  We present here a model for multivalent diffusive transport whereby a central
point-like hub is coupled to multiple feet, which bind to complementary sites
on a two-dimensional landscape. The available number of binding interactions is
dependent on the number of feet (multivalency), and on their allowed distance
from the central hub (span). Using Monte Carlo simulations that implement the
Gillespie algorithm, we simulate multivalent diffusive transport processes for
100 distinct walker designs. Informed by our simulation results we derive an
analytical expression for the diffusion coefficient of a general multivalent
diffusive process as a function of multivalency, span, and dissociation
constant Kd. Our findings can be used to guide experimental design of
multivalent transporters, in particular providing insight into how to overcome
trade-offs between diffusivity and processivity.
