Modeling of kinetic processes in biological systems

多位点磷酸化动力学。 多位点磷酸化动力学通常用进行性和分布性机制来解释，这实际上是一般磷酸化动力学的特殊极限情况。我们一般地研究了磷酸化动力学，重点是这些极限情况是如何发生的，因为参数的特殊选择 由片状表面限制扩散的陷阱。 在生物系统中，扩散的溶质通常被反射表面上的活性中心捕获。我们研究了斑块表面的俘获，重点研究了捕获率如何依赖于斑块表面的分数。 简单细胞网络中的集体生长。 我们研究简单细胞网络中的集体生长，目的是合理解释为什么网络中不同的细胞以不同的速度生长。 底物解离速率对酶速度的影响不是很小。 基于一般的争论，最近有人提出可以通过增加底物解离速率来提高酶的速度。我们研究了多态酶动力学的一般模型，目的是明确这种酶反应加速发生的条件。 散装介导的表面运输。 我们研究溶质分子的表面传输，这些分子被允许从表面解离，然后又回来。我们的目标是了解不同研究小组报告的这类系统中分子异常次扩散的起源。 随机门控对通道促进膜转运的影响。 尽管通道促进的膜传输中的随机门控已经被研究了几十年，但还没有理论来解释通过通道的溶质通量如何依赖于该门控速率和通道中的溶质动力学。我们发展了这样一个理论，它表明，如果门控速率与溶质通过通道的速率相当，则在快速门控时可能会出现显著偏离常识预期的情况。

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.