When transporting cellular cargoes along the cytoskeletal filament track, motor proteins produce additional frictional drag. This “protein friction” determines the mean speed of a cargo for a given force and the energy dissipated per chemical cycle. Motor protein friction has been measured directly in an optical tweezer experiment, and can also be estimated from the force-velocity curve, close to stall. We present a mathematical and computational study of this phenomenon. In our model, a motor protein is elastically linked to a μm-sized cargo particle, and undergoes tightly coupled, biased random walk-like motion on the microtubule filament, the bias being contributed by nucleotide hydrolysis as well as stretching of the linker “spring”, with spring constant κ. The cytoplasm is assumed to be a Newtonian fluid, which exerts a damping force on the cargo moving with velocity V. The effective drag coefficient is measured in our numerical simulations, where F is the net external force on the cargo, including motor-induced force, near F=0. The motor friction is predicted theoretically and compared with simulation data for a range of values of κ and γ. The predicted values for small γ are found to be similar to experimental results, though smaller in magnitude. Numerical simulations also show that is a weakly increasing function of γ, and is additive when multiple motors are involved in transportation.

当沿着细胞骨架细丝轨道运输细胞货物时，运动蛋白会产生额外的摩擦阻力。这种“蛋白质摩擦”决定了货物在给定力下的平均速度和每个化学循环耗散的能量。运动蛋白摩擦已在光镊实验中直接测量，也可以从接近失速的力-速度曲线估计。我们对这种现象进行了数学和计算研究。在我们的模型中，运动蛋白与μ m 大小的货物颗粒弹性连接，并在微管丝上进行紧密耦合的、有偏差的随机游走式运动，这种偏差是由核苷酸水解以及接头的拉伸造成的“弹簧”，弹簧常数κ. 细胞质被假定为牛顿流体，它对以速度V移动的货物施加阻尼力。在我们的数值模拟中测量了有效阻力系数，其中F是货物上的净外力，包括电机引起的力，接近F = 0。从理论上预测电机摩擦并与κ和γ值范围的模拟数据进行比较。发现小γ的预测值与实验结果相似，但幅度较小。数值模拟还表明是γ的弱递增函数, 并且当多个电机参与运输时是相加的。