Essential dynamics: foundation and applications

The role of hydrophobicity in the cold denaturation of proteins under high pressure: A study on apomyoglobin

An exciting debate arises when microscopic mechanisms involved in the denaturation of proteins at high pressures are explained. In particular, the issue emerges when the hydrophobic effect is invoked, given that hydrophobicity cannot elucidate by itself the volume changes measured during protein unfolding. In this work, we study by the use of molecular dynamics simulations and essential dynamics analysis the relation between the solvation dynamics, volume, and water structure when apomyoglobin is subjected to a hydrostatic pressure regime. Accordingly, the mechanism of cold denaturation of proteins under high-pressure can be related to the disruption of the hydrogen-bond network of water favoring the coexistence of two states, low-density and high-density water, which directly implies in the formation of a molten globule once the threshold of 200 MPa has been overcome.

Analyzing Biomolecular Ensembles

Several techniques are available to generate conformational ensembles of proteins and other biomolecules either experimentally or computationally. These methods produce a large amount of data that need to be analyzed to identify structure-dynamics-function relationship. In this chapter, we will cover different tools to unveil the information hidden in conformational ensemble data and to guide toward the rationalization of the data. We included routinely used approaches such as dimensionality reduction, as well as new methods inspired by high-order statistics and graph theory.

Molecular Determinants of the Promiscuity of MexB and MexY Multidrug Transporters of Pseudomonas aeruginosa

Secondary multidrug transporters of the resistance-nodulation-cell division (RND) superfamily contribute crucially to antibiotic resistance in Gram-negative bacteria. Compared to the most studied transporter AcrB of Escherichia coli, little is known about the molecular determinants of distinct polyspecificities of the most important RND transporters MexB and MexY of Pseudomonas aeruginosa. In an effort to add knowledge on this topic, we performed an exhaustive atomic-level comparison of the main putative recognition sites (access and deep binding pockets) in these two Mex transporters. We identified an underlying link between some structural, chemical and dynamical features of the binding pockets and the physicochemical nature of the corresponding substrates recognized by either one or both pumps. In particular, mosaic-like lipophilic and electrostatic surfaces of the binding pockets provide for both proteins several multifunctional sites for diffuse binding of diverse substrates. Specific lipophilicity signatures of the weakly conserved deep pocket suggest a key role of this site as a selectivity filter as in Acr transporters. Finally, the different dynamics of the bottom-loop in MexB and MexY support its possible role in binding of large substrates. Our work represents the first comparative study of the major RND transporters in P. aeruginosa and also the first structure-based study of MexY, for which no experimental structure is available yet.

Universality and Specificity in Protein Fluctuation Dynamics

We investigate the universal scaling of protein fluctuation dynamics with a site-specific diffusive model of protein motion, which predicts an initial subdiffusive regime in the configurational relaxation. The long-time dynamics of proteins is controlled by an activated regime. We argue that the hierarchical free energy barriers set the time scales of biological processes and establish an upper limit to the size of single protein domains. We find it compelling that the scaling behavior for the protein dynamics is in close agreement with the Kardar-Parisi-Zhang scaling exponents.

Molecular Rationale behind the Differential Substrate Specificity of Bacterial RND Multi-Drug Transporters

Resistance-Nodulation-cell Division (RND) transporters AcrB and AcrD of Escherichia coli expel a wide range of substrates out of the cell in conjunction with AcrA and TolC, contributing to the onset of bacterial multidrug resistance. Despite sharing an overall sequence identity of ~66% (similarity ~80%), these RND transporters feature distinct substrate specificity patterns whose underlying basis remains elusive. We performed exhaustive comparative analyses of the putative substrate binding pockets considering crystal structures, homology models and conformations extracted from multi-copy μs-long molecular dynamics simulations of both AcrB and AcrD. The impact of physicochemical and topographical properties (volume, shape, lipophilicity, electrostatic potential, hydration and distribution of multi-functional sites) within the pockets on their substrate specificities was quantitatively assessed. Differences in the lipophilic and electrostatic potentials among the pockets were identified. In particular, the deep pocket of AcrB showed the largest lipophilicity convincingly pointing out its possible role as a lipophilicity-based selectivity filter. Furthermore, we identified dynamic features (not inferable from sequence analysis or static structures) such as different flexibilities of specific protein loops that could potentially influence the substrate recognition and transport profile. Our findings can be valuable for drawing structure (dynamics)-activity relationship to be employed in drug design.

