pK_A in proteins solving the Poisson–Boltzmann equation with finite elements

Abstract

Knowledge on pK(A) values is an eminent factor to understand the function of proteins in living systems. We present a novel approach demonstrating that the finite element (FE) method of solving the linearized Poisson-Boltzmann equation (lPBE) can successfully be used to compute pK(A) values in proteins with high accuracy as a possible replacement to finite difference (FD) method. For this purpose, we implemented the software molecular Finite Element Solver (mFES) in the framework of the Karlsberg+ program to compute pK(A) values. This work focuses on a comparison between pK(A) computations obtained with the well-established FD method and with the new developed FE method mFES, solving the lPBE using protein crystal structures without conformational changes. Accurate and coarse model systems are set up with mFES using a similar number of unknowns compared with the FD method. Our FE method delivers results for computations of pK(A) values and interaction energies of titratable groups, which are comparable in accuracy. We introduce different thermodynamic cycles to evaluate pK(A) values and we show for the FE method how different parameters influence the accuracy of computed pK(A) values.

Empirical Conversion of pKa Values between Different Solvents and Interpretation of the Parameters: Application to Water, Acetonitrile, Dimethyl Sulfoxide, and Methanol

“…This is particularly the case if the protein model is solely based on the crystal structures. Alternating the protein crystal structures by modeling , or molecular dynamics (MD) simulations helps reduce the p K a -RMSD, which for MD simulations is significantly below 1 pH unit.…”

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

“…The interplay of so many titratable sites of several ionizable objects will slow down even more the already difficult sampling. The best Krieger et al (2006), Burger andAyers (2011), andOlsson et al (2011) b See Bashford (1997), Baker et al (2001), Anandakrishnan et al (2012), Wang et al (2015), and Sakalli and Knapp (2015) c See Svensson et al (1990), Kesvatera et al (1996Kesvatera et al ( , 1999Kesvatera et al ( , 2001, Teixeira et al (2010), Carnal et al (2015), Barroso da Silva et al (2017a), and Barroso da Silva and MacKernan (2017b) d See Baptista et al (1997, Baptista and Soares (2001), Machuqueiro and Baptista (2007), and Santos et al (2015) e See Lee et al (2004), Shen (2009), Dashti et al (2012), Goh et al (2013a), Chen et al (2013Chen et al ( , 2014Chen et al ( , 2016, Chen and Roux (2015), Socher and Stich (2016), and Donnini et al (2016) f See Tummanapelli and Vasudevan (2015), Kamerlin et al (2009), andLi et al (2002) alternative in this case is the MC titration schemes, particularly the FPTS. From this mesoscopic scheme, other intermediate models can also be derived in order to improve accuracy for specific tasks at higher CPU expenses.…”

“…Different methods are available. For example, the "finite element method", (Davis and McCammon 1990;Project 1995;Harvey 1989;Orttung 1977;Terán et al 1989) the "finite difference method", (Davis and McCammon 1990;Project 1995;Harvey 1989;Warwicker and Watson 1982;Holst 1993;Davis et al 1991;Sakalli and Knapp 2015) and the "boundary element method" (Davis and McCammon 1990;Project 1995;Harvey 1989;Juffer 1993Juffer , 1998Juffer et al 1991) are applied to solve the PB equation for biomolecular systems. There are also a number of generalized program packages available to study biomolecular phenomena (Warwicker and Watson 1982;Holst 1993;Davis et al 1991;Bashford and Gerwert 1992;Honig and Nicholls 1995;Juffer 1992) and web-servers (Calixto 2010;Anandakrishnan et al 2012;Smith et al 2012;Wang et al 2016).…”