SPECTRUS: A Dimensionality Reduction Approach for Identifying Dynamical Domains in Protein Complexes from Limited Structural Datasets

Predicting binding events in very flexible, allosteric, multi-domain proteins

Knowledge of the structures formed by proteins and small ligands is of fundamental importance for understanding molecular principles of chemotherapy and for designing new and more effective drugs. Due to the still high costs and to the several limitations of experimental techniques, it is most often desirable to predict these ligand-protein complexes in silico, particularly when screening for new putative drugs from databases of millions of compounds. While virtual screening based on molecular docking is widely used for this purpose, it generally fails in mimicking binding events associated with large conformational changes in the protein, particularly when the latter involve multiple domains. In this work, we describe a new methodology aimed at generating bound-like conformations of very flexible and allosteric proteins bearing multiple binding sites. Validation was performed on the enzyme adenylate kinase (ADK), a paradigmatic example of proteins that undergo very large conformational changes upon ligand binding. By only exploiting the unbound structure and the putative binding sites of the protein, we generated a significant fraction of bound-like structures, which employed in ensemble-docking calculations allowed to find native-like poses of substrates, inhibitors, and catalytically incompetent binders. Our protocol provides a general framework for the generation of bound-like conformations of flexible proteins that are suitable to host different ligands, demonstrating high sensitivity to the fine chemical details that regulate protein's activity. We foresee applications in virtual screening for difficult targets, prediction of the impact of amino acid mutations on structure and dynamics, and protein engineering.

Surveying the energy landscape of coarse-grained mappings

Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.

pyCapsid: identifying dominant dynamics and quasi-rigid mechanical units in protein shells

SUMMARY

pyCapsid is a Python package developed to facilitate the characterization of the dynamics and quasi-rigid mechanical units of protein shells and other protein complexes. The package was developed in response to the rapid increase of high-resolution structures, particularly capsids of viruses, requiring multiscale biophysical analyses. Given a protein shell, pyCapsid generates the collective vibrations of its amino-acid residues, identifies quasi-rigid mechanical regions associated with the disassembly of the structure, and maps the results back to the input proteins for interpretation. pyCapsid summarizes the main results in a report that includes publication-quality figures.

AVAILABILITY AND IMPLEMENTATION

pyCapsid's source code is available under MIT License on GitHub. It is compatible with Python 3.8-3.10 and has been deployed in two leading Python package-management systems, PIP and Conda. Installation instructions and tutorials are available in the online documentation and in the pyCapsid's YouTube playlist. In addition, a cloud-based implementation of pyCapsid is available as a Google Colab notebook. pyCapsid Colab does not require installation and generates the same report and outputs as the installable version. Users can post issues regarding pyCapsid in the repository's issues section.

Macromolecular crowding impact on anti-CRISPR AcrIIC3/NmeCas9 complex: Insights from scaled particle theory, molecular dynamics, and elastic networks models

The coupling of Cas9 and its inhibitor AcrIIC3, both from the bacterium Neisseria meningitidis (Nme), form a homodimer of the (NmeCas9/AcrIIC3)₂ type. This coupling was studied to assess the impact of their interaction with the crowders in the following environments: (1) homogeneous crowded, (2) heterogeneous, and (3) microheterogeneous cytoplasmic. For this, statistical thermodynamic models based on the scaled particle theory (SPT) were used, considering the attractive and repulsive protein-crowders contributions and the stability of the formation of spherocylindrical homodimers and the effects of changes in the size of spherical dimers were estimated. Studies based on models of dynamics, elastic networks, and statistical potentials to the formation of complexes NmeCas9/AcrIIC3 using PEG as the crowding agent support the predictions from SPT. Macromolecular crowding stabilizes the formation of the dimers, being more significant when the attractive protein-crowder interactions are weaker and the crowders are smaller. The coupling is favored towards the formation of spherical and compact dimers due to crowding addition (excluded-volume effects) and the thermodynamic stability of the dimers is markedly dependent on the size of the crowders. These results support the experimental mechanistic proposal of inhibition of NmeCas9 mediated by AcrIIC3.

