Modeling of kinetic processes in biological systems

通道促进的膜转运。(I)我们发展了膜通道离子电流波动的一般理论，这是由于分子移位导致通道部分阻塞所致。(Ii)我们发展了分子通过锥形通道的传输理论，并表明粒子间的相互作用破坏了非相互作用的粒子通过这种通道传输所固有的通量对称性。 两态蛋白质折叠。我们发展了一个两态蛋白质折叠理论，假设潜在的动力学是根据蛋白质粗粒离散状态网络上的速率方程来表示的。我们的理论允许人们找到折叠和展开速率以及最可能的折叠/展开路径。 果蝇胚胎中形态原梯度的动态变化。我们发展了两态反应扩散系统级联中的信号梯度理论，为Shvartsman教授的实验室的实验观察提供了新的见解。在普林斯顿大学。 具有熵陷阱和势垒的复杂介质中的传输。我们发展了一个理论，解释了粒子扩散系数与其半径的反常关系，用于在有死端的管子中扩散。 树突棘的弥漫性逃逸。我们发展了一种理论，解释了树枝状脊柱中的粒子寿命如何取决于脊柱的几何参数、粒子的初始位置以及它在脊柱颈部和头部的扩散系数。

Channel-facilitated membrane transport. (i) We developed a general theory of fluctuations of ion current through a membrane channel due to partial blocking of the channel by translocating molecules. (ii) We developed a theory of transport of molecules through conical channels and showed that inter-particle interactions break the flux symmetry inherent in transport of non-interacting particles through such channels. Two-state protein folding. We developed a theory of two-state protein folding assuming that underlying dynamics is formulated in terms of rate equations on a network of coarse-grained discrete states of the protein. Our theory allows one to find folding and unfolding rates as well as most probable folding/unfolding pathways. Dynamics of morphogen gradients in the Drosophila Embrio. We developed a theory of signaling gradients in cascades of two-state reaction-diffusion systems that provides a new insight into the experimental observations made in Professor Shvartsman's Lab. at Princeton University. Transport in complex media with entropy traps and barriers. We developed a theory that explains anomalous dependence of the particle diffusivity on its radius for diffusion in tubes with dead ends. Diffusive escape from dendritic spines. We developed a theory that explains how the particle lifetime in a dendritic spine depends on geometric parameters of the spine, initial position of the particle, and its diffusivity in the spine neck and head.