A model for biased diffusion of collagenase along collagen fibrils

We present a model to describe the biased diffusion of a collagenase along collagen fibrils. Based on the structures of collagen fibril and collagenase, the interaction is described by a one-dimensional potential that is symmetric in the region of no cleavage and asymmetric in the cleavage region. We show that the mean velocity of the unidirectional diffusion of the collagenase depends on the three parameters: the asymmetric ratio of the local potential in the cleavage region, the chemical reaction rate of proteolysis and the jumping rate of collagenase between two neighboring tracks. We calculate the correlation function and the mean transport velocity for both wild-type and mutant collagenases along collagen fibrils, the results of which are consistent with the previous experiments.