Pseudo-time-coupled nonlinear models for biomolecular surface representation and solvation analysis. (English) Zbl 1241.92007
Summary: This paper presents an improved mathematical model for biomolecular surface representation and solvation analysis. Based on the Eulerian formulation, the polar and nonpolar contributions to the solvation process can be equally accounted for via a unified free energy functional. Using variational analysis, two nonlinear partial differential equations, that is, a Poisson-Boltzmann (PB) type equation for the electrostatic potential and a geometric flow type equation defining the solute-solvent interface, can be derived. To achieve a more efficient and stable coupling, we propose a time-dependent PB equation by introducing a pseudo-time. The system of nonlinear partial differential equations can then be coupled via the standard time integration. Furthermore, the numerical treatment of nonlinear terms becomes easier in the present model. Based on a hypersurface function, the biomolecular surface is represented as a smooth interface. However, for the nonlinear PB equation, such a smooth interface may cause unphysical blowup because of the existence of nonvanishing values within the solute domain. A filtering process is proposed to circumvent this problem. An example solvation analysis of various compounds and proteins was carried out to validate the proposed model. The contributions of electrostatic interactions to the protein-protein binding affinity are studied for selected protein complexes.
MSC:
| 92C05 | Biophysics |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35A15 | Variational methods applied to PDEs |
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
Keywords:
biological surface formation and evolution; potential driving geometric flows; generalized nonlinear Poisson; Boltzmann equation; multiscale models; solvation free energyReferences:
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