Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes; sophisticated enhanced sampling methods have been proposed to generate these macromolecular transition paths. As such paths are curves in a high-dimensional space, they have been difficult to compare quantitatively, a prerequisite to, for instance, assess the quality of different sampling algorithms. The Path Similarity Analysis (PSA) approach alleviates these difficulties by utilizing the full information in 3N-dimensional trajectories in configuration space. PSA employs the Hausdorff or Fr\'echet path metrics---adopted from computational geometry---enabling us to quantify path (dis)similarity, while the new concept of a Hausdorff-pair map permits the extraction of atomic-scale determinants responsible for path differences. Combined with clustering techniques, PSA facilitates the comparison of many paths, including collections of transition ensembles. We use the closed-to-open transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for the assessment enhanced sampling algorithms---to examine multiple microsecond equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free form alongside transition ensembles from the MD-based dynamic importance sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for instance, that differences in DIMS-MD and FRODA paths were mediated by a set of conserved salt bridges whose charge-charge interactions are fully modeled in DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis methods relying on pre-defined collective variables, such as native contacts or geometric quantities, can be used synergistically with PSA, as well as the application of PSA to more complex systems such as membrane transporter proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also available from journal site

On the conservation of the slow conformational dynamics within the amino acid kinase family: NAGK the paradigm

N-Acetyl-L-Glutamate Kinase (NAGK) is the structural paradigm for examining the catalytic mechanisms and dynamics of amino acid kinase family members. Given that the slow conformational dynamics of the NAGK (at the microseconds time scale or slower) may be rate-limiting, it is of importance to assess the mechanisms of the most cooperative modes of motion intrinsically accessible to this enzyme. Here, we present the results from normal mode analysis using an elastic network model representation, which shows that the conformational mechanisms for substrate binding by NAGK strongly correlate with the intrinsic dynamics of the enzyme in the unbound form. We further analyzed the potential mechanisms of allosteric signalling within NAGK using a Markov model for network communication. Comparative analysis of the dynamics of family members strongly suggests that the low-frequency modes of motion and the associated intramolecular couplings that establish signal transduction are highly conserved among family members, in support of the paradigm sequence→structure→dynamics→function © 2010 Marcos et al

Low-frequency harmonic perturbations drive protein conformational changes

Protein dynamics has been investigated since almost half a century, as it is believed to constitute the fundamental connection between structure and function. Elastic network models (ENMs) have been widely used to predict protein dynamics, flexibility and the biological mechanism, from which remarkable results have been found regarding the prediction of protein conformational changes. Starting from the knowledge of the reference structure only, these conformational changes have been usually predicted either by looking at the individual mode shapes of vibrations (i.e., by considering the free vibrations of the ENM) or by applying static perturbations to the protein network (i.e., by considering a linear response theory). In this paper, we put together the two previous approaches and evaluate the complete protein response under the application of dynamic perturbations. Harmonic forces with random directions are applied to the protein ENM, which are meant to simulate the single frequency-dependent components of the collisions of the surrounding particles, and the protein response is computed by solving the dynamic equations in the underdamped regime, where mass, viscous damping and elastic stiffness contributions are explicitly taken into account. The obtained motion is investigated both in the coordinate space and in the sub-space of principal components (PCs). The results show that the application of perturbations in the low-frequency range is able to drive the protein conformational change, leading to remarkably high values of direction similarity. Eventually, this suggests that protein conformational change might be triggered by external collisions and favored by the inherent low-frequency dynamics of the protein structure

New Monte Carlo Based Technique To Study DNA–Ligand Interactions

We present a new all-atom Monte Carlo technique capable of performing quick and accurate DNA–ligand conformational sampling. In particular, and using the PELE software as a frame, we have introduced an additional force field, an implicit solvent, and an anisotropic network model to effectively map the DNA energy landscape. With these additions, we successfully generated DNA conformations for a test set composed of six DNA fragments of A-DNA and B-DNA. Moreover, trajectories generated for cisplatin and its hydrolysis products identified the best interacting compound and binding site, producing analogous results to microsecond molecular dynamics simulations. Furthermore, a combination of the Monte Carlo trajectories with Markov State Models produced noncovalent binding free energies in good agreement with the published molecular dynamics results, at a significantly lower computational cost. Overall our approach will allow a quick but accurate sampling of DNA–ligand interactions.The authors thank the Barcelona Supercomputing Center for computational resources. This work was supported by grants from the European Research Council—2009-Adg25027-PELE European project and the Spanish Ministry of Economy and Competitiveness CTQ2013-48287 and “Juan de la Cierva” to F.L.Peer ReviewedPostprint (author's final draft

A coarse-grained methodology identifies intrinsic mechanisms that dissociate interacting protein pairs

We address the problem of triggering dissociation events between proteins that have formed a complex. We have collected a set of 25 non-redundant, functionally diverse protein complexes having high-resolution three-dimensional structures in both the unbound and bound forms. We unify elastic network models with perturbation response scanning (PRS) methodology as an efficient approach for predicting residues that have the propensity to trigger dissociation of an interacting protein pair, using the three-dimensional structures of the bound and unbound proteins as input. PRS reveals that while for a group of protein pairs, residues involved in the conformational shifts are confined to regions with large motions, there are others where they originate from parts of the protein unaffected structurally by binding. Strikingly, only a few of the complexes have interface residues responsible for dissociation. We find two main modes of response: In one mode, remote control of dissociation in which disruption of the electrostatic potential distribution along protein surfaces play the major role; in the alternative mode, mechanical control of dissociation by remote residues prevail. In the former, dissociation is triggered by changes in the local environment of the protein, e.g., pH or ionic strength, while in the latter, specific perturbations arriving at the controlling residues, e.g., via binding to a third interacting partner is required for decomplexation. We resolve the observations by relying on an electromechanical coupling model which reduces to the usual elastic network result in the limit of the lack of coupling. We validate the approach by illustrating the biological significance of top residues selected by PRS on select cases where we show that the residues whose perturbation leads to the observed conformational changes correspond to either functionally important or highly conserved residues in the complex

