Resolution of Maximum Entropy Method-Derived Posterior Conformational Ensembles of a Flexible System Probed by FRET and Molecular Dynamics Simulations

Maximum entropy methods (MEMs) determine posterior distributions by combining experimental data with prior information. MEMs are frequently used to reconstruct conformational ensembles of molecular systems for experimental information and initial molecular ensembles. We performed time-resolved Fo''rster resonance energy transfer (FRET) experiments to probe the interdye distance distributions of the lipase-specific foldase Lif in the apo state, which likely has highly flexible, disordered, and/or ordered structural elements. Distance distributions estimated from ensembles of molecular dynamics (MD) simulations serve as prior information, and FRET experiments, analyzed within a Bayesian framework to recover distance distributions, are used for optimization. We tested priors obtained by MD with different force fields (FFs) tailored to ordered (FF99SB, FF14SB, and FF19SB) and disordered proteins (IDPSFF and FF99SBdisp). We obtained five substantially different posterior ensembles. As in our FRET experiments the noise is characterized by photon counting statistics, for a validated dye model, MEM can quantify consistencies between experiment and prior or posterior ensembles. However, posterior populations of conformations are uncorrelated to structural similarities for individual structures selected from different prior ensembles. Therefore, we assessed MEM simulating varying priors in synthetic experiments with known target ensembles. We found that (i) the prior and experimental information must be carefully balanced for optimal posterior ensembles to minimize perturbations of populations by overfitting and (ii) only ensemble-integrated quantities like inter-residue distance distributions or density maps can be reliably obtained but not ensembles of atomistic structures. This is because MEM optimizes ensembles but not individual structures. This result for a highly flexible system suggests that structurally varying priors calculated from varying prior ensembles, e.g., generated with different FFs, may serve as an ad hoc estimate for MEM reconstruction robustness.