Coarse-grained normal mode analysis in structural biology

Knot data analysis using multiscale Gauss link integral

In the past decade, topological data analysis has emerged as a powerful algebraic topology approach in data science. Although knot theory and related subjects are a focus of study in mathematics, their success in practical applications is quite limited due to the lack of localization and quantization. We address these challenges by introducing knot data analysis (KDA), a paradigm that incorporates curve segmentation and multiscale analysis into the Gauss link integral. The resulting multiscale Gauss link integral (mGLI) recovers the global topological properties of knots and links at an appropriate scale and offers a multiscale geometric topology approach to capture the local structures and connectivities in data. By integration with machine learning or deep learning, the proposed mGLI significantly outperforms other state-of-the-art methods across various benchmark problems in 13 intricately complex biological datasets, including protein flexibility analysis, protein-ligand interactions, human Ether-à-go-go-Related Gene potassium channel blockade screening, and quantitative toxicity assessment. Our KDA opens a research area-knot deep learning-in data science.

Analysis of mapping atomic models to coarse-grained resolution

Low-resolution coarse-grained (CG) models provide significant computational and conceptual advantages for simulating soft materials. However, the properties of CG models depend quite sensitively upon the mapping, M, that maps each atomic configuration, r, to a CG configuration, R. In particular, M determines how the configurational information of the atomic model is partitioned between the mapped ensemble of CG configurations and the lost ensemble of atomic configurations that map to each R. In this work, we investigate how the mapping partitions the atomic configuration space into CG and intra-site components. We demonstrate that the corresponding coordinate transformation introduces a nontrivial Jacobian factor. This Jacobian factor defines a labeling entropy that corresponds to the uncertainty in the atoms that are associated with each CG site. Consequently, the labeling entropy effectively transfers configurational information from the lost ensemble into the mapped ensemble. Moreover, our analysis highlights the possibility of resonant mappings that separate the atomic potential into CG and intra-site contributions. We numerically illustrate these considerations with a Gaussian network model for the equilibrium fluctuations of actin. We demonstrate that the spectral quality, Q, provides a simple metric for identifying high quality representations for actin. Conversely, we find that neither maximizing nor minimizing the information content of the mapped ensemble results in high quality representations. However, if one accounts for the labeling uncertainty, Q(M) correlates quite well with the adjusted configurational information loss, Îmap(M), that results from the mapping.

Genome structural dynamics: insights from Gaussian network analysis of Hi-C data

Characterization of the spatiotemporal properties of the chromatin is essential to gaining insights into the physical bases of gene co-expression, transcriptional regulation and epigenetic modifications. The Gaussian network model (GNM) has proven in recent work to serve as a useful tool for modeling chromatin structural dynamics, using as input high-throughput chromosome conformation capture data. We focus here on the exploration of the collective dynamics of chromosomal structures at hierarchical levels of resolution, from single gene loci to topologically associating domains or entire chromosomes. The GNM permits us to identify long-range interactions between gene loci, shedding light on the role of cross-correlations between distal regions of the chromosomes in regulating gene expression. Notably, GNM analysis performed across diverse cell lines highlights the conservation of the global/cooperative movements of the chromatin across different types of cells. Variations driven by localized couplings between genomic loci, on the other hand, underlie cell differentiation, underscoring the significance of the four-dimensional properties of the genome in defining cellular identity. Finally, we demonstrate the close relation between the cell type-dependent mobility profiles of gene loci and their gene expression patterns, providing a clear demonstration of the role of chromosomal 4D features in defining cell-specific differential expression of genes.

Molecular interaction studies of L-proline in water and ethanol at different temperatures using dielectric relaxation, refractive index and DFT methods

