分子马达驱动囊泡进入闭合收缩区的动力学
Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors
摘要：
我们研究了一个模型的膜泡运输到树突棘，这是球状的细胞内室在神经元驱动的分子马达的动力学。我们简化了[Fai et al.，狭窄盲缩中囊泡的主动弹性流体动力学。Phys. Rev. Fluids，2（2017），113601]到一个快-慢系统，产生一个解析和数值上易于处理的方程，相当于过阻尼极限下的原始模型。该模型的关键参数是倾向于向树突棘头部推动的马达与倾向于向相反方向推动的马达的比率。我们在这些参数进行了数值分岔分析，发现稳态囊泡速度出现和消失，通过几个鞍结分岔。这一过程使我们能够确定存在多个稳定速度的参数空间区域。我们表明，通过直接计算，只能有足够接近的囊泡脊柱直径比的单向运动。我们的分析预测的临界囊泡脊柱直径比，在那里有一个从单向到双向运动的过渡，与文献中的囊泡轨迹的实验观察一致。
英文摘要：
We study the dynamics of a model of membrane vesicle transport into dendritic spines, which are bulbous intracellular compartments in neurons driven by molecular motors. We reduce the lubrication model proposed in [Fai et al., Active elastohydrodynamics of vesicles in narrow, blind constrictions. Phys. Rev. Fluids, 2 (2017), 113601] to a fast-slow system, yielding an analytically and numerically tractable equation equivalent to the original model in the overdamped limit. The model's key parameters are the ratio of motors that prefer to push toward the head of the dendritic spine to the ratio of motors that prefer to push in the opposite direction. We perform a numerical bifurcation analysis in these parameters and find that steady-state vesicle velocities appear and disappear through several saddle-node bifurcations. This process allows us to identify the region of parameter space in which multiple stable velocities exist. We show by direct calculations that there can only be unidirectional motion for sufficiently close vesicle-to-spine diameter ratios. Our analysis predicts the critical vesicle-to-spine diameter ratio, at which there is a transition from unidirectional to bidirectional motion, consistent with experimental observations of vesicle trajectories in the literature.
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