Pathway Modeling and Problem Solving Environments

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Pathway Modeling andProblem Solving Environments

• Cliff Shaffer
• Department of Computer Science
• Virginia Tech
• Blacksburg, VA 24061

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The Fundamental Goal of Molecular Cell Biology
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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.

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G1
cell division
S
DNA replication
M (mitosis)
G2
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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
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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

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Mathematical Model
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Simulation of the budding yeast cell cycle
mass
CKI
Cln2
Clb2
Cdh1
Cdc20
Time (min)
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Experimental Data
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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

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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

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Modeling Lifecycle
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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

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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.

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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

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

• From a wiring diagram

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JigCell Model Builder

• to a reaction mechanism

N.B. Parameters are given names, not numerical
values!
to ordinary differential equations
(ode files, SBML)
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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

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Run Manager

• Inheritance patterns

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JigCell Run Manager
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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

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Comparator

• Visualize results

Kumagai1
Kumagai2
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Comparator
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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

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Parameter Optimization
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Error Function
Parameter Optimization
orthogonal distance regression
Levenberg-Marquardt algorithm
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Parameter Optimization
Only 1 experiment shown here. The model must be
fitted simultaneously to many different
experiments.
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Global DIRECT Search(DIViding RECTangles)
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Global DIRECT Search(DIViding RECTangles)
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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).

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Model Composition

• Notice that the yeast cell diagram contains
  natural components

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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

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Composition Processes
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Sample Sub-models
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Aggregated Submodels
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Final Aggregated Model
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Aggregation Connector
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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

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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

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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.

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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