Institute of Bioengineering, Swiss Federal Institute of Technology (EPFL), 1015 Lausanne, Switzerland.
Chemical and Biological Engineering, Koc University, Istanbul, Turkey.
J Chem Phys. 2022 May 14;156(18):185101. doi: 10.1063/5.0088522.
Based on Schreiber's work on transfer entropy, a molecular theory of nonlinear information transfer between residue pairs in proteins is developed. The joint distribution function for residue fluctuations required by the theory is expressed in terms of tensor Hermite polynomials that conveniently separate harmonic and nonlinear contributions to information transfer. The harmonic part of information transfer is expressed as the difference between time dependent and independent mutual information. Third order nonlinearities are discussed in detail. The amount and speed of information transfer between residues, which are important for understanding allosteric activity in proteins, are discussed. Mutual information between two residues is commonly used for information transfer. While mutual information shows the maximum amount of information that may be transferred between two residues, it does not explain the actual amount of transfer nor the transfer rate of information. For this, dynamic equations of the system are needed. The solution of the Langevin equation and molecular dynamics trajectories are used in the present work for this purpose. Allosteric communication in human NAD-dependent isocitrate dehydrogenase is studied as an example. Calculations show that several paths contribute collectively to information transfer. Important residues on these paths are identified. Time resolved information transfer between these residues, their amplitudes, and transfer rates, which are in agreement with time resolved ultraviolet resonance Raman measurements in general, are estimated. Peak values of calculated information transfer, ∼0.01-0.04 bits, are about two orders of magnitude smaller than the information content of residues. They are comparable to mutual information values, however. Estimated transfer rates are in the order of 1-20 megabits per second, and sustained transfer during the activity time-span of proteins may be significant. Information transfer from third order contributions is one to two orders of magnitude smaller than the harmonic terms, showing that harmonic analysis is a good approximation to information transfer.
基于施赖伯（Schreiber）的转移熵理论，建立了一种用于蛋白质中残基对之间非线性信息传递的分子理论。该理论所需的残基波动联合分布函数表示为张量 Hermite 多项式，这些多项式方便地分离了信息传递的谐波和非线性贡献。信息传递的谐波部分表示为随时间变化的和独立的互信息之间的差异。详细讨论了三阶非线性。讨论了残基之间信息传递的数量和速度，这对于理解蛋白质中的变构活性非常重要。两个残基之间的互信息通常用于信息传递。虽然互信息显示了两个残基之间可能传递的最大信息量，但它并不能解释实际的传递量或信息传递的速度。为此，需要系统的动力学方程。本工作使用 Langevin 方程的解和分子动力学轨迹来实现这一目的。以人类 NAD 依赖性异柠檬酸脱氢酶的变构通讯为例进行研究。计算表明，几条路径共同贡献于信息传递。确定了这些路径上的重要残基。估计了这些残基之间的时间分辨信息传递、它们的幅度和传递速率，总体上与时间分辨紫外共振拉曼测量结果一致。计算出的信息传递的峰值约为 0.01-0.04 位，大约比残基的信息量小两个数量级。然而，它们与互信息值相当。估计的传递速率在 1-20 兆位/秒之间，并且在蛋白质的活性时间跨度内持续传递可能是重要的。三阶贡献的信息传递比谐波项小一到两个数量级，这表明谐波分析是信息传递的一个很好的近似。