Intrinsic Dynamics of the ClpXP Proteolytic Machine Using Elastic Network Models

ClpXP complex is an ATP-dependent mitochondrial matrix protease that binds, unfolds, translocates, and subsequently degrades specific protein substrates. Its mechanisms of operation are still being debated, and several have been proposed, including the sequential translocation of two residues (SC/2R), six residues (SC/6R), and even long-pass probabilistic models. Therefore, it has been suggested to employ biophysical-computational approaches that can determine the kinetics and thermodynamics of the translocation. In this sense, and based on the apparent inconsistency between structural and functional studies, we propose to apply biophysical approaches based on elastic network models (ENM) to study the intrinsic dynamics of the theoretically most probable hydrolysis mechanism. The proposed models ENM suggest that the ClpP region is decisive for the stabilization of the ClpXP complex, contributing to the flexibility of the residues adjacent to the pore, favoring the increase in pore size and, therefore, with the energy of interaction of its residues with a larger portion of the substrate. It is predicted that the complex may undergo a stable configurational change once assembled and that the deformability of the system once assembled is oriented, to increase the rigidity of the domains of each region (ClpP and ClpX) and to gain flexibility of the pore. Our predictions could suggest under the conditions of this study the mechanism of the interaction of the system, of which the substrate passes through the unfolding of the pore in parallel with a folding of the bottleneck. The variations in the distance calculated by molecular dynamics could allow the passage of a substrate with a size equivalent to ∼3 residues. The theoretical behavior of the pore and the stability and energy of binding to the substrate based on ENM models suggest that in this system, there are thermodynamic, structural, and configurational conditions that allow a possible translocation mechanism that is not strictly sequential.

Structural deformability induced in proteins of potential interest associated with COVID-19 by binding of homologues present in ivermectin: Comparative study based in elastic networks models

The COVID-19 pandemic has accelerated the study of the potential of multi-target drugs (MTDs). The mixture of homologues called ivermectin (avermectin-B1a + avermectin-B1b) has been shown to be a MTD with potential antiviral activity against SARS-CoV-2 in vitro. However, there are few reports on the effect of each homologue on the flexibility and stiffness of proteins associated with COVID-19, described as ivermectin targets. We observed that each homologue was stably bound to the proteins studied and was able to induce detectable changes with Elastic Network Models (ENM). The perturbations induced by each homologue were characteristic of each compound and, in turn, were represented by a disruption of native intramolecular networks (interactions between residues). The homologues were able to slightly modify the conformation and stability of the connection points between the Cα atoms of the residues that make up the structural network of proteins (nodes), compared to free proteins. Each homologue was able to modified differently the distribution of quasi-rigid regions of the proteins, which could theoretically alter their biological activities. These results could provide a biophysical-computational view of the potential MTD mechanism that has been reported for ivermectin.

A graph-based algorithm for detecting rigid domains in protein structures

Background

Conformational transitions are implicated in the biological function of many proteins. Structural changes in proteins can be described approximately as the relative movement of rigid domains against each other. Despite previous efforts, there is a need to develop new domain segmentation algorithms that are capable of analysing the entire structure database efficiently and do not require the choice of protein-dependent tuning parameters such as the number of rigid domains.

Results

We develop a graph-based method for detecting rigid domains in proteins. Structural information from multiple conformational states is represented by a graph whose nodes correspond to amino acids. Graph clustering algorithms allow us to reduce the graph and run the Viterbi algorithm on the associated line graph to obtain a segmentation of the input structures into rigid domains. In contrast to many alternative methods, our approach does not require knowledge about the number of rigid domains. Moreover, we identified default values for the algorithmic parameters that are suitable for a large number of conformational ensembles. We test our algorithm on examples from the DynDom database and illustrate our method on various challenging systems whose structural transitions have been studied extensively.

Conclusions

The results strongly suggest that our graph-based algorithm forms a novel framework to characterize structural transitions in proteins via detecting their rigid domains. The web server is available at http://azifi.tz.agrar.uni-goettingen.de/webservice/.

An Information-Theory-Based Approach for Optimal Model Reduction of Biomolecules

In theoretical modeling of a physical system, a crucial step consists of the identification of those degrees of freedom that enable a synthetic yet informative representation of it. While in some cases this selection can be carried out on the basis of intuition and experience, straightforward discrimination of the important features from the negligible ones is difficult for many complex systems, most notably heteropolymers and large biomolecules. We here present a thermodynamics-based theoretical framework to gauge the effectiveness of a given simplified representation by measuring its information content. We employ this method to identify those reduced descriptions of proteins, in terms of a subset of their atoms, that retain the largest amount of information from the original model; we show that these highly informative representations share common features that are intrinsically related to the biological properties of the proteins under examination, thereby establishing a bridge between protein structure, energetics, and function.

