Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA. Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX13LB, UK.
Phys Biol. 2010 Aug 23;7(3):036004. doi: 10.1088/1478-3975/7/3/036004.
The tug-of-war model of motor-driven cargo transport is formulated as an intermittent trapping process. An immobile trap, representing the cellular machinery that sequesters a motor-driven cargo for eventual use, is located somewhere within a microtubule track. A particle representing a motor-driven cargo that moves randomly with a forward bias is introduced at the beginning of the track. The particle switches randomly between a fast moving phase and a slow moving phase. When in the slow moving phase, the particle can be captured by the trap. To account for the possibility that the particle avoids the trap, an absorbing boundary is placed at the end of the track. Two local signaling mechanisms--intended to improve the chances of capturing the target--are considered by allowing the trap to affect the tug-of-war parameters within a small region around itself. The first is based on a localized adenosine triphosphate (ATP) concentration gradient surrounding a synapse, and the second is based on a concentration of tau--a microtubule-associated protein involved in Alzheimer's disease--coating the microtubule near the synapse. It is shown that both mechanisms can lead to dramatic improvements in the capture probability, with a minimal increase in the mean capture time. The analysis also shows that tau can cause a cargo to undergo random oscillations, which could explain some experimental observations.
动力货物运输的拔河模型被构造成间歇捕获过程。一个不动的陷阱，代表将动力货物隔离以供最终使用的细胞机制，位于微管轨道的某个位置。一个代表随机向前偏置运动的动力货物的粒子在轨道的开始处被引入。粒子在快速移动相和缓慢移动相之间随机切换。当处于缓慢移动相时，粒子可以被陷阱捕获。为了考虑粒子避开陷阱的可能性，在轨道的末端放置了一个吸收边界。通过允许陷阱影响自身周围的小区域内的拔河参数，考虑了两种局部信号机制——旨在提高捕获目标的机会。第一种机制基于围绕突触的局部三磷酸腺苷（ATP）浓度梯度，第二种机制基于微管附近的tau——一种与阿尔茨海默病有关的微管相关蛋白——的浓度。结果表明，这两种机制都可以显著提高捕获概率，而平均捕获时间仅略有增加。分析还表明，tau 可以导致货物发生随机振荡，这可以解释一些实验观察结果。
