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Pathway Modeling and Problem Solving Environments

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Title: 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
ApplicationCell 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
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
Mathematical Model
8
Simulation of the budding yeast cell cycle
mass
CKI
Cln2
Clb2
Cdh1
Cdc20
Time (min)
9
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10
Experimental Data
11
Tysons Budding Yeast Model
  • Tysons 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
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
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)
32
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33
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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
Sample Composed Model
40
Composition Wizard
  • Final Species Mapping Table

41
Composition Wizard
  • Final Reaction Mapping Table

42
Aggregated Submodels
43
Final Aggregated Model
44
Aggregation Connector
45
Composition in SBML
  • Virginia Techs proposed language features to
    support composition/aggregation being written
    into forthcoming SBML Level 3 definition

46
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

47
Gillespies 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

48
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.

49
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
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