Sampling Assessment for Molecular Simulations Using Conformational Entropy Calculations

Emerging Conformational-Analysis Protocols from the RTCONF55-16K Reaction Thermochemistry Conformational Benchmark Set

RTCONF55-16K is a new, reactive conformational data set based on cost-efficient methods to assess different conformational analysis protocols. Our reference calculations underpinned the accuracy of the CENSO (Grimme et al. J. Phys. Chem. A, 2021, 125, 4039) procedure and resulted in alternative recipes with different cost-accuracy compromises. Our general-purpose and economical protocols (CENSO-light and zero, respectively) were found to be 10-30 times faster than the original algorithm, adding only 0.4-0.7 kcal/mol absolute error to the relative free energy estimates.

Addressing Challenges of Macrocyclic Conformational Sampling in Polar and Apolar Solvents: Lessons for Chameleonicity

We evaluated a workflow to reliably sample the conformational space of a set of 47 peptidic macrocycles. Starting from SMILES strings, we use accelerated molecular dynamics simulations to overcome high energy barriers, in particular, the cis-trans isomerization of peptide bonds. We find that our approach performs very well in polar solvents like water and dimethyl sulfoxide. Interestingly, the protonation state of a secondary amine in the ring only slightly influences the conformational ensembles of our test systems. For several of the macrocycles, determining the conformational distribution in chloroform turns out to be considerably more challenging. Especially, the choice of partial charges crucially influences the ensembles in chloroform. We address these challenges by modifying initial structures and the choice of partial charges. Our results suggest that special care has to be taken to understand the configurational distribution in apolar solvents, which is a key step toward a reliable prediction of membrane permeation of macrocycles and their chameleonic properties.

Toward Reliable and Insightful Entropy Calculations on Flexible Molecules

The absolute entropy of a flexible molecule can be approximated by the sum of a rigid-rotor-harmonic-oscillator (RRHO) entropy and a Gibbs-Shannon entropy associated to the Boltzmann distribution for the occupation of the conformational energy levels. Herein, we show that such partitioning, which has received renewed interest, leads to accurate entropies of single molecules of increasing size provided that the conformational part is estimated by means of a set of discretization and expansion techniques that are able to capture the significant correlation effects among the torsional motions. To ensure a reliable entropy estimation, we rely on extensive sampling as that produced by classical molecular dynamics simulations on the microsecond time scale, which is currently affordable for small- and medium-sized molecules. According to test calculations, the gas-phase entropy of simple organic molecules is predicted with a mean unsigned error of 0.9 cal/(mol K) when the RRHO entropies are computed at the B3LYP-D3/cc-pVTZ level. Remarkably, the same protocol gives small errors [<1 cal/(mol K)] for the extremely flexible linear alkane molecules (C_nH_2n+2, n = 14, 16, and 18). Similarly, we obtain well-converged entropies for a more challenging test of drug molecules, which exhibit more pronounced correlation effects. We also perform equivalent entropy calculations on a 76 amino acid protein, ubiquitin, by taking advantage of the cutoff-dependent formulation of an expansion technique (correlation-consistent multibody local approximation, CC-MLA), which incorporates genuine correlation effects among the neighboring dihedral angles. Moreover, we show that insightful descriptors of the coupled torsional motions can be obtained with the CC-MLA approach.

Calculation of absolute molecular entropies and heat capacities made simple

We propose a fully-automated composite scheme for the accurate and numerically stable calculation of molecular entropies by efficiently combining density-functional theory (DFT), semi-empirical methods (SQM), and force-field (FF) approximations. The scheme is systematically expandable and can be integrated seamlessly with continuum-solvation models. Anharmonic effects are included through the modified rigid-rotor-harmonic-oscillator (msRRHO) approximation and the Gibbs-Shannon formula for extensive conformer ensembles (CEs), which are generated by a metadynamics search algorithm and are extrapolated to completeness. For the first time, variations of the ro-vibrational entropy over the CE are consistently accounted-for through a Boltzmann-population average. Extensive tests of the protocol with the two standard DFT approaches B97-3c and B3LYP-D3 reveal an unprecedented accuracy with mean deviations <1 cal mol-1 K-1 (about <1-2%) for the total gas phase molecular entropy of medium-sized molecules. Even for the hardship case of extremely flexible linear alkanes (C14H30-C16H34), errors are only about 3 cal mol-1 K-1. Comprehensive tests indicate a relatively strong variation of the conformational entropy on the underlying level of theory for typical drug molecules, inferring the complex potential energy surfaces as the main source of error. Furthermore, we show some application examples for the calculation of free energy differences in typical chemical reactions.

