The communication within a cell is realized by an intricate system of messages known as intracellular signaling. This signaling system is coupled to other biochemical reaction systems that regulate specific intracellular processes. The interplay between those processes is very complicated and a mathematical model may help to unravel the secrets of intracellular signaling and regulation.
The most commonly used methods for mathematical modeling of biochemical reaction systems are deterministic, using differential equations for concentrations etc. However, of some types of molecules that are involved in intracellular signaling and regulation, only several hundred or a few thousand copies are present in a cell. In those cases, random events (intrinsic noise) may play an important role and so-called stochastic modeling methods may provide a better description of the behavior of the reaction network. Such stochastic methods take into account that from an initial state various other states can be visited subsequently.
In this research, we investigate biochemical reaction systems for which both deterministic and stochastic models are constructed. In particular we study how the behavior of the stochastic model depends on the total number of molecules. The relation between stochastic models of intracellular signalling and regulation and their more common deterministic counterparts have been extensively studied. In particular bi-stable systems formed by phosphorylation cycles.
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