The model of stochastic particle movement (Equation 7, Materials and methods) was simulated with equal transition probabilities () for various values of and particle numbers in an infinite cable with 1 µm compartments and 1 s time steps. The expected run length is given by the mean of a negative binomial distribution. For each simulation, a mass-action approximation was fit by matching the first two moments of the cargo distribution, as described in the Materials and methods. In both panels, dots represent simulated triplicates, and lines denote the average outcome with colors denoting the simulated ensemble size (see legend). (A) The mass-action model (Equation 1, Results) provides a reasonably accurate fit after 100 s of simulation with moderately long run lengths and low particle numbers. The fit improves for longer simulations and larger particle numbers, since the cargo distribution is better approximated by a normal distribution under these conditions due to the central limit theorem. The coefficient of determination, , reflects the proportion of explained variance by the mass-action model (equivalent to a Gaussian fit to the concentration profile). (B) The estimated diffusion coefficient of the mass-action model (i.e. the variance of the Gaussian fit in panel A) increases as expected run length increases.