Long-range correlation in protein dynamics: Confirmation by structural data and normal mode analysis

Modulation of the conformational landscape of the PDZ3 domain by perturbation on a distal non-canonical α3 helix: decoding the microscopic mechanism of allostery in the PDZ3 domain

While allosteric signal transduction is crucial for protein signaling and regulation, the dynamic process of allosteric communication remains poorly understood. The third PDZ domain (PDZ stands for the common structural domain shared by the postsynaptic density protein (PSD95), Drosophila disc large tumor suppressor (DlgA), and zonula occludens-1 protein (ZO-1)) serves as a classic example of a single-domain allosteric protein, demonstrating a long-range coupling between the C-terminal α helix (known as the α3 helix) and ligand binding. A molecular level understanding of how the α3 helix modulates the ligand binding affinity of the PDZ3 domain is still lacking. In this study, extensive molecular dynamics simulations corroborated with principal component analysis (PCA), ligand binding free energy calculations, energetic frustration analysis and Markov state model analysis are employed to uncover such molecular details. We demonstrate the definite presence of a binding competent closed-like state in the conformational landscape of wild-type PDZ3. The population modulations of this closed state and other binding incompetent states in the landscape due to α3-truncation/mutation of PDZ3 are explored. A correlation between the closed state population and calculated binding free energy is established, which supports the conformation selection mechanism. Covariance analysis identified the presence of correlated motion between two distant loops (β1-β2 and β2-β3) in the wild-type PDZ3 system, which weakened due to truncation/mutation in the distant α3 helix. It has also been observed that whenever the α3 helix was perturbed, the β2-β3 loop got further away from the binding groove and it is found to be correlated with the binding free energy values. Energetic frustration analysis of the PDZ3 domain also showed that the β2-β3 loop is highly frustrated. Finally, MSM analysis revealed a relevant timescale (closed to open state transition), which is similar to the observed experimental signal transduction timescale for the system. These observations led to the conclusion that the distantly located α3 helix plays a pivotal role in regulating the conformational landscape of the PDZ3 domain, determining the ligand binding affinity and resulting in allosteric behavior of the domain.

Computational Analysis of the Accumulation of Mutations in Therapeutically Important RNA Viral Proteins During Pandemics with Special Emphasis on SARS-CoV-2

Single stranded RNA viruses are primary causative agents for pandemics, causing extensive morbidity and mortality worldwide. A pivotal question in pandemic preparedness and therapeutic intervention is what are the specific mutations which are more likely to emerge during such global health crises? This study aims to identify markers for mutations with the highest probability of emergence in these pandemics, focusing on the SARS-CoV-2 spike protein, an essential and therapeutically significant viral protein, starting from sequence information from the onset of the pandemic until July 2022. Quite consistently, we observed that emerged mutations tended to demonstrate a high genetic score, which reflects high similarity of the type of codon required for translation between an amino acid and to the mutated one. Further, this pattern is also observed in therapeutically significant proteins of other ssRNA pandemic viruses, including influenza (HA, NA), spike proteins of Ebola, envelope of Dengue and Chikungunya. We propose that the genetic score serves as an initial indicator, preceding the actual impact of the mutation on viral fitness. Finally, we developed a comprehensive computational pipeline to further explore and predict the subsequent effects of mutations on viral fitness. We believe that our pipeline can narrow down and predict future mutations in therapeutically important viral proteins during a pandemic.

Evolutionary rewiring of the dynamic network underpinning allosteric epistasis in NS1 of influenza A virus

