Modeling of kinetic processes in biological systems

里程碑理论 里程碑是一种潜在地大大扩大了可以使用分子动力学模拟进行分析的过程的时间范围的方法。它的主要思想是使用MD模拟将原始动力学映射到速率方程，然后可以用来研究感兴趣的过程。我们的理论解释了状态转变的物理意义，其中状态转变由速率方程描述。 膜通道中封闭分子的动力学研究 当大分子进入膜通道时，它会阻止小离子通过通道的电流。Bezrukov博士的团队在单通道实验中对这种现象进行了实验研究。我们建立了通道中阻滞剂寿命的双位模型，该模型比精确的扩散模型简单得多，因此对于分析阻塞剂在通道中的持续时间的实验数据是有用的。 跃迁路径时间的前后对称性 转移路径是扩散轨道的最后一部分，它从点a开始，在第一次到达点b时终止，在此期间，轨道从a点到达点be，而不与点a相接。我们证明了a到b转移路径的持续时间的分布等于b到a转移路径的持续时间的分布。这是扩散动力学的时间反转对称性的结果。 粗糙表面的扩散限制陷阱 我们研究了粗糙的非均匀吸收表面对扩散粒子的捕获，证明了在适当选择参数：有效表面位置及其捕获率的情况下，它与光滑的均匀吸收表面的捕获是等价的。我们的理论建立了这些参数与原始表面参数之间的关系，原始表面是粗糙的和非均匀的。

Theory of milestoning Milestoning is a method that potentially allows significantly enlarge the time range of processes that can be analyzed using molecular dynamics simulations. Its main ides is to use MD simulations to map the original dynamics onto rate equations which then can be used to study the process of interest. Our theory explains physical meaning of the states transitions among which are described by the rate equations. Dynamics of blocking molecules in a membrane channel When a large molecule enters a membrane channel, it blocks the current of small ions through the channels. This phenomenon is studied experimentally in single-channel experiments in the Dr. Bezrukov's group. We developed a two-site model of the blocker lifetime in the channel, which is much simpler than the exact diffusion model and, therefore, useful for the analysis of experimental data on the blockade duration. Forward-backward symmetry of transition path time Transition path is a final part of a diffusion trajectory that starts form point a and is terminated when it comes to point b for the first time, during which the trajectory goes from point a to point be without touching point a. We show that the distribution of the duration of a-to-b transition path is equal to that for the duration of b-to-a transition path. This is a consequence of time-reversal symmetry of diffusion dynamics. Diffusion-limited trapping by rough surfaces We study trapping of diffusing particles by rough non-uniformly absorbing surfaces and show that it is equivalent to that by smooth uniformly absorbing surfaces with properly chosen parameters: effective surface location and its trapping rate. Our theory establishes the relation between these parameters and the parameters of the original surface which is rough and non-uniform.