Multidimensional Scaling of the Molecular Structures

AbstractThis paper introduces a discrete, multidimensional geometric scaling model that correlates the molecular mass (expressed in Daltons, Da) of biological entities with their linear physical dimensions (expressed in nanometers, nm). By establishing a primary structural quantum step derived from fundamental physical constants (the mass of one Dalton, electron rest mass, and the classical electron radius), we demonstrate that macrostructures undergo proportional dimensional compression. We define a 6-tier dimensional framework (6 Floors) based on scaling reductions governed by powers of five, providing direct validation against experimental data ranging from simple molecules (H2O) to complex macromolecular machinery and whole virions (HIV-1).