Viral proteins frequently mutate to evade or antagonize host innate immune responses, yet the impact of these mutations on the molecular energy landscape remains unclear. Epistasis, the intramolecular communications between mutations, often renders the combined mutational effects unpredictable. Nonstructural protein 1 (NS1) is a major virulence factor of the influenza A virus (IAV) that activates host PI3K by binding to its p85β subunit. Here, we present the deep analysis for the impact of evolutionary mutations in NS1 that emerged between the 1918 pandemic IAV strain and its descendant PR8 strain. Our analysis reveal how the mutations rewired inter-residue communications which underlies long-range allosteric and epistatic networks in NS1. Our findings show that PR8 NS1 binds to p85β with approximately 10-fold greater affinity than 1918 NS1 due to allosteric mutational effects. Notably, these mutations also exhibited long-range epistatic effects. NMR chemical shift perturbation and methyl-axis order parameter analyses revealed that the mutations induced long-range structural and dynamic changes in PR8 NS1, enhancing its affinity to p85β. Complementary MD simulations and graph-based network analysis uncover how these mutations rewire dynamic residue interaction networks, which underlies the long-range epistasis and allosteric effects on p85β-binding affinity. Significantly, we find that conformational dynamics of residues with high betweenness centrality play a crucial role in communications between network communities and are highly conserved across influenza A virus evolution. These findings advance our mechanistic understanding of the allosteric and epistatic communications between distant residues and provides insight into their role in the molecular evolution of NS1.

A strategy for Cas13 miniaturization based on the structure and AlphaFold

The small size of the Cas nuclease fused with various effector domains enables a broad range of function. Although there are several ways of reducing the size of the Cas nuclease complex, no efficient or generalizable method has been demonstrated to achieve protein miniaturization. In this study, we establish an Interaction, Dynamics and Conservation (IDC) strategy for protein miniaturization and generate five compact variants of Cas13 with full RNA binding and cleavage activity comparable the wild-type enzymes based on a combination of IDC strategy and AlphaFold2. In addition, we construct an RNA base editor, mini-Vx, and a single AAV (adeno-associated virus) carrying a mini-RfxCas13d and crRNA expression cassette, which individually shows efficient conversion rate and RNA-knockdown activity. In summary, these findings highlight a feasible strategy for generating downsized CRISPR/Cas13 systems based on structure predicted by AlphaFold2, enabling targeted degradation of RNAs and RNA editing for basic research and therapeutic applications.

Increasing the O2 Resistance of the [FeFe]-Hydrogenase CbA5H through Enhanced Protein Flexibility

The high turnover rates of [FeFe]-hydrogenases under mild conditions and at low overpotentials provide a natural blueprint for the design of hydrogen catalysts. However, the unique active site (H-cluster) degrades upon contact with oxygen. The [FeFe]-hydrogenase fromClostridium beijerinckii (CbA5H) is characterized by the flexibility of its protein structure, which allows a conserved cysteine to coordinate to the active site under oxidative conditions. Thereby, intrinsic cofactor degradation induced by dioxygen is minimized. However, the protection from O₂ is only partial, and the activity of the enzyme decreases upon each exposure to O₂. By using site-directed mutagenesis in combination with electrochemistry, ATR-FTIR spectroscopy, and molecular dynamics simulations, we show that the kinetics of the conversion between the oxygen-protected inactive state (cysteine-bound) and the oxygen-sensitive active state can be accelerated by replacing a surface residue that is very distant from the active site. This sole exchange of methionine for a glutamate residue leads to an increased resistance of the hydrogenase to dioxygen. With our study, we aim to understand how local modifications of the protein structure can have a crucial impact on protein dynamics and how they can control the reactivity of inorganic active sites through outer sphere effects.

Finite-size correlation behavior near a critical point: A simple metric for monitoring the state of a neural network

In this article, a correlation metric κ_{c} is proposed for the inference of the dynamical state of neuronal networks. κ_{C} is computed from the scaling of the correlation length with the size of the observation region, which shows qualitatively different behavior near and away from the critical point of a continuous phase transition. The implementation is first studied on a neuronal network model, where the results of this new metric coincide with those obtained from neuronal avalanche analysis, thus well characterizing the critical state of the network. The approach is further tested with brain optogenetic recordings in behaving mice from a publicly available database. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