The complex dielectric permittivity of L-Proline in water and ethanol solutions with molar concentrations ranging from 0.025 M to 0.15 M was measured by open-ended coaxial probe technique. The measurements were carried out across a frequency span of 0.02 < ν/GHz < 20 and temperatures varying from 298.15 K to 323.15 K. The densities (ρ) and refractive index (nD) of the L-proline in aqueous and ethanol solutions were also determined to provide insights into the solute-solvent interactions in the system. The Havriliak-Negami equation was employed to compute the dielectric relaxation time of the mixtures. The relaxation time of L-Proline in an ethanol medium was found to be higher than that of L-Proline in an aqueous medium due to the greater degree of self-association of ethanol molecules. Additionally, the relaxation time of the mixtures lengthened with rising molar concentration, which is attributed to the presence of hydrogen bonds among L-Proline and aqueous/ethanol molecules. The strength of the hydrogen bond interaction of L-Proline in both mediums was calculated using single-point energy calculations employing IEFPCM/PCM solvation models through DFT/B3LYP and MP2 approaches with a 6-311 G ++ (d, p) basis set. The results were correlated with the hydrogen bond strength, Gibbs' free energy of activation parameter, and dipole-dipole interactions.Communicated by Ramaswamy H. Sarma.

Reused Protein Segments Linked to Functional Dynamics

Protein space is characterized by extensive recurrence, or "reuse," of parts, suggesting that new proteins and domains can evolve by mixing-and-matching of existing segments. From an evolutionary perspective, for a given combination to persist, the protein segments should presumably not only match geometrically but also dynamically communicate with each other to allow concerted motions that are key to function. Evidence from protein space supports the premise that domains indeed combine in this manner; we explore whether a similar phenomenon can be observed at the sub-domain level. To this end, we use Gaussian Network Models (GNMs) to calculate the so-called soft modes, or low-frequency modes of motion for a dataset of 150 protein domains. Modes of motion can be used to decompose a domain into segments of consecutive amino acids that we call "dynamic elements", each of which belongs to one of two parts that move in opposite senses. We find that, in many cases, the dynamic elements, detected based on GNM analysis, correspond to established "themes": Sub-domain-level segments that have been shown to recur in protein space, and which were detected in previous research using sequence similarity alone (i.e. completely independently of the GNM analysis). This statistically significant correlation hints at the importance of dynamics in evolution. Overall, the results are consistent with an evolutionary scenario where proteins have emerged from themes that need to match each other both geometrically and dynamically, e.g. to facilitate allosteric regulation.

Normal Mode Analysis Elicits Conformational Shifts in Proteins at Both Proximal and Distal Regions to the Phosphosite Stemming from Single-Site Phosphorylation

Phosphorylation, a fundamental biochemical switch, intricately regulates protein function and signaling pathways. Our study employs extensive computational structural analyses on a curated data set of phosphorylated and unphosphorylated protein pairs to explore the multifaceted impact of phosphorylation on protein conformation. Using normal mode analysis (NMA), we investigated changes in protein flexibility post-phosphorylation, highlighting an enhanced level of structural dynamism. Our findings reveal that phosphorylation induces not only local changes at the phosphorylation site but also extensive alterations in distant regions, showcasing its far-reaching influence on protein structure-dynamics. Through in-depth case studies on polyubiquitin B and glycogen synthase kinase-3 beta, we elucidate how phosphorylation at distinct sites leads to variable structural and dynamic modifications, potentially dictating functional outcomes. While phosphorylation largely preserves the residue motion correlation, it significantly disrupts low-frequency global modes, presenting a dualistic impact on protein dynamics. We also explored alterations in the total accessible surface area (ASA), emphasizing region-specific changes around phosphorylation sites. This study sheds light on phosphorylation-induced conformational changes, dynamic modulation, and surface accessibility alterations, leveraging an integrated computational approach with RMSD, NMA, and ASA, thereby contributing to a comprehensive understanding of cellular regulation and suggesting promising avenues for therapeutic interventions.

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.

Protein dynamics underlying allosteric regulation

Allostery is the mechanism by which information and control are propagated in biomolecules. It regulates ligand binding, chemical reactions, and conformational changes. An increasing level of experimental resolution and control over allosteric mechanisms promises a deeper understanding of the molecular basis for life and powerful new therapeutics. In this review, we survey the literature for an up-to-date biological and theoretical understanding of protein allostery. By delineating five ways in which the energy landscape or the kinetics of a system may change to give rise to allostery, we aim to help the reader grasp its physical origins. To illustrate this framework, we examine three systems that display these forms of allostery: allosteric inhibitors of beta-lactamases, thermosensation of TRP channels, and the role of kinetic allostery in the function of kinases. Finally, we summarize the growing power of computational tools available to investigate the different forms of allostery presented in this review.

