A review of geometric, topological and graph theory apparatuses for the modeling and analysis of biomolecular data

摘要: Geometric, topological and graph theory modeling analysis of biomolecules are essential importance in the conceptualization molecular structure, function, dynamics, transport. On one hand, geometric provides surface structural representation, offers basis for visualization, which is crucial understanding structure interactions. other it bridges gap between data theoretical/mathematical models. Topological give rise to atomic critical points connectivity, shed light on intrinsic invariants such as independent components (atoms), rings (pockets) cavities. Graph analyzes biomolecular interactions reveals structure-function relationship. In this paper, we review certain geometric, apparatuses analysis. These categorized into discrete continuous ones. For approaches, theory, Gaussian network model, anisotropic normal mode analysis, quasi-harmonic flexibility rigidity index, nonlinear spectral persistent homology discussed. mathematical tools, present continuum mapping, high dimensional homology, modeling, differential geometry surfaces, curvature evaluation, variational derivation minimal atoms molecule quantum chemical topology. Four new including analytical surface, Hessian matrix eigenvalue map, map virtual particle introduced first time bridge gaps