Model based analysis of stochastic biochemical reactions often ends up with approximation due to the lack of closed form solutions to the governing chemical master equation. This leads to erroneous prediction of reaction dynamics and delays the design-build-test cycles in synthetic biology. To overcome this issue , this paper proposes a computational method for predicting rigorous upper and lower bounds of dynamic moments . We combine the differential equation model of the moment dynamics with a so-called moment condition to derive linear matrix inequalities that the moments of molecular copy numbers must satisfy . Using these conditions, we formulate a semidefinite program that efficiently and rigorously computes the bounds of transient moment dynamics. The proposed method is demonstrated with a stochastic protein dimerization process .
The predictive ability of stochastic chemical reactions is currently limited by the lack of closed form solutions to the governing chemical master equation. To overcome this limitation , this paper proposes a computational method capable of predicting mathematically rigorous upper and lower bounds of transient moments for reactions governed by the law of mass action. We first derive an equation that transient moments must satisfy based on the moment equation. Although this equation is underdetermined, we introduce a set of semidefinite constraints known as moment condition to narrow the feasible set of the variables in the equation . Using these conditions, we formulate a semidefinite program that efficiently and rigorously computes the bounds of transient moment dynamics. The proposed method is demonstrated with illustrative numerical examples and is compared with related works to discuss advantages and limitations .
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Model based analysis of stochastic biochemical reactions often ends up with approximation due to
The predictive ability of stochastic chemical reactions is currently limited by
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This leads to erroneous prediction of reaction dynamics and delays the design-build-test cycles in synthetic biology.
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issue
limitation
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for predicting
capable of predicting mathematically
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dynamic moments . We combine the differential equation model of the moment dynamics with a so-called
transient moments for reactions governed by the law of mass action. We first derive an equation that transient moments must satisfy based on the moment equation. Although this equation is underdetermined, we introduce a set of semidefinite constraints known as
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derive linear matrix inequalities that the moments of molecular copy numbers must satisfy
narrow the feasible set of the variables in the equation
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a stochastic protein dimerization process
illustrative numerical examples and is compared with related works to discuss advantages and limitations