Mathematics of Ions in Protein Channels

描述(申请人提供)：离子通道是中间有孔(直径约0.4-1纳米)的蛋白质，控制着广泛的生物功能，因此每天都有数千个实验室进行研究。离子通道是物理和数学研究的理想对象，因为它们的结构简单且非常不变。离子通道是生物学研究的理想对象，因为它们控制着如此多的细胞功能，是大量蛋白质的原型，占据了人类基因组的相当大一部分。离子通道是临床上非常重要的对象，因为它们直接参与了如此多的疾病。 离子通道可以在物理传统中研究，因为离子通过一个简单的不变结构进行电扩散，遵循众所周知的电场扩散定律。如果系统要包括明确定义的离子浓度和电势，那么在毫秒的生物时间尺度上直接模拟原子在通道中的运动是不可行的。问题是要知道要平均什么以及如何平均，这样才能理解和控制渠道的功能。在这里，我们采用了多分辨分析的工程方法，提出了化学传统的平均场理论和随机物理的数学传统的随机理论。这两个传统的中心问题是扩展以前的平衡系统理论，以便能够预测在生物通道中测量的大电流。

DESCRIPTION (provided by applicant): Ion channels are proteins with holes down their middle (some 0.4 - 1 nm in diameter) that control a wide range of biological function and so are studied in thousands of laboratories every day. Ion channels are ideal objects for physical and mathematical investigation because their structure is simple and quite invariant. Ion channels are ideal objects for biological investigation because they control so many cellular functions and are archetypes of an enormous number of proteins, occupying a substantial fraction of the human genome. Ion channels are objects of great clinical importance because they are involved directly in so many diseases. Ion channels can be studied in the physical tradition because ions move by electrodiffusion through a simple invariant structure following well known laws of diffusion in an electric field. Direct simulation of atomic motion in channels is not feasible on the biological time scale of msec if the system is to include well defined concentrations of ions and electrical potentials. The problem is to know what to average and how to average so the function of channels can be understood and controlled. Here we adopt the engineering approach of multiresolution analysis, proposing a mean field theory in the chemical tradition and stochastic theory in the mathematical tradition of stochastic physics. The central issue in both traditions is to extend previous theories of equilibrium systems to allow prediction of the large currents measured in biological channels.