1. Pathway Modeling and Problem 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. 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

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. Mathematical Model synthesis degradation binding activation
inactivation

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

10. Differential equations Parameter values
k1 = , 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

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)

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

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. 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)

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