Detection of long-range concerted motions in protein by a distance covariance

Adaptive Workflows of Machine Learning Illuminate the Sequential Operation Mechanism of the TAK1's Allosteric Network

Allostery is a fundamental mechanism driving biomolecular processes that holds significant therapeutic concern. Our study rigorously investigates how two distinct machine-learning algorithms uniquely classify two already close-to-active DFG-in states of TAK1, differing just by the presence or absence of its allosteric activator TAB1, from an ensemble mixture of conformations (obtained from 2.4 μs molecular dynamics (MD) simulations). The novelty, however, lies in understanding the deeper algorithmic potentials to systematically derive a diverse set of differential residue connectivity features that reconstruct the essential mechanistic architecture for TAK1-TAB1 allostery in such a close-to-active biochemical scenario. While the recursive, random forest-based workflow displays the potential of conducting discretized, hierarchical derivation of allosteric features, a multilayer perceptron-based approach gains considerable efficacy in revealing fluid connected patterns of features when hybridized with mutual information scoring. Interestingly, both pipelines benchmark similar directions of functional conformational changes for TAK1's activation. The findings significantly advance the depth of mechanistic understanding by highlighting crucial activation signatures along a directed C-lobe → activation loop → ATP pocket channel of information flow, including (1) the αF-αE biterminal alignments and (2) the "catalytic" drift of the activation loop toward kinase active site. Besides, some novel allosteric hotspots (K253, Y206, N189, etc.) are further recognized as TAB1 sensors, transducers, and responders, including a benchmark E70 mutation site, precisely mapping the important structural segments for sequential allosteric execution. Hence, our work demonstrates how to navigate through greater structural depths and dimensions of dynamic allosteric machineries just by leveraging standard ML methods in suitable streamlined workflows adaptive to the specific system and objectives.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Virtual repurposing of ursodeoxycholate and chenodeoxycholate as lead candidates against SARS-Cov2-Envelope protein: A molecular dynamics investigation

Drug repurposing is an apt choice to combat the currently prevailing global threat of COVID-19, caused by SARS-Cov2in absence of any specific medication/vaccine. The present work employs state of art computational methods like homology modelling, molecular docking and molecular dynamics simulations to evaluate the potential of two widely used surfactant drugs namely chenodeoxycholate(CDC) and ursodeoxycholate (UDC), to bind to the envelope protein of SARS-Cov2(SARS-Cov2-E).The monomeric unit of SARS-Cov2-E was modelled from a close homologue (>90% sequence identity) and a pentameric assembly was modelled using symmetric docking, followed by energy minimization in a DPPC membrane environment. The minimized structure was used to generate best scoring SARS-Cov2-E-CDC/UDC complexes through blind docking. These complexes were subjected to 230 ns molecular dynamics simulations in triplicates in a DPPC membrane environment. Comparative analyses of structural properties and molecular interaction profiles from the MD trajectories revealed that, both CDC and UDC could stably bind to SARS-Cov2-E through H-bonds, water-bridges and hydrophobic contacts with the transmembrane-channelresidues.T30 was observed to be a key residue for CDC/UDC binding. CDC/UDC binding affected the H-bonding pattern between adjacent monomeric chains, slackening the compact transmembrane region of SARS-Cov2-E. Additionally, the polar functional groups of CDC/UDC facilitated entry of a large number of water molecules into the channel. These observations suggest CDC/UDC as potential candidates to hinder the survival of SARS-Cov2 by disrupting the structure of SARS-Cov2-E and facilitating the entry of solvents/polar inhibitors inside the viral cell.Communicated by Ramaswamy H. Sarma.

