Constant pH Molecular Dynamics in Explicit Solvent with λ-Dynamics

Abstract

pH is an important parameter in condensed-phase systems, because it determines the protonation state of titratable groups and thus influences the structure, dynamics, and function of molecules in solution. In most force field simulation protocols, however, the protonation state of a system (rather than its pH) is kept fixed and cannot adapt to changes of the local environment. Here, we present a method, implemented within the MD package GROMACS, for constant pH molecular dynamics simulations in explicit solvent that is based on the λ-dynamics approach. In the latter, the dynamics of the titration coordinate λ, which interpolates between the protonated and deprotonated states, is driven by generalized forces between the protonated and deprotonated states. The hydration free energy, as a function of pH, is included to facilitate constant pH simulations. The protonation states of titratable groups are allowed to change dynamically during a simulation, thus reproducing average protonation probabilities at a certain pH. The accuracy of the method is tested against titration curves of single amino acids and a dipeptide in explicit solvent.

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

“…16 Most recently, two groups have reported on the development of CpHMD techniques based solely on explicit-solvent models and testing on small model systems. 17,18 In these implementations the GB-based single-site CpHMD method 7 was extended to explicit-solvent simulations by replacing the calculation of solvation forces due to the GB model with deriving forces on real and λ particles from interactions involving explicit water molecules. A noted key ingredient is the alternative functional form (other than sin 2 θ ) for the λ variable.…”

“…The long-range electrostatics was calculated using truncation with force shift 18 or Ewald summation without accounting for the additional forces on λ particles. 17 Potential artifacts due to the fluctuation in overall net charge were also neglected.…”

Role of Deprotonation Free Energies in pKa Prediction and Molecule Ranking

“…A parabolic potential with a 3 kJ/mol energy barrier between the two limiting λ-states was used to bias the sampling toward the two end points. 1 The reference pK a for the glutamic acid dipeptide was taken to be 4.4 43 and used in eq 2. The standard error was calculated from the averages over at least four simulations, commenced from independent initial states randomly chosen at the end of the equilibration process.…”

“…This is similar to the approach of Briggs et al 13,14 and Lim et al 15 The proton-donor bond dissociation free energy is assumed to be the same in the reference compound as the protein, which obviates the need to carry out computationally expensive QM calculations. 1 The are two main categories of constant-pH simulation: the first uses the Metropolis Monte Carlo (MC) procedure to sample the protonation state of the residue, within the framework of a molecular dynamics (MD) simulation. 23,24,28,31−34 Periodically, a MC move is attempted to change the protonation state of the residue, 35 based upon the free energy change in the protein and the corresponding free energy change in the reference compound.…”

Communication: Estimating the initial biasing potential for λ-local-elevation umbrella-sampling (λ-LEUS) simulations via slow growth

“…The introduction of a coordinate transformation [12][13][14][15][16][17] λ(θ ), where θ is the actual dynamical variable, determina) Electronic mail: phil@igc.phys.chem.ethz.ch ing indirectly the value of the coupling parameter λ. This leads to the extended Hamiltonian (omitting r and p for the simplicity of the notation)…”