Mathematical Sciences: Theories of the Open Channel

艾森伯格9514145研究员和他的同事结合实验和数学模型研究了膜中开放通道的行为。明渠理论的起点是电扩散理论。人们早就知道，一个理论应该包括屏蔽或屏蔽现象，即通道蛋白质内部和周围离子大气中的离子有助于确定其孔的势能分布，但数学上的困难是严重的，分析通常集中在膜表面或通道末端的离子大气，而不是通道孔内的共离子和反离子。这些困难最近都被克服了。该项目发展了PNP理论来预测通过通道的电流，给出了通道的结构和固定(即永久)电荷的分布。该项目使用泊松方程来描述离子和通道蛋白质上的电荷如何决定电场，并使用能斯特-普朗克方程来描述离子在电位和浓度梯度中的迁移和扩散。对开放通道的研究是生物技术的一个重要组成部分，因为通道在扮演细胞守门人的角色方面具有重要的生物学意义：它们负责神经系统中的信号传递；它们协调心脏的收缩，因此心脏可以充当泵；一般来说，它们是许多药物和控制细胞生命的天然物质的受体或效应器。通道是高速计算研究的极好对象，因为它们使用如此简单的物理(扩散)来执行重要的生物功能。扩散的计算比涉及这么多酶函数的量子力学计算简单得多。通道也是天然的纳米管，因此在新兴的纳米结构、材料和制造领域具有重要意义。在这方面，Porin特别适合，因为它可以大量获得，它可以很容易地通过生物技术的方法进行修饰，并且它的结构是原子细节已知的。

Eisenberg 9514145 The investigator and his colleagues study the behavior of open channels in membranes, combining experiments and mathematical modeling. The starting place for a theory of open channels is a theory of electrodiffusion. It has long been known that a theory should include the phenomena of shielding or screening, whereby the ions in the ionic atmosphere in and around the channel protein help determine the potential profile of its pore, but mathematical difficulties were severe, and analysis was usually focused on the ionic atmosphere at the surface of the membrane or end of the channel and not the co- and counter-ions within the channel's pore. These difficulties have recently been overcome. The project develops PNP theory to predict the current through the channel, given its structure and distribution of fixed (i.e., permanent) charge. The project uses Poisson's equation to describe how charge on ions and the channel protein determines the electric field; and the Nernst-Planck equations to describe migration and diffusion of ions in gradients of potential and concentration. The study of open channels is an important component of biotechnology because channels have great biological importance in their role as gatekeepers to cells: they are responsible for signaling in the nervous system; they coordinate the contraction of the heart, so it can act as a pump; in general, they are receptors or effectors for many drugs and natural substances that control the life of cells. Channels are wonderful objects to study by high speed computing because they use such simple physics (diffusion) to perform important biological function. The computation of diffusion is much simpler than the computation of the quantum mechanics involved in so many enzymatic functions. Channels are also natural nanotubes and so are of importance in the emerging area of nanostructures, materials and manufacturing. Porin is particularly well suited in this regard since it is available in large quantities, it can be easily modified by the methods of biotechnology, and its structure is known in atomic detail.