How adding a single methylene to dihydrofolate reductase can change its conformational dynamics

Studies of the effects of pressure on proteins from piezophilic (pressure-loving) microbes compared with homologous proteins from mesophilic microbes have been relatively rare. Interestingly, such studies of dihydrofolate reductase show that a single-site mutation from an aspartic acid to a glutamic acid can reverse the pressure-dependent monotonic decrease in activity to that in a monotonic pressure-dependent activation. This residue is near the active site but is not thought to directly participate in the catalytic mechanism. Here, the ways that addition of one carbon to the entire protein could lead to such a profound difference in pressure effects are explored using molecular dynamics simulations. The results indicate that the glutamate changes the coupling between a helix and the β-sheet due to the extra flexibility of the side chain, which further changes correlated motions of other regions of the protein.

Inter-domain dynamics drive cholesterol transport by NPC1 and NPC1L1 proteins

Transport of LDL-derived cholesterol from lysosomes into the cytoplasm requires NPC1 protein; NPC1L1 mediates uptake of dietary cholesterol. We introduced single disulfide bonds into NPC1 and NPC1L1 to explore the importance of inter-domain dynamics in cholesterol transport. Using a sensitive method to monitor lysosomal cholesterol efflux, we found that NPC1's N-terminal domain need not release from the rest of the protein for efficient cholesterol export. Either introducing single disulfide bonds to constrain lumenal/extracellular domains or shortening a cytoplasmic loop abolishes transport activity by both NPC1 and NPC1L1. The widely prescribed cholesterol uptake inhibitor, ezetimibe, blocks NPC1L1; we show that residues that lie at the interface between NPC1L1's three extracellular domains comprise the drug's binding site. These data support a model in which cholesterol passes through the cores of NPC1/NPC1L1 proteins; concerted movement of various domains is needed for transfer and ezetimibe blocks transport by binding to multiple domains simultaneously.

Cholesterol Transport in Wild-Type NPC1 and P691S: Molecular Dynamics Simulations Reveal Changes in Dynamical Behavior

The Niemann–Pick C1 (NPC1) protein is the main protein involved in NPC disease, a fatal lysosomal lipid storage disease. NPC1, containing 1278 amino acids, is comprised of three lumenal domains (N-terminal, middle lumenal, C-terminal) and a transmembrane (TM) domain that contains a five helix bundle referred to as the sterol-sensing domain (SSD). The exact purpose of the SSD is not known, but it is believed that the SSD may bind cholesterol, either as a part of the lipid trafficking pathway or as part of a signaling mechanism. A recent cryo-EM structure has revealed an itraconazole binding site (IBS) in the SSD of human NPC1. Using this structural data, we constructed a model of cholesterol-bound wild-type (WT) and mutant P691S and performed molecular dynamics (MD) simulations of each cholesterol-bound protein. For WT NPC1, cholesterol migrates laterally, in the direction of the lipid bilayer. In the case of P691S, cholesterol is observed for the first time to migrate away from the SSD toward the N-terminal domain via a putative tunnel that connects the IBS with the lumenal domains. Structural features of the IBS are analyzed to identify the causes for different dynamical behavior between cholesterol-bound WT and cholesterol-bound P691S. The side chain of Ser691 in the P691S mutant introduces a hydrogen bond network that is not present in the WT protein. This change is likely responsible for the altered dynamical behavior observed in the P691S mutant and helps explain the disrupted cholesterol trafficking behavior observed in experiments.

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.

Entropic allostery dominates the phosphorylation-dependent regulation of Syk tyrosine kinase release from immunoreceptor tyrosine-based activation motifs

