Numerical Solvers

The Virtual Cell converts the biological description defined in a BioModel into a corresponding mathematical system of equations (e.g. ordinary and/or partial differential equations), VCell will then solve the equations by applying numerical solvers to perform and analyze simulations.

In Virtual Cell, numerical solvers can be divided into the following 4 types.

Deterministic Compartmental Solvers The compartmental simulation executes a single point simulation based on the defined physiological model, the geometric assumptions, and structure sizes or surface to volume ratios and volume fractions. The ordinary differential equations (ODE), for single point approximations, representing the reactions kinetics are generated and passed to an interpreted ODE solver. The set of nonlinear ODE equations are typically solved in seconds. It allows an interactive modification of parameters and a quick determination of the effect over time. In addition, the Virtual Cell software computes the local sensitivity (Sensitivity Analysis) of any species concentration to any parameter as a function of time evaluated at the nominal solution.

Stochastic Compartmental Solvers

Different numerical methods are required to simulate different biological systems. Deterministic simulation is valid as long as the concentrations of simulated populations are high. However, the concentrations of these factors could be very low in living cells. In these latter cases, the biology is more accurately simulated by discrete approaches. As a result, stochastic simulation has been implemented in Virtual Cell to allow users to describe the discrete nature of changes in cell systems.

Note: to exercise hybrid solvers you need to go to species specifications and check the checkbox for "Force Continuous" for at least one species. See Species Specifications.

Deterministic Spatial Solvers

Virtual Cell uses the finite volume method to deterministically solve spatial problems. The finite volume method is a method of spatial discretization of partial differential equations which exactly preserves conservation laws. Similar to the finite difference method, values are calculated at discrete places on a meshed geometry. The standalone version of the finite volume method is a little slower but gives better error messages.

Stochastic Spatial Solvers

Virtual Cell incorporates the Smoldyn(Smoluchowski Dynamics) to stochastically solve spatial problems. Smoldyn is a computer program for cell-scale biochemical simulations. It simulates each molecule of interest individually to capture natural stochasticity and for nanometer-scale spatial resolution. It treats other molecules implicity, so it can simulate tens of thousands of molecules over several minutes of real time. Simulated molecules diffuse, react, are confined by surfaces, and bind to membranes much as they would in a real biological system.