A stochastic chemo-mechanical model for microtubule dynamics on the dimer level: hydrolysis, catastrophes, and regulation

微管是细胞骨架中的丝状蛋白质，具有复杂的动态聚合行为，涉及所谓的灾难和救援事件，这对它们的生物学功能是必不可少的，例如在有丝分裂期间。本研究致力于在二聚体水平上建立和分析微管动力学的随机化学力学模型。微管蛋白二聚体的水解会在微管内产生机械力，在灾难事件中释放出来，此时微管进入快速解聚阶段，微管蛋白二聚体发生明显弯曲。理论和模拟模型将这些机械力耦合到二聚体的添加和移除的化学动力学，特别是微管内的进一步水解事件。到目前为止，文献中还没有提到这后一个方面。在化学-力学模拟模型中，在每个时间步，微管将被机械松弛，聚合和水解事件将根据其受机械力调节的动力学速率随机地进行。理论模型的参数将受到现有实验数据的限制，例如聚合和解聚速度。关于微管力学，我们将实施和比较变构模型和晶格模型，其中水解会引起单个微管蛋白二聚体的弯曲，而晶格模型则会削弱固有弯曲的微管蛋白二聚体之间稳定的侧键。关于水解的化学动力学，我们将实现并比较随机水解序和矢量水解法。特别是，我们将研究力学和水解之间的耦合在多大程度上可以为灾难的开始提供微观模型，即过渡到快速解聚阶段。最后，我们将使用化学机械微管模型来建立微管调节蛋白如stathmin或XMAP215的功能的理论模型；stathmin是一种重要的微管生长抑制因子，而XMAP215则促进MT的生长速度。有证据表明，这两种蛋白质都与局部弯曲相结合，因此也与微管的力学相结合。

Microtubules are filamentous proteins in the cytoskeleton with a complex dynamical polymerization behavior involving so-called catastrophe and rescue events, which is essential for their biological function, for example during mitosis. This research project is focused on the development and analysis of a stochastic chemo-mechanical model for microtubule dynamics on the dimer level. Hydrolysis of tubulin dimers gives rise to mechanical forces within the microtubule, which are released in catastrophe events, where the microtubule enters a phase of rapid depolymerization and tubulin dimer bending becomes apparent. The theoretical and simulation model will couple these mechanical forces to the chemical kinetics of addition and removal of dimers and, in particular, further hydrolysis events within the microtubule. This latter aspect has not been addressed in the literature so far. Within the chemo-mechanical simulation model, at each time step, the microtubule will be mechanically relaxed and polymerization and hydrolysis events are performed stochastically according to their kinetic rates, which are modulated by mechanical forces. Parameters of the theoretical model will be constrained by available experimental data, for example, for polymerization and depolymerization velocities. Regarding the microtubule mechanics, we will implement and compare the allosteric model, where hydrolysis gives rise to bending of individual tubulin dimers and the lattice model, where hydrolysis weakens the stabilizing lateral bonds between intrinsically bent tubulin dimers. Regarding the chemical kinetics of hydrolysis, we will implement and compare both random hydrolysis order and a vectorial hydrolysis scheme. In particular, we will investigate to what extend the coupling between mechanics and hydrolysis can provide a microscopic model for the initiation of catastrophes, i.e., the transition into a rapid depolymerization phase. Finally, we will use the chemo-mechanical microtubule model to develop theoretical models for the function of microtubule regulating proteins such as stathmin or XMAP215; stathmin is an important microtubule growth inhibitor, whereas XMAP215 increases the MT growth rate. There is evidence, that both proteins couple to the local curvature and, thus, also to the mechanics of the microtubule.