Accurate free energy calculations for biomolecular catalysis of electron transfer

蛋白质之间的长距离和短距离电子转移（ET）对所有生命系统都至关重要，并在光合作用和生物同化中起着至关重要的作用。ET也是在先进材料中转移和储存太阳能的核心过程。我们对相应的生物电子传输的理解可以启发开发和推进节能技术的新方法。然而，仍然需要强大的，准确的，和预测的基础理论和计算模型，以确定材料和生物系统中的ET过程的结构，能量学和动力学。我们引入了一种新的分析方法DHAM，可用于从有偏或无偏模拟轨迹计算速率和自由能（罗斯塔和Hummer，JCTC 2015）。DHAM方法是当前最先进的加权直方图分析方法（WHAM）的概括，该方法被广泛用于从偏置分子模拟中获得准确的自由能。我们表明，WHAM计算的自由能可以表现出显着的错误，例如，当分析模拟弱偏置-一个问题，克服了使用DHAM。我们的方法是设计来确定一个全球马尔可夫链的最大似然法的基础上分析多个模拟轨迹。我们沿着一个离散化的反应坐标构造马尔可夫转移矩阵沿着，并获得相应的平稳分布，以确定自由能的轮廓。重要的是，我们的形式主义提供了有偏见的模拟动力学信息。在此基础上，本研究的主要目的是发展一种新的研究电子传递的方法。作为第一个应用，我们将研究FNR的催化反应，FNR是光合作用电子传递过程的最后一步，利用光能将高能电子以化学键的形式储存在NADPH中。我们的新的计算方法将提供准确的自由能以及光合系统的动力学信息。重要的是，它将使我们能够理解潜在的机制，包括难以捉摸的耦合质子转移步骤，这些步骤与FNR中的电子转移反应一起发生。

Long- and short-range electron transfer (ET) between proteins is vital for all living systems, and plays an essential role in photosynthesis and bio-assimilation. ET is a central process for the transfer and storage of solar energy in advanced materials as well. Our understanding of the corresponding biological electron transport can inspire new approaches for developing and advancing energy efficient technologies. However, robust, accurate, and predictive underlying theoretical and computational models are still needed to determine structure, energetics and kinetics of ET processes in materials and biological systems. We introduced a new analysis method, DHAM, which can be used to calculate rates and free energies from biased or unbiased simulation trajectories (Rosta and Hummer, JCTC 2015). The DHAM method is a generalisation of the current state-of-the-art weighted histogram analysis method (WHAM), which is widely used to obtain accurate free energies from biased molecular simulations. We showed that WHAM-computed free energies can exhibit significant errors, e.g. when analysing simulations under weak bias - a problem overcome by using DHAM. Our method is designed to determine a global Markov chain based on a maximum likelihood approach to analyse multiple simulation trajectories. We construct the Markov transition matrix along a discretized reaction coordinate, and obtain the corresponding stationary distribution to determine the free energy profile. Importantly, our formalism provides kinetic information of biased simulations. By building on this approach, my main aim is to develop a new method to study electron transfer.As a first application, we will study the catalytic reaction of FNR, a central enzyme in the final step of the photosynthetic electron transfer processes using the energy of light to store high-energy electrons in the form of chemical bonds in NADPH. Our novel computational methods will provide accurate free energies as well as kinetic information about the dynamics of the photosynthetic systems. Importantly, it will allow us to understand the underlying mechanism, including the elusive coupled proton transfer steps that occur together with the electron transfer reactions in FNR.