A general model for the motion of multivalent cargo interacting with substrates

Multivalent interactions are common in biology at many different length scales, and can result in the directional motion of multivalent cargo along substrates. Here, a general analytical model has been developed that can describe the directional motion of multivalent cargo as a response to position dependence in the binding and unbinding rates exhibited by their interaction sites. Cargo exhibit both an effective velocity, which acts in the direction of increasing cargo-substrate binding rate and decreasing cargo-substrate unbinding rate, and an effective diffusivity. This model can reproduce previously published experimental findings using only the binding and unbinding rate distributions of cargo interaction sites, and without any further parameter fitting. Extension of the cargo binding model to two dimensions reveals an effective velocity with the same properties as that derived for the one-dimensional case.