Structural dynamics of wild type and mutated forms of human L1 endonuclease and insights into its sequence specific nucleic acid binding mechanism: A molecular dynamics study

Biomolecular recognition of proteins and nucleic acids is mainly mediated by their structural features and the molecular dynamics simulations approach has been used to explore this recognition processes at the atomic level. L1-Endonuclease, an enzyme involved in L1 retrotransposition, cleaves the TA junction DNA (5'-TTTT/AA-3') and expresses high specificity for target site recognition. The present study highlights the structural features of L1-endonuclease as well as DNA responsible for such specific recognition. Especially, the importance of βB6-B5 hairpin loop in DNA recognition has been elucidated by analyzing the dynamics of Thr192 mutated L1-endonuclease. In addition, simulations of the endonuclease complexed with DNA substrates (sequences having TA and CG junctions) revealed the specificity of L1 endonuclease towards TA junction. Molecular dynamics simulations revealed that the βB6-B5 hairpin loop protrudes well into the minor groove of DNA having TA junction and induces DNA bending such that the width of minor groove is increased. Such endonuclease induced bending of TA junction DNA sequence positions the scissile phosphodiester bond of DNA for cleavage. The innate property of minor groove widening in TA junction than in CG junction is utilized by the βB6-βB5 hairpin loop of endonuclease while recognizing the DNA sequences. The present study also highlights the role of Mg²⁺ cation in catalysis and attempts to explore the possible target site DNA cleavage mechanism.

Consistent Principal Component Modes from Molecular Dynamics Simulations of Proteins

Principal component analysis is a technique widely used for studying the movements of proteins using data collected from molecular dynamics simulations. In spite of its extensive use, the technique has a serious drawback: equivalent simulations do not afford the same PC-modes. In this article, we show that concatenating equivalent trajectories and calculating the PC-modes from the concatenated one significantly enhances the reproducibility of the results. Moreover, the consistency of the modes can be systematically improved by adding more individual trajectories to the concatenated one.

Folding propensity of anoplin: A molecular dynamics study of the native peptide and four mutated isoforms

Anoplin, a cationic decapeptide amide GLLKRIKTLL-NH2 derived from venom sac of the solitary wasp Anoplius samariensis has been investigated through Molecular Dynamics. The wild-type (WT) and four isoforms were simulated both in water and in the membrane-mimicking solvent trifluoroethanol (TFE). In water all the investigated species, found to be in rapid equilibrium between different conformational states, can be considered as unfolded. On the other hand, in TFE all the systems enhance their rigidity and, in general, show α-helix as the main folded conformation. Interestingly, a semi-quantitative thermodynamic analysis has suggested that the folding driving force is not always the same being in some cases (e.g., the WT Anoplin) of entropic nature and in other cases of energetic nature.

Structural variability of C3larvin toxin. Intrinsic dynamics of the α/β fold of the C3-like group of mono-ADP-ribosyltransferase toxins

C3larvin toxin is a new member of the C3 class of the mono-ADP-ribosyltransferase toxin family. The C3 toxins are known to covalently modify small G-proteins, e.g. RhoA, impairing their function, and serving as virulence factors for an offending pathogen. A full-length X-ray structure of C3larvin (2.3 Å) revealed that the characteristic mixed α/β fold consists of a central β-core flanked by two helical regions. Topologically, the protein can be separated into N and C lobes, each formed by a β-sheet and an α-motif, and connected by exposed loops involved in the recognition, binding, and catalysis of the toxin/enzyme, i.e. the ADP-ribosylation turn-turn and phosphate-nicotinamide PN loops. Herein, we provide two new C3larvin X-ray structures and present a systematic study of the toxin dynamics by first analyzing the experimental variability of the X-ray data-set followed by contrasting those results with theoretical predictions based on Elastic Network Models (GNM and ANM). We identify residues that participate in the stability of the N-lobe, putative hinges at loop residues, and energy-favored deformation vectors compatible with conformational changes of the key loops and 3D-subdomains (N/C-lobes), among the X-ray structures. We analyze a larger ensemble of known C3bot1 conformations and conclude that the characteristic 'crab-claw' movement may be driven by the main intrinsic modes of motion. Finally, via computational simulations, we identify harmonic and anharmonic fluctuations that might define the C3larvin 'native state.' Implications for docking protocols are derived.