SARS-CoV-2 Main Protease: A Molecular Dynamics Study

Herein, we investigate the structure and flexibility of the hydrated SARS-CoV-2 main protease by means of 2.0 μs molecular dynamics (MD) simulations in explicit solvent. After having performed electrostatic pKa calculations on several X-ray structures, we consider both the native (unbound) configuration of the enzyme and its noncovalent complex with a model peptide, Ace-Ala-Val-Leu-Gln∼Ser-Nme, which mimics the polyprotein sequence recognized at the active site. For each configuration, we also study their monomeric and homodimeric forms. The simulations of the unbound systems show that the relative orientation of domain III is not stable in the monomeric form and provide further details about interdomain motions, protomer-protomer interactions, inter-residue contacts, accessibility at the catalytic site, etc. In the presence of the peptide substrate, the monomeric protease exhibits a stable interdomain arrangement, but the relative orientation between the scissile peptide bond and the catalytic dyad is not favorable for catalysis. By means of comparative analysis, we further assess the catalytic impact of the enzyme dimerization, the actual flexibility of the active site region, and other structural effects induced by substrate binding. Overall, our computational results complement previous crystallographic studies on the SARS-CoV-2 enzyme and, together with other simulation studies, should contribute to outline useful structure-activity relationships.

Protonation state effects of estrogen receptor α on the recognition mechanisms by perfluorooctanoic acid and perfluorooctane sulfonate: A computational study

Perfluorooctanoic acid (PFOA) and perfluorooctane sulfonate (PFOS) have been reported to cause adverse health effects on wildlife as well as humans. Numerous studies demonstrated that PFOA and PFOS could interfere with the transcriptional activation of estrogen receptor α (ERα) by mimicking the function of endogenous ligand, whereas some reports suggested that the two compounds present non-estrogenic activities. These conflicting results bring a confusion to understand their molecular mechanism on the ERα-mediated signaling pathway. To address this issue, we performed the molecular docking and molecular dynamics simulations to elaborate the structural characteristics for the binding of PFOA and PFOS to ERα. Our results indicated that the two opposite binding orientations were modulated by the protonation states of key residue His524. In sub-acidic condition, PFOA and PFOS prefer to form the H-bonding interactions with the protonated His524, whereas Arg394 provided the H-bonding interactions for stable binding in sub-alkaline condition. Conformational analyses implied that the diverse binding modes were closely related to the conformational propensity of ERα for subsequent coactivator recruitment and transcription activation. Generally, our findings provide a flexible strategy to assess the pH impacts of microenvironment on the toxicities of perfluoroalkyl acids by their interactions with proteins.

Affinity Calculations of Cyclodextrin Host-Guest Complexes: Assessment of Strengths and Weaknesses of End-Point Free Energy Methods

The end-point methods like MM/PBSA or MM/GBSA estimate the free energy of a biomolecule by combining its molecular mechanics energy with solvation free energy and entropy terms. On the one hand, their performance largely depends on the particular system of interest, and despite numerous attempts to improve their reliability that have resulted in many variants, there is still no clear alternative to improve their accuracy. On the other hand, the relatively small cyclodextrin host-guest complexes, for which high-quality binding calorimetric data are usually available, are becoming reference models for testing the accuracy of free energy methods. In this work, we further assess the performance of various MM/PBSA-like approaches as applied to cyclodextrin complexes. To this end, we select a set of complexes between β-cyclodextrin and 57 small organic molecules that has been previously studied with the binding energy distribution analysis method in combination with an implicit solvent model ( Wickstrom, L.; He, P.; Gallicchio, E.; Levy, R. M. J. Chem. Theory Comput. 2013 , 9 , 3136 - 3150 ). For each complex, a conventional 1.0 μs molecular dynamics simulation in explicit solvent is performed. Then we employ semiempirical quantum chemical calculations, several variants of the MM-PB(GB)SA methods, entropy estimations, etc., to assess the reliability of the end-point affinity calculations. The best end-point protocol in this study, which combines DFTB3 energies with entropy corrections, yields estimations of the binding free energies that still have substantial errors (RMSE = 2.2 kcal/mol), but it exhibits a good prediction capacity in terms of ligand ranking ( R² = 0.66) that is close to or even better than that of rigorous free energy methodologies. Our results can be helpful to discriminate between the intrinsic limitations of the end-point methods and other sources of error, such as the underlying energy and continuum solvation methods.