Unravelling the effect of the E545K mutation on PI3Kα kinase

PI3Kα controls several cellular processes and its aberrant signalling is implicated in tumorigenesis. One of its hotspot mutations, E545K, increases PI3Kα lipid kinase activity, but its mode of action is only partially understood. Here, we perform biased and unbiased molecular dynamics simulations of PI3Kα and uncover, for the first time, the free energy landscape of the E545K PI3Kα mutant. We reveal the mechanism by which E545K leads to PI3Kα activation in atomic-level detail, which is considerably more complex than previously thought.

Spectral analysis of molecular dynamics simulations on PDZ: MD sectors

The idea of protein "sectors" posits that sparse subsets of amino acid residues form cooperative networks that are key elements of protein stability, ligand binding, and allosterism. To date, protein sectors have been calculated by the statistical coupling analysis (SCA) method of Ranganathan and co-workers via the spectral analysis of conservation-weighted evolutionary covariance matrices obtained from a multiple sequence alignments of homologous families of proteins. SCA sectors, a knowledge-based protocol, have been indentified with functional properties and allosterism for a number of systems. In this study, we investigate the utility of the sector idea for the analysis of physics-based molecular dynamics (MD) trajectories of proteins. Our test case for this procedure is PSD95- PDZ3, one of the smallest proteins for which allosterism has been observed. It has served previously as a model system for a number of prediction algorithms, and is well characterized by X-ray crystallography, NMR spectroscopy and site specific mutagenisis. All-atom MD simulations were performed for a total of 500 nanoseconds using AMBER, and MD-calculated covariance matrices for the fluctuations of residue displacements and non-bonded interaction energies were subjected to spectral analysis in a manner analogous to that of SCA. The composition of MD sectors was compared with results from SCA, site specific mutagenesis, and allosterism. The concordance indicates that MD sectors are a viable protocol for analyzing MD trajectories and provide insight into the physical origin of the phenomenon.Communicated by Ramaswamy H. Sarma.

All Atom Motion Tree detects side chain-related motions and their coupling with domain motion in proteins

Structural changes of proteins are closely related with their molecular function. We previously developed a computational tool, Motion Tree (MT), to compare protein structures and describe structural changes using solely the Cα atoms. Here, we have extended MT to incorporate all heavy atoms to analyze side chain-related (SCR) motions. All Atom Motion Tree (AAMT) was applied to 76 proteins that exhibited a simple domain motion identified by MT. AAMT also detected 921 SCR motions. We examined the coupling of domain and SCR motions and classified the structural changes in terms of coupling. The statistical results indicated that it is common for coupled SCR motions to also couple with the domain motion. The classification correlates properties of domain motions and SCR motions. The AAMT results suggest that a large domain motion with a sizable domain boundary is accompanied by SCR motions composed of more than a single residue, which induces further couplings of SCR motions.

InfleCS: Clustering Free Energy Landscapes with Gaussian Mixtures

Free energy landscapes provide insights into conformational ensembles of biomolecules. In order to analyze these landscapes and elucidate mechanisms underlying conformational changes, there is a need to extract metastable states with limited noise. This has remained a formidable task, despite a plethora of existing clustering methods. We present InfleCS, a novel method for extracting well-defined core states from free energy landscapes. The method is based on a Gaussian mixture free energy estimator and exploits the shape of the estimated density landscape. The core states that naturally arise from the clustering allow for detailed characterization of the conformational ensemble. The clustering quality is evaluated on three toy models with different properties, where the method is shown to consistently outperform other conventional and state-of-the-art clustering methods. Finally, the method is applied to a temperature enhanced molecular dynamics simulation of Ca²⁺-bound Calmodulin. Through the free energy landscape, we discover a pathway between a canonical and a compact state, revealing conformational changes driven by electrostatic interactions.

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

Structure and dynamics of Helicobacter pylori nickel-chaperone HypA: an integrated approach using NMR spectroscopy, functional assays and computational tools

