(A) Polarized distributions of NA (top) result in sialic acid distributions (middle) that decrease abruptly within a few tens of nanometers of the NA cluster. While most HAs sample from uniform distributions of sialic acid, those close to the NA cluster have a higher probability of binding to sialic acid that is offset from the HA in the positive direction. This results in a persistent bias in the direction of virus diffusion (bottom). (B) and (C) Similar to (A), but with two different types of symmetric NA distributions. In both cases, symmetric distributions of sialic acid (middle) result in symmetric random walks (bottom). In the one-dimensional case shown here, although the probability of positive or negative displacements are initially equal, once a displacement direction is established, the virus will tend to continue in the established direction. (D) Results of two-dimensional simulations with varying organizations of NA on the virus’s surface. Although localizing NA to one of the virus’s poles (‘polar’ configuration) produces consistent oriented motion, introducing separation between HA-rich and NA-rich regions with the same NA localization (‘gapped’ configuration) eliminates this tendency, as does localizing NA to both viral poles (‘bipolar’ configuration). Having moderately polarized NA distributions also suppresses oriented motion, since this configuration (‘off-center’) creates gradients in sialic acid density that partially cancel out over the length of the virus. Finally, NA in a random, uniformly-distributed configuration results in diffusion in a random direction. Because this configuration leads to more efficient cleavage of sialic acid and thus weaker virus adhesion, these simulations were performed with a lower number of total NAs (6 vs. 16) to prevent the virus from detaching altogether.