Microtubules interacting with a boundary: mean length and mean first-passage times.
Microtubules interacting with a boundary: mean length and mean first-passage times.
复制标题
与边界相互作用的微管：平均长度和平均首次通过时间。
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发表时间：
2012
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通讯作者：
B. Mulder
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作者：
B. Mulder
我建立了一个微管与突变诱发边界相互作用的动力学模型。在这个模型中，微管要么等待成核，要么活跃生长或收缩，要么在边界处停滞不前。我首先确定这些不同态的稳态占有率和由此产生的长度分布。然后，用一组合适的分裂概率和条件平均首次通过时间来表示到达边界的平均首次通过时间问题，并用微分方程法对这些量进行显式求解。作为应用，我重温了最近提出的微管和目标染色体之间相互作用的搜索和捕获模型[M.Gopalakrishnan和B.S.Govindan，Bull]。数学课。比奥尔。73,2483(2011)]。我展示了我的方法是如何直接而紧凑地解决这个问题的。
I formulate a dynamical model for microtubules interacting with a catastrophe-inducing boundary. In this model microtubules are either waiting to be nucleated, actively growing or shrinking, or stalled at the boundary. I first determine the steady-state occupation of these various states and the resultant length distribution. Next, I formulate the problem of the mean first-passage time to reach the boundary in terms of an appropriate set of splitting probabilities and conditional mean first-passage times and solve explicitly for these quantities using a differential equation approach. As an application, I revisit a recently proposed search-and-capture model for the interaction between microtubules and target chromosomes [M. Gopalakrishnan and B. S. Govindan, Bull. Math. Biol. 73, 2483 (2011)]. I show how my approach leads to a direct and compact solution of this problem.