CNRS, INP, Inst Neurophysiopathol, Faculté de Pharmacie de Marseille, Aix Marseille University, 13385, Marseille, France.
Service pharmacie, CHU Hôpital de La Timone, APHM, Marseille, France.
Bull Math Biol. 2019 Mar;81(3):722-758. doi: 10.1007/s11538-018-0531-2. Epub 2018 Nov 27.
Microtubules (MTs) are protein filaments found in all eukaryotic cells which are crucial for many cellular processes including cell movement, cell differentiation, and cell division. Due to their role in cell division, they are often used as targets for chemotherapy drugs used in cancer treatment. Experimental studies of MT dynamics have played an important role in the development and administration of many novel cancer drugs; however, a complete description of MT dynamics is lacking. Here, we propose a new mathematical model for MT dynamics, that can be used to study the effects of chemotherapy drugs on MT dynamics. Our model consists of a growth-fragmentation equation describing the dynamics of a length distribution of MTs, coupled with two ODEs that describe the dynamics of free GTP- and GDP-tubulin concentrations (the individual dimers that comprise of MTs). Here, we prove the well-posedness of our system and perform a numerical exploration of the influence of certain model parameters on the systems dynamics. In particular, we focus on a qualitative description for how a certain class of destabilizing drugs, the vinca alkaloids, alter MT dynamics. Through variation of certain model parameters which we know are altered by these drugs, we make comparisons between simulation results and what is observed in in vitro studies.
微管（MTs）是所有真核细胞中发现的蛋白质丝，对于许多细胞过程至关重要，包括细胞运动、细胞分化和细胞分裂。由于它们在细胞分裂中的作用，它们经常被用作癌症治疗中化疗药物的靶点。对 MT 动力学的实验研究在许多新型癌症药物的开发和管理中发挥了重要作用；然而，对 MT 动力学的描述还不完整。在这里，我们提出了一个新的 MT 动力学数学模型，可用于研究化疗药物对 MT 动力学的影响。我们的模型由一个描述 MT 长度分布动力学的生长-断裂方程组成，与两个描述游离 GTP-和 GDP-微管蛋白浓度（构成 MT 的单个二聚体）动力学的 ODE 耦合。在这里，我们证明了我们系统的适定性，并对某些模型参数对系统动力学的影响进行了数值探讨。特别是，我们关注一类不稳定药物（长春花生物碱）如何改变 MT 动力学。通过改变我们知道这些药物会改变的某些模型参数，我们将模拟结果与体外研究中的观察结果进行比较。
