Balancing Accuracy and Cost of Confinement Simulations by Interpolation and Extrapolation of Confinement Energies

Improvements to the confinement method for the calculation of
conformational free energy differences are presented. By taking
advantage of phase space overlap between simulations at different
frequencies, significant gains in accuracy and speed are reached. The
optimal frequency spacing for the simulations is obtained from
extrapolations of the confinement energy, and relaxation time analysis
is used to determine time steps, simulation lengths, and friction
coefficients. At postprocessing, interpolation of confinement energies
is used to significantly reduce discretization errors in the calculation
of conformational free energies. The efficiency of this protocol is
illustrated by applications to alanine n-peptides and lactoferricin. For
the alanine-n-peptide, errors were reduced between 2- and 10-fold and
sampling times between 8- and 67-fold, while for lactoferricin the long
sampling times at low frequencies were reduced 10100-fold.