Using the Maximum Entropy Principle to Combine Simulations and Solution Experiments

Abstract

Molecular dynamics (MD) simulations allow investigating the structural dynamics of biomolecular systems with unrivaled time and space resolution. However, in order to compensate for the inaccuracies of the utilized empirical force fields, it is becoming common to integrate MD simulations with experimental data obtained from ensemble measurements. We here review the approaches that can be used to combine MD and experiment under the guidance of the maximum entropy principle. We mostly focus on methods based on Lagrangian multipliers, either implemented as reweighting of existing simulations or through an on-the-fly optimization. We discuss how errors in the experimental data can be modeled and accounted for. Finally, we use simple model systems to illustrate the typical difficulties arising when applying these methods.

Structural Interpretation of Hydrogen-Deuterium Exchange with Maximum-Entropy Simulation Reweighting

“…The HDXer method is equipped to do so, specifically through the calculation of the app required to achieve a given MSD. app , and other metrics of reweighting robustness, such as the Kish effective sample size (51,67), may be used to identify situations in which the relevant structural states are not part of the reference ensemble. For the TeaA model system, this situation can be exemplified by removing all the closed-state conformations from the reference ensemble before applying the HDXer method exactly as above, i.e., targeting a data set reflecting a 60% population of that state (Fig.…”

“…Deuteration levels measured at different timepoints could be separated into training and validation sets, and inconsistencies in the resultant reweighted ensembles may reveal sources of experimental error. However, as has been extensively discussed for other ensemble refinement methods (50,51,57,58,67), disentangling the exact sources of error in a given set of reweighting results is a challenging proposition and likely to require comparison and cross-validation with multiple reference ensembles and experimental datasets.…”

“…Here, we develop and test a simulation methodology to construct conformational ensembles that faithfully reflect a given set of target HDX-MS data, for a given empirical model of " . This approach, which we refer to as HDX ensemble reweighting (HDXer), is based on concepts outlined in previous studies and applied to other types of biophysical data (44)(45)(46)(47)(48)(49)(50)(51)(52)(53)(54), but not yet to HDX-MS. In brief, our approach uses a maximum-entropy criterion to reweight the configurations obtained computationally post-hoc, so that calculated ensemble-averaged peptide deuterated fractions reproduce measured values, within a given level of uncertainty.…”

Tandem CTCF sites function as insulators to balance spatial chromatin contacts and topological enhancer-promoter selection

“…On the contrary, the model-based simulation includes known mechanisms to set up the model but predicts the macroscopic variables usually deviating from the observations. We use the relative maximum entropy approach [83] that combines the advantages of both the maximum entropy approach and the model-based simulations. The basic idea is quite similar to the maximum entropy approach.…”

“…The relative maximum entropy approach actually selects a distribution closest to the least informative one among those satisfying the experimental observations. We apply the relative maximum entropy approach [83] to correct polymer simulations by the rescaled QHR-4C data. Pairs with 0 contact frequencies in both replicates are excluded.…”