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Curvature Concentrations on the HIV-1 Capsid

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It is known that the retrovirus capsids possess a fullerene-like structure. These caged polyhedral arrangements are built entirely from hexagons and exactly 12 pentagons according to the Euler theorem. Viral capsids are composed of capsid proteins, which create the hexagon and pentagon shapes by groups of six (hexamer) and five (pentamer) proteins. Different distributions of these 12 pentamers result in icosahedral, tubular, or conical shaped capsids. These pentamer clusters introduce declination and hence curvature on the capsids. This paper provides explicit and quantitative characterization of curvature on virus capsids. The concept of curvature concentration is also introduced. For the HIV (5,7)-cone, it is shown that the curvature concentration at the narrow end is about at least four times higher than that at the broad end. Our modeling results about curvature concentrations on HIV-1 capsids echo the results in the literature that the pentamers are in the regions with the highest stress, although the connection between the two approaches (curvature concentration and stress) is to be explored. This also leads to a conjecture that “HIV-1 capsid narrow end may close last during maturation but open first during entry into a host cell".

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  • Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874,
  • Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874,
  • Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874,
  • Department of Biochemistry and Molecular Biology, Colorado State University, Fort Collins, CO 80523-1870,


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