The Solution And Applications Of A Dielectric Continuum Model Considering The Steric And Correlation Effects

One commonly-used mathematical model for estimating the electrostatic potential in an ionic solvent is the Poisson-Boltzmann equation(PBE),which has been widely employed in many important bioengineering applications,such as protein docking,ion channel modeling,and rational drug design.However,due to ignoring the ion size and the ion-ion correlations,the PBE model has some drawbacks.So far,the traditional PBE model has been improved in many researches,but,only the influence of ion size or ion-ion correlations has been considered,and the two factors are not taken into account comprehensively.Based on this situat.ion,how to construct a more reasonable model and solve it efficiently becomes a very important.topic.As an improvement,in this thesis,a nonlocal size-modified PB model(NSMPB)is proposed,which is a new dielectric continuum model considering the steric and correlation effects.NSMPB is turned out to be very difficult and expensive to solve due to its solution singularity caused by point charge terms and its integro-differential term.To deal with the convolution term,by using its properties,the nonlocal term is treated as an unknown function so that the NSMPB model can be equivalently reformulated into a system of coupled equations.And the three term decomposition scheme of the solution in the previous work is used to deal with the singularity caused by Dirac-delta distribution.At the same time,a new block preconditioner is constructed,and proved that the eigenvalues of its preconditioned linear system have the bound independent of mesh size.More importantly,we propose an effective algorithm for solving the NSMPB model based on finite element method.Finally,in numerical experiments,we construct a Born ball test model which has analytical solutions to validate our algorithm and program.Then,the performances of our new model and algorithm on six biomolecular systems with different net charges were compared.The solvation free energies of the six biomolecules with different ionic strengths and ionic sizes were calculated by our new model,and then compared with the results calculated by the SMPBE and NMPBE packages.