Integrating Electron Paramagnetic Resonance Spectroscopy and Computational Modeling to Measure Protein Structure and Dynamics

Electron paramagnetic resonance (EPR) has become a powerful probe of conformational heterogeneity and dynamics of biomolecules. In this Review, we discuss different computational modeling techniques that enrich the interpretation of EPR measurements of dynamics or distance restraints. A variety of spin labels are surveyed to provide a background for the discussion of modeling tools. Molecular dynamics (MD) simulations of models containing spin labels provide dynamical properties of biomolecules and their labels. These simulations can be used to predict EPR spectra, sample stable conformations and sample rotameric preferences of label sidechains. For molecular motions longer than milliseconds, enhanced sampling strategies and de novo prediction software incorporating or validated by EPR measurements are able to efficiently refine or predict protein conformations, respectively. To sample large-amplitude conformational transition, a coarse-grained or an atomistic weighted ensemble (WE) strategy can be guided with EPR insights. Looking forward, we anticipate an integrative strategy for efficient sampling of alternate conformations by de novo predictions, followed by validations by systematic EPR measurements and MD simulations. Continuous pathways between alternate states can be further sampled by WE-MD including all intermediate states.

Normal mode analysis and comparative study of intrinsic dynamics of alcohol oxidase enzymes from GMC protein family

Glucose-Methanol-Choline (GMC) family enzymes are very important in catalyzing the oxidation of a wide range of structurally diverse substrates. Enzymes that constitute the GMC family, share a common tertiary fold but < 25% sequence identity. Cofactor FAD, FAD binding signature motif, and similar structural scaffold of the active site are common features of oxidoreductase enzymes of the GMC family. Protein functionality mainly depends on protein three-dimensional structures and dynamics. In this study, we used the normal mode analysis method to search the intrinsic dynamics of GMC family enzymes. We have explored the dynamical behavior of enzymes with unique substrate catabolism and active site characteristics from different classes of the GMC family. Analysis of individual enzymes and comparative ensemble analysis of enzymes from different classes has shown conserved dynamic motion at FAD binding sites. The present study revealed that GMC enzymes share a strong dynamic similarity (Bhattacharyya coefficient >90% and root mean squared inner product >52%) despite low sequence identity across the GMC family enzymes. The study predicts that local deformation energy between atoms of the enzyme may be responsible for the catalysis of different substrates. This study may help that intrinsic dynamics can be used to make meaningful classifications of proteins or enzymes from different organisms.Communicated by Ramaswamy H. Sarma.

Synergism between x-ray crystallography and NMR residual dipolar couplings in characterizing protein dynamics

The important role of structural dynamics in protein function is widely recognized. Thermal or B-factors and their anisotropy, seen in x-ray analysis of protein structures, report on the presence of atomic coordinate heterogeneity that can be attributed to motion. However, their quantitative evaluation in terms of protein dynamics by x-ray ensemble refinement remains challenging. NMR spectroscopy provides quantitative information on the amplitudes and time scales of motional processes. Unfortunately, with a few exceptions, the NMR data do not provide direct insights into the atomic details of dynamic trajectories. Residual dipolar couplings, measured by solution NMR, are very precise parameters reporting on the time-averaged bond-vector orientations and may offer the opportunity to derive correctly weighted dynamic ensembles of structures for cases where multiple high-resolution x-ray structures are available. Applications to the SARS-CoV-2 main protease, Mpro, and ubiquitin highlight this complementarity of NMR and crystallography for quantitative assessment of internal motions.

Internal Normal Mode Analysis Applied to RNA Flexibility and Conformational Changes

We investigated the capability of internal normal modes to reproduce RNA flexibility and predict observed RNA conformational changes and, notably, those induced by the formation of RNA-protein and RNA-ligand complexes. Here, we extended our iNMA approach developed for proteins to study RNA molecules using a simplified representation of the RNA structure and its potential energy. Three data sets were also created to investigate different aspects. Despite all the approximations, our study shows that iNMA is a suitable method to take into account RNA flexibility and describe its conformational changes opening the route to its applicability in any integrative approach where these properties are crucial.

