Accurate p$K_a$ Computation Using Matched Interface and Boundary (MIB) Method Based Poisson-Boltzmann Solver

Abstract

The pK a values are important quantities characterizing the ability of protein active sites to give up protons. pK a can be measured using NMR by tracing chemicalshifts of some special atoms, which is however expensive and time-consuming. Alternatively, pK a can be calculated numerically by electrostatic free energy changes subject to the protonation and deprotonation of titration sites. To this end, the Poisson-Boltzmann (PB) model is an effective approach for the electrostatics. However, numerically solving PB equation is challenging due to the jump conditions across the dielectric interfaces, irregular geometry of the molecular surface, and charge singularities. Our recently developed matched interface and boundary (MIB) method treats these challenges rigorously, resulting in a solid second order MIBPB solver. Since the MIBPB solver uses Green's function based regularization of charge singularities by decomposing the solution into a singular component and a regularized component, it is particularly efficient in treating the accuracy-sensitive, numerous, and complicated charge distributions from the pK a calculation. Our numerical results demonstrate that accurate free energies and pK a values are achieved at coarse grid rapidly. In addition, the resulting software, which pipelines the entire pK a calculation procedure, is available to all potential users from the greater bioscience community.

Milk Protein Analysis: an Overview of the Methods - Development and Application

“…In principle, free amino acids and protein-bound amino acids and peptides react with formaldehyde, producing methylene amino acid derivatives and changing the pK a of these amino groups (Moore et al, 2010). The value pK a = -log 10 K a is the co-logarithm of acid dissociation constant (acid dissociation constant K a is a quantitative measure of the strength of an acid in solution), which measures the tendency for a group to give up a proton (Hu et al, 2018). The method can be applied to raw milk, drinking milk (whole, semi-skimmed and skimmed milk), milk powder or ice cream.…”

Bridging Eulerian and Lagrangian Poisson–Boltzmann solvers by ESES

“…This application is inspired by work from Juffer et al 62 and has potential application in computing protein pKa. 5,62,63 Consider the discretized forms of Equations ( 20a) and (20b) for governing potential and its normal derivatives as…”

“…With the trending of the studies and findings in biology and health care at the molecular levels, the PB model has shown its broad applications in biomolecular simulations such as protein structure, 2 chromatin packing, 3 pKa, [4][5][6] membrane, 7 binding energy, 8 solvation free energy, 9 ion channel profiling, 10 etc.…”

A Cartesian FMM-accelerated Galerkin boundary integral Poisson-Boltzmann solver

“…In this model, the explicit water molecules are treated as continuum and the dissolved electrolytes are approximated using the statistical Boltzmann distribution. The PB model has broad applications in biomolecular simulations such as protein structure [2], protein-protein interaction [3], chromatin packing [4], pKa [5][6][7], membrane [8], binding energy [9], solvation free energy [10], ion channel profiling [11], etc.…”