Clarkson University, 8 Clarkson Avenue, Potsdam, NY, United States of America.
Clarkson University, 8 Clarkson Avenue, Potsdam, NY, United States of America.
J Theor Biol. 2022 Nov 21;553:111257. doi: 10.1016/j.jtbi.2022.111257. Epub 2022 Aug 31.
Microtubules (MTs) are protein polymers found in all eukaryotic cells. They are crucial for normal cell development, providing structural support for the cell and aiding in the transportation of proteins and organelles. In order to perform these functions, MTs go through periods of relatively slow polymerization (growth) and very fast depolymerization (shortening), where the switch from growth to shortening is called a catastrophe and the switch from shortening to growth is called a rescue. Although MT dynamic instability has traditionally been described solely in terms of growth and shortening, MTs have been shown to pause for extended periods of time, however the reason for pausing is not well understood. Here, we present a new mathematical model to describe MT dynamics in terms of growth, shortening, and pausing. Typically, MT dynamics are defined by four key parameters which include the MT growth rate, shortening rate, frequency of catastrophe, and the frequency of rescue. We derive a mathematical expression for the catastrophe frequency in the presence of pausing, as well as expressions to describe the total time that MTs spend in a state of growth and pause. In addition to exploring MT dynamics in a control-like setting, we explore the implicit effect of stabilizing MT associated proteins (MAPs) and stabilizing and destabilizing chemotherapeutic drugs that target MTs on MT dynamics through variations in model parameters.
微管（MTs）是存在于所有真核细胞中的蛋白质聚合物。它们对正常细胞发育至关重要，为细胞提供结构支撑，并有助于蛋白质和细胞器的运输。为了发挥这些功能，MT 经历相对缓慢的聚合（生长）和非常快速的解聚（缩短）期，其中从生长到缩短的转变称为崩溃，从缩短到生长的转变称为救援。尽管 MT 的动态不稳定性传统上仅以生长和缩短来描述，但已经表明 MT 会暂停很长一段时间，然而暂停的原因尚不清楚。在这里，我们提出了一个新的数学模型，根据生长、缩短和暂停来描述 MT 的动力学。通常，MT 动力学由四个关键参数定义，包括 MT 的生长速度、缩短速度、崩溃频率和救援频率。我们推导出了在存在暂停的情况下崩溃频率的数学表达式，以及描述 MT 处于生长和暂停状态的总时间的表达式。除了在类似控制的环境中探索 MT 动力学外，我们还通过模型参数的变化来探索稳定 MT 相关蛋白（MAPs）和稳定及不稳定针对 MT 的化疗药物对 MT 动力学的隐含影响。
