Anneal-MaxCal: kinetic ensembles from a Markov model learned along a solute-tempering ladder
- 1[1] Department of Biotechnology, Agricultural University of Athens, 75 Iera Odos Str., 11855 Athens, Greece. [2] Archimedes Unit, Athena Research Center, 15125
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 s 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 {Delta}F 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 {Delta}F by 1.892 kBT and shorten relaxation from 4818 to 289 ps.
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BibTeX
@misc{brotzakis2026annealmaxcal,
title = {{Anneal-MaxCal: kinetic ensembles from a Markov model learned along a solute-tempering ladder}},
author = {Z. F. Brotzakis and N. Rekatsinas},
howpublished = {bioRxiv},
year = {2026},
month = oct,
doi = {10.64898/2026.10.05.756723},
url = {https://www.biorxiv.org/content/10.64898/2026.10.05.756723v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Anneal-MaxCal: kinetic ensembles from a Markov model learned along a solute-tempering ladder
AU - Z. F. Brotzakis
AU - N. Rekatsinas
PY - 2026
DA - 2026/10/05
PB - bioRxiv
DO - 10.64898/2026.10.05.756723
UR - https://www.biorxiv.org/content/10.64898/2026.10.05.756723v1
AB - 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 s 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 {Delta}F 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 {Delta}F by 1.892 kBT and shorten relaxation from 4818 to 289 ps.
ER -