Natalia Díaz

Molecular dynamics simulations of the dinuclear zinc-β-lactamase from Bacteroides fragilis complexed with imipenem

Herein, we present results from MD simulations of the Michaelis complex formed between the dizinc β‐lactamase from B. fragilis and imipenem. We considered two catalytically important configurations, which differ in the presence or absence of a hydroxide bridge connecting the two zinc ions in the active site. The structural and dynamical effects induced by substrate binding, the specific roles of the conserved residues and the zinc‐bound water molecules, the near attack conformers of the Michaelis complex, and so forth, are discussed in detail. The relative stability of the two configurations was estimated from QM linear scaling calculations on the enzyme‐substrate complex combined with Poisson‐Boltzmann electrostatic calculations and normal mode calculations. Importantly, we find that the two configurations have similar energies, indicating that these two structures could readily be interchanged, thereby facilitating catalysis. The configuration with the hydroxide bound to the two zinc ions is predicted to be the resting form of the enzyme, while the configuration without the bridge is the reactive form that was found to place the hydroxide in position to attack the carbonyl of the β‐lactam ring. Thus, we propose that the enzyme initiates catalysis by converting from the hydroxide bridge form into the configuration that lacks the hydroxide bridge. This interconversion increases the nucleophilicity of the hydroxide ion and exposes it to the β‐lactam carbonyl, which ultimately facilitates nucleophilic attack. The implications of the observed modes of binding, the possible influence of mutating the Lys184 and Asn193 residues on substrate binding, and the reaction mechanism are also discussed in detail.

Entropy Calculations of Single Molecules by Combining the Rigid-Rotor and Harmonic-Oscillator Approximations with Conformational Entropy Estimations from Molecular Dynamics Simulations.

As shown by previous theoretical and computational work, absolute entropies of small molecules that populate different conformers can be predicted accurately on the basis of the partitioning of the intramolecular entropy into vibrational and conformational contributions. Herein, we further elaborate on this idea and propose a protocol for entropy calculations of single molecules that combines the rigid rotor harmonic oscillator (RRHO) entropies with the direct sampling of the molecular conformational space by means of classical molecular dynamics simulations. In this approach, the conformational states are characterized by discretizing the time evolution of internal rotations about single bonds, and subsequently, the mutual information expansion (MIE) is used to approach the full conformational entropy from the converged probability density functions of the individual torsion angles, pairs of torsions, triads, and so on. This RRHO&MIE protocol could have broad applicability, as suggested by our test calculations on systems ranging from hydrocarbon molecules in the gas phase to a polypeptide molecule in aqueous solution. For the hydrocarbon molecules, the ability of the RRHO&MIE protocol to predict absolute entropies is assessed by carefully comparing theoretical and experimental values in the gas phase. For the rest of the test systems, we analyze the advantages and limitations of the RRHO&MIE approach in order to capture high order correlation effects and yield converged conformational entropies within a reasonable simulation time. Altogether, our results suggest that the RRHO&MIE strategy could be useful for estimating absolute and/or relative entropies of single molecules either in the gas phase or in solution.

Hydration of zinc ions: theoretical study of [Zn(H2O)4](H2O)82+ and [Zn(H2O)6](H2O)62+

Abstract Herein, a quantum-mechanical (QM) investigation of the title complexes is reported. Several different levels of QM theory (HF/6-31G ∗ , B3LYP/6-31G ∗ , MP2/6-31G ∗ , etc.) were employed in order to gain insights into the origin of the preference for six-coordination of hydrated Zn2+ ions which has been observed experimentally. B3LYP/6-311+G(2d,2p)//B3LYP/6-31G ∗ calculations predict that the four coordinated structure [Zn(H2O)4](H2O)82+ is the most favorable one by 8 kJ/mol. At MP2/6-311+G(2d,2p)//MP2/6-31G ∗ , the [Zn(H2O)6](H2O)62+ complex is 28 kJ/mol more stable than the four-coordinated configuration [Zn(H2O)4](H2O)82+, thereby, satisfactorily reproducing the experimental observed preference for six-coordination. According to our analyses, the HF and B3LYP methods overestimate the contribution of hard and soft interactions to the Zn–water interactions, respectively, whereas the MP2 method gives a more balanced description.

Thermochemical Fragment Energy Method for Biomolecules: Application to a Collagen Model Peptide.

