Improving efficiency of large time-scale molecular dynamics simulations of hydrogen-rich systems

Abstract

A systematic analysis is performed on the effectiveness of removing degrees of freedom from hydrogen atoms and/or increasing hydrogen masses to increase the efficiency of molecular dynamics simulations of hydrogen‐rich systems such as proteins in water. In proteins, high‐frequency bond‐angle vibrations involving hydrogen atoms limit the time step to 3 fs, which is already a factor of 1.5 beyond the commonly used time step of 2 fs. Removing these degrees of freedom from the system by constructing hydrogen atoms as dummy atoms, allows the time step to be increased to 7 fs, a factor of 3.5 compared with 2 fs. Additionally, a gain in simulation stability can be achieved by increasing the masses of hydrogen atoms with remaining degrees of freedom from 1 to 4 u. Increasing hydrogen mass without removing the high‐frequency degrees of freedom allows the time step to be increased only to 4 fs, a factor of two, compared with 2 fs. The net gain in efficiency of sampling configurational space may be up to 15% lower than expected from the increase in time step due to the increase in viscosity and decrease in diffusion constant. In principle, introducing dummy atoms and increasing hydrogen mass do not influence thermodynamical properties of the system and dynamical properties are shown to be influenced only to a moderate degree. Comparing the maximum time step attainable with these methods (7 fs) to the time step of 2 fs that is routinely used in simulation, and taking into account the increase in viscosity and decrease in diffusion constant, we can say that a net gain in simulation efficiency of a factor of 3 to 3.5 can be achieved. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 786–798, 1999

A Quantitative Coarse-Grain Model for Lipid Bilayers

“…The mass and principal moments of inertia of water sites are increased to optimize the stability of molecular dynamics integration. 81 In particular, the water mass is set to 50 amu (the real value being 18 amu). The chosen principal moments of inertia correspond to a redistribution of water masses as follows: 15 amu for each hydrogen and 20 amu for the oxygen.…”

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

“…An unwanted side-effect of the increase in total mass, however, was the scale down of the whole motion of the system (not only the fast, but also the meaningful dynamics). Subsequent studies led to the exploration of the repartitioning of masses (Feenstra et al 1999), such that a heavier mass was assigned to hydrogen atoms and smaller masses were assigned to heavy atoms, with the result being that the total mass was kept constant. The long-time MD simulation with the hydrogen-mass repartitioning (HMR) method (Hopkins et al 2015) reported that a 4-fs time-step provided a numerically safe result and did not influence thermodynamic properties.…”

Exact and efficient calculation of lagrange multipliers in biological polymers with constrained bond lengths and bond angles: Proteins and nucleic acids as example cases

“…Therefore, much related to eq. (2.8), we can compute the first derivative of σ I(α,β) : 11) and also the second derivative:…”

“…For a Verlet-like integrator [9,10], stability requires the time step to be at least about five times smaller than the period of the fastest vibration in the studied system [11]. Here is where constraints come into play.…”

“…If constraints are imposed on bond lengths involving hydrogens, the time step can typically be increased by a factor of 2 to 3 (from 1 fs to 2 or 3 fs) [12]. Constraining additional internal degrees of freedom, such as heavy atoms bond lengths and bond angles, allows even larger timesteps [11,13], but one has to be careful, since, as more and softer degrees of freedom are constrained, the more likely it is that the physical properties of the simulated system could be severely distorted [14][15][16].…”