Why Discrete Stochastic Simulation

1
Multiscale Simulation for Biochemical Systems

• Why Discrete Stochastic Simulation?
• An ODE model cannot capture effects due to small
  numbers of key chemical species
• A molecular dynamics model is too slow given the
  model complexities, time scales of interest, and
  need for repeated runs
• Why Multiscale?
• A discrete stochastic model of all species and
  all reactions may be too slow. Accelerate
  and/or couple to ODE model
• Parameters could be coming from finer scale (MD)
  simulations

2
Software What do we have?

• Discrete stochastic simulation of well-mixed
  systems MCell, StochKit, Cain/SSALIB, JigCell,
  CellDesigner, CellMC, STOCKS, StochSim, SynBioSS,
  TinkerCell, Moleculizer,
• Some limited multiscale capabilities

3
Software What do we need?

• Stiff stochastic systems
• Adaptive multiscale
• Probabilities of rare events
• Sensitivity analysis, uncertainty quantification,
  reduced order stochastic models
• Parameter estimation
• High performance, for example GPU

4
Spatial stochastic simulation

• Huge problem of computational complexity
• Large numbers of diffusive transfers must be
  aggregated to enable parallelism
• Intrinsic physical limitations put lower bound on
  spatial grid size
• Mathematical and software infrastructure must
  support complicated geometries, unstructured
  meshes
• Molecular crowding effects reaction propensities,
  but by how much?

Unfolded protein response in the endoplasmic
reticulum C. Young, A. Robinson, U. Delaware
Polarization in yeast mating T. M. Yi, UC Irvine
5
We need a collection of community models!

• Why?
• Facilitate development and extension of models
• Experiment with published models and
  validate/invalidate with new experimental data
• Demonstrate the issues that computational
  infrastructure need to address
• Test the viability and efficiency of new
  algorithms and software on realistic models
• Issues
• Requires a common modeling language and/or
  standards and expectations for publication
• The language must be extensible to accommodate
  unforseen future needs