Herein, we first review different methodologies that have been proposed for computing the quantum mechanical (QM) energy and other molecular properties of large systems through a linear combination of subsystem (fragment) energies, which can be computed using conventional QM packages. Particularly, we emphasize the similarities among the different methods that can be considered as variants of the multibody expansion technique. Nevertheless, on the basis of thermochemical arguments, we propose yet another variant of the fragment energy methods, which could be useful for, and readily applicable to, biomolecules using either QM or hybrid quantum mechanical/molecular mechanics methods. The proposed computational scheme is applied to investigate the stability of a triple-helical collagen model peptide. To better address the actual applicability of the fragment QM method and to properly compare with experimental data, we compute average energies by carrying out single-point fragment QM calculations on structures generated by a classical molecular dynamics simulation. The QM calculations are done using a density functional level of theory combined with an implicit solvent model. Other free-energy terms such as attractive dispersion interactions or thermal contributions are included using molecular mechanics. The importance of correcting both the intermolecular and intramolecular basis set superposition error (BSSE) in the QM calculations is also discussed in detail. On the basis of the favorable comparison of our fragment-based energies with experimental data and former theoretical results, we conclude that the fragment QM energy strategy could be an interesting addition to the multimethod toolbox for biomolecular simulations in order to investigate those situations (e.g., interactions with metal clusters) that are beyond the range of applicability of common molecular mechanics methods.

CENCALC: a computational tool for conformational entropy calculations from molecular simulations.

We present the CENCALC software that has been designed to estimate the conformational entropy of single molecules from extended Molecular Dynamics (MD) simulations in the gas‐phase or in solution. CENCALC uses both trajectory coordinates and topology information in order to characterize the conformational states of the molecule of interest by discretizing the time evolution of internal rotations. The implemented entropy methods are based on the mutual information expansion, which is built upon the converged probability density functions of the individual torsion angles, pairs of torsions, triads, and so on. Particularly, the correlation‐corrected multibody local approximation selects an optimum cutoff in order to retrieve the maximum amount of genuine correlation from a given MD trajectory. We illustrate these capabilities by carrying out conformational entropy calculations for a decapeptide molecule either in its unbound form or in complex with a metalloprotease enzyme. CENCALC is distributed under the GNU public license at http://sourceforge.net/projects/cencalc/.

Entropic Control of the Relative Stability of Triple-helical Collagen Peptide Models

Herein, we show that current methodologies in atomistic simulations can yield reliable standard free energy values in aqueous solution for the transition from the dissociated monomeric form to the triple-helix state of collagen model peptides. The calculations are performed on a prototypical highly stable triple-helical peptide, [(Pro-Hyp-Gly)10]3 (POG10), and on the so-called T3-785 triple-helix mimicking a fragment from the type III human collagen, which is more thermally labile. On the basis of extensive MD simulations in explicit solvent followed by molecular-mechanical and electrostatic Poisson-Boltzmann calculations complemented with an accurate estimation of the nonpolar contributions to solvation, the computed free energy change for the aggregation processes of the POG10 and T3-785 peptides leading to their triple-helices is -6.6 and -6.1 kcal/mol, respectively. For POG10, this value is in agreement with differential scanning calorimetric data. However, it is shown that conformational entropy, which is estimated by means of an expansion of mutual information functions, preferentially destabilizes the triple-helical state of T3-785 by around 4.6 kcal/mol, thus explaining its lower thermal stability. Altogether, our computational results allow us to ascertain, for the first time, the actual thermodynamic forces controlling the absolute and relative stability of collagen model peptides.

An Integrated Computational and Experimental Approach to Gaining Selectivity for MMP‐2 within the Gelatinase Subfamily

