Modeling of kinetic processes in biological systems

平均跃迁路径时间与势垒高度的关系 粒子在a点和b点之间扩散的过渡路径是粒子轨迹的最后一段，当它离开a点并到达b点而不接触a点时，反之亦然。研究了平均跃迁路径时间对势垒高度的依赖关系。我们发现，这种依赖关系从高维空间中随着势垒高度的单调减小到二维空间中的单调增加是非常不平凡的。 系统的动力学，如分子马达，在具有不同速度和扩散系数的状态之间随机跳跃 在很长一段时间内，系统的随机动力学可以用两个参数来描述：有效漂移速度和扩散系数。我们发展了一种理论，解释了这些有效参数如何与各个状态的漂移速度和扩散系数以及状态间跃迁的速率有关。 拥挤环境中的随机游走 我们发展了拥挤环境下的循环随机游走理论，并证明了拥挤对无拥挤时随机游走的主要特征有影响。我们解释了如何在单分子实验中观察到所发现的效应。 跃迁路径时间的前后对称性 对过渡路径时间的传统考虑假定扩散粒子是守恒的。由于详细的平衡，跃迁路径的分布具有正反向对称性。我们将传统的考虑推广到扩散粒子可以被捕获的情况，并证明了在存在任意形状的分布汇的情况下，细节平衡是满足的。这使得我们能够证明，即使在存在陷阱的情况下，跃迁路径时间分布的前后对称性也是守恒的。

Dependence of the mean transition path time on the height of the entropy barrier Transition path of a particle diffusing between points a and b is the final segment of the particle trajectory when it leaves point a and goes to point b without touching point a and vice versa. We studied the mean transition path time in entropy potentials focusing on its dependence of the entropy barrier height. We found that this dependence is highly non-trivial changing from monotonic decrease with the barrier height in high-dimensional spaces to monotonic increase in two dimensions. Dynamics of systems, like molecular motors, that randomly jump between states with different velocities and diffusivities At long times, stochastic dynamics of systems mentioned in the title can be characterized by two parameters: effective drift velocity and diffusivity. We developed a theory that explains how these effective parameters are related to the drift velocities and diffusivities in individual states and the rates of inter-state transitions. Random walk in crowded environment We developed a theory of cyclic random walk in crowded environment and demonstrated that crowding affects main features of the random walk in the absence of crowding. We explained how one can observe the discovered effects in single-molecule experiments. Forward-backward symmetry of the transition path time Conventional consideration of the transition path time assumes conservation of diffusing particles. Because of the detailed balance, the distribution of the transition path possesses the forward-backward symmetry. We generalized the conventional consideration to the case where diffusing particles can be trapped and proved that the detailed balance is fulfilled in the presence of a distributed sink of an arbitrary shape. This allowed us to show that the forward-backward symmetry of the distribution of the transition path time is conserved even in the presence of trapping.