米氏单步酶循环中噪声诱导的双稳态分析
Analysis of noise-induced bistability in Michaelis Menten single-step enzymatic cycle
摘要：
在本文中，我们研究了噪声诱导的双稳态在一个特定的电路，具有许多生物学意义，即一个单步酶循环描述的米氏方程与准稳态假设。我们研究了系统的主方程形式主义，并与福克-普朗克连续近似，其特征的条件下，连续的方法是一个很好的近似精确的离散模型。对这两种情况下的平稳分布的分析表明，双峰性在这样的系统中不可能发生。我们讨论了额外的要求可以产生随机双峰，通过耦合系统与化学反应，涉及酶的生产和营业额。这个扩展的系统只在特定的参数窗口中显示了依赖于所涉及的分子数量的行为，提供了关于哪个应该是可行的系统大小的提示，以便这种现象可以在实际的生物系统中被利用。
英文摘要：
In this paper we study noise-induced bistability in a specific circuit with many biological implications, namely a single-step enzymatic cycle described by Michaelis Menten equations with quasi-steady state assumption. We study the system both with a Master Equation formalism, and with the Fokker-Planck continuous approximation, characterizing the conditions in which the continuous approach is a good approximation of the exact discrete model. An analysis of the stationary distribution in both cases shows that bimodality can not occur in such a system. We discuss which additional requirements can generate stochastic bimodality, by coupling the system with a chemical reaction involving enzyme production and turnover. This extended system shows a bistable behaviour only in specific parameter windows depending on the number of molecules involved, providing hints about which should be a feasible system size in order that such a phenomenon could be exploited in real biological systems.
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