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

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

abstract: Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example, showed that the geometry-based FRODA occasionally sampled the pathway space of force field-based DIMS MD. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.The article is published at http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.100456

Unfolding simulations reveal the mechanism of extreme unfolding cooperativity in the kinetically stable alpha-lytic protease.

Kinetically stable proteins, those whose stability is derived from their slow unfolding kinetics and not thermodynamics, are examples of evolution's best attempts at suppressing unfolding. Especially in highly proteolytic environments, both partially and fully unfolded proteins face potential inactivation through degradation and/or aggregation, hence, slowing unfolding can greatly extend a protein's functional lifetime. The prokaryotic serine protease alpha-lytic protease (alphaLP) has done just that, as its unfolding is both very slow (t(1/2) approximately 1 year) and so cooperative that partial unfolding is negligible, providing a functional advantage over its thermodynamically stable homologs, such as trypsin. Previous studies have identified regions of the domain interface as critical to alphaLP unfolding, though a complete description of the unfolding pathway is missing. In order to identify the alphaLP unfolding pathway and the mechanism for its extreme cooperativity, we performed high temperature molecular dynamics unfolding simulations of both alphaLP and trypsin. The simulated alphaLP unfolding pathway produces a robust transition state ensemble consistent with prior biochemical experiments and clearly shows that unfolding proceeds through a preferential disruption of the domain interface. Through a novel method of calculating unfolding cooperativity, we show that alphaLP unfolds extremely cooperatively while trypsin unfolds gradually. Finally, by examining the behavior of both domain interfaces, we propose a model for the differential unfolding cooperativity of alphaLP and trypsin involving three key regions that differ between the kinetically stable and thermodynamically stable classes of serine proteases

EnGens: a computational framework for generation and analysis of representative protein conformational ensembles

Proteins are dynamic macromolecules that perform vital functions in cells. A protein structure determines its function, but this structure is not static, as proteins change their conformation to achieve various functions. Understanding the conformational landscapes of proteins is essential to understand their mechanism of action. Sets of carefully chosen conformations can summarize such complex landscapes and provide better insights into protein function than single conformations. We refer to these sets as representative conformational ensembles. Recent advances in computational methods have led to an increase in the number of available structural datasets spanning conformational landscapes. However, extracting representative conformational ensembles from such datasets is not an easy task and many methods have been developed to tackle it. Our new approach, EnGens (short for ensemble generation), collects these methods into a unified framework for generating and analyzing representative protein conformational ensembles. In this work, we: (1) provide an overview of existing methods and tools for representative protein structural ensemble generation and analysis; (2) unify existing approaches in an open-source Python package, and a portable Docker image, providing interactive visualizations within a Jupyter Notebook pipeline; (3) test our pipeline on a few canonical examples from the literature. Representative ensembles produced by EnGens can be used for many downstream tasks such as protein–ligand ensemble docking, Markov state modeling of protein dynamics and analysis of the effect of single-point mutations

Machine learning in the analysis of biomolecular simulations

Machine learning has rapidly become a key method for the analysis and organization of large-scale data in all scientific disciplines. In life sciences, the use of machine learning techniques is a particularly appealing idea since the enormous capacity of computational infrastructures generates terabytes of data through millisecond simulations of atomistic and molecular-scale biomolecular systems. Due to this explosion of data, the automation, reproducibility, and objectivity provided by machine learning methods are highly desirable features in the analysis of complex systems. In this review, we focus on the use of machine learning in biomolecular simulations. We discuss the main categories of machine learning tasks, such as dimensionality reduction, clustering, regression, and classification used in the analysis of simulation data. We then introduce the most popular classes of techniques involved in these tasks for the purpose of enhanced sampling, coordinate discovery, and structure prediction. Whenever possible, we explain the scope and limitations of machine learning approaches, and we discuss examples of applications of these techniques.Peer reviewe

Visualisation of variable binding pockets on protein surfaces by probabilistic analysis of related structure sets

Background: Protein structures provide a valuable resource for rational drug design. For a protein with no known ligand, computational tools can predict surface pockets that are of suitable size and shape to accommodate a complementary small-molecule drug. However, pocket prediction against single static structures may miss features of pockets that arise from proteins’ dynamic behaviour. In particular, ligand-binding conformations can be observed as transiently populated states of the apo protein, so it is possible to gain insight into ligand-bound forms by considering conformational variation in apo proteins. This variation can be explored by considering sets of related structures: computationally generated conformers, solution NMR ensembles, multiple crystal structures, homologues or homology models. It is non-trivial to compare pockets, either from different programs or across sets of structures. For a single structure, difficulties arise in defining particular pocket’s boundaries. For a set of conformationally distinct structures the challenge is how to make reasonable comparisons between them given that a perfect structural alignment is not possible. Results: We have developed a computational method, Provar, that provides a consistent representation of predicted binding pockets across sets of related protein structures. The outputs are probabilities that each atom or residue of the protein borders a predicted pocket. These probabilities can be readily visualised on a protein using existing molecular graphics software. We show how Provar simplifies comparison of the outputs of different pocket prediction algorithms, of pockets across multiple simulated conformations and between homologous structures. We demonstrate the benefits of use of multiple structures for protein-ligand and protein-protein interface analysis on a set of complexes and consider three case studies in detail: i) analysis of a kinase superfamily highlights the conserved occurrence of surface pockets at the active and regulatory sites ii) a simulated ensemble of unliganded Bcl2 structures reveals extensions of a known ligand-binding pocket not apparent in the apo crystal structure; iii) visualisations of interleukin-2 and its homologues highlight conserved pockets at the known receptor interfaces and regions whose conformation is known to change on inhibitor binding. Conclusions: Through post-processing of the output of a variety of pocket prediction software, Provar provides a flexible approach to the analysis and visualization of the persistence or variability of pockets in sets of related protein structures