F429 Regulation of Tunnels in Cytochrome P450 2B4: A Top Down Study of Multiple Molecular Dynamics Simulations

The root causes of the outcomes of the single-site mutation in enzymes remain by and large not well understood. This is the case of the F429H mutant of the cytochrome P450 (CYP) 2B4 enzyme where the substitution, on the proximal surface of the active site, of a conserved phenylalanine 429 residue with histidine seems to hamper the formation of the active species, Compound I (porphyrin cation radical-Fe^(IV) = O, Cpd I) from the ferric hydroperoxo (Fe^(III)OOH^-, Cpd 0) precursor. Here we report a study based on extensive molecular dynamic (MD) simulations of 4 CYP-2B4 point mutations compared to the WT enzyme, having the goal of better clarifying the importance of the proximal Phe429 residue on CYP 2B4 catalytic properties. To consolidate the huge amount of data coming from five simulations and extract the most distinct structural features of the five species studied we made an extensive use of cluster analysis. The results show that all studied single polymorphisms of F429, with different side chain properties: i) drastically alter the reservoir of conformations accessible by the protein, perturbing global dynamics ii) expose the thiolate group of residue Cys436 to the solvent, altering the electronic properties of Cpd0 and iii) affect the various ingress and egress channels connecting the distal sites with the bulk environment, altering the reversibility of these channels. In particular, it was observed that the wild type enzyme exhibits unique structural features as compared to all mutant species in terms of weak interactions (hydrogen bonds) that generate a completely different dynamical behavior of the complete system. Albeit not conclusive, the current computational investigation sheds some light on the subtle and critical effects that proximal single-site mutations can exert on the functional mechanisms of human microsomal CYPs which should go rather far beyond local structure characterization.

Comparison of the Internal Dynamics of Metalloproteases Provides New Insights on Their Function and Evolution

Metalloproteases have evolved in a vast number of biological systems, being one of the most diverse types of proteases and presenting a wide range of folds and catalytic metal ions. Given the increasing understanding of protein internal dynamics and its role in enzyme function, we are interested in assessing how the structural heterogeneity of metalloproteases translates into their dynamics. Therefore, the dynamical profile of the clan MA type protein thermolysin, derived from an Elastic Network Model of protein structure, was evaluated against those obtained from a set of experimental structures and molecular dynamics simulation trajectories. A close correspondence was obtained between modes derived from the coarse-grained model and the subspace of functionally-relevant motions observed experimentally, the later being shown to be encoded in the internal dynamics of the protein. This prompted the use of dynamics-based comparison methods that employ such coarse-grained models in a representative set of clan members, allowing for its quantitative description in terms of structural and dynamical variability. Although members show structural similarity, they nonetheless present distinct dynamical profiles, with no apparent correlation between structural and dynamical relatedness. However, previously unnoticed dynamical similarity was found between the relevant members Carboxypeptidase Pfu, Leishmanolysin, and Botulinum Neurotoxin Type A, despite sharing no structural similarity. Inspection of the respective alignments shows that dynamical similarity has a functional basis, namely the need for maintaining proper intermolecular interactions with the respective substrates. These results suggest that distinct selective pressure mechanisms act on metalloproteases at structural and dynamical levels through the course of their evolution. This work shows how new insights on metalloprotease function and evolution can be assessed with comparison schemes that incorporate information on protein dynamics. The integration of these newly developed tools, if applied to other protein families, can lead to more accurate and descriptive protein classification systems.

Protein Flexibility in Drug Discovery: From Theory to Computation

Nowadays it is widely accepted that the mechanisms of biomolecular recognition are strongly coupled to the intrinsic dynamic of proteins. In past years, this evidence has prompted the development of theoretical models of recognition able to describe ligand binding assisted by protein conformational changes. On a different perspective, the need to take into account protein flexibility in structure-based drug discovery has stimulated the development of several and extremely diversified computational methods. Herein, on the basis of a parallel between the major recognition models and the simulation strategies used to account for protein flexibility in ligand binding, we sort out and describe the most innovative and promising implementations for structure-based drug discovery.

