The roto-conformational diffusion tensor as a tool to interpret molecular flexibility

Stochastic modeling approaches can be used to rationalize complex molecular dynamical behaviours in solution, helping to interpret the coupling mechanisms among internal and external degrees of freedom, providing insight into reaction mechanisms and extracting structural and dynamical data from spectroscopic observables. However, the definition of comprehensive models is usually limited by (i) the difficulty in defining - without resorting to phenomenological assumptions - a representative reduced ensemble of molecular coordinates able to capture essential dynamical properties and (ii) the complexity of numerical or approximate treatments of the resulting equations. In this paper, we address the first of these two issues. Building on a previously defined systematic approach to construct rigorous stochastic models of flexible molecules in solutions from basic principles, we define a manageable diffusive framework leading to a Smoluchowski equation determined by one main tensorial parameter, namely the scaled roto-conformational diffusion tensor, which accounts for the influence of both conservative and dissipative forces and describes the molecular mobility via a precise definition of internal-external and internal-internal couplings. We then show the usefulness of the roto-conformational scaled diffusion tensor as an efficient gauge of molecular flexibility through the analysis of a set of molecular systems of increasing complexity ranging from dimethylformamide to a protein domain.