Role of distal sites in enzyme engineering

The limitations associated with natural enzyme catalysis have triggered the rise of the field of protein engineering. Traditional rational design was based on the analysis of protein structural information and catalytic mechanisms to identify key active sites or ligand binding sites to reshape the substrate pocket. The role and significance of functional sites in the active center have been studied extensively. With a deeper understanding of the structure-catalysis relationship map, the entire protein molecule can be filled with residues that play a substantial role in its structure and function. However, the catalytic mechanism underlying distal mutations remains unclear. The aim of this review was to highlight the criticality of the distal site in enzyme engineering based on the following three aspects: What can distal mutations exert on function from mutability landscape? How do distal sites influence enzyme function? How to predict and design distal mutations? This review provides insights into the catalytic mechanism of enzymes from the global interaction network, knowledge from sequence-structure-dynamics-function relationships, and strategies for distal mutation-based protein engineering.

Surveying nonvisual arrestins reveals allosteric interactions between functional sites

Arrestins are important scaffolding proteins that are expressed in all vertebrate animals. They regulate cell-signaling events upon binding to active G-protein coupled receptors (GPCR) and trigger endocytosis of active GPCRs. While many of the functional sites on arrestins have been characterized, the question of how these sites interact is unanswered. We used anisotropic network modeling (ANM) together with our covariance compliment techniques to survey all the available structures of the nonvisual arrestins to map how structural changes and protein-binding affect their structural dynamics. We found that activation and clathrin binding have a marked effect on arrestin dynamics, and that these dynamics changes are localized to a small number of distant functional sites. These sites include α-helix 1, the lariat loop, nuclear localization domain, and the C-domain β-sheets on the C-loop side. Our techniques suggest that clathrin binding and/or GPCR activation of arrestin perturb the dynamics of these sites independent of structural changes.

Key Residues in δ Opioid Receptor Allostery Explored by the Elastic Network Model and the Complex Network Model Combined with the Perturbation Method

Opioid receptors, a kind of G protein-coupled receptors (GPCRs), mainly mediate an analgesic response via allosterically transducing the signal of endogenous ligand binding in the extracellular domain to couple to effector proteins in the intracellular domain. The δ opioid receptor (DOP) is associated with emotional control besides pain control, which makes it an attractive therapeutic target. However, its allosteric mechanism and key residues responsible for the structural stability and signal communication are not completely clear. Here we utilize the Gaussian network model (GNM) and amino acid network (AAN) combined with perturbation methods to explore the issues. The constructed fcfGNM_MD, where the force constants are optimized with the inverse covariance estimation based on the correlated fluctuations from the available DOP molecular dynamics (MD) ensemble, shows a better performance than traditional GNM in reproducing residue fluctuations and cross-correlations and in capturing functionally low-frequency modes. Additionally, fcfGNM_MD can consider implicitly the environmental effects to some extent. The lowest mode can well divide DOP segments and identify the two sodium ion (important allosteric regulator) binding coordination shells, and from the fastest modes, the key residues important for structure stabilization are identified. Using fcfGNM_MD combined with a dynamic perturbation-response method, we explore the key residues related to the sodium ion binding. Interestingly, we identify not only the key residues in sodium ion binding shells but also the ones far away from the perturbation sites, which are involved in binding with DOP ligands, suggesting the possible long-range allosteric modulation of sodium binding for the ligand binding to DOP. Furthermore, utilizing the weighted AAN combined with attack perturbations, we identify the key residues for allosteric communication. This work helps strengthen the understanding of the allosteric communication mechanism in δ opioid receptor and can provide valuable information for drug design.

Explicit versus implicit consideration of binding partners in protein-protein complex to elucidate intrinsic dynamics

The binding of many proteins to their protein partners is tightly regulated via control of their relative intrinsic dynamics during the binding process, a phenomenon which can in turn be modulated. Therefore, investigating the intrinsic dynamics of proteins is necessary to understand function in a comprehensive way. By intrinsic dynamics herein, we principally refer to the vibrational signature of a protein molecule popularly obtained from normal modes or essential modes. For normal modes, one often considers that the molecule under investigation is a collection of springs in a solvent-free or implicit-solvent medium. In the context of a protein-binding partner, the analysis of vibration of the target protein is often complicated due to molecular interaction within the complex. Generally, it is assumed that the isolated bound conformation of the target protein captures the implicit effect of the binding partner on the intrinsic dynamics, therefore suggesting that any influence of the partner molecule is also already integrated. Such an assumption allows large-scale studies of the conservation of protein flexibility. However, in cases where a partner protein directly influences the vibration of the target via critical contacts at the protein-protein interface, the above assumption falls short of providing a detailed view. In this review article, we discuss the implications of considering the dynamics of a protein in a protein-protein complex, as modelled implicitly and explicitly with methods dependent on elastic network models. We further propose how such an explicit consideration can be applied to understand critical protein-protein contacts that can be targeted in future studies.

