Toward accurate free energy calculations in biomolecular simulation: advances in Markov model reweighting and expanded ensemble method

The rational design of stable, preorganized peptides/ligands demands precise atomistic insights into their folded and unfolded conformational ensembles, which are often challenging to obtain from simulations alone due to timescale limitations and force field inaccuracies. This dissertation advances computational tools for molecular design by integrating molecular dynamics (MD) simulations with experimental data and developing enhanced sampling methods for reliable free energy landscapes. In Chapter 2, we present the Bayesian Inference of Conformational Populations (BICePs) framework to reweight Markov state models constructed from extensive MD trajectories against nuclear magnetic resonance (NMR) measurements. Applied to ten linear and cyclic beta-hairpin peptide mimics, BICePs refines Karplus parameters for scalar couplings and reweights ensembles using NOE distances, chemical shifts, and ³JHN H^α couplings. The resulting folding landscapes accurately capture the effects of subtle chemical modifications on stability (≤2 kJ/mol changes), aligning with experimental trends and outperforming prior NAMFIS estimates, demonstrating robustness for experiment-guided simulation refinement. Chapter 3 introduces a hybrid 1/t-modified Wang-Landau (WL) algorithm designed to mitigate error saturation in expanded-ensemble methods. We test this algorithm in both a toy model of harmonic potentials and all-atom alchemical simulations to estimate the hydration free energy of paracetamol. In each case, we find that the hybrid 1/t WL algorithm reduces saturation errors by up to 30%, enabling sub-0.1 kT precision without plateaus. Systematic analysis of switching thresholds reveals optimal strategies for convergence of the method. Together, these approaches provide a unified pipeline for accurate simulation-based prediction of thermodynamic quantities, with implications for de novo design.