Modeling of kinetic processes in biological systems

通道促进的膜转运。(I)我们发展了膜通道转运的一般随时间变化的理论。我们用这个理论证明了涨落定理同样适用于相互作用和非相互作用粒子的输运。(Ii)我们还解决了由于分子移位导致膜通道部分堵塞而导致通过膜通道的离子电流波动的问题。 两态蛋白质折叠。我们将激活速率过程的Kramers-Langer理论推广到离散基础随机动力学的情形。将我们的理论应用于两态蛋白质的折叠，可以得到折叠和解折叠的速率以及最可能的折叠/解折叠路径。 非马尔可夫非对称随机游动。我们提出了一种新的方法，它允许我们找到有边界和无边界的非马尔可夫非对称随机游动的传播子和相关描述子的拉普拉斯变换。这些结果被用于发展上述膜通道传输的一般依赖于时间的理论。 悬浮细胞培养中的细胞间通讯。我们发展了一种在悬浮细胞培养中配体内化的理论，悬浮细胞通过扩散配体进行通信。我们的理论表明，表征配体内化的时间和长度尺度如何取决于细胞和配体的性质以及细胞浓度等检测参数。该理论被用来分析在培养的人树突状细胞对病毒感染的早期反应实验中关于干扰素信号的实验数据。 果蝇胚胎中形态原梯度的动态变化。我们分析了果蝇胚胎中不同母体形态原梯度的动态变化的各个方面。我们分析的目的是使在Shvartsman教授实验室进行的实验观察合理化。在普林斯顿大学。 具有熵陷阱和势垒的多孔结构中的输运。我们发展了由死端形成周期性熵陷阱的管内扩散理论和由球体接触形成的周期性熵势垒的管内扩散理论。在未来，我们将使用这些结果来分析第二信使在粘液脊椎中的区划。

Channel-facilitated membrane transport. (i) We developed a general time-dependent theory of transport through membrane channels. We used the theory to demonstrate that the fluctuation theorem is equally applicable for transport of both interacting and non-interacting particles. (ii) We also worked out the problem of fluctuations of the ion current through a membrane channel due to partial blocking of the channel by translocating molecules. Two-state protein folding. We generalized Kramers-Langer theory of activated rate processes to the case of discrete underlying stochastic dynamics. Application of our theory to folding of two-state proteins allows one to find folding and unfolding rates as well as most probable folding/unfolding pathways. Non-Markovian asymmetric random walks. We suggested a new approach which allowed us to find the Laplace transform of the propagator and related descriptors for non-Markovian asymmetric random walks with and without boundaries. These results were used when developing the general time-dependent theory of transport through membrane channels mentioned above. Cell-to cell communication in cultures of suspended cells. We developed a theory of ligand internalization in cultures of suspended cells, which communicate by diffusing ligands. Our theory shows how the time and length scales characterizing the ligand internalization depend on the properties of the cells and ligands as well as on the parameters of the assay like the cell concentration, etc.. The theory was used to analyze experimental data on Interferon signaling in experiments on early response of cultured human dendritic cells to virial infection. Dynamics of morphogen gradients in the Drosophila Embrio. We analyzed various aspects of the dynamics of different maternal morphogen gradients in the Drosophila Embryo. The goal of our analysis was to rationalize experimental observations made in Professor Shvartsman's Lab. at Princeton University. Transport in porous structures with entropy traps and barriers. We developed theories of diffusion in tubes with periodic entropy traps formed by dead ends and in tubes with periodic entropy barriers formed by contacting spheres. In the future we are going to use these results to analyze compartmentalization of second messengers in dedritic spines.