Studies of pathogen-host specificity, virulence, and transmissibility are critical for basic research as well as for assessing the pandemic potential of emerging infectious diseases. This is especially true for viruses such as influenza, which continue to affect millions of people annually through both seasonal and occasional pandemic events. Although the influenza virus has been fairly well studied for decades, our understanding of host-cell binding and its relation to viral transmissibility and infection is still incomplete. Assessing the binding mechanisms of complex biological systems with atomic-scale detail is challenging given current experimental limitations. Much remains to be learned, for example, about how the terminal residue of influenza-binding host-cell receptors (sialic acid) interacts with the viral surface. Here, we present an integrative structural-modeling and physics-based computational assay that reveals the sialic acid association rate constants (k on) to three influenza sites: the hemagglutinin (HA), neuraminidase (NA) active, and NA secondary binding sites. We developed a series of highly detailed (atomic-resolution) structural models of fully intact influenza viral envelopes. Brownian dynamics simulations of these systems showed how structural properties, such as stalk height and secondary-site binding, affect sialic acid k on values. Comparing the k on values of the three sialic acid binding sites across different viral strains suggests a detailed model of encounter-complex formation and indicates that the secondary NA binding site may play a compensatory role in host-cell receptor binding. Our method elucidates the competition among these sites, all present on the same virion, and provides a new technology for directly studying the functional balance between HA and NA.