Linear noise approximation is valid over limited times for any chemical system that is sufficiently large.
Linear noise approximation is valid over limited times for any chemical system that is sufficiently large.
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DOI：
10.1049/iet-syb.2011.0038
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发表时间：
2012-08
影响因子：
2.3
通讯作者：
E. Wallace;D. Gillespie;Kevin R. Sanft;L. Petzold
中科院分区：
文献类型：
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作者：
E. Wallace;D. Gillespie;Kevin R. Sanft;L. Petzold
线性噪声近似(LNA)是一种近似充分搅拌的化学反应体系的随机时间演化的方法。它既可以作为van Kampens对化学主方程(CME)的体系规模展开中确定的化学反应速率方程(RRE)的最低阶修正，也可以通过线性化两项截断的化学Kramers-MoYal方程来获得。然而，这两个推论都没有让人们对LNA的有效性有太多了解。对于某些化学体系，CME的系统规模展开式的问题特性，化学Kramers-MoYal方程两项截断的任意性，以及LNA与CME解有时较差的一致性，都引起了人们对LNA的有效性和有用性的关注。在这里，作者认为，这些问题可以通过将LNA视为化学朗之万方程(CLE)的近似值来解决。这一观点已经隐含在Gardiner从截断的Kramers-MoYal方程推导出的LNA中，因为该方程在数学上等价于CLE。然而，CLE可以以一种既不涉及截断的Kramers-MoYal方程也不涉及系统规模展开的方式得到更令人信服的推导。这一推导表明，CLE对于任何足够接近热力学(大系统)极限的系统都是有效的，至少在有限的时间跨度内是有效的。从CLE相对容易地推导出LNA表明，LNA与CLE的有效性条件相同，这也表明LNA真正给我们的是当我们从热力学极限退回到一个大的但有限的系统时，CLE从RRE开始偏离的描述。作者表明，LNA的这种方法简化了其推导，澄清了其局限性，并提供了一条更容易解决其问题的途径。
The linear noise approximation (LNA) is a way of approximating the stochastic time evolution of a well-stirred chemically reacting system. It can be obtained either as the lowest order correction to the deterministic chemical reaction rate equation (RRE) in van Kampen's system-size expansion of the chemical master equation (CME), or by linearising the two-term-truncated chemical Kramers-Moyal equation. However, neither of those derivations sheds much light on the validity of the LNA. The problematic character of the system-size expansion of the CME for some chemical systems, the arbitrariness of truncating the chemical Kramers-Moyal equation at two terms, and the sometimes poor agreement of the LNA with the solution of the CME, have all raised concerns about the validity and usefulness of the LNA. Here, the authors argue that these concerns can be resolved by viewing the LNA as an approximation of the chemical Langevin equation (CLE). This view is already implicit in Gardiner's derivation of the LNA from the truncated Kramers-Moyal equation, as that equation is mathematically equivalent to the CLE. However, the CLE can be more convincingly derived in a way that does not involve either the truncated Kramers-Moyal equation or the system-size expansion. This derivation shows that the CLE will be valid, at least for a limited span of time, for any system that is sufficiently close to the thermodynamic (large-system) limit. The relatively easy derivation of the LNA from the CLE shows that the LNA shares the CLE's conditions of validity, and it also suggests that what the LNA really gives us is a description of the initial departure of the CLE from the RRE as we back away from the thermodynamic limit to a large but finite system. The authors show that this approach to the LNA simplifies its derivation, clarifies its limitations, and affords an easier path to its solution.