Ligand Strain and Entropic Effects on the Binding of Macrocyclic and Linear Inhibitors: Molecular Modeling of Penicillopepsin Complexes

Using extensive molecular dynamics simulations, we investigate the structure and dynamics of the complexes formed between penicillopepsin and two peptidomimetic inhibitors: a linear compound, isovaleryl(P₄)-valine(P₃)-asparagine(P₂)-leucine(P₁)-phosphonate-phenylalanine(P₁'), and its macrocylic analog that includes a methylene bridge between the Asn(P₂) and Phe(P₁') side chains. The macrocyclic inhibitor, which has a 420-fold stronger affinity than that of the acyclic one, has been considered to lower the entropic penalty for binding. To better understand this binding preference, the solution structure of the inhibitors is studied by molecular dynamics simulations. Subsequently, we assess the influence of the enzyme/inhibitor contacts, the enzyme-induced inhibitor strain, the variation of the ligand configurational entropy and the enzyme reorganization by combining molecular-mechanics Poisson-Boltzmann surface area and normal mode calculations with conformational entropy calculations. We find that there is no relevant entropic stabilization on the binding of the cyclic inhibitor with respect to the acyclic analog because the methylene bridge does not reduce appreciably the conformational flexibility of the free inhibitor. The most important factors explaining the stronger affinity of the macrocyclic inhibitor are the conformational filtering and the lower ligand strain induced by the methylene bridge.

Computer Simulations of Intrinsically Disordered Proteins

The investigation of intrinsically disordered proteins (IDPs) is a new frontier in structural and molecular biology that requires a new paradigm to connect structural disorder to function. Molecular dynamics simulations and statistical thermodynamics potentially offer ideal tools for atomic-level characterizations and thermodynamic descriptions of this fascinating class of proteins that will complement experimental studies. However, IDPs display sensitivity to inaccuracies in the underlying molecular mechanics force fields. Thus, achieving an accurate structural characterization of IDPs via simulations is a challenge. It is also daunting to perform a configuration-space integration over heterogeneous structural ensembles sampled by IDPs to extract, in particular, protein configurational entropy. In this review, we summarize recent efforts devoted to the development of force fields and the critical evaluations of their performance when applied to IDPs. We also survey recent advances in computational methods for protein configurational entropy that aim to provide a thermodynamic link between structural disorder and protein activity.

Conformational and entropy analyses of extended molecular dynamics simulations of α-, β- and γ-cyclodextrins and of the β-cyclodextrin/nabumetone complex

The conformational entropies of cyclodextrins and of the β-CD/nabumetone complex are assessed by means of extensive MD simulations.

Dihedral angle entropy measures for intrinsically disordered proteins

Protein stability is based on a delicate balance between energetic and entropic factors. Intrinsically disordered proteins (IDPs) interacting with a folded partner protein in the act of binding can order the IDP to form the correct functional interface by decrease in the overall free energy. In this work, we evaluate the part of the entropic cost of ordering an IDP arising from their dihedral states. The IDP studied is a leucine zipper dimer that we simulate with molecular dynamics and find that it does show disorder in six phi and psi dihedral angles of the N terminal sequence of one monomer. Essential to ascertain is the degree of disorder in the IDP, and we do so by considering the entire, discretized probability distribution function of N dihedrals with M conformers per dihedral. A compositional clustering method is introduced, whereby the NS = N(M) states are formed from the Cartesian product of each dihedral's conformational space. Clustering is carried out with a version of a k-means algorithm that accounts for the circular nature of dihedral angles. For the 12 dihedrals each found to have three conformers, among the resulting 531441 states, their populations show that the first 100 (500) most populated states account for ∼65% (∼90%) of the entire population, indicating that there are strong dependencies among the dihedrals' conformations. These state populations are used to evaluate a Kullback-Leibler divergence entropy measure and obtain the dihedral configurational entropy S. At 300 K, TS ∼ 3 kcal/mol, showing that IDP entropy, while roughly half that would be expected from independently distributed dihedrals, can be a decisive contributor to the free energy of this IDP binding and ordering.