The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations
The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations
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DOI：
10.1016/j.bpj.2014.06.012
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发表时间：
2014-08-05
影响因子：
3.4
通讯作者：
Bennett, Matthew R.
中科院分区：
文献类型：
--
作者：
Kim, Jae Kyoung;Josic, Kresimir;Bennett, Matthew R.
在生物化学网络中，反应通常发生在不同的时间尺度上，并且可以被表征为快或慢。准稳态近似（QSSA）利用时间尺度分离的生化网络模型投影到低维慢流形。因此，快速基元反应没有被明确地建模，并且它们的效果被非基元反应速率函数（例如，Hill函数）。QSSA应用于确定性系统的精度取决于时间尺度的分离程度。最近，有人提出使用通过确定性QSSA获得的非初等速率函数来定义生化网络随机模拟中的倾向函数。在这种方法中，称为随机QSSA，快速反应的一部分，非基元反应不模拟，大大减少了计算时间。然而，目前还不清楚，当随机QSSA提供了一个准确的近似的原始随机模拟。我们发现，不同于确定性QSSA，随机QSSA的有效性不遵循从时间尺度分离，但也取决于非基元反应速率函数的灵敏度在缓慢的物种的变化。当该灵敏度较小时，随机QSSA变得更准确。不同类型的QSSA导致具有不同灵敏度的非初等函数，并且总QSSA导致比标准或前因子QSSA更不灵敏的函数。我们证明，作为一个结果，随机QSSA变得更准确的非基元反应函数时，使用总QSSA。我们的工作提供了一个明显的新颖条件的有效性QSSA在随机模拟不同的时间尺度的生化反应网络。
In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.