Department of Mathematics and Statistics, Cleveland State University, Cleveland, OH, 44115, USA.
Center for Applied Data Analysis and Modeling, Cleveland State University, Cleveland, OH, 44115, USA.
Bull Math Biol. 2021 Jan 7;83(2):9. doi: 10.1007/s11538-020-00838-4.
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.
许多细胞过程依赖于细胞将物质在细胞核内外运输的能力。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，细胞内运输的抑制被认为与神经退行性疾病如阿尔茨海默病和肌萎缩性侧索硬化症有关。此外，微管可能包含所谓的缺陷区域，由于其他马达和微管相关蛋白的积累，马达蛋白的速度在此处降低。在这项工作中，我们提出了一个新的数学模型来描述包含缺陷区域的微管上的马达蛋白的运动。我们采用源于基本晶格模型的平均场方法来研究马达蛋白动力学和密度分布。特别是，给定一组模型参数，我们得到了沿着给定微管的平衡密度分布的闭式表达式。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解析结果。这项工作将有助于对不均匀微管的基本理解，为可能导致神经退行性疾病的微观相互作用提供深入了解。我们对不均匀微管的结果与研究均匀情况的先前工作一致。
