Prescott Thomas P, Papachristodoulou Antonis
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom; Life Sciences Interface Doctoral Training Centre, University of Oxford, Parks Road, Oxford OX1 3QU, United Kingdom.
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom.
J Theor Biol. 2014 Sep 7;356:113-22. doi: 10.1016/j.jtbi.2014.04.007. Epub 2014 Apr 13.
Biochemical reaction networks tend to exhibit behaviour on more than one timescale and they are inevitably modelled by stiff systems of ordinary differential equations. Singular perturbation is a well-established method for approximating stiff systems at a given timescale. Standard applications of singular perturbation partition the state variable into fast and slow modules and assume a quasi-steady state behaviour in the fast module. In biochemical reaction networks, many reactants may take part in both fast and slow reactions; it is not necessarily the case that the reactants themselves are fast or slow. Transformations of the state space are often required in order to create fast and slow modules, which thus no longer model the original species concentrations. This paper introduces a layered decomposition, which is a natural choice when reaction speeds are separated in scale. The new framework ensures that model reduction can be carried out without seeking state space transformations, and that the effect of the fast dynamics on the slow timescale can be described directly in terms of the original species.
生化反应网络往往会在多个时间尺度上展现出行为，并且不可避免地要用刚性常微分方程组来建模。奇异摄动是一种在给定时间尺度上近似刚性系统的成熟方法。奇异摄动的标准应用将状态变量划分为快速和慢速模块，并假设快速模块中存在准稳态行为。在生化反应网络中，许多反应物可能同时参与快速反应和慢速反应；反应物本身不一定是快速或慢速的。为了创建快速和慢速模块，通常需要进行状态空间变换，这样就不再对原始物种浓度进行建模了。本文介绍了一种分层分解方法，当反应速度在尺度上分离时，这是一种自然的选择。新框架确保了无需寻求状态空间变换就能进行模型简化，并且快速动力学在慢时间尺度上的影响可以直接根据原始物种来描述。
