In the intracellular environment, the intrinsic dynamics of microtubule filaments is often hindered by the presence of barriers of various kind, such as kinetochore complexes and cell cortex, which impact their polymerisation force and dynamical properties such as catastrophe frequency. We present a theoretical study of the effect of a forced barrier, also subjected to thermal noise, on the statistics of catastrophe events in a single microtubule as well as a ‘bundle’ of two parallel microtubules. For microtubule dynamics, which includes growth, detachment, hydrolysis and the consequent dynamic instability, we employ a one-dimensional discrete stochastic model. The dynamics of the barrier is captured by over-damped Langevin equation, while its interaction with a growing filament is assumed to be hard-core repulsion. A unified treatment of the continuum dynamics of the barrier and the discrete dynamics of the filament is realized using a hybrid Fokker–Planck equation. An explicit mathematical formula for the force-dependent catastrophe frequency of a single microtubule is obtained by solving the above equation, under some assumptions. The prediction agrees well with results of numerical simulations in the appropriate parameter regime. More general situations are studied via numerical simulations. To investigate the extent of ‘load-sharing’ in a microtubule bundle, and its impact on the frequency of catastrophes, the dynamics of a two-filament bundle is also studied. Here, two parallel, non-interacting microtubules interact with a common, forced barrier. The equations for the two-filament model, when solved using a mean-field assumption, predicts equal sharing of load between the filaments. However, numerical results indicate the existence of a wide spectrum of load-sharing behaviour, which is characterized using a dimensionless parameter.

在细胞内环境中，微管丝的内在动力学经常受到各种障碍的阻碍，例如动粒复合物和细胞皮层，这会影响它们的聚合力和动力学特性，例如突变频率。我们提出了一个受热噪声影响的强制屏障对单个微管以及两个平行微管“束”中灾难事件统计的影响的理论研究。对于微管动力学，包括生长、脱离、水解和随之而来的动态不稳定性，我们采用一维离散随机模型。屏障的动力学由过阻尼朗之万方程捕获，而它与生长细丝的相互作用被假定为硬核排斥。使用混合 Fokker-Planck 方程实现了对屏障的连续动力学和灯丝的离散动力学的统一处理。在一些假设下，通过求解上述方程，获得了单个微管的力相关突变频率的明确数学公式。该预测与适当参数范围内的数值模拟结果非常吻合。通过数值模拟研究更一般的情况。为了研究微管束中“负载共享”的程度及其对灾难频率的影响，还研究了双丝束的动力学。在这里，两个平行的、非相互作用的微管与一个共同的、强制的屏障相互作用。双灯丝模型的方程，当使用平均场假设求解时，预测灯丝之间的负载均摊。然而，数值结果表明存在广泛的负载共享行为，其特征在于使用无量纲参数。