More than one token can move at a time

21. Petri Nets Animation: Wikipedia

22. Petri Nets http://upload.wikimedia.org/wikipedia/commons/f/fe/Detailed_petri_net.png

23. Petri Nets • Generalization of Boolean networks • Visual design and analysis • Non-deterministic • Colored tokens, stochastic nets • But • Still can’t compose networks

24. Interacting state machines www.odetocode.com/Articles/460.aspx

25. Interacting state machines • Multiple state machines • Communication between machines Fisher et al

26. Interacting state machines Fisher et al

27. Interacting State machines • Natural abstraction and hierarchy • Qualitative • Easy to run model checking on • Mature and well tested tools and languages

28. Process calculi • Languages that model communicating processes • Interactions between molecules • Process is a state machine • Some state changes are events • Events allow communication between processes

29. Process calculi • Interactions as message passing • No shared variables • Small set of primitives • Operators to combine primitives • Algebraic laws • Parallel and sequential composition • Directed communication

30. Hybrid Models • Combine computational and mathematical models • Discrete state changes update differential equations Fisher et al

31. Challenges and Open Questions What about GFP? What are the biological abstraction layers?

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34. Quantitative measures • Experimental data is often unit less ratios • Direct measurements make parameter setting easier • Need better experimental methods to get direct measurement of signals • Convert observed fluorescence into number of molecules

35. Bio Logic Gates Fisher et al

36. Biology as engineering • Design and build systems • Very large scale integration • Hierarchy and levels of abstraction • Robust and fully characterized

37. Regulation of Gene Expression in Flux Balance Models of Metabolism Markus Covert, Christophe Schilling, Bernhard Palsson Journal of Theoretical Biology, 2001

38. Flux Balance Analysis • Cells obey the laws of physics and chemistry • We can write down the reactions • We know the basic governing laws • Conservation of mass • Conservation of energy • Redox potential So, cell behavior is constrained

39. Flux Balance Analysis http://covertlab.stanford.edu/projects/iFBA/

40. Flux Balance Analysis Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

41. Advances in flux balance analysis, 2003 Kenneth J Kauffman, Purusharth Prakash and Jeremy S Edwards

42. Flux Balance Analysis http://covertlab.stanford.edu/projects/iFBA/

43. Regulation • FBA assumes all gene products are available to contribute to a solution • E. Coli has 600 metabolic genes • 400 regulatory genes • High levels of transcriptional regulation

44. Regulation • Constraints change shape of solution space Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

45. Representing transcriptional Regulatory Constraints • Boolean logic equations If all products present, flux determined by FBA If all products not present, place a temporary constraint Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

46. Carbon core metabolic network Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

48. Simulating different Conditions Two carbon sources, aerobic Two carbon sources, diauxic shift Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

49. Amino Acid biosynthesis Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

50. Further Advances • Explicit incorporation of thermodynamics • Different objective functions • Maximization of biomass • Maximization of ATP • Maximizing rate of synthesis of a product