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摘要翻译：
本文证明，对于一类反应网络，反应物种和反应的离散随机性质导致精确随机模拟的平均值与相应确定性系统的预测之间存在定性和定量的差异。这种差异与所考虑的系统中每个物种的分子数量无关。这些反应网络是开放的化学反应系统，没有零级反应速率系统。它们的特征是至少有两个驻点，其中一个为非零稳定点，和一个不稳定的平凡解（基于确定性系统线性稳定性分析的稳定性）。从一个非零初始条件开始，确定性系统由于其不稳定性质而永远不会到达零驻点。相反，本文的结果证明了该零态是离散随机系统唯一稳定的定态。这一结果推广了以往对特定系统的理论研究和仿真，为分析一类表现出这种不一致行为的系统提供了理论基础。这一结果对感染、凋亡和群体动力学的模拟有一定的意义，因为它可以表明，对于某些模型，随机模拟总是会产生不同于确定性模拟的对平均行为的预测。
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英文标题：
《Size-independent differences between the mean of discrete stochastic
systems and the corresponding continuous deterministic systems》
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作者：
Chetan J Gadgil
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Biology 数量生物学
二级分类：Other Quantitative Biology 其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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一级分类：Quantitative Biology 数量生物学
二级分类：Quantitative Methods 定量方法
分类描述：All experimental, numerical, statistical and mathematical contributions of value to biology
对生物学价值的所有实验、数值、统计和数学贡献
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英文摘要：
In this paper I show that, for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the prediction of the corresponding deterministic system. The differences are independent of the number of molecules of each species in the system under consideration. These reaction networks are open systems of chemical reactions with no zero-order reaction rates systems. They are characterized by at least two stationary points, one of which is a nonzero stable point, and one unstable trivial solution (stability based on a linear stability analysis of the deterministic system). Starting from a nonzero initial condition, the deterministic system never reaches the zero stationary point due to its unstable nature. In contrast, the result presented here proves that this zero-state is the only stable stationary state for the discrete stochastic system. This result generalizes previous theoretical studies and simulations of specific systems and provides a theoretical basis for analyzing a class of systems that exhibit such inconsistent behavior. This result has implications in the simulation of infection, apoptosis, and population kinetics, as it can be shown that for certain models the stochastic simulations will always yield different predictions for the mean behavior than the deterministic simulations.
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PDF链接：
https://arxiv.org/pdf/0801.0277
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