Differential geometry based solvation model II: Lagrangian formulation

摘要: Solvation is an elementary process in nature and of paramount importance to more sophisticated chemical, biological biomolecular processes. The understanding solvation essential prerequisite for the quantitative description analysis systems. This work presents a Lagrangian formulation our differential geometry based models. representation surfaces has few utilities/advantages. First, it provides basis visualization, surface electrostatic potential map visual perception biomolecules. Additionally, consistent with conventional setting implicit solvent theories thus, many existing theoretical algorithms computational software packages can be directly employed. Finally, does not need resort artificially enlarged van der Waals radii as often required by Eulerian analysis. main goal present analyze connection, similarity difference between formalisms model. Such important model extends scaled particle theory nonpolar solvent–solute interaction potential. completed Poisson–Boltzmann (PB) polar employed provide natural interfaces. optimization total free energy functional, which encompasses contributions, leads coupled driven geometric flow PB equations. Due development singularities nonsmooth manifolds representation, resulting potential-driven equation embedded into purpose computation, thanks equivalence Laplace–Beltrami operator two representations. partial equations (PDEs) are solved iterative procedure reach steady state, delivers desired interface problems interest. These quantities utilized evaluate energies protein–protein binding affinities. A number methods described interconversion representations, solution PDE system. proposed approaches have been extensively validated. We also verify that mean curvature indeed gives rise minimal molecular variational offers energy. applications considered set 17 small compounds 23 proteins. salt effect on affinity investigated protein complexes using Numerical results compared experimental measurements those obtained other literature.