Helicobacter pylori HypA (HpHypA) is a metallochaperone necessary for maturation of [Ni,Fe]-hydrogenase and urease, the enzymes required for colonization and survival of H. pylori in the gastric mucosa. HpHypA contains a structural Zn(II) site and a unique Ni(II) binding site at the N-terminus. X-ray absorption spectra suggested that the Zn(II) coordination depends on pH and on the presence of Ni(II). This study was performed to investigate the structural properties of HpHypA as a function of pH and Ni(II) binding, using NMR spectroscopy combined with DFT and molecular dynamics calculations. The solution structure of apo,Zn-HpHypA, containing Zn(II) but devoid of Ni(II), was determined using 2D, 3D and 4D NMR spectroscopy. The structure suggests that a Ni-binding and a Zn-binding domain, joined through a short linker, could undergo mutual reorientation. This flexibility has no physiological effect on acid viability or urease maturation in H. pylori. Atomistic molecular dynamics simulations suggest that Ni(II) binding is important for the conformational stability of the N-terminal helix. NMR chemical shift perturbation analysis indicates that no structural changes occur in the Zn-binding domain upon addition of Ni(II) in the pH 6.3-7.2 range. The structure of the Ni(II) binding site was probed using ¹H NMR spectroscopy experiments tailored to reveal hyperfine-shifted signals around the paramagnetic metal ion. On this basis, two possible models were derived using quantum-mechanical DFT calculations. The results provide a comprehensive picture of the Ni(II) mode to HpHypA, important to rationalize, at the molecular level, the functional interactions of this chaperone with its protein partners.

Effect of Ca2+ on the promiscuous target-protein binding of calmodulin

Calmodulin (CaM) is a calcium sensing protein that regulates the function of a large number of proteins, thus playing a crucial part in many cell signaling pathways. CaM has the ability to bind more than 300 different target peptides in a Ca2+-dependent manner, mainly through the exposure of hydrophobic residues. How CaM can bind a large number of targets while retaining some selectivity is a fascinating open question. Here, we explore the mechanism of CaM selective promiscuity for selected target proteins. Analyzing enhanced sampling molecular dynamics simulations of Ca2+-bound and Ca2+-free CaM via spectral clustering has allowed us to identify distinct conformational states, characterized by interhelical angles, secondary structure determinants and the solvent exposure of specific residues. We searched for indicators of conformational selection by mapping solvent exposure of residues in these conformational states to contacts in structures of CaM/target peptide complexes. We thereby identified CaM states involved in various binding classes arranged along a depth binding gradient. Binding Ca2+ modifies the accessible hydrophobic surface of the two lobes and allows for deeper binding. Apo CaM indeed shows shallow binding involving predominantly polar and charged residues. Furthermore, binding to the C-terminal lobe of CaM appears selective and involves specific conformational states that can facilitate deep binding to target proteins, while binding to the N-terminal lobe appears to happen through a more flexible mechanism. Thus the long-ranged electrostatic interactions of the charged residues of the N-terminal lobe of CaM may initiate binding, while the short-ranged interactions of hydrophobic residues in the C-terminal lobe of CaM may account for selectivity. This work furthers our understanding of the mechanism of CaM binding and selectivity to different target proteins and paves the way towards a comprehensive model of CaM selectivity.

Structural dynamics is a determinant of the functional significance of missense variants

Discrimination of clinically relevant mutations from neutral mutations is of paramount importance in precision medicine and pharmacogenomics. Our study shows that current computational predictions of pathogenicity, mostly based on analysis of sequence conservation, may be improved by considering the changes in the structural dynamics of the protein due to point mutations. We introduce and demonstrate the utility of a classifier that takes advantage of efficient evaluation of structural dynamics by elastic network models.

Accurate evaluation of the effect of point mutations on protein function is essential to assessing the genesis and prognosis of many inherited diseases and cancer types. Currently, a wealth of computational tools has been developed for pathogenicity prediction. Two major types of data are used to this aim: sequence conservation/evolution and structural properties. Here, we demonstrate in a systematic way that another determinant of the functional impact of missense variants is the protein’s structural dynamics. Measurable improvement is shown in pathogenicity prediction by taking into consideration the dynamical context and implications of the mutation. Our study suggests that the class of dynamics descriptors introduced here may be used in conjunction with existing features to not only increase the prediction accuracy of the impact of variants on biological function, but also gain insight into the physical basis of the effect of missense variants.

A Data-Driven Perspective on the Hierarchical Assembly of Molecular Structures

Macromolecular systems are composed of a very large number of atomic degrees of freedom. There is strong evidence suggesting that structural changes occurring in large biomolecular systems at long time scale dynamics may be captured by models coarser than atomistic, although a suitable or optimal coarse-graining is a priori unknown. Here we propose a systematic approach to learning a coarse representation of a macromolecule from microscopic simulation data. In particular, the definition of effective coarse variables is achieved by partitioning the degrees of freedom both in the structural (physical) space and in the conformational space. The identification of groups of microscopic particles forming dynamical coherent states in different metastable states leads to a multiscale description of the system, in space and time. The application of this approach to the folding dynamics of two proteins provides a revised view of the classical idea of prestructured regions (foldons) that combine during a protein-folding process and suggests a hierarchical characterization of the assembly process of folded structures.

