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，具有复杂的动态聚合行为，涉及所谓的灾难和救援事件，这对其生物学功能至关重要，例如在有丝分裂期间。本研究项目的重点是在二聚体水平上开发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在微管内产生机械力，这些力在突变事件中释放，微管进入快速解聚阶段，微管蛋白二聚体弯曲变得明显。理论和模拟模型将这些机械力耦合到二聚体的添加和去除的化学动力学，特别是微管内的进一步水解事件。到目前为止，这后一个方面还没有在文献中得到解决。在化学-力学模拟模型中，在每个时间步，微管将机械放松，聚合和水解事件根据其动力学速率随机进行，动力学速率由机械力调节。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，我们将实现并比较变构模型，其中水解引起单个微管蛋白二聚体的弯曲和晶格模型，其中水解削弱了内在弯曲的微管蛋白二聚体之间的稳定横向键。关于水解的化学动力学，我们将实现并比较随机水解顺序和矢量水解方案。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-机械微管模型来开发微管调节蛋白（如stathmin或XMAP215）功能的理论模型；stathmin是一种重要的微管生长抑制剂，而XMAP215可以提高MT的生长速度。有证据表明，这两种蛋白质都与局部曲率偶联，因此也与微管的力学偶联。

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.