针对生物振荡网络分析的周期系统目标敏感性方法研究
doi: 10.3724/SP.J.1004.2012.01065
Developing Objective Sensitivity Analysis of Periodic Systems: Case Studies of Biological Oscillators
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摘要: 生物学实验和模型计算结果表明振荡是一种常见的生物学现象, 越来越多的研究人员关注生物系统内部的振荡现象是如何产生的、引起振荡的关键因素是什么等问题. 敏感性分析定量分析系统行为在模型参数、系统输入或者初始条件发生变化时受影响的程度. 对周期系统进行传统的状态敏感性计算时, 得到的灵敏度指标随着时间的增加而发散, 因而对其进行敏感性分析是一项具有挑战性的工作. 本文针对这类系统, 首先提出基本状态敏感性的概念, 由此进一步推导出一种相敏感性分析方法. 在计算周期灵敏度过程中, 提出了一种基于奇异值分解的的改进算法, 简化了基本状态灵敏度的计算. 本文中的目标敏感性分析方法克服了因累积效应引起的发散问题. 通过对一个生物节律模型和一个复杂的信号转导网络系统模型进行敏感性分析, 可以看到改进的周期灵敏度计算方法得到的结果与已有方法一致, 并且新提出的目标敏感性分析方法及其计算在处理存在反应守恒的复杂生物振荡系统分析时是有效的.Abstract: Sensitivity analysis is a powerful tool in investigating the impact of parameter variations on the change of system behaviours quantitatively. For a periodic system, sensitivity analysis is a challenging problem since the standard sensitivity metrics grow unbounded when time tends to infinity. Objective sensitivity analyses using various oscillation features such as period, phase, amplitude, etc. are therefore needed to circumvent this problem. In this work, a new concept of basal state sensitivity is proposed based on which a phase sensitivity calculation is derived. The improved period sensitivity calculation following an existing algorithm using singular value decomposition (SVD) is also presented, which provides a simple calculation for the basal state sensitivity. These new sensitivity calculations are developed with the purpose to analyse biological oscillators since there is an increasing interest in understanding how oscillations occur and what the main controlling factors are following a growing experimental and computational evidence of oscillations in biological systems. The improved calculation of period sensitivity is shown to be consistent with the previous methods through a well studied circadian rhythm model. The calculation of new objective sensitivities are also testified by the same circadian rhythm model as well as an oscillatory signal transduction pathway model, which further illustrates the efficiency of this approach in handling complex biological oscillators in the presence of reaction conservations.
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Key words:
- Sensitivity analysis /
- periodic systems /
- phase sensitivity /
- period sensitivity /
- biological oscillator
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