Constant pH Simulation with FMM Electrostatics in GROMACS. (B) GPU Accelerated Hamiltonian Interpolation
Bartosz Kohnke, Eliane Briand, Carsten Kutzner, Helmut Grubmüller
TL;DR
This article presents MAHI, a GPU-accelerated MAHI method that enables rigorous Hamiltonian Interpolation for constant-pH MD within GROMACS by leveraging Fast Multipole Method electrostatics. MAHI starts from a charge-scaled Hamiltonian and applies targeted P2P, lattice, and dipole corrections to recover HI forces, achieving near-linear scaling with the number of titratable sites and forms. Accuracy benchmarks show MAHI closely reproduces reference HI/PME results across random and biomolecular test systems, while performance evaluations reveal modest overhead (often under 10–25%) that remains nearly constant as system size grows; a hybrid PME+MAHI approach can yield further speedups. The work demonstrates practical, scalable constant-pH MD suitable for large biomolecular systems and opens avenues for exascale-ready constant-pH simulations with flexible electrostatics solvers.
Abstract
The structural dynamics of biological macromolecules, such as proteins, DNA/RNA, or their complexes, are strongly influenced by protonation changes of their typically many titratable groups, which explains their pH sensitivity. In turn, conformational and environmental changes in the biomolecule affect the protonation state of these groups. With a few exceptions, conventional force field-based molecular dynamics (MD) simulations do not account for these effects, nor do they allow for coupling to a pH buffer. The $λ$-dynamics method implements this coupling and thus allows for MD simulations at constant pH. It uses separate Hamiltonians for the protonated and deprotonated states of each titratable group, with a $λ$ variable that continuously interpolates between them. However, rigorous implementations of Hamiltonian Interpolation (HI) $λ$-dynamics are prohibitively slow when used with Particle Mesh Ewald (PME). To circumvent this problem, it has been proposed to interpolate the charges instead of the Hamiltonians (QI). Here, we propose a rigorous yet efficient Multipole-Accelerated Hamiltonian Interpolation (MAHI) method to perform $λ$-dynamics in GROMACS. Starting from a charge-scaled Hamiltonian, precomputed with the Fast Multipole Method (FMM) or with PME, the correct HI forces are calculated with negligible computational overhead. We compare HI with QI and show that HI leads to more frequent transitions between protonation states, resulting in better sampling and accuracy. Our performance benchmarks show that introducing, e.g., 512 titratable sites to a one million atom MD system increases runtime by less than 20% compared to a regular FMM-based simulation. We have integrated the scheme into our GPU-FMM code for the simulation software GROMACS, allowing an easy and effortless transition from standard force field simulations to constant pH simulations.