The recent development of artificial intelligence provides us with new and powerful tools for studying the mysterious relationship between organism evolution and protein evolution. In this work, based on the AlphaFold Protein Structure Database (AlphaFold DB), we perform comparative analyses of the proteins of different organisms. The statistics of AlphaFold-predicted structures show that, for organisms with higher complexity, their constituent proteins will have larger radii of gyration, higher coil fractions, and slower vibrations, statistically. By conducting normal mode analysis and scaling analyses, we demonstrate that higher organismal complexity correlates with lower fractal dimensions in both the structure and dynamics of the constituent proteins, suggesting that higher functional specialization is associated with higher organismal complexity. We also uncover the topology and sequence bases of these correlations. As the organismal complexity increases, the residue contact networks of the constituent proteins will be more assortative, and these proteins will have a higher degree of hydrophilic-hydrophobic segregation in the sequences. Furthermore, by comparing the statistical structural proximity across the proteomes with the phylogenetic tree of homologous proteins, we show that, statistical structural proximity across the proteomes may indirectly reflect the phylogenetic proximity, indicating a statistical trend of protein evolution in parallel with organism evolution. This study provides new insights into how the diversity in the functionality of proteins increases and how the dimensionality of the manifold of protein dynamics reduces during evolution, contributing to the understanding of the origin and evolution of lives.

Functional Loop Dynamics and Characterization of the Inactive State of the NS2B-NS3 Dengue Protease due to Allosteric Inhibitor Binding

Dengue virus, a flavivirus that causes dengue shock syndrome and dengue hemorrhagic fever, is currently prevalent worldwide. A two-component protease (NS2B-NS3) is essential for maturation, representing an important target for designing anti-flavivirus drugs. Previously, consideration has been centered on developing active-site inhibitors of NS2B-NS3pro. However, the flat and charged nature of its active site renders difficulties in developing inhibitors, suggesting an alternative strategy for identifying allosteric inhibitors. The allosterically sensitive site of the dengue protease is located near Ala125, between the 120s loop and 150s loop. Using atomistic molecular dynamics simulations, we have explored the protease's conformational dynamics upon binding of an allosteric inhibitor. Furthermore, characterization of the inherent flexible loops (71-75s loop, 120s loop, and 150s loop) is carried out for allosteric-inhibitor-bound wild-type and mutant A125C variants and a comparison is performed with its unbound state to extract the structural changes describing the inactive state of the protease. Our study reveals that compared to the unliganded system, the inhibitor-bound system shows large structural changes in the 120s loop and 150s loop in contrast to the rigid 71-75s loop. The unliganded system shows a closed-state pocket in contrast to the open state for the wild-type complex that locks the protease into the open and inactive-state conformations. However, the mutant complex fluctuates between open and closed states. Also, we tried to see how mutation and binding of an allosteric inhibitor perturb the connectivity in a protein structure network (PSN) at contact levels. Altogether, our study reveals the mechanism of conformational rearrangements of loops at the molecular level, locking the protein in an inactive conformation, which may be useful for developing allosteric inhibitors.

Edge weights in a protein elastic network reorganize collective motions and render long-range sensitivity responses

The effects of inter-residue interactions on protein collective motions are analyzed by comparing two elastic network models (ENM)—structural contact ENM (SC-ENM) and molecular dynamics (MD)-ENM—with the edge weights computed from an all-atom MD trajectory by structure-mechanics statistical learning. A theoretical framework is devised to decompose the eigenvalues of ENM Hessian into contributions from individual springs and to compute the sensitivities of positional fluctuations and covariances to spring constant variation. Our linear perturbation approach quantifies the response mechanisms as softness modulation and orientation shift. All contacts of C α positions in SC-ENM have an identical spring constant by fitting the profile of root-of-mean-squared-fluctuation calculated from an all-atom MD simulation, and the same trajectory data are also used to compute the specific spring constant of each contact as an MD-ENM edge weight. We illustrate that the soft-mode reorganization can be understood in terms of gaining weights along the structural contacts of low elastic strengths and loosing magnitude along those of high rigidities. With the diverse mechanical strengths encoded in protein dynamics, MD-ENM is found to have more pronounced long-range couplings and sensitivity responses with orientation shift identified as a key player in driving the specific residues to have high sensitivities. Furthermore, the responses of perturbing the springs of different residues are found to have asymmetry in the action–reaction relationship. In understanding the mutation effects on protein functional properties, such as long-range communications, our results point in the directions of collective motions as a major effector.

