Mathematical determination of the HIV-1 matrix shell structure and its impact on the biology of HIV-1

Abstract

Since its discovery in the early 1980s, there has been significant progress in understanding the biology of type 1 human immunodeficiency virus (HIV-1). Structural biologists have made tremendous contributions to this challenge, guiding the development of current therapeutic strategies. Despite our efforts, there are unresolved structural features of the virus and consequently, significant knowledge gaps in our understanding. The superstructure of the HIV-1 matrix (MA) shell has not been elucidated. Evidence by various high-resolution microscopy techniques support a model composed of MA trimers arranged in a hexameric configuration consisting of 6 MA trimers forming a hexagon. In this manuscript we review the mathematical limitations of this model and propose a new model consisting of a 6-lune hosohedra structure, which aligns with available structural evidence. We used geometric and rotational matrix computation methods to construct our model and predict a new mechanism for viral entry that explains the increase in particle size observed during CD4 receptor engagement and the most common HIV-1 ellipsoidal shapes observed in cryo-EM tomograms. A better understanding of the HIV-1 MA shell structure is a key step towards better models for viral assembly, maturation and entry. Our new model will facilitate efforts to improve understanding of the biology of HIV-1.

Challenging the Existing Model of the Hexameric HIV-1 Gag Lattice and MA Shell Superstructure: Implications for Viral Entry

“…Ellipsoidal shapes were more affected than spherical shapes because of the more drastic change in angles starting from the initial tile ( Figure 1 B,C, yellow tile). In a previously published Supplemental Figure S2 [ 14 ], we showed that regular hexagons could not be used to build the HIV model unless one of the hexagon sides had a shorter side length.…”

“…Scripts and calculations: All scripts and calculations were developed in the python language as previously described [ 14 ]. Coordinates were exported to PyMol for the construction of structures.…”

“…Mathematical algorithm used to generate coordinates for vectors to assemble the HIV-1 MA shell: We followed similar algorithms as previously described [ 14 ], with some modifications. To achieve the incorporation of Env glycoproteins in the structure in random locations, MA trimer incorporations were terminated with a probability of 1.36% (14 stops out of 1028 possible locations).…”

“…Presently, the precise arrangement of the HIV-1 MA shell remains unknown. In a recent publication [ 14 ], we examined the geometrical restrictions presented by Gag and MA trimers in the existing model for the superstructure of the shell, which involves hexagonally arranged trimers. The hexagonal arrangement, first observed by Alfadhli et al [ 4 ], presented compelling electron microscopy images of myristoylated-MA or Gag trimers assembled into a flat two-dimensional arrangement.…”

“…The HIV-1 MA shell is thought to emerge from an initial superstructure of hexameric Gag trimers, a model that warrants a careful re-examination. Previously, we analyzed the geometrical limitations of the hexameric Gag lattice and demonstrated that this arrangement is not mathematically feasible [ 14 ]. We proposed a new MA shell model consisting of a six-lune MA hosohedron that explained a number of microscopy observations, including HIV-1 viral expansion during entry [ 15 ], rearrangement of Env glycoproteins to form clusters during maturation [ 16 , 17 , 18 ], the pleomorphic nature of viral structures including spherical and ellipsoidal shapes [ 19 ], and the correct number of MA trimers per viral particle [ 20 ].…”