Sequence-sensitive elastic network captures dynamical features necessary for miR-125a maturation

The Elastic Network Contact Model (ENCoM) is a coarse-grained normal mode analysis (NMA) model unique in its all-atom sensitivity to the sequence of the studied macromolecule and thus to the effect of mutations. We adapted ENCoM to simulate the dynamics of ribonucleic acid (RNA) molecules, benchmarked its performance against other popular NMA models and used it to study the 3D structural dynamics of human microRNA miR-125a, leveraging high-throughput experimental maturation efficiency data of over 26 000 sequence variants. We also introduce a novel way of using dynamical information from NMA to train multivariate linear regression models, with the purpose of highlighting the most salient contributions of dynamics to function. ENCoM has a similar performance profile on RNA than on proteins when compared to the Anisotropic Network Model (ANM), the most widely used coarse-grained NMA model; it has the advantage on predicting large-scale motions while ANM performs better on B-factors prediction. A stringent benchmark from the miR-125a maturation dataset, in which the training set contains no sequence information in common with the testing set, reveals that ENCoM is the only tested model able to capture signal beyond the sequence. This ability translates to better predictive power on a second benchmark in which sequence features are shared between the train and test sets. When training the linear regression model using all available data, the dynamical features identified as necessary for miR-125a maturation point to known patterns but also offer new insights into the biogenesis of microRNAs. Our novel approach combining NMA with multivariate linear regression is generalizable to any macromolecule for which relatively high-throughput mutational data is available.

Slow dynamics measured by phosphorescence lifetime reveals global conformational changes in human adult hemoglobin induced by allosteric effectors

The mechanism underlying allostery in hemoglobin (Hb) is still not completely understood. Various models describing the action of allosteric effectors on Hb function have been published in the literature. It has also been reported that some allosteric effectors-such as chloride ions, inositol hexaphosphate, 2,3-diphospho-glycerate and bezafibrate-considerably lower the oxygen affinity of Hb. In this context, an important question is the extent to which these changes influence the conformational dynamics of the protein. Earlier, we elaborated a challenging method based on phosphorescence quenching, which makes characterizing protein-internal dynamics possible in the ms time range. The experimental technique involves phosphorescence lifetime measurements in thermal equilibrium at varied temperatures from 10 K up to 273 K, based on the signal of Zn-protoporphyrin substituted for the heme in the β-subunits of Hb. The thermal activation of protein dynamics was observed by the enhancement of phosphorescence quenching attributed to O2 diffusion. It was shown that the thermal activation of protein matrix dynamics was clearly distinguishable from the dynamic activation of the aqueous solvent, and was therefore highly specific for the protein. In the present work, the same method was used to study the changes in the parameters of the dynamic activation of human HbA induced by binding allosteric effectors. We interpreted the phenomenon as phase transition between two states. The fitting of this model to lifetime data yielded the change of energy and entropy in the activation process and the quenching rate in the dynamically activated state. The fitted parameters were particularly sensitive to the presence of allosteric effectors and could be interpreted in line with results from earlier experimental studies. The results suggest that allosteric effectors are tightly coupled to the dynamics of the whole protein, and thus underline the importance of global dynamics in the regulation of Hb function.

