Modeling of kinetic processes in biological systems

通道促进膜运输。 （i）我们发展了由于分子易位部分阻塞通道而导致通过膜通道的离子电流波动的一般理论。 （ii）我们发展了分子通过锥形通道传输的理论，并表明粒子间相互作用打破了非相互作用粒子通过此类通道传输所固有的通量对称性。 两种状态的蛋白质折叠。我们开发了一种二态蛋白质折叠理论，假设潜在的动力学是根据蛋白质粗粒度离散状态网络上的速率方程来表述的。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。 果蝇胚胎中形态发生素梯度的动力学。我们开发了一种二态反应扩散系统级联中的信号梯度理论，为 Shvartsman 教授实验室的实验观察提供了新的见解。在普林斯顿大学。 在具有熵陷阱和势垒的复杂介质中传输。我们提出了一种理论，解释了在有死角的管子中扩散时粒子扩散率对其半径的异常依赖性。 树突棘的扩散逃逸。我们开发了一种理论，解释了树突棘中的粒子寿命如何取决于树突棘的几何参数、粒子的初始位置及其在树突颈部和头部的扩散率。

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.