Mathematical models for HIV-1 viral capsid structure and assembly
Date
2015
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Abstract
HIV-1 (human immunodeficiency virus type 1) is a retrovirus that causes the acquired immunodeficiency syndrome (AIDS). This infectious disease has high mortality rates, encouraging HIV-1 to receive extensive research interest from scientists of multiple disciplines. Group-specific antigen (Gag) polyprotein precursor is the major structural component of HIV. This protein has 4 major domains, one of which is called the capsid (CA). These proteins join together to create the peculiar structure of HIV-1 virions. It is known that retrovirus capsid arrangements represent a fullerene-like structure. These caged polyhedral arrangements are built entirely from hexamers (6 joined proteins) and exactly 12 pentamers (5 proteins) by the Euler theorem. Different distributions of these 12 pentamers result in icosahedral, tubular, or the unique HIV-1 conical shaped capsids. In order to gain insight into the distinctive structure of the HIV capsid, we develop and analyze mathematical models to help understand the underlying biological mechanisms in the formation of viral capsids. The pentamer clusters introduce declination and hence curvature on the capsids. The HIV-1 capsid structure follows a (5,7)-cone pattern, with 5 pentamers in the narrow end and 7 in the broad end. We show that the curvature concentration at the narrow end is about five times higher than that at the broad end. This leads to a conclusion that the narrow end is the weakest part on the HIV-1 capsid and a conjecture that “the narrow end closes last during maturation but opens first during entry into a host cell.” Models for icosahedral capsids are established and well-received, but models for tubular and conical capsids need further investigation. We propose new models for the tubular and conical capsid based on an extension of the Caspar-Klug quasi-equivalence theory. In particular, two and three generating vectors are used to characterize respectively the lattice structures of tubular and conical capsids. Comparison with published HIV-1 data demonstrates a good agreement of our modeling results with experimental data. It is known that there are two stages in the viral capsid assembly: nucleation (formation of a nuclei: hexamers) and elongation (building the closed shell). We develop a kinetic model for modeling HIV-1 viral capsid nucleation using a 6-species dynamical system. Numerical simulations of capsid protein (CA) multimer concentrations closely match experimental data. Sensitivity and elasticity analysis of CA multimer concentrations with respect to the association and disassociation rates further reveals the importance of CA dimers in the nucleation stage of viral capsid self-assembly.
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Subject
cone
dynamical systems
sensitivity analysis
curvature
capsid
HIV-1