A geometric criterion links HIV-1 capsid topography to its biophysical properties and function

Mathematical models of virus capsid structure are pillars of modern virology, aiding the understanding of viral mechanisms and the design of antiviral interventions. Traditionally, the HIV-1 capsid core geometry is represented as a fullerene lattice, akin to the icosahedral models of spherical viruses in Caspar-Klug theory. However, recent studies revealed that many viral capsids deviate from such idealised lattices, with important functional implication. Here we demonstrate that this is the case also for the conical HIV-1 core geometries, in which the hexamer and pentamer boundaries form a pseudo-tiling rather than a perfectly aligned fullerene network. We introduce a triangular geometric criterion that quantifies local deviations of an HIV-1 atomic model from its idealised fullerene backbone. Using this criterion, we demonstrate that this difference in geometric organisation between idealised (fullerene) and actual (data-derived) capsid model has implications for the capsids biophysical properties. We also discuss the use of the geometric criterion as a predictive tool regarding cofactor binding, exploiting its correlation with local curvature and topography. Our results establish a quantitative framework linking capsid geometry, curvature, and biophysical function, offering new perspectives for assembly inhibitor design and lentiviral vector engineering.