Main Content

Derive ODEs from SimBiology Reactions

For model simulation, SimBiology® derives ordinary differential equations (ODEs) from model reactions using mass-balance principles. The left-hand-side (LHS) of each ODE is the time-derivative of a model quantity and the right-hand-side (RHS) is defined using reaction fluxes that are derived from reaction rates and rate rules. In other words, SimBiology represents a system of ODEs as follows.

x˙=Sv

x˙ is an M-by-1 vector containing the rates of change for model quantities, S is an M-by-R stoichiometry matrix, v is an R-by-1 flux vector. M equals the total number of species, and R equals the total number of reactions in the model

During the conversion of model reactions into ODEs, SimBiology performs a dimensional analysis to ensure each reaction flux has the dimension of substance/time such as amount/time or mass/time. If the reaction rate has the dimension of concentration/time, then SimBiology multiplies it by the compartment volume to get the reaction flux. If the reaction rate has the dimension of substance/time, then the flux is identical to the rate, and no volume-correction is performed. If there are no units specified with the model, the default dimension for a species (DefaultSpeciesDimension) is concentration, and that for a flux is substance/time. For such cases, the ODE is the flux divided by a compartment volume to make the dimension of LHS and RHS consistent. See the following figure for an illustration.

Suppose there is a reaction x —> y, with the reaction rate R1. The following figure explains the dimensional analysis performed by SimBiology to make the dimensions of LHS and RHS of an ODE consistent.

See Also

Related Topics