Inferring couplings in networks across order-disorder phase transitions

Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods, and the structure in the data. To this end, we characterize the efficacy of direct coupling analysis (DCA) - a highly successful method for analyzing amino acid sequence data-in inferring pairwise interactions from samples of ferromagnetic Ising models on random graphs. Our approach allows for physically motivated exploration of qualitatively distinct data regimes separated by phase transitions. We show that inference quality depends strongly on the nature of data-generating distributions: optimal accuracy occurs at an intermediate temperature where the detrimental effects from macroscopic order and thermal noise are minimal. Importantly our results indicate that DCA does not always outperform its local-statistics-based predecessors; while DCA excels at low temperatures, it becomes inferior to simple correlation thresholding at virtually all temperatures when data are limited. Our findings offer insights into the regime in which DCA operates so successfully, and more broadly, how inference interacts with the structure in the data.

Functional Dynamics of Substrate Recognition in TEM Beta-Lactamase

The beta-lactamase enzyme provides effective resistance to beta-lactam antibiotics due to substrate recognition controlled by point mutations. Recently, extended-spectrum and inhibitor-resistant mutants have become a global health problem. Here, the functional dynamics that control substrate recognition in TEM beta-lactamase are investigated using all-atom molecular dynamics simulations. Comparisons are made between wild-type TEM-1 and TEM-2 and the extended-spectrum mutants TEM-10 and TEM-52, both in apo form and in complex with four different antibiotics (ampicillin, amoxicillin, cefotaxime and ceftazidime). Dynamic allostery is predicted based on a quasi-harmonic normal mode analysis using a perturbation scan. An allosteric mechanism known to inhibit enzymatic function in TEM beta-lactamase is identified, along with other allosteric binding targets. Mechanisms for substrate recognition are elucidated using multivariate comparative analysis of molecular dynamics trajectories to identify changes in dynamics resulting from point mutations and ligand binding, and the conserved dynamics, which are functionally important, are extracted as well. The results suggest that the H10-H11 loop (residues 214-221) is a secondary anchor for larger extended spectrum ligands, while the H9-H10 loop (residues 194-202) is distal from the active site and stabilizes the protein against structural changes. These secondary non-catalytically-active loops offer attractive targets for novel noncompetitive inhibitors of TEM beta-lactamase.

Quantitative Analysis of Dynamic Allostery

Dynamic allostery refers to one important class of allosteric regulation that does not involve noticeable conformational changes upon effector binding. In recent years, many "quasi"-dynamic allosteric proteins have been found to only experience subtle conformational changes during allosteric regulation. However, as enthalpic and entropic contributions are coupled to each other and even tiny conformational changes could bring in noticeable free energy changes, a quantitative description is essential to understand the contribution of pure dynamic allostery. Here, by developing a unified anisotropic elastic network model (uANM) considering both side-chain information and ligand heavy atoms, we quantitatively estimated the contribution of pure dynamic allostery in a dataset of known allosteric proteins by excluding the conformational changes upon ligand binding. We found that the contribution of pure dynamic allostery is generally small (much weaker than previously expected) and robustly exhibits an allosteric activation effect, which exponentially decays with the distance between the substrate and the allosteric ligand. We further constructed toy models to study the determinant factors of dynamic allostery in monomeric and oligomeric proteins using the uANM. Analysis of the toy models revealed that a short distance, a small angle between the two ligands, strong protein-ligand interactions, and weak protein internal interactions lead to strong dynamic allostery. Our study provides a quantitative estimation of pure dynamic allostery and facilitates the understanding of dynamic-allostery-controlled biological processes and the design of allosteric drugs and proteins.

