Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network provided the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily complicated systems by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) the time evolution can be easily discretized, rendering the dynamics suitable for computer simulation in a simple and direct way. Finally, it is shown that one obtains the classical rate equations form the stochastic models by averaging over an ensemble .
Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) the time evolution can be easily discretized, rendering the dynamics suitable for computer simulation in a simple and direct way. Finally, it is shown that one obtains the classical rate equations form the corresponding stochastic versions as the equations satisfied by the mean values of the random variables .
R
provided
given
R
complicated systems
large networks
R
stochastic models by averaging over an ensemble
corresponding stochastic versions as the equations satisfied by the mean values of the random variables