Nonlinear dynamics of selectivity, conductivity, and gating in biological ion channels

我们建议研究生物离子通道的物理。这些天然的导电纳米管控制着广泛的生物功能。与纳米级晶体管类似，它们存在于所有生物细胞的细胞膜中。移动手指涉及到数十亿个离子通道的协调操作。人类大脑消耗的代谢能量的一半被离子泵用来将K+和Na+移入和移出神经细胞。了解离子通道的结构和操作不仅与治愈疾病有关，还可能为生物计算机及其与纳米电子学的集成铺平道路。通道是非常复杂的装置，由数千个原子组成，灵活，充满离子和水偶极子，根据离子和通道壁的运动调整它们的位置。他们非常有选择性，对外部条件非常敏感。例如，KCSA钾通道对K+和Na+离子的区别是1000倍，即使它们具有相同的极性，并且Na+的直径实际上小0.4A。然而，通道传导高达1亿离子/秒，即几乎以自由扩散的速度进行，并显示出非常强劲的性能。通道建模是一个从根本上困难的多体问题，具有长距离相互作用和变化很大的时间尺度，从亚微秒原子运动到亚毫秒门控动力学。尽管取得了令人印象深刻的科学进展，但通道的理论模型往往过于简单化，无法捕捉结构和功能之间的重要关系，例如，传统的通道扩散模型将离子视为点电荷，将水视为连续介质，将蛋白质视为具有刚性壁的介质--尽管离子大小、水合作用以及与孔道中蛋白质振动的相互作用起着至关重要的作用。我们的主要目标是通过使用分子动力学(MD)分离生物相关的自由度来开发通道的新的布朗动力学(BD)描述，并从理论和数值上证明选择性过滤器处的蛋白质振动、离子大小和水合作用，和电荷波动(在早期工作中基本上被忽略)，为通道在相同极性的离子之间的高电导率和选择性提供了领先的顺序贡献。我们现在提议一项全面的研究计划，其强大的基础是：(I)我们EPSRC资助的(GR/S86174/01)关于BD模拟、泊松-能斯特-普朗克和离子通道反应速率理论的初步项目；(Ii)Lancaster小组在非平衡随机动力学方面的毕生专长；(Iii)他们与拉什大学医学院的长期合作；以及(Iv)Warwick小组在MD模拟方面的国际知名度和丰富经验。通过发展一种基于BD和MD模拟相结合的新方法，我们将寻求一个自洽的解释，说明类似离子之间的强烈选择性如何与通道中的高电导率、应力松弛和能量耗散相结合。我们还将尝试建立如何通过蛋白质壁的振动耦合到离子渗透来改变门控的能量和统计数据。我们的理论和模拟结果将与牛津、芝加哥、教堂山和格罗宁根的实验者合作，与真实的钾、钙和人工通道数据进行比较。研究带来了非平衡物理的新想法，将重点放在生物学中具有核心重要性的长期存在的问题上。这项工作将自由地利用该小组在非线性动力学、涨落理论、耦合振荡器及其生物医学应用方面的专门知识。即使在提高对开放离子通道中传导的理解方面取得部分成功，也将具有非常重要的意义，并将证明该企业是合理的。

We propose to investigate the physics of biological ion channels. These natural conducting nanotubes control a vast range of biological functions. Analogous to nano-scale transistors, they are present in the membranes of all biological cells. Moving a finger involves the coordinated operation of billions of ion channels. Half of the metabolic energy consumed by the human brain is used by ion pumps moving K+ and Na+ in and out of nerve cells. Understanding ion channel structure and operation is not only relevant to curing disease, but may also pave the way to bio-computers and their integration with nano-electronics. Channels are extraordinarily complicated devices, built of thousands of atoms, flexible, and filled with ions and water dipoles that adjust their positions to movements of the ions and channel walls. They are very selective and sensitive to external conditions. E.g. the KcsA potassium channel discriminates between K+ and Na+ ions by a factor of 1000, even though they are of the same polarity and Na+ is actually smaller in diameter by 0.4A. Yet channels conduct up to 100 million ions/sec, i.e. almost at the rate of free diffusion, and display very robust performance. Modelling channels is a fundamentally difficult many-body problem with long range interactions and widely-varying timescales, ranging from sub-ps atomic motion to sub-ms gating dynamics. Despite impressive scientific progress, theoretical models of channels are often too simplistic to capture the all-important relationship between structure and function, e.g. traditional models of channel diffusion consider ions as point charges, water as continuous dielectric, and protein as a dielectric with rigid walls - although ion size, hydration, and interaction with protein vibrations in the pore are known to play crucial roles.Our main goal is to develop a novel Brownian dynamics (BD) description of channels by isolating biologically relevant degrees of freedom using molecular dynamics (MD), and to demonstrate theoretically and numerically that protein vibration, ion size and hydration at the selectivity filter, and charge fluctuations (all largely neglected in earlier work), provide leading order contributions to the channel's high conductivity and selectivity between ions of the same polarity. We now propose a full-scale research programme, building on the strong base of: (i) our EPSRC-funded (GR/S86174/01) preliminary project on BD simulations, Poisson-Nernst-Planck and reaction rate theories of ion channels; (ii) the Lancaster group's life-time expertise in non-equilibrium stochastic dynamics; (iii) their long-term collaboration with Rush University Medical College; and (iv) the international distinction and enormous experience of the Warwick group in MD simulation. We will seek a self-consistent explanation of how strong selectivity between alike ions can be combined with high conductivity, stress relaxation and energy dissipation in the channel by developing a novel approach based on a combination of BD and MD simulations. We will also try to establish how coupling to the ion permeation via vibrations of the protein walls changes the energetics and statistics of the gating. Our theoretical and simulation results will be compared with real potassium, calcium, and artificial channel data in collaboration with experimentalists in Oxford, Chicago, Chapel Hill and Groningen.The investigations bring new ideas from non-equilibrium physics to focus on long-standing problems that are of central importance in biology. The work will draw freely on the group's special expertise in nonlinear dynamics, fluctuation theory, coupled oscillators, and their biomedical applications. Even partial success in improving the understanding of conduction in open ion channels will be highly significant, and will more than justify the enterprise.