Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.
Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.
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DOI：
10.1371/journal.pcbi.1005676
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发表时间：
2017-07
影响因子：
4.3
通讯作者：
Rand DA
中科院分区：
文献类型：
--
作者：
Minas G;Rand DA
为了分析诸如系统生物学中研究的大型复杂随机动力学模型，目前非常需要准确、快速的模拟和估计的分析工具和算法。我们提出了一个新的随机近似的生物振荡器，以解决这些需求。我们的方法，称为相位校正LNA (pcLNA)，克服了标准线性噪声近似（LNA）在长时间保持均匀精度的主要局限性，仍然保持LNA的速度和分析可跟踪性。作为其中的一部分，我们开发了关键概率分布和相关量的解析表达式，如Fisher信息矩阵和Kullback-Leibler散度，并引入了一种新的系统全局敏感性分析方法。我们还提出了用于统计推断和振荡系统长期模拟的算法，这些算法被证明与跳跃算法和扩散方程积分算法一样准确，但速度要快得多。我们使用已发表的生物钟和NF-κB系统模型的随机版本来说明我们的结果。许多细胞和分子系统，如生物钟和细胞周期，都是用非线性动力系统建模的振荡器。此外，振荡系统在科学领域无处不在。对于完全无噪声的动力系统有广泛的理论和非常有效的算法来模拟它们的时间行为。另一方面，生物系统本质上是随机的，随机噪声的存在可能起着至关重要的作用。不幸的是，对于随机模型的分析工具和理解都少得多，特别是当它们是非线性的，并且有很多状态变量和参数时。此外，如果系统较大，仿真效果不佳，并且速度很慢。在本文中，我们描述了如何以一种促进快速模拟，参数估计和新分析方法的方式准确地近似此类系统，例如计算描述系统随机行为的概率分布以及描述这些分布在系统参数变化时如何变化。
In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA) overcomes the main limitations of the standard Linear Noise Approximation (LNA) to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results. Many cellular and molecular systems such as the circadian clock and the cell cycle are oscillators that are modelled using nonlinear dynamical systems. Moreover, oscillatory systems are ubiquitous elsewhere in science. There is an extensive theory for perfectly noise-free dynamical systems and very effective algorithms for simulating their temporal behaviour. On the other hand, biological systems are inherently stochastic and the presence of stochastic noise can play a crucial role. Unfortunately, there are far fewer analytical tools and much less understanding for stochastic models especially when they are nonlinear and have lots of state variables and parameters. Moreover simulation is not so effective and can be very slow if the system is large. In this article we describe how to accurately approximate such systems in a way that facilitates fast simulation, parameter estimation and new approaches to analysis, such as calculating probability distributions that describe the system’s stochastic behaviour and describing how these distributions change when the parameters of the system are varied.
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影响因子：
3.9
作者：
Rand, D. A.
通讯作者：
Rand, D. A.
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