Information-theoretic approach in allometric scaling relations of DNA and proteins

Allometric scaling relations can be observed in between molecular parameters. Hence, we looked for presence of such relation among sizes (i.e., lengths) of proteins and genes. Protein lengths exist in the literature as the number of amino acids. They can also be derived from the mRNA lengths. Here, we looked for allometric scaling relation by using such data and simultaneously, the data was compared with the sizes of genes and proteins that were obtained from our modified information-theoretic approach. Results implied presence of scaling relation in the calculated results. This was expected due to the implemented modification in the information-theoretic calculation. Relation in the literature-based data was lacking high goodness of fit value. It could be due to physical factors and selective pressures, which ended up in deviations of the literature-sourced values from those in the model. Genome size is correlated with cell size. Intracellular volume, which is related to the DNA size, would require certain number of proteins, the sizes of which can therefore be correlated with the protein sizes. Cell sizes, genome sizes, and average protein and gene sizes, along with the number of proteins, namely the expression levels of the genes, are the physical factors, and the molecular factors influence those physical factors. The selective pressures on those can act through the connection between those physical factors and limit the dynamic ranges. Biological measures could be prone to such forces and are likely to deviate from expected models, regardless of the validity of assumptions, unless those are also implemented in the models. Yet, present discrepancies could be pointing at the need for model improvement, data imperfection, invalid assumptions, etc. Still, current work highlights possible use of information-theoretic approach in allometric scaling relations' studies.

Dynamics-Evolution Correspondence in Protein Structures

The genotype-phenotype mapping of proteins is a fundamental question in structural biology. In this Letter, with the analysis of a large dataset of proteins from hundreds of protein families, we quantitatively demonstrate the correlations between the noise-induced protein dynamics and mutation-induced variations of native structures, indicating the dynamics-evolution correspondence of proteins. Based on the investigations of the linear responses of native proteins, the origin of such a correspondence is elucidated. It is essential that the noise- and mutation-induced deformations of the proteins are restricted on a common low-dimensional subspace, as confirmed from the data. These results suggest an evolutionary mechanism of the proteins gaining both dynamical flexibility and evolutionary structural variability.

Box scaling as a proxy of finite size correlations

The scaling of correlations as a function of size provides important hints to understand critical phenomena on a variety of systems. Its study in biological structures offers two challenges: usually they are not of infinite size, and, in the majority of cases, dimensions can not be varied at will. Here we discuss how finite-size scaling can be approximated in an experimental system of fixed and relatively small extent, by computing correlations inside of a reduced field of view of various widths (we will refer to this procedure as "box-scaling"). A relation among the size of the field of view, and measured correlation length, is derived at, and away from, the critical regime. Numerical simulations of a neuronal network, as well as the ferromagnetic 2D Ising model, are used to verify such approximations. Numerical results support the validity of the heuristic approach, which should be useful to characterize relevant aspects of critical phenomena in biological systems.

Modelling conformational state dynamics and its role on infection for SARS-CoV-2 Spike protein variants

The SARS-CoV-2 Spike protein needs to be in an open-state conformation to interact with ACE2 to initiate viral entry. We utilise coarse-grained normal mode analysis to model the dynamics of Spike and calculate transition probabilities between states for 17081 variants including experimentally observed variants. Our results correctly model an increase in open-state occupancy for the more infectious D614G via an increase in flexibility of the closed-state and decrease of flexibility of the open-state. We predict the same effect for several mutations on glycine residues (404, 416, 504, 252) as well as residues K417, D467 and N501, including the N501Y mutation recently observed within the B.1.1.7, 501.V2 and P1 strains. This is, to our knowledge, the first use of normal mode analysis to model conformational state transitions and the effect of mutations on such transitions. The specific mutations of Spike identified here may guide future studies to increase our understanding of SARS-CoV-2 infection mechanisms and guide public health in their surveillance efforts.

