Pathway Modeling and Problem Solving Environments

1. Pathway Modeling andProblem Solving Environments Cliff Shaffer Department of Computer Science Virginia Tech Blacksburg, VA 24061

2. The Fundamental Goal of Molecular Cell Biology

3. Application:Cell Cycle Modeling • How do cells convert genes into behavior? • Create proteins from genes • Protein interactions • Protein effects on the cell • Our study organism is the cell cycle of the budding yeast Saccharomyces cerevisiae.

4. G1 cell division S DNA replication M (mitosis) G2

5. Pds1 Esp1 Esp1 Sister chromatid separation unaligned chromosomes SBF Cdh1 Pds1 Mcm1 Cdc20 PPX Net1P Tem1-GDP Cdc15/MEN Lte1 Bub2 Tem1-GTP Net1 Cdc14 RENT Sic1 Sic1 P Mcm1 Cdh1 Cdc20 Cln2 Clb2 Clb5 Mitosis Mad2 growth APC-P unaligned chromosomes Mcm1 Cdc20 Cdh1 Clb2 APC Inactive trimer Cdc14 and Cln3 Swi5 CDKs SCF P Cdc14 Bck2 Inactive trimer ? MBF Clb5 DNA synthesis Clb2 SBF Cln2 Budding

6. Modeling Techniques • One method: Use ODEs that describe the rate at which each protein concentration changes • Protein A degrades protein B: … with initial condition [A](0) = A0. Parameter c determines the rate of degradation. • Sometimes modelers use “creative” rate laws to approximate subsystems

7. synthesis synthesis binding degradation degradation inactivation activation Mathematical Model

8. G1 S/M Simulation of the budding yeast cell cycle mass CKI Cln2 Clb2 Cdh1 Cdc20 Time (min)

10. k1 = 0.0013, v2’ = 0.001, v2” = 0.17, k3’ = 0.02, k3” = 0.85, k4’ = 0.01, k4” = 0.9, J3 = 0.01, J4 = 0.01, k9 = 0.38, k10 = 0.2, k5’ = 0.005, k5” = 2.4, J5 = 0.5, k6 = 0.33, k7 = 2.2, J7 = 0.05, k8 = 0.2, J8 = 0.05, … Parameter values Differential equations Experimental Data

11. Tyson’s Budding Yeast Model • Tyson’s model contains over 30 ODEs, some nonlinear. • Events can cause concentrations to be reset. • About 140 rate constant parameters • Most are unavailable from experiment and must set by the modeler

12. Fundamental Activities • Collect information • Search literature (databases), Lab notebooks • Define/modify models • A user interface problem • Run simulations • Equation solvers (ODEs, PDEs, deterministic, stochastic) • Compare simulation results to experimental data • Analysis

13. Modeling Lifecycle

14. Our Mission: Build Software to Help the Modelers • Typical cycle time for changing the model used to be one month • Collect data on paper lab notebooks • Convert to differential equations by hand • Calibrate the model by trial and error • Inadequate analysis tools • Goal: Change the model once per day. • Bottleneck should shift to the experimentalists

15. Another View • Current models of simple organisms contain a few 10s of equations. • To model mammalian systems might require two orders of magnitude in additional complexity. • We hope our current vision for tools can supply one order of magnitude. • The other order of magnitude is an open problem.

16. JigCell Current Primary Software Components: • JigCell Model Builder • JigCell Run Manager • JigCell Comparator • Automated Parameter Estimation (PET) • Bifurcation Analysis (Oscill8) http://jigcell.biol.vt.edu

17. Model Builder Optimum Parameter Values Parameter Values Run Manager Comparator Parameter Optimizer

18. JigCell Model Builder • From a wiring diagram…

19. JigCell Model Builder • …to a reaction mechanism N.B. Parameters are given names, not numerical values! … to ordinary differential equations (ode files, SBML)

20. Mutations • Wild type cell • Mutations • Typically caused by gene knockout • Consider a mutant with no B to degrade A. • Set c = 0 • We have about 130 mutations • each requires a separate simulation run

21. Derived Set (mutant A) Derived Set (mutant B) Derived Set (mutant C) Derived Set (mutant A’) Derived Set (mutant AB) Derived Set (mutant A’C) Basal Set (wild-type) Run Manager • Inheritance patterns

22. JigCell Run Manager

23. Phenotypes • Each mutant has some observed outcome (“experimental” data). Generally qualitative. • Cell lived • Cell died in G1 phase • Model should match the experimental data. • Model should not be overly sensitive to the rate constants. • Overly sensitive biological systems tend not to survive

24. Comparator • Visualize results Kumagai1 Kumagai2

25. Comparator

26. Optimization • How to decide on parameter values? • Key features of optimization • Each problem is a point in multidimensional space • Each point can be assigned a value by an objective function • The goal is to find the best point in the space as defined by the objective function • We usually settle for a “good” point

27. Parameter Optimization

28. Error Function Parameter Optimization orthogonal distance regression Levenberg-Marquardt algorithm

29. Parameter Optimization Only 1 experiment shown here. The model must be fitted simultaneously to many different experiments.

30. Global DIRECT Search(DIViding RECTangles)

31. Global DIRECT Search(DIViding RECTangles)

34. Composition Motivation • Models are reaching the limits of manageability due to an increase in: • Size • Complexity • Making a model suitable for stochastic simulation increases the number of reactions by a factor of 3-5. • Models of the mammalian cell cycle will require 100-1000 reactions (even more for stochastic simulation).

35. Model Composition • Notice that the yeast cell diagram contains natural components

36. Composition Processes • Fusion • Merging two or more existing models • Composition • Build up model hierarchy from existing models by describing their interactions and connections • Aggregation • Connects modular blocks using controlled interfaces (ports) • Flattening • Convert hierarchy back into a single “flat” model for use with standard simulators

37. Composition Processes

38. Sample Sub-models

39. Aggregated Submodels

40. Final Aggregated Model

41. Aggregation Connector

42. Stochastic Simulation • ODE-based (deterministic) models cannot explain behaviors introduced by random nature of the system. • Variations in mass of division • Variations in time of events • Differences in gross outcomes

43. Gillespie’s Stochastic Simulation Algorithm • There is a population for each chemical species • There is a “propensity” for each reaction, in part determined by population • Each reaction changes population for associated species • Loop: • Pick next reaction (random, propensity) • Update populations, propensities • Slow, there are approximations to speed it up

44. Comments on Collaboration • Domain team routinely underestimates how difficult it is to create reliable and usable software. • CS team routinely underestimates how difficult it is to stay focused on the needs of the domain team. • Partial solution: truly integrate.

45. How to Succeed in CBB • Programming skills are necessary but not sufficient • Math is usually the biggest bottleneck • Statistics for Bioinformatics • Numerical analysis, optimization, differential equations for computational biology • Chemistry/biochemistry are good choices for domain knowledge • You have to have an “interdisciplinary attitude”