Patterns of coevolving amino acids unveil structural and dynamical domains

Patterns of interacting amino acids are so preserved within protein families that the sole analysis of evolutionary comutations can identify pairs of contacting residues. It is also known that evolution conserves functional dynamics, i.e., the concerted motion or displacement of large protein regions or domains. Is it, therefore, possible to use a pure sequence-based analysis to identify these dynamical domains? To address this question, we introduce here a general coevolutionary coupling analysis strategy and apply it to a curated sequence database of hundreds of protein families. For most families, the sequence-based method partitions amino acids into a few clusters. When viewed in the context of the native structure, these clusters have the signature characteristics of viable protein domains: They are spatially separated but individually compact. They have a direct functional bearing too, as shown for various reference cases. We conclude that even large-scale structural and functionally related properties can be recovered from inference methods applied to evolutionary-related sequences. The method introduced here is available as a software package and web server (spectrus.sissa.it/spectrus-evo_webserver).

A probabilistic model for detecting rigid domains in protein structures

MOTIVATION

Large-scale conformational changes in proteins are implicated in many important biological functions. These structural transitions can often be rationalized in terms of relative movements of rigid domains. There is a need for objective and automated methods that identify rigid domains in sets of protein structures showing alternative conformational states.

RESULTS

We present a probabilistic model for detecting rigid-body movements in protein structures. Our model aims to approximate alternative conformational states by a few structural parts that are rigidly transformed under the action of a rotation and a translation. By using Bayesian inference and Markov chain Monte Carlo sampling, we estimate all parameters of the model, including a segmentation of the protein into rigid domains, the structures of the domains themselves, and the rigid transformations that generate the observed structures. We find that our Gibbs sampling algorithm can also estimate the optimal number of rigid domains with high efficiency and accuracy. We assess the power of our method on several thousand entries of the DynDom database and discuss applications to various complex biomolecular systems.

AVAILABILITY AND IMPLEMENTATION

The Python source code for protein ensemble analysis is available at: https://github.com/thachnguyen/motion_detection

CONTACT

: mhabeck@gwdg.de.

Unifying view of mechanical and functional hotspots across class A GPCRs

G protein-coupled receptors (GPCRs) are the largest superfamily of signaling proteins. Their activation process is accompanied by conformational changes that have not yet been fully uncovered. Here, we carry out a novel comparative analysis of internal structural fluctuations across a variety of receptors from class A GPCRs, which currently has the richest structural coverage. We infer the local mechanical couplings underpinning the receptors’ functional dynamics and finally identify those amino acids whose virtual deletion causes a significant softening of the mechanical network. The relevance of these amino acids is demonstrated by their overlap with those known to be crucial for GPCR function, based on static structural criteria. The differences with the latter set allow us to identify those sites whose functional role is more clearly detected by considering dynamical and mechanical properties. Of these sites with a genuine mechanical/dynamical character, the top ranking is amino acid 7x52, a previously unexplored, and experimentally verifiable key site for GPCR conformational response to ligand binding.

The biological functionality of several receptors and enzymes depends on their capability to sustain large-scale structural fluctuations and adopt different conformational states in response to ligand binding. This is the case for G protein-coupled receptors (GPCRs), the largest superfamily of signaling proteins in mammals and a primary pharmaceutical target. To better understand the functional dynamics of GPCRs, we have analysed the inter-residue distance variations across the available structures for several receptors of the rhodopsin-like family (class A). We first reconstructed the network of mechanical, rigid-like couplings between nearby amino acids and then identified those acting as dynamical/mechanical hubs. These were the sites whose virtual removal led to a significant softening of the overall mechanical network. After validating the biological relevance of these sites by comparison against known key functional sites, we singled out those regions which emerge as prominent mechanical hubs and yet have an otherwise still unknown functional role. The most relevant of such novel putative functional sites, which could be probed by mutagenesis experiments, is at interface of two transmembrane helices and we expect it to be crucial for assisting GPCRs conformational response to agonist binding.

Conformational ensemble of human α-synuclein physiological form predicted by molecular simulations

We perform here enhanced sampling simulations of N-terminally acetylated human α-synuclein, an intrinsically disordered protein involved in Parkinson's disease. The calculations, consistent with experiments, suggest that the post-translational modification leads to the formation of a transient amphipathic α-helix. The latter, absent in the non-physiological form, alters protein dynamics at the N-terminal and intramolecular interactions.