Changes in Dynamics upon Oligomerization Regulate Substrate Binding and Allostery in Amino Acid Kinase Family Members

Oligomerization is a functional requirement for many proteins. The interfacial interactions and the overall packing geometry of the individual monomers are viewed as important determinants of the thermodynamic stability and allosteric regulation of oligomers. The present study focuses on the role of the interfacial interactions and overall contact topology in the dynamic features acquired in the oligomeric state. To this aim, the collective dynamics of enzymes belonging to the amino acid kinase family both in dimeric and hexameric forms are examined by means of an elastic network model, and the softest collective motions (i.e., lowest frequency or global modes of motions) favored by the overall architecture are analyzed. Notably, the lowest-frequency modes accessible to the individual subunits in the absence of multimerization are conserved to a large extent in the oligomer, suggesting that the oligomer takes advantage of the intrinsic dynamics of the individual monomers. At the same time, oligomerization stiffens the interfacial regions of the monomers and confers new cooperative modes that exploit the rigid-body translational and rotational degrees of freedom of the intact monomers. The present study sheds light on the mechanism of cooperative inhibition of hexameric N-acetyl-L-glutamate kinase by arginine and on the allosteric regulation of UMP kinases. It also highlights the significance of the particular quaternary design in selectively determining the oligomer dynamics congruent with required ligand-binding and allosteric activities

Studying protein-ligand interactions using a Monte Carlo procedure

[eng] Biomolecular simulations have been widely used in the study of protein-ligand interactions; comprehending the mechanisms involved in the prediction of binding affinities would have a significant repercussion in the pharmaceutical industry. Notwithstanding the intrinsic difficulty of sampling the phase space, hardware and methodological developments make computer simulations a promising candidate in the resolution of biophysically relevant problems. In this context, the objective of the thesis is the development of a protocol that permits studying protein-ligand interactions, in view to be applied in drug discovery pipelines. The author contributed to the rewriting PELE, our Monte Carlo sampling procedure, using good practices of software development. These involved testing, improving the readability, modularity, encapsulation, maintenance and version control, just to name a few. Importantly, the recoding resulted in a competitive cutting-edge software that is able to integrate new algorithms and platforms, such as new force fields or a graphical user interface, while being reliable and efficient. The rest of the thesis is built upon this development. At this point, we established a protocol of unbiased all-atom simulations using PELE, often combined with Markov (state) Models (MSM) to characterize the energy landscape exploration. In the thesis, we have shown that PELE is a suitable tool to map complex mechanisms in an accurate and efficient manner. For example, we successfully conducted studies of ligand migration in prolyl oligopeptidases and nuclear hormone receptors (NHRs). Using PELE, we could map the ligand migration and binding pathway in such complex systems in less than 48 hours. On the other hand, with this technique we often run batches of 100s of simulations to reduce the wall-clock time. MSM is a useful technique to join these independent simulations in a unique statistical model, as individual trajectories only need to characterize the energy landscape locally, and the global characterization can be extracted from the model. We successfully applied the combination of these two methodologies to quantify binding mechanisms and estimate the binding free energy in systems involving NHRs and tyorsinases. However, this technique represents a significant computational effort. To reduce the computational load, we developed a new methodology to overcome the sampling limitations caused by the ruggedness of the energy landscape. In particular, we used a procedure of iterative simulations with adaptive spawning points based on reinforcement learning ideas. This permits sampling binding mechanisms at a fraction of the cost, and represents a speedup of an order of magnitude in complex systems. Importantly, we show in a proof-of-concept that it can be used to estimate absolute binding free energies. Overall, we hope that the methodologies presented herein help streamline the drug design process.[spa] Las simulaciones biomoleculares se han usado ampliamente en el estudio de interacciones proteína-ligando. Comprender los mecanismos involucrados en la predicción de afinidades de unión tiene una gran repercusión en la industria farmacéutica. A pesar de las dificultades intrínsecas en el muestreo del espacio de fases, mejoras de hardware y metodológicas hacen de las simulaciones por ordenador un candidato prometedor en la resolución de problemas biofísicos con alta relevancia. En este contexto, el objetivo de la tesis es el desarrollo de un protocolo que introduce un estudio más eficiente de las interacciones proteína-ligando, con vistas a diseminar PELE, un procedimiento de muestreo de Monte Carlo, en el diseño de fármacos. Nuestro principal foco ha sido sobrepasar las limitaciones de muestreo causadas por la rugosidad del paisaje de energías, aplicando nuestro protocolo para hacer analsis detallados a nivel atomístico en receptores nucleares de hormonas, receptores acoplados a proteínas G, tirosinasas y prolil oligopeptidasas, en colaboración con una compañía farmacéutica y de varios laboratorios experimentales. Con todo ello, esperamos que las metodologías presentadas en esta tesis ayuden a mejorar el diseño de fármacos