Anneal-MaxCal: kinetic ensembles from a Markov model learned along a solute-tempering ladder

Abstract

A full characterisation of a molecular system requires its metastable states, their populations and their interconversion rates. Molecular Dynamics can in principle provide this characterisation but is limited by sampling and by force-field inaccuracies. Enhanced sampling addresses the first problem, but typically requires prior knowledge of reaction coordinates or metastable states and often sacrifices the kinetics, while maximum-caliber reweighting by Brotzakis, Vendruscolo and Bolhuis [Proc. Natl. Acad. Sci. U.S.A., 118(2):e2012423118, 2021] has been implemented to that matter on reweighting continuous pathways by imposing rate constants as kinetic constraints in two-state protein folding. Here, we introduce Anneal-MaxCal, which tackles both problems by imposing rate constants or time-resolved data on a Markov model learned along an annealed solute-tempering ladder spanning softer to physical interactions. MBAR assigns physical free energies to all 160 cells of a slow TICA subspace, against 79 visited at the physical coupling. The square-root approximation (SqRA), a discretised diffusion on this free-energy landscape, converts these populations into a detailed-balance rate matrix. Its prefactors, which act as a position-dependent diffusivity across each cell face, are learned from transitions at the softer couplings and extrapolated log-linearly to the physical coupling. This yields rates and a committor across the TICA space, although the physical rung contains a single barrier crossing. For alanine dipeptide, 665 ns of simulation give a relaxation time of 5430 ± 996 ps against 4413 ± 446 ps from 15.4 μs of unbiased dynamics, whereas a constant prefactor is 2.5 times too slow. Maximum caliber then minimally perturbs this prior, with the posterior populations following from a generalised Doob transform. A synthetic time-resolved density with a tenfold slower back-transition lowers ΔF from 5.191 to 2.885 kBT , raises the product-basin population from 0.0055 to 0.0529 and slows relaxation 9.47-fold, leaving the reactant basin unchanged. Forward and backward rates accelerated 3 and 20-fold raise ΔF by 1.892 kBT and shorten relaxation from 4818 to 289 ps.