Essential dynamics for the study of microstructures in liquids

Essential Dynamics (ED) is a powerful tool for analyzing molecular dynamics (MD) simulations and it is widely adopted for conformational analysis of large molecular systems such as, for example, proteins and nucleic acids. In this study, we extend the use of ED to the study of clusters of arbitrary size constituted by weakly interacting particles, for example, atomic clusters and supramolecular systems. The key feature of the method we present is the identification of the relevant atomic-molecular clusters to be analyzed by ED for extracting the information of interest. The application of this computational approach allows a straightforward and unbiased conformational study of the local microstructures in liquids, as emerged from semiclassical MD simulations. The good performance of the method is demonstrated by calculating typical observables of liquid water, that is, NMR, NEXAFS O1s, and IR spectra, known to be rather sensitive both to the presence and to the conformational features of hydrogen-bonded clusters.

New insights into the meaning and usefulness of principal component analysis of concatenated trajectories

A comparison between different conformations of a given protein, relating both structure and dynamics, can be performed in terms of combined principal component analysis (combined-PCA). To that end, a trajectory is obtained by concatenating molecular dynamics trajectories of the individual conformations under comparison. Then, the principal components are calculated by diagonalizing the correlation matrix of the concatenated trajectory. Since the introduction of this approach in 1995 it has had a large number of applications. However, the interpretation of the eigenvectors and eigenvalues so obtained is based on intuitive foundations, because analytical expressions relating the concatenated correlation matrix with those of the individual trajectories under consideration have not been provided yet. In this article, we present such expressions for the cases of two, three, and an arbitrary number of concatenated trajectories. The formulas are simple and show what is to be expected and what is not to be expected from a combined-PCA. Their correctness and usefulness is demonstrated by discussing some representative examples. The results can be summarized in a simple sentence: the correlation matrix of a concatenated trajectory is given by the average of the individual correlation matrices plus the correlation matrix of the individual averages. From this it follows that the combined-PCA of trajectories belonging to different free energy basins provides information that could also be obtained by alternative and more straightforward means.

Random Matrix Theory in molecular dynamics analysis

It is well known that, in some situations, principal component analysis (PCA) carried out on molecular dynamics data results in the appearance of cosine-shaped low index projections. Because this is reminiscent of the results obtained by performing PCA on a multidimensional Brownian dynamics, it has been suggested that short-time protein dynamics is essentially nothing more than a noisy signal. Here we use Random Matrix Theory to analyze a series of short-time molecular dynamics experiments which are specifically designed to be simulations with high cosine content. We use as a model system the protein apoCox17, a mitochondrial copper chaperone. Spectral analysis on correlation matrices allows to easily differentiate random correlations, simply deriving from the finite length of the process, from non-random signals reflecting the intrinsic system properties. Our results clearly show that protein dynamics is not really Brownian also in presence of the cosine-shaped low index projections on principal axes.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Reconstructing the free-energy landscape of Met-enkephalin using dihedral principal component analysis and well-tempered metadynamics

Well-Tempered Metadynamics (WTmetaD) is an efficient method to enhance the reconstruction of the free-energy surface of proteins. WTmetaD guarantees a faster convergence in the long time limit in comparison with the standard metadynamics. It still suffers, however, from the same limitation, i.e., the non-trivial choice of pertinent collective variables (CVs). To circumvent this problem, we couple WTmetaD with a set of CVs generated from a dihedral Principal Component Analysis (dPCA) on the Ramachandran dihedral angles describing the backbone structure of the protein. The dPCA provides a generic method to extract relevant CVs built from internal coordinates, and does not depend on the alignment to an arbitrarily chosen reference structure as usual in Cartesian PCA. We illustrate the robustness of this method in the case of a reference model protein, the small and very diffusive Met-enkephalin pentapeptide. We propose a justification a posteriori of the considered number of CVs necessary to bias the metadynamics simulation in terms of the one-dimensional free-energy profiles associated with Ramachandran dihedral angles along the amino-acid sequence.

Theoretical-computational modeling of photo-induced charge separation spectra and charge recombination kinetics in solution

A computational approach, based on molecular dynamics simulations and quantum-chemical calculations, is proposed for modelling the photo-induced charge separation and the kinetics of the subsequent charge recombination (CR) processes in solution.