Looking for water‐soluble inhibitors of matrix metalloproteinase‐2 (MMP‐2 or gelatinase A), we have previously reported compound 1, a potent MMP‐2 inhibitor with a promising selectivity over the structurally homologous MMP‐9 (gelatinase B). Here we report the results of Molecular Dynamics (MD) simulations for both gelatinases (MMP‐2 and MMP‐9), and for the corresponding MMP/1 complexes, in an attempt to shed light on the observed selectivity between the two enzymes. These studies indicated a higher plasticity of MMP‐2 at the S1′ pocket and suggested an induced‐fit effect at the “back door” of this pocket. On the basis of these observations, we designed 11 a–d to aid further discrimination between MMP‐2 and MMP‐9. Those compounds displayed notably lower inhibitory activities against MMP‐9; in particular, 11 b proved to be over 100 times more active against MMP‐2 than against MMP‐9. MD simulations of the MMP/11 b complexes and thermodynamic integration calculations provided structural insight and relative binding energies consistent with the experimentally observed activity data. These findings demonstrate that structural differences in the S1′ pocket bottom permit an improvement in selectivity in the inhibition of MMP‐2 over that of MMP‐9; this is of great relevance for future structure‐based drug design because MMP‐2 is a validated target for cancer therapy, whereas MMP‐9 plays both detrimental and protective roles in cancer. This study also supports the need to consider the dynamics of the S1′ pocket in order to achieve selectivity in the inhibition of MMPs.

Kinetic and binding effects in peptide substrate selectivity of matrix metalloproteinase-2: Molecular dynamics and QM/MM calculations†

Herein, we examine computationally the binding and hydrolysis reaction of the MMP‐2 enzyme with two peptide substrates selected by the enzyme from a phage peptide library. Molecular dynamics simulations of the Michaelis complexes (25 ns) allow us to characterize the main enzyme/substrate contacts. Subsequently MM‐PBSA calculations using independent trajectories for the complexes and the free substrates provide relative binding energies in good agreement with the experimental KM results. Computational alanine scanning analyses of the enzyme/substrate interaction energies confirm the relevance of the P3, P2, and P1′ side chains for ligand binding. Finally, the hydrolysis of both peptides taking place at the MMP‐2 active site is explored by means of hybrid quantum mechanical/molecular mechanics calculations. The computed reaction mechanisms result in rate‐determining energy barriers being in consonance with the experimental kcat values. Overall, the computational protocol seems to capture the subtle differences in binding and catalysis experimentally observed for the two peptide substrates. Some implications of our results for the future design of novel and more specific MMP‐2 inhibitors are also discussed. Proteins 2010.

Direct methods for computing single-molecule entropies from molecular simulations

Assessing the actual role of entropic forces in controlling both the stability and activity of flexible molecules and macromolecules is a theoretical challenge that is gradually gaining more attention. The continuous improvements in computational algorithms and in hardware technologies are greatly expanding the sampling capability of molecular simulations, thereby making a direct positive impact on the feasibility and reliability of entropy predictions. However, more sophisticated theoretical approaches are also required in order to make substantial progress in the type and accuracy of entropy calculations. Focusing on the evaluation of the configurational entropy of single molecules, we highlight recent advances in different methodologies including Gaussian parametric approaches, nonparametric methods and normal mode calculations. For the nonparametric methodologies, we analyze more specifically the importance of correlation effects, the various formulations of the expansion approaches, the combination of nonparametric estimations of conformational entropy with normal mode calculations, the convenience of including bias corrections for mitigating the impact of insufficient sampling and, finally, their close relationship with the experimental measures of conformational motion. The overall consideration of these and other aspects shows that addition of the direct entropy methods to the standard palette of tools used in molecular modeling for data analysis and property estimation, will increase both the level of detail of the computer simulations and our understanding of molecular functions. WIREs Comput Mol Sci 2015, 5:1–26. doi: 10.1002/wcms.1195

From the X-ray compact structure to the elongated form of the full-length MMP-2 enzyme in solution: a molecular dynamics study.

Current understanding on the collagenolytic activity performed by the MMPs assumes some degree of relative motion between the catalytic and the hemopexin-like domains of the enzyme. However, all the crystal structures available for the full-length enzymes display a compact arrangement of the protein domains. Herein, we employ Molecular Dynamics simulations to investigate the structure of the full-length MMP-2 enzyme in aqueous solution. This simulation, together with previous experimental results that have been obtained very recently for the MMP-9 and MMP-12 enzymes, gives strong support to the hypothesis that the interdomain dynamics of the MMP enzymes in solution can result in a manifold of conformations including some structures with a large interdomain separation. The simulation of MMP-2 provides also a detailed molecular picture of the structures involved in the transition from the compact X-ray arrangement to the extended form in solution. Such information could be helpful in future studies of the regulation and/or the collagenolytic activity of these important enzymes.