Compute-Intensive Simulations for Cellular Models - Parallel Computing for Bioinformatics and Computational Biology - page 80

Figure 4.1 Three-dimensional image of a mammalian insulin-secreting cell, produced by
Dr. Brad Marsh (University of Queensland).
modeling regimes: systems with small numbers of molecules, systems where in any
small time interval all the reactions can fire many times but none of the propensity
functions changes appreciably, and systems with large numbers of molecules. These
three regimes are sometimes called the discrete regime (described by discrete Markov
processes), the chemical Langevin regime (CLE, described by stochastic differential
equations driven by Wiener processes), and the standard chemical kinetic rate equa-
tions regime (described by ordinary differential equations). Thus at the end of this
section we describe multi-scaled simulation approaches that allow us to move back
and forth between these regimes as appropriate.
Section 4.3 gives a brief overview of some of the modeling and simulation issues
associated with genetic regulation. Because of its simplicity we focus on bacterio-
phage λ , which is a virus that infects the bacterium Escherichia coli . This phage can
be in two states: lysis or lysogen, and in this section we review some of the model-
ing and simulation approaches applied to this system in terms of some of the issues
raised in Section 4.2. In particular, we show that there are still issues in developing
mathematical models that agree with experimental results for biologically reasonable
values of the model parameters.