Geometric characterization of the HSV - 1 glycoprotein B - amyloid β interaction in Alzheimer's disease using Forman-Ricci curvature

Alzheimer's disease is characterized by the accumulation and aggregation of amyloid-{beta}(A{beta}), but the molecular mechanisms linking environmental and infectious factors to A$\beta$ conformational changes remain incompletely understood. Herpes simplex virus type 1 (HSV-1) has been proposed as a potential contributor to AD pathology, and interactions between the viral glycoprotein B (gB) and A$\beta$ may influence the conformational behaviour of the peptide. Molecular dynamics (MD) simulations provide atomic-scale information on such interactions, but conventional structural descriptors may not fully capture changes in the organization of residue interaction networks. Here, we introduce a graph-geometric framework based on Forman-Ricci curvature to characterize the evolution of residue interaction networks during MD simulations. Each simulation frame is represented as a residue interaction graph based on C--C contacts, and residue-wise curvature profiles are analysed across time. We apply the framework to A{beta}1-42 in isolation and in complex with HSV-1 gB. Conventional MD analyses indicate stable association of the simulated complex, favourable interaction energetics, and conformational changes in A{beta}, including a transition from -helical structure toward {beta}-turn-rich conformations over the simulated timescale. Forman-Ricci curvature reveals pronounced and spatially localized remodelling of the A{beta} residue interaction network in the complex, with the strongest changes concentrated in the C-terminal region. These regions also exhibit reduced temporal curvature fluctuations and progressively distinct geometric behaviour throughout the simulation. Hierarchical clustering further identifies cooperative groups of residues with coordinated curvature dynamics, including a prominent C-terminal domain. Together, these results demonstrate that Forman-Ricci curvature provides a complementary description of biomolecular dynamics by capturing changes in the geometric organization of residue interaction networks that are not directly represented by conventional structural descriptors. The framework provides a general computational approach for studying network-level structural remodelling in protein molecular dynamics and offers a quantitative perspective on the conformational consequences of HSV-1 gB--A{beta} association.