The present work explores the molecular mechanisms underlying and potentially helping new strains of SARS-CoV-2 to gain an evolutionary advantage during the ongoing COVID-19 pandemics. We show how a computational method called normal mode analysis that treats protein dynamics in a simplified manner is capable to predict the higher propensity of the Spike protein to be in the open state in which it is capable to interact with the human ACE2 receptor and thus facilitate cell entry. Because the simulation of the simplified computational model is relatively less demanding on resources than alternative methods, we were able to simulate over 17000 mutations in the SARS-CoV-2 Spike protein to identify multiple mutations that if they were to appear as the virus continues to evolve, could confer an evolutionary advantage. As a matter of fact, our predictions foresaw the emergence of particular mutations such as N501Y that appeared in several variants of concern. Our results can inform public health regarding new variants and serves as a proof of concept for the application of normal mode analysis to study the effect of mutations on both, protein dynamics and conformational transitions in a high-throughput manner.

Comparative protein structure network analysis on 3CLpro from SARS-CoV-1 and SARS-CoV-2

The main protease M^pro, 3CL^pro is an important target from coronaviruses. In spite of having 96% sequence identity among M^pros from SARS‐CoV‐1 and SARS‐CoV‐2; the inhibitors used to block the activity of SARS‐CoV‐1 M^pro so far, were found to have differential inhibitory effect on M^pro of SARS‐CoV‐2. The possible reason could be due to the difference of few amino acids among the peptidases. Since, overall 3‐D crystallographic structure of M^pro from SARS‐CoV‐1 and SARS‐CoV‐2 is quite similar and mapping a subtle structural variation is seemingly impossible. Hence, we have attempted to study a structural comparison of SARS‐CoV‐1 and SARS‐CoV‐2 M^pro in apo and inhibitor bound states using protein structure network (PSN) based approach at contacts level. The comparative PSNs analysis of apo M^pros from SARS‐CoV‐1 and SARS‐CoV‐2 uncovers small but significant local changes occurring near the active site region and distributed throughout the structure. Additionally, we have shown how inhibitor binding perturbs the PSG and the communication pathways in M^pros. Moreover, we have also investigated the network connectivity on the quaternary structure of M^pro and identified critical residue pairs for complex formation using three centrality measurement parameters along with the modularity analysis. Taken together, these results on the comparative PSN provide an insight into conformational changes that may be used as an additional guidance towards specific drug development.

Dynamical Correlations Reveal Allosteric Sites in G Protein-Coupled Receptors

G protein-coupled Receptors (GPCRs) play a central role in many physiological processes and, consequently, constitute important drug targets. In particular, the search for allosteric drugs has recently drawn attention, since they could be more selective and lead to fewer side effects. Accordingly, computational tools have been used to estimate the druggability of allosteric sites in these receptors. In spite of many successful results, the problem is still challenging, particularly the prediction of hydrophobic sites in the interface between the protein and the membrane. In this work, we propose a complementary approach, based on dynamical correlations. Our basic hypothesis was that allosteric sites are strongly coupled to regions of the receptor that undergo important conformational changes upon activation. Therefore, using ensembles of experimental structures, normal mode analysis and molecular dynamics simulations we calculated correlations between internal fluctuations of different sites and a collective variable describing the activation state of the receptor. Then, we ranked the sites based on the strength of their coupling to the collective dynamics. In the β2 adrenergic (β2AR), glucagon (GCGR) and M2 muscarinic receptors, this procedure allowed us to correctly identify known allosteric sites, suggesting it has predictive value. Our results indicate that this dynamics-based approach can be a complementary tool to the existing toolbox to characterize allosteric sites in GPCRs.

Predicting the stability of mutant proteins by computational approaches: an overview

A very large number of computational methods to predict the change in thermodynamic stability of proteins due to mutations have been developed during the last 30 years, and many different web servers are currently available. Nevertheless, most of them suffer from severe drawbacks that decrease their general reliability and, consequently, their applicability to different goals such as protein engineering or the predictions of the effects of mutations in genetic diseases. In this review, we have summarized all the main approaches used to develop these tools, with a survey of the web servers currently available. Moreover, we have also reviewed the different assessments made during the years, in order to allow the reader to check directly the different performances of these tools, to select the one that best fits his/her needs, and to help naïve users in finding the best option for their needs.