Spleen tyrosine kinase (Syk) is an essential player in immune signaling through its ability to couple multiple classes of membrane immunoreceptors to intracellular signaling pathways. Ligand binding leads to the recruitment of Syk to a phosphorylated cytoplasmic region of the receptors called ITAM. Syk binds to ITAM with high-affinity (nanomolar Kd ) via its tandem pair of SH2 domains. The affinity between Syk and ITAM is allosterically regulated by phosphorylation at Y130 in a linker connecting the tandem SH2 domains; when Y130 is phosphorylated, the binding affinity decreases (micromolar Kd ). Previous equilibrium binding studies attribute the increase in the binding free energy to an intra-molecular binding (isomerization) step of the tandem SH2 and ITAM, but a physical basis for the increased free energy is unknown. Here, we provide evidence that Y130 phosphorylation imposes an entropy penalty to isomerization, but surprisingly, has negligible effect on the SH2 binding interactions with ITAM and thus on the binding enthalpy. An analysis of NMR chemical shift differences characterized conformational effects of ITAM binding, and binding thermodynamics were measured from isothermal titration calorimetry. Together the data support a previously unknown mechanism for the basis of regulating protein-protein interactions through protein phosphorylation. The decreased affinity for Syk association with immune receptor ITAMs by Y130 phosphorylation is an allosteric mechanism driven by an increased entropy penalty, likely contributed by conformational disorder in the SH2-SH2 inter-domain structure, while SH2-ITAM binding contacts are not affected, and binding enthalpy is unchanged.

Oscillatory Diffusion and Second-Order Cyclostationarity in Alanine Tripeptide from Molecular Dynamics Simulation

Molecular dynamics (MD) simulation distinctly describes motions of biomolecules at high resolution and can potentially be used to explain allosteric mechanism in subcellular processes. Statistical methods are necessary to realize this potential because MD simulations generate a large volume of data and because the analysis is never efficient, objective, or thorough without using appropriate statistical approaches. Tracing the flow of information within a biomolecule requires not only a description of an overall mechanism but also a multiscale statistical description from atomic interactions to the overall mechanism. The foundation of this multiscale description, in general, is a measure of correlation between motions of atoms or residues, as reflected by dynamic cross-correlation, Pearson correlation, or mutual information. However, these correlations can be inadequate because they assume wide sense stationarity, which means that the instantaneous average and correlation of a particular property are time-independent. Consequently, these measures of correlation cannot account for correlation between motions of different frequencies, since frequency implies oscillation and variation over time. Here, we characterize the nonstationarity in the form of pure oscillatory instantaneous variance in the signed dihedral angular accelerations (SDAA) along the main chain of alanine tripeptide in MD simulations by power spectrum, corrected squared envelope spectrum (CSES), and cross-CSES. This oscillation has a physical interpretation of an oscillatory diffusion. The fraction of this oscillation in all motions is as high as about 40% at some frequencies. This shows that oscillatory instantaneous variance exists in the SDAA and that significant correlation may not be accounted for in current correlation analysis. This oscillation is also found to transmit between dihedral angles. These results could have implications in the understanding of the dynamics of biomolecules.

Analysis of Multidomain Protein Dynamics

Proteins with a modular architecture of multiple domains connected by linkers often exhibit diversity in the relative positions of domains, while the domain tertiary structure remains unchanged. The biological function of these modular proteins, or the regulation of their activity, depends on the variation in domain orientation and separation. Accordingly, careful characterization of interdomain motion and correlated fluctuations of multidomain systems is relevant for understanding the functional behavior of modular proteins. Molecular dynamics (MD) simulations provides a powerful approach to study these motions in atomic detail. Nevertheless, the common procedure for analyzing fluctuations from MD simulations after rigid-body alignment fails for multidomain proteins; it greatly overestimates correlated positional fluctuations in the presence of relative domain motion. We show here that expressing the atomic motions of a multidomain protein as a combination of displacement within the domain reference frame and motion of the relative domains correctly separates the internal motions to allow a useful description of correlated fluctuations. We illustrate the methodology of separating the domain fluctuations and local fluctuations by application to the tandem SH2 domains of human Syk protein kinase and by characterizing an effect of phosphorylation on the dynamics. Correlated motions are assessed from a distance covariance rather than the more common vector-coordinate covariance. The approach makes it possible to calculate the proper correlations in fluctuations internal to a domain as well as between domains.

