Title of article :
Single-variable reaction systems: Deterministic and stochastic models
Author/Authors :
Monique M. C. Steijaert، نويسنده , , M.N. and Liekens، نويسنده , , A.M.L. and Bo?na?ki، نويسنده , , D. and Hilbers، نويسنده , , P.A.J. and ten Eikelder، نويسنده , , H.M.M.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2010
Pages :
12
From page :
105
To page :
116
Abstract :
Biochemical reaction networks are often described by deterministic models based on macroscopic rate equations. However, for small numbers of molecules, intrinsic noise can play a significant role and stochastic methods may thus be required. In this work, we analyze the differences and similarities between a class of macroscopic deterministic models and corresponding mesoscopic stochastic models. We derive expressions that provide a clear and intuitive view upon the behavior of the stochastic model. In particular, these expressions show the dependence of both the dynamics and the stationary distribution of the stochastic model on the number of molecules in the system. As expected, most properties of the stochastic model correspond well with those in the deterministic model if the number of molecules is large enough. However, for some properties, both models are inconsistent, even if the number of molecules in the stochastic model tends to infinity. Throughout this paper, we use a bistable autophosphorylation cycle as a running example. For such a bistable system, we give an explicit proof that the rate of convergence to the stationary distribution (or the second eigenvalue of the transition matrix) depends exponentially on the number of molecules.
Keywords :
Chemical master equation , Bistability , Reaction kinetics , Quasi-stationarity , Potential function
Journal title :
Mathematical Biosciences
Serial Year :
2010
Journal title :
Mathematical Biosciences
Record number :
1589645
Link To Document :
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