Constant pH Simulation with FMM Electrostatics in GROMACS. (A) Design and Applications

The structural dynamics of biological macromolecules,
such as proteins,
DNA/RNA, or complexes thereof, are strongly influenced by protonation
changes of their typically many titratable groups, which explains
their sensitivity to pH changes. Conversely, conformational and environmental
changes of the biomolecule affect the protonation state of these groups.
With few exceptions, conventional force field-based molecular dynamics
(MD) simulations neither account for these effects nor do they allow
for coupling to a pH buffer. Here, we present design decisions and
applications of a rigorous Hamiltonian interpolation λ-dynamics
constant pH method in GROMACS, which rests on GPU-accelerated Fast
Multipole Method (FMM) electrostatics. Our implementation supports
both CHARMM36m and Amber99sb*-ILDN force fields and is largely automated
to enable seamless switching from regular MD to constant pH MD, involving
minimal changes to the input files. Here, the first of two companion
papers describes the underlying constant pH protocol and sample applications
to several prototypical benchmark systems such as cardiotoxin V, lysozyme,
and staphylococcal nuclease. Enhanced convergence is achieved through
a new dynamic barrier height optimization method, and high pKa accuracy is demonstrated. We use Functional
Mode Analysis (FMA) and Mutual Information (MI) to explore the complex
intra- and intermolecular couplings between the protonation states
of titratable groups as well as those between protonation states and
conformational dynamics. We identify striking conformation-dependent
pKa variations and unexpected inter-residue
couplings. Conformation–protonation coupling is identified
as a primary cause of the slow protonation convergence notorious to
constant pH simulations involving multiple titratable groups, suggesting
enhanced sampling methods to accelerate convergence.