Many cellular processes rely on the cell's ability to transport material to and from the nucleus. Networks consisting of many microtubules and actin filaments are key to this transport. Recently, the inhibition of intracellular transport has been implicated in neurodegenerative diseases such as Alzheimer's disease and Amyotrophic Lateral Sclerosis. Furthermore, microtubules may contain so-called defective regions where motor protein velocity is reduced due to accumulation of other motors and microtubule-associated proteins. In this work, we propose a new mathematical model describing the motion of motor proteins on microtubules which incorporate a defective region. We take a mean-field approach derived from a first principle lattice model to study motor protein dynamics and density profiles. In particular, given a set of model parameters we obtain a closed-form expression for the equilibrium density profile along a given microtubule. We then verify the analytic results using mathematical analysis on the discrete model and Monte Carlo simulations. This work will contribute to the fundamental understanding of inhomogeneous microtubules providing insight into microscopic interactions that may result in the onset of neurodegenerative diseases. Our results for inhomogeneous microtubules are consistent with prior work studying the homogeneous case.

中文翻译：

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沿非均质微管的运动蛋白转运

许多细胞过程依赖于细胞运输物质进出细胞核的能力。由许多微管和肌动蛋白丝组成的网络是这种运输的关键。最近，细胞内转运的抑制与神经退行性疾病如阿尔茨海默病和肌萎缩侧索硬化有关。此外，微管可能包含所谓的缺陷区域，其中由于其他马达和微管相关蛋白的积累，运动蛋白速度降低。在这项工作中，我们提出了一个新的数学模型，描述了包含缺陷区域的微管上运动蛋白的运动。我们采用源自第一原理晶格模型的平均场方法来研究运动蛋白质动力学和密度分布。特别是，给定一组模型参数，我们获得了沿给定微管的平衡密度分布的封闭形式表达式。然后，我们使用离散模型的数学分析和蒙特卡罗模拟来验证分析结果。这项工作将有助于对非均质微管的基本理解，提供对可能导致神经退行性疾病发作的微观相互作用的深入了解。我们对非均质微管的结果与先前研究均质情况的工作一致。这项工作将有助于对非均质微管的基本理解，提供对可能导致神经退行性疾病发作的微观相互作用的深入了解。我们对非均质微管的结果与先前研究均质情况的工作一致。这项工作将有助于对非均质微管的基本理解，提供对可能导致神经退行性疾病发作的微观相互作用的深入了解。我们对非均质微管的结果与先前研究均质情况的工作一致。