Best Practices in Constant pH MD Simulations: Accuracy and Sampling

Various approaches
have been proposed to include the
effect of
pH in molecular dynamics (MD) simulations. Among these, the λ-dynamics approach proposed
by Brooks and
co-workers [Kong, X.; Brooks III, C. L. J. Chem. Phys. 1996, 105, 2414−2423] can be performed
with little computational overhead and hfor each typeence be used
to routinely perform MD simulations at microsecond time scales, as
shown in the accompanying paper [Aho, N. et al. J. Chem. Theory
Comput. 2022, DOI: 10.1021/acs.jctc.2c00516]. At
such time scales, however, the accuracy of the molecular mechanics
force field and the parametrization becomes critical. Here, we address
these issues and provide the community with guidelines on how to set
up and perform long time scale constant pH MD simulations. We found
that barriers associated with the torsions of side chains in the CHARMM36m
force field are too high for reaching convergence in constant pH MD
simulations on microsecond time scales. To avoid the high computational
cost of extending the sampling, we propose small modifications to
the force field to selectively reduce the torsional barriers. We demonstrate
that with such modifications we obtain converged distributions of
both protonation and torsional degrees of freedom and hence consistent
pKa estimates, while the sampling of the
overall configurational space accessible to proteins is unaffected
as compared to normal MD simulations. We also show that the results
of constant pH MD depend on the accuracy of the correction potentials.
While these potentials are typically obtained by fitting a low-order
polynomial to calculated free energy profiles, we find that higher
order fits are essential to provide accurate and consistent results.
By resolving problems in accuracy and sampling, the work described
in this and the accompanying paper paves the way to the widespread
application of constant pH MD beyond pKa prediction.