In this article, we introduce a new method to model stochastic gene expression  . The protein concentration dynamics follows a backward stochastic differential equation (BSDE).  To validate our approach we employ the Gillespiemethod to generate benchmark data. The numerical simulation shows that the data produced by both methods agree quite well .
In this article, we introduce a novel backward method to model stochastic gene expression and protein level dynamics . The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of endpoint ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time reversed simulations, allowing, for example, the assessment of the biological conditions (e.g. protein concentrations) that preceded an experimentally measured event of interest (e.g. mitosis, apoptosis, etc.) .
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new
novel backward
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and protein level dynamics
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concentration dynamics follows a
amount is regarded as a diffusion process and is described by a
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Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of endpoint ("final") conditions, in addition to the model parametrization.
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the Gillespiemethod to generate benchmark data. The numerical simulation shows that the data produced by both methods agree quite well
Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time reversed simulations, allowing, for example, the assessment of the biological conditions (e.g. protein concentrations) that preceded an experimentally measured event of interest (e.g. mitosis, apoptosis, etc.)