Role of trap recharge time on the statistics of captured particles
Role of trap recharge time on the statistics of captured particles
复制标题
DOI：
10.1103/physreve.99.022420
复制
发表时间：
2019-02-25
影响因子：
2.4
通讯作者：
Borisyuk, Alla
中科院分区：
文献类型：
--
作者：
Handy, Gregory;Lawley, Sean D.;Borisyuk, Alla
我们考虑n个粒子在一个区域内自由扩散。边界包含吸收逃逸区域，在那里粒子可以逃逸，和陷阱，在那里粒子可以被捕获。这些陷阱或捕获区域模仿生物学的例子，如突触间隙中的受体和等待猎物的伏击捕食者，必须在捕获之间充电。我们有兴趣在表征的时间过程中的粒子的数量留在域中，累积捕获的数量，和可用的捕获区域的数量。我们发现，在某些条件下，累积捕获的数量随时间线性增加的斜率和持续时间明确确定的充电率的捕获区域。该充电速率还确定清除时间的均值和方差，清除时间定义为所有粒子离开该区域所需的时间。此外，我们发现，虽然有限的充电率将总是导致在一个较低的数量的捕获粒子相比，瞬时充电，它可以增加或减少的变异量。最后，我们将该模型扩展到部分吸收陷阱，以研究理想突触间隙内受体激活的动态变化。我们发现，域的宽度控制这些受体被激活的时间量，而受体的数量控制激活的幅度。我们的数学结果来自考虑这个系统在几个方面：作为一个完整的空间扩散过程与充电陷阱，作为一个连续时间马尔可夫过程的离散状态空间，并作为一个系统的常微分方程的平均场近似。
We consider n particles diffusing freely in a domain. The boundary contains absorbing escape regions, where the particles can escape, and traps, where the particles can be captured. Modeled after biological examples such as receptors in the synaptic cleft and ambush predators waiting for prey, these traps, or capture regions, must recharge between captures. We are interested in characterizing the time courses of the number of particles remaining in the domain, the number of cumulative captures, and the number of available capture regions. We find that under certain conditions, the number of cumulative captures increases linearly in time with a slope and duration determined explicitly by the recharge rate of the capture regions. This recharge rate also determines the mean and variance of the clearance time, defined as the time it takes for all particles to leave the domain. Further, we find that while a finite recharge rate will always result in a lower number of captured particles when compared to instantaneous recharging, it can either increase or decrease the amount of variability. Lastly, we extend the model to partially absorbing traps in order to investigate the dynamics of receptor activation within an idealized synaptic cleft. We find that the width of the domain controls the amount of time that these receptors are activated, while the number of receptors controls the amplitude of activation. Our mathematical results are derived from considering this system in several ways: as a full spatial diffusion process with recharging traps, as a continuous-time Markov process on a discrete state space, and as a system of ordinary differential equations in a mean-field approximation.