A natural unification of GNM and ANM and the role of inter-residue forces

The Gaussian network model (GNM) and anisotropic network model (ANM) are two elastic network models that have been widely used to study protein fluctuation dynamics. Both models have strengths and weaknesses. Attempts have been made in the past to unify the two models but they had severe limitations. This work presents a novel theoretical result that shows how GNM and ANM can be unified through taking into account the effect of inter-residue forces. The unified model, called the force spring model, or FSM, is reduced to ANM when all the inter-residue forces are set to zero. Moreover, the unification reveals the role of inter-residue forces in protein fluctuation dynamics. Specifically, the effect of inter-residue forces is closely examined by studying the changes in mean-square fluctuations when inter-residue forces are present.