The origins of the large differences observed in the rates at which diverse particles are conveyed along axonal microtubules are still a matter of debate in the literature. There is evidence that certain neurodegenerative diseases may be triggered by disturbances in the related transport processes. Motivated by this, we employ a model to investigate mobility properties of certain cargoes whose dynamics are coupled with that of molecular motors on crowded microtubules. For certain initial and boundary conditions, we use the method of characteristics to resolve perturbatively the pair of equations of Burgers type resulting from a mean-field approach to the original microscopic stochastic model. Extensions to nonperturbative limits are explored numerically. In this context, we are able to figure out conditions under which the cargoes' average velocities may differ up to orders of magnitude just by changing the number of motors on the considered track. We then discuss possibilities to connect these theoretical predictions with available experimental data about axon transport.

中文翻译：

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快速和缓慢的轴突运输：基于货物和分子马达耦合动力学的统一方法

在沿轴突微管输送不同颗粒的速率上观察到的巨大差异的根源仍然是文献中争论的问题。有证据表明，某些神经退行性疾病可能是由相关运输过程的紊乱引起的。因此，我们采用了一个模型来研究某些货物的流动性，这些货物的动力学与拥挤的微管上的分子电动机的动力学耦合。对于某些初始条件和边界条件，我们使用特征方法微扰地求解由原始微观随机模型的均值场方法得到的Burgers型方程对。通过数字探索了对非摄动极限的扩展。在这种情况下，我们能够找出货物 仅通过改变所考虑的轨道上的电动机数量，平均速度可能会相差一个数量级。然后，我们讨论将这些理论预测与有关轴突运输的可用实验数据联系起来的可能性。