Steady-state is an essential concept in reaction networks. Its properties, number and stability , reflect fundamental characteristics of several biological phenomena such as molecular switches, cell differentiation, and memory . Because biochemical reactions occur at the cellular level, they are affected by unavoidable fluctuations. Although several methods have been proposed to detect and analyze the stability of steady-states for deterministic models, these methods cannot be applied to stochastic reaction networks. In this paper, we propose an algorithm based on algebraic methods to detect steady-states of stochastic reaction networks . The proposed method can be used to calculate necessary and sufficient parameters such that the stochastic reaction network has a prescribed number of steady-states . To evaluate our proposed method, we perform computer simulations for three typical chemical reactions and demonstrate that the results obtained with our method are consistent with the simulation results.
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression . Because biochemical reactions occur at the cellular level, they are affected by unavoidable fluctuations. Although several methods have been proposed to detect and analyze the stability of steady states for deterministic models, these methods cannot be applied to stochastic reaction networks. In this paper, we propose an algorithm based on algebraic computations to calculate parameter regions for constrained steady-state distribution of stochastic reaction networks , in which the means and variances satisfy some given inequality constraints . To evaluate our proposed method, we perform computer simulations for three typical chemical reactions and demonstrate that the results obtained with our method are consistent with the simulation results.
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Steady-state
Steady state
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properties, number and stability , reflect
stability reflects
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molecular switches, cell differentiation, and memory
cellular signal transduction and gene expression
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steady-states
steady states
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methods to detect steady-states
computations to calculate parameter regions for constrained steady-state distribution
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. The proposed method can be used to calculate necessary and sufficient parameters such that the stochastic reaction network has a prescribed number of steady-states
, in which the means and variances satisfy some given inequality constraints