The model is considered to have three major interlinked components:
The input is a builtin parametrised, time-dependent, algebraic function that describes (models) the conditions the system was subjected to when it was measured.
The model's state is described by a number of state variables, which entirely describe everything that is within the model's scope (which is tied to the modeling purpose). The state of the model is time varying and the change over time is described by a differential equation. The types of differential equation are: ordinary (ode), partial (pde) and stochastic (sde); where ode is easiest to solve (simulate). Simulating a model in this case means solving a boundary value problem of the appropriate type. Simple ODEs omit the spatial properties of a systems biology model and model the averages of substance concentrations. Stochastic differential equations retain the probabilistic view of random reactions but would usually also omit the system's geometry when modeling.
Ordinary and Stochastic Differential Equations can approximate the geometry through the use of compartments. Creating a large number of compartments can approximate PDEs. Any attempt of doing that will increase the computational burden and it is recommended to try simple models first (i.e. ODEs, if possible).
A qualitative model is best represented by a directed graph. The graph shows reactions between the model's state variables (substances) and possibly also modifiers (ligands, substrates, etc.). A reaction typically changes the concnetration of more than one substance and is parametrised by often a priori unknown kinetic rate coefficients.
Because it can be reused, it is best to introduce intermediate flux variables that describe the actual reaction (in terms of M/s=mol/(l*s)
).
The kinetic rate coefficients k
that are needed to calculate fluxes typically have different units. Since their values can vary a lot, but are always strictly positive, they should be determined in logarithmic space: k=exp(theta)
. And then we find theta by either sampling (ABC, MCMC), Profile Likelihood method or even simple optimization if that makes sense (i.e. if there is one well defined global optimum).