Pathway Modeling and Problem Solving Environments Cliff Shaffer Department of Computer Science Virginia Tech Blacksburg, VA 24061

The Fundamental Goal of Molecular Cell Biology

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.

G1 cell division S DNA replication M (mitosis) G2

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

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

Mathematical Model synthesis degradation binding activation inactivation

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

Differential equations Parameter values 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, … Experimental Data

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

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

Modeling Lifecycle

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

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.

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

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

JigCell Model Builder From a wiring diagram…

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

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

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

JigCell Run Manager

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

Comparator Visualize results Kumagai1 Kumagai2

Comparator