Transfer entropy methods provide an approach to understanding asymmetric information flow in coupled systems, with particular application to understanding allosteric interactions in biomolecular systems. Transfer entropy analysis holds the potential to reveal pathways or networks of residues that are coupled in their information flow and thus give new insights into folding and binding dynamics. Most current methods for calculating transfer entropy require very long simulations and almost equally long calculations of joint probability histograms to compute the information transfer that make these methods either functionally intractable or statistically unreliable. Available approximate methods based on graph and network theory approaches are rapid but lose sensitivity to the chemical nature of the biomolecules and thus are not applicable in mutation studies. We show that reliable estimates of the transfer entropy can be obtained from the variance-covariance matrix of atomic fluctuations, which converges quickly and retains sensitivity to the full chemical profile of the biomolecular system. We validate our method on ERK2, a well-studied kinase involved in the MAPK signaling cascade for which considerable computational, experimental, and mutation data are available. We present the results of transfer entropy analysis on data obtained from molecular dynamics simulations of wild type active and inactive ERK2, along with mutants Q103A, I84A, L73P, and G83A. We show that our method is consistent with the results of computational and experimental studies on ERK2, and we provide a method for interpreting networks of interconnected residues in the protein from a perspective of allosteric coupling. We introduce new insights about possible allosteric activity of the extreme N-terminal region of the kinase, which to date has been under-explored in the literature and may provide an important new direction for kinase studies. We also describe evidence that suggests activation may occur by different paths or routes in different mutants. Our results highlight systematic advantages and disadvantages of each method for calculating transfer entropy and show the important role of transfer entropy analysis for understanding allosteric behavior in biomolecular systems.

中文翻译：

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通过方差-协方差矩阵计算转移熵可深入了解ERK2中的变构通讯

传递熵方法提供了一种理解耦合系统中不对称信息流的方法，特别是可以用于理解生物分子系统中的变构相互作用。转移熵分析有潜力揭示残基的路径或网络，这些残基在其信息流中耦合在一起，从而为折叠和结合动力学提供了新的见识。当前大多数用于计算传递熵的方法都需要很长时间的模拟，并且对联合概率直方图的计算也几乎需要同样长的时间，以计算信息传递，这使得这些方法在功能上难以处理或在统计上不可靠。基于图论和网络理论方法的可用近似方法是快速的，但是对生物分子的化学性质不敏感，因此不适用于突变研究。我们表明，可以从原子涨落的方差-协方差矩阵获得可靠的转移熵估计，该矩阵快速收敛并保留了对生物分子系统完整化学特征的敏感性。我们在ERK2上验证了我们的方法，ERK2是一种经过深入研究的激酶，参与MAPK信号级联反应，可提供大量的计算，实验和突变数据。我们介绍了从野生型有功和无功ERK2，以及突变体Q103A，I84A，L73P和G83A的分子动力学模拟获得的数据的转移熵分析的结果。我们表明我们的方法与对ERK2的计算和实验研究的结果一致，并且我们提供了从变构偶联的角度解释蛋白质中相互连接的残基网络的方法。我们介绍了有关激酶的极端N端区域可能的变构活性的新见解，迄今为止，在文献中尚未对此进行深入探讨，这可能为激酶研究提供重要的新方向。我们还描述了证据表明，激活可能通过不同的突变体中的不同路径或途径发生。我们的结果凸显了每种用于计算转移熵的方法的系统优缺点，并显示了转移熵分析对于理解生物分子系统中的变构行为的重要作用。