VCell: an introduction and its capabilities

Introduction

VCell primary documents are the BioModel, MathModel, Geometry, Application and Simulation.

BioModel consists of the

• Physiology - conceptual representation of the model: structures, molecules, connectivity map, kinetics.
• One or more Applications - virtual experiments that can be simulated: initial conditions, actual morphologies, electrical protocols, etc.
  • An Application can be compartmental or it can use a Geometry (see below).
  • Each Application has a mathematical representation that is automatically generated and can be viewed.
  • For each Application you can specify one or more
    • Simulations (time length, resolution, solvers to use, parameter overrides, etc.) that will run and produce Results. Results can be viewed in VCell or exported to a variety of formats.

MathModel is somewhat equivalent to the math description of a BioModel Application – it is a direct specification of the equations to be solved, using the VCell modeling language. It can be compartmental or it can use a spatial Geometry. One or more Simulations must be defined for each MathModel to run and produce Results.

• The math from a BioModel Application is a valid MathModel, but MathModel can not be extended to a BioModels. MathModels are needed to override biology-driven limitations of BioModels.

Geometry is a representation of a spatial structure which a BioModel Application (or a MathModel) can use for spatially resolved simulation. It can be 1-D, 2-D, or 3-D, and either analytically defined or based on a digital image.

 

Capabilities

Non-Spatial Deterministic (ODE) Solvers

• Forward Euler (First Order, Fixed Time Step)
• Runge-Kutta (Second Order, Fixed Time Step)
• Runge-Kutta (Fourth Order, Fixed Time Step)
• Adams-Moulton (Fifth Order, Fixed Time Step)
• Runge-Kutta-Fehlberg (Fifth Order, Variable Time Step)
• IDA (Variable Order, Variable Time Step, ODE/DAE)
• CVODE (Variable Order, Variable Time Step)
• Combined stiff solver CVODE/IDA

 

Spatial Deterministic (PDE) Solvers

• Semi-Implicit Finite Volume, Regular Grid (Fixed Time Step)
• Semi-Implicit Finite Volume Compiled, Regular Grid (Fixed Time Step)
• Fully-Implicit Finite Volume, Regular Grid (Fixed Time Step).

 

Non-Spatial Stochastic Solvers

• Gibson (Next Reaction Stochastic Method)
• Hybrid (Gibson + Euler-Matuyama Method)
• Hybrid (Gibson + Milstein Method)
• Hybrid (Adaptive Gibson + Milstein Method)

 

Spatial Stochastic Solvers

• Smoldyn ("Smoluchowski Dynamics" written by Dr. Steve Andrews)

 

Parameter Estimation using COPASI for Non-Spatial Deterministic Problems

(Only available in VCell 5.1 Beta version or later)
The Virtual Cell incorporates the COPASI parameter estimation capabilites to optimize parameters in non-spatial deterministic models to best fit experimental data. The available optmization solvers are listed below:

• Evolutionary Programming
• Evolution Strategy (SRES)
• Genetic Algorithm
• Genetic Algorithm SR
• Hooke and Jeeves
• Levenberg - Marquardt
• Nelder - Mead
• Particle Swarm
• Random Search
• Simulated Annealing
• Steepest Descent
• Praxis
• Truncated Newton

 

Model specification

• Comaprtmental volumes and membrane sizes
• Concentrations and/or molecule counts for species
• 3D Diffusion
• 2D Membrane Diffusion
• Advection (Velocity)
• Local and global parameters
• Initial conditions can be specified in terms of other model parameters, reserved symbols and species.

 

Geometry

• Creating analytic shapes in geometry editor.
• Protein Subcellular Location Image Database (PSLID) import and data handling in FieldData.
• Allow membrane field data from simulation results.
• Predefined ROIs for existing spatial compartments.
• ROIs from user defined Boolean functions.
• ROIs from user drawn polygons.
• Improved spatial data analysis for ROIs.

 

User Interface

• Auto-complete text
• Sort and search in Math Viewer and Math Model editor.

 

Export-Import Features

• Links to BioModels.net database
• Basic CellML import into MathModels.
• Formalize VCML as XML document
• Annotations (MIRIAM compliant)
• Create pdf report of models

 

Simulations

• Field data (using images data as input to simulations)
• CVODE solver used for Optimization in parameter estimation.
• Parameter scans
• 3D Surface Visualization for spatial simulation results