Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This manuscript contributes an alternative approach from these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and interaction among these components are given by logical rules representing the biochemical mechanisms governing their regulation ; stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update function guarantee activation or degradation there is a probability that the process will not occur due to stochasticity in the process, for instance, some of the chemical reactions encoded by the function fail to occur which lead to a function failure . This approach allows a finer analysis of discrete models and provide a natural set up for cell population simulations  . We applied our methods to two of the best studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.
Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This paper contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects . This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability . We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.
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interaction among these components are given by logical rules representing the biochemical mechanisms governing their regulation ; stochasticity
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stochasticity in the process, for instance, some of the chemical reactions encoded by the function fail to occur which lead to a function failure
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provides a natural setup
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to study cell-to-cell variability
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