Biochemical fluctuations, optimisation and the linear noise approximation.
Biochemical fluctuations, optimisation and the linear noise approximation.
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DOI：
10.1186/1752-0509-6-86
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发表时间：
2012-07-17
影响因子：
--
通讯作者：
McKane AJ
中科院分区：
文献类型：
--
作者：
Pahle J;Challenger JD;Mendes P;McKane AJ
在许多情况下，分子数量的随机波动对于理解生物化学系统至关重要。然而，这些波动的系统研究严重阻碍了随机模拟算法的高计算需求。这在某些或许多模型参数不为人所知的情况下尤其成问题。在这里，我们提出了一个解决这个问题，即线性噪声近似与优化方法的组合。线性噪声近似用于有效地估计系统中粒子数的协方差。将其与闭环中的优化方法相结合，以在可能的高维参数空间内找到协方差的极值，使我们能够回答各种问题。例如，在给定的参数范围内，随机波动的最低幅度是多少？或者，参数值的哪些具体变化导致某些化学物种之间的相关性增加？与随机模拟方法不同，这对少量分子没有要求，因此可以应用于随机模拟禁止的情况。我们实施了我们的战略，在软件COPASI和显示其适用性的两种不同模型的丝裂原活化激酶（MAPK）信号-一个通用模型的细胞外信号调节激酶（ERK）和一个模型的信号通过p38 MAPK。使用我们的方法，我们能够快速找到的ERK模型中的颗粒数之间的协方差的局部最大值取决于磷酸-MKKK和其相应的磷酸酶的活动。利用p38 MAPK模型，我们的方法能够有效地找到信号系统输出的变异系数，即HSP 27的颗粒数，可以最小化的条件。我们还研究了该模型中两个并行信号分支（MKK 3和MKK 6）之间的相关性。我们的策略是一个实用的方法，即使在一些或许多模型参数尚未完全特征化的生物化学模型的波动进行有效的调查。
Stochastic fluctuations in molecular numbers have been in many cases shown to be crucial for the understanding of biochemical systems. However, the systematic study of these fluctuations is severely hindered by the high computational demand of stochastic simulation algorithms. This is particularly problematic when, as is often the case, some or many model parameters are not well known. Here, we propose a solution to this problem, namely a combination of the linear noise approximation with optimisation methods. The linear noise approximation is used to efficiently estimate the covariances of particle numbers in the system. Combining it with optimisation methods in a closed-loop to find extrema of covariances within a possibly high-dimensional parameter space allows us to answer various questions. Examples are, what is the lowest amplitude of stochastic fluctuations possible within given parameter ranges? Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species? Unlike stochastic simulation methods, this has no requirement for small numbers of molecules and thus can be applied to cases where stochastic simulation is prohibitive. We implemented our strategy in the software COPASI and show its applicability on two different models of mitogen-activated kinases (MAPK) signalling -- one generic model of extracellular signal-regulated kinases (ERK) and one model of signalling via p38 MAPK. Using our method we were able to quickly find local maxima of covariances between particle numbers in the ERK model depending on the activities of phospho-MKKK and its corresponding phosphatase. With the p38 MAPK model our method was able to efficiently find conditions under which the coefficient of variation of the output of the signalling system, namely the particle number of Hsp27, could be minimised. We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this model. Our strategy is a practical method for the efficient investigation of fluctuations in biochemical models even when some or many of the model parameters have not yet been fully characterised.
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