Explicit-solvent molecular dynamics simulation at constant pH: Methodology and application to small amines

Abstract

A method is developed for performing classical explicit-solvent molecular dynamics ͑MD͒ simulations at constant pH, where the protonation state of each ionizable ͑titratable͒ group in a simulated compound is allowed to fluctuate in time, depending on the instantaneous system configuration and the imposed pH. In this method, each ionizable group is treated as a mixed state, i.e., the interaction-function parameters for the group are a linear combination of those of the protonated state and those of the deprotonated state. Free protons are not handled explicitly. Instead, the extent of deprotonation of each group is relaxed towards its equilibrium value by weak coupling to a ''proton bath.'' The method relies on precalibrated empirical functions, one for each type of ionizable group present in the simulated compound, which are obtained through multiple MD simulations of monofunctional model compounds. In this study, the method is described in detail and its application illustrated by a series of constant-pH MD simulations of small monofunctional amines. In particular, we investigate the influence of the relaxation time used in the weak-coupling scheme, the choice of appropriate model compounds for the calibration of the required empirical functions, and corrections for finite-size effects linked with the small size of the simulation box.

Charge-leveling and proper treatment of long-range electrostatics in all-atom molecular dynamics at constant pH

“…[1][2][3][4][5] In the continuous approach, an additional titration degree of freedom is added for every titratable site and the titration degrees of freedom are propagated alongside conformational dynamics. [6][7][8] Among these methods, the continuous pH molecular dynamics (pHMD) method 7,8 based on λ dynamics, 9 which will be referred to as CpHMD hereafter, has been successfully applied to pK a predictions 10 and pH-dependent protein folding 11 and conformational dynamics. 12,13 The first version of the CpHMD technique makes use of the generalized Born (GB) implicit-solvent model for propagating both conformational and titration coordinates and the temperature-based a) Present address: Department of Pharmaceutical Sciences, University of Maryland, Baltimore, Maryland 21201, USA.…”

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

“…The differences between the ones already presented are often seen in small technical details. For the sake of completeness, we should cite the work with coarsegrained models done by Delle Site (for peptides) (Enciso et al 2013), the Donnini's version (Donnini et al 2016) of the "λ"'s dynamics for the MARTINI force field applied to study oleic acid aggregates (Bennett et al 2013), and the initiatives with the empirical "λ" dynamics method of Börjesson & Hünenberger (for amines) (Börjesson and Hünenberger 2001;Baptista 2002), and the classical MD method coupled with quantum mechanically derived proton hopping (Q-HOP) method of Lill & Helms (applied on small molecules and protein) (Lill and Helms 2001;De Groot et al 2003;Gu et al 2007).…”

Aplicação da equação de Poisson-Boltzmann ao cálculo de propriedades dependentes do pH em proteínas

“…Os valores das energias livres padrão em fase gasosa podem ser obtidos através de métodos ab-initio 4,38 ou medidas experimentais 35 (e.g. espectroscopia de ressonância magnética ou cinética enzimática), enquanto que as energias livres de solvatação podem ser calculadas por méto-dos Monte Carlo 39,40 ou perturbação termodinâmica 56 . Contudo, a energia livre de solvatação do próton ∆G g,s (H + ) é uma quantidade difícil de ser determinada, tanto experimental quanto computacionalmente, de modo que a relação resultante da diferença entre os pK a s de dois grupos AH e BH é preferivelmente expressa como: (8) Analogamente, o pK a do grupo AH na proteína, pK a (p) , é descrito pela equação: (9) Os valores de pK a (s) são obtidos a partir de medidas experimentais para cada um dos 20 aminoácidos naturais em solução 35 .…”

“…No entanto, as conformações obtidas por Dinâmica Molecular ou Monte Carlo são, por sua vez, dependentes dos estados de protonação escolhidos para a conformação inicial do sistema. Recentemente, métodos de dinâmica molecular em pH constante foram propostos, nos quais os estados de protonação podem variar ao longo da simulação 56,57 . Estes métodos tratam o pH como um parâmetro termodinâmico, de modo similar à pressão e temperatura ("proton bath"), sem fazer uso da equação de PoissonBoltzmann e estão fora do âmbito deste artigo.…”