Modeling of kinetic processes in biological systems

多位点磷酸化的动力学。 多位点磷酸化动力学通常被解释为进行性和分布性机制，事实上，这是一般磷酸化动力学的特殊限制情况。我们研究了磷酸化动力学的一般，重点是如何这些限制情况下出现的特殊选择的参数 通过斑片状表面的扩散限制捕获。 在生物系统中，扩散溶质通常被反射表面上的活性位点捕获。我们研究捕捉斑片状表面的捕获率如何取决于补丁表面分数。 简单细胞网络中的集体增长。 我们研究了一个简单的细胞网络中的集体增长，目的是合理化为什么网络中的不同细胞以不同的速率增长。 底物解离速率对酶促速度的重要影响。 基于一般的论点，最近有人提出，可以通过增加底物解离速率来增加酶促速度。我们研究了一般模型的多态酶动力学的目标，以指定的条件下，这种加速的酶促反应可以发生。 体积介导的表面转运。 我们研究溶质分子的表面输运，溶质分子被允许从表面解离，然后回来。我们的目标是了解不同团体报道的这种系统中分子的异常亚扩散的起源。 随机门控对通道易化膜转运的影响。 虽然通道促进的膜转运中的随机门控已经研究了几十年，但是没有理论解释通过通道的溶质通量如何取决于通道中的门控速率和溶质动力学。我们开发了这样一个理论，它表明，从常识的预期可能会发生显着偏差，在快速门控，如果门控速率变得可比的溶质通过通道的速率。

Dynamics of multisite phosphorylation. Multi-site phosphorylation dynamics is usually interpreted in terms of the processive and distributive mechanisms, which, in fact, are special limiting cases of the general phosphorylation dynamics. We study the phosphorylation dynamics in general, focusing on how these limiting cases arise for the special choice of the parameters Diffusion-limited trapping by patchy surfaces. In biological systems, diffusing solutes are typically trapped by active sites on the otherwise reflecting surfaces. We study trapping by patchy surfaces focusing on how the trapping rate depends on the patch surface fraction. Collective growth in simple cell networks. We study collective growth in a simple cell network with the goal to rationalize why different cells of the network grow with different rates. Non-trivial effects of the substrate dissociation rate on the enzymatic velocity. Based on general arguments, it was recently proposed that the enzymatic velocity can be increased by increasing the substrate dissociation rate. We study a general model of the multistate enzyme dynamics with the goal to specify the conditions under which such acceleration of the enzymatic reaction can occur. Bulk-mediated surface transport. We study surface transport of solute molecules which are allowed to dissociate from the surface and then come back. Our goal was to understand the origin of the anomalous subdiffusion of the molecules in such systems reported by different groups. Effect of stochastic gating on channel-facilitated membrane transport. Although stochastic gating in channel-facilitated membrane transport has been studied for many decades, there is no theory that explains how the solute flux through the channel depends on that gating rate and the solute dynamics in the channel. We developed such a theory which shows that significant deviations from the common sense expectation may occur at fast gating if the gating rate becomes comparable with the rate of the solute passage through the channel.