(Dis)similarity Index To Compare Correlated Motions in Molecular Simulations

Molecular dynamics (MD) simulations are widely used to complement or guide experimental studies in the characterization of protein dynamics, thanks to improvements in force-field accuracy, along with in the software and hardware to sample the conformational landscape of proteins. Among the different applications of MD simulations, the study of correlated motions is largely employed for different purposes. Several metrics have been developed to describe correlated motions in the MD ensemble, such as methods based on Pearson Correlation or Mutual Information. Cross-correlation analysis of MD trajectories is indeed appealing not only to identify residues characterized by coupled fluctuations in protein structures but also since it can be used to extrapolate motions along directions in which major conformational changes should occur, for example on longer time scales than the ones that are actually simulated. Nevertheless, most of the MD studies employ average correlation maps and mostly in a qualitative way, even when different systems or different replicates of the same system are compared. The broad application of correlation metrics in the analysis of MD simulations, especially for comparative purposes, requires a step forward toward more quantitative and accurate comparisons. We thus here employed a simple but effective index, which is based on a normalized Frobenius norm of the differences between protein correlation maps, to compare correlated motions. We applied this index for a quantitative comparison of correlated motions from MD simulations of seven proteins of different size and fold. We also employed the index to assess the robustness of correlation description when multi-replicate MD simulations of a same system are used, and we compared our index to metrics for comparison of structural ensembles such as Root Mean Square Inner Product and the Bhattacharyya Coefficient.

Reverse engineering and identification in systems biology: strategies, perspectives and challenges

The interplay of mathematical modelling with experiments is one of the central elements in systems biology. The aim of reverse engineering is to infer, analyse and understand, through this interplay, the functional and regulatory mechanisms of biological systems. Reverse engineering is not exclusive of systems biology and has been studied in different areas, such as inverse problem theory, machine learning, nonlinear physics, (bio)chemical kinetics, control theory and optimization, among others. However, it seems that many of these areas have been relatively closed to outsiders. In this contribution, we aim to compare and highlight the different perspectives and contributions from these fields, with emphasis on two key questions: (i) why are reverse engineering problems so hard to solve, and (ii) what methods are available for the particular problems arising from systems biology?

Quantification of Drive-Response Relationships Between Residues During Protein Folding

Mutual correlation and cooperativity are commonly used to describe residue-residue interactions in protein folding/function. However, these metrics do not provide any information on the causality relationships between residues. Such drive-response relationships are poorly studied in protein folding/function and difficult to measure experimentally due to technical limitations. In this study, using the information theory transfer entropy (TE) that provides a direct measurement of causality between two times series, we have quantified the drive-response relationships between residues in the folding/unfolding processes of four small proteins generated by molecular dynamics simulations. Instead of using a time-averaged single TE value, the time-dependent TE is measured with the Q-scores based on residue-residue contacts and with the statistical significance analysis along the folding/unfolding processes. The TE analysis is able to identify the driving and responding residues that are different from the highly correlated residues revealed by the mutual information analysis. In general, the driving residues have more regular secondary structures, are more buried, and show greater effects on the protein stability as well as folding and unfolding rates. In addition, the dominant driving and responding residues from the TE analysis on the whole trajectory agree with those on a single folding event, demonstrating that the drive-response relationships are preserved in the non-equilibrium process. Our study provides detailed insights into the protein folding process and has potential applications in protein engineering and interpretation of time-dependent residue-based experimental observables for protein function.

Reverse engineering cellular networks with information theoretic methods

Building mathematical models of cellular networks lies at the core of systems biology. It involves, among other tasks, the reconstruction of the structure of interactions between molecular components, which is known as network inference or reverse engineering. Information theory can help in the goal of extracting as much information as possible from the available data. A large number of methods founded on these concepts have been proposed in the literature, not only in biology journals, but in a wide range of areas. Their critical comparison is difficult due to the different focuses and the adoption of different terminologies. Here we attempt to review some of the existing information theoretic methodologies for network inference, and clarify their differences. While some of these methods have achieved notable success, many challenges remain, among which we can mention dealing with incomplete measurements, noisy data, counterintuitive behaviour emerging from nonlinear relations or feedback loops, and computational burden of dealing with large data sets.