Deep mutational scanning and machine learning reveal structural and molecular rules governing allosteric hotspots in homologous proteins

A fundamental question in protein science is where allosteric hotspots - residues critical for allosteric signaling - are located, and what properties differentiate them. We carried out deep mutational scanning (DMS) of four homologous bacterial allosteric transcription factors (aTFs) to identify hotspots and built a machine learning model with this data to glean the structural and molecular properties of allosteric hotspots. We found hotspots to be distributed protein-wide rather than being restricted to 'pathways' linking allosteric and active sites as is commonly assumed. Despite structural homology, the location of hotspots was not superimposable across the aTFs. However, common signatures emerged when comparing hotspots coincident with long-range interactions, suggesting that the allosteric mechanism is conserved among the homologs despite differences in molecular details. Machine learning with our large DMS datasets revealed global structural and dynamic properties to be a strong predictor of whether a residue is a hotspot than local and physicochemical properties. Furthermore, a model trained on one protein can predict hotspots in a homolog. In summary, the overall allosteric mechanism is embedded in the structural fold of the aTF family, but the finer, molecular details are sequence-specific.

Comprehensive evaluation of end-point free energy techniques in carboxylated-pillar[6]arene host-guest binding: I. Standard procedure

Despite the massive application of end-point free energy methods in protein-ligand and protein-protein interactions, computational understandings about their performance in relatively simple and prototypical host-guest systems are limited. In this work, we present a comprehensive benchmark calculation with standard end-point free energy techniques in a recent host-guest dataset containing 13 host-guest pairs involving the carboxylated-pillar[6]arene host. We first assess the charge schemes for solutes by comparing the charge-produced electrostatics with many ab initio references, in order to obtain a preliminary albeit detailed view of the charge quality. Then, we focus on four modelling details of end-point free energy calculations, including the docking procedure for the generation of initial condition, the charge scheme for host and guest molecules, the water model used in explicit-solvent sampling, and the end-point methods for free energy estimation. The binding thermodynamics obtained with different modelling schemes are compared with experimental references, and some practical guidelines on maximizing the performance of end-point methods in practical host-guest systems are summarized. Further, we compare our simulation outcome with predictions in the grand challenge and discuss further developments to improve the prediction quality of end-point free energy methods. Overall, unlike the widely acknowledged applicability in protein-ligand binding, the standard end-point calculations cannot produce useful outcomes in host-guest binding and thus are not recommended unless alterations are performed.

Local Normal Mode Analysis for Fast Loop Conformational Sampling

We propose and validate a novel method to efficiently explore local protein loop conformations based on a new formalism for constrained normal mode analysis (NMA) in internal coordinates. The manifold of possible loop configurations imposed by the position and orientation of the fixed loop ends is reduced to an orthogonal set of motions (or modes) encoding concerted rotations of all the backbone dihedral angles. We validate the sampling power on a set of protein loops with highly variable experimental structures and demonstrate that our approach can efficiently explore the conformational space of closed loops. We also show an acceptable resemblance of the ensembles around equilibrium conformations generated by long molecular simulations and constrained NMA on a set of exposed and diverse loops. In comparison with other methods, the main advantage is the lack of restrictions on the number of dihedrals that can be altered simultaneously. Furthermore, the method is computationally efficient since it only requires the diagonalization of a tiny matrix, and the modes of motions are energetically contextualized by the elastic network model, which includes both the loop and the neighboring residues.

Principal Component Analysis and Related Methods for Investigating the Dynamics of Biological Macromolecules

Principal component analysis (PCA) is used to reduce the dimensionalities of high-dimensional datasets in a variety of research areas. For example, biological macromolecules, such as proteins, exhibit many degrees of freedom, allowing them to adopt intricate structures and exhibit complex functions by undergoing large conformational changes. Therefore, molecular simulations of and experiments on proteins generate a large number of structure variations in high-dimensional space. PCA and many PCA-related methods have been developed to extract key features from such structural data, and these approaches have been widely applied for over 30 years to elucidate macromolecular dynamics. This review mainly focuses on the methodological aspects of PCA and related methods and their applications for investigating protein dynamics.

The effect of dimerization and ligand binding on the dynamics of Kaposi's sarcoma-associated herpesvirus protease

The Kaposi's sarcoma-associated herpesvirus protease is essential for virus maturation. This protease functions under allosteric regulation that establishes its enzymatic activity upon dimerization. It exists in equilibrium between an inactive monomeric state and an active, weakly associating, dimeric state that is stabilized upon ligand binding. The dynamics of the protease dimer and its monomer were studied using the Gaussian network model and the anisotropic network model , and its role in mediating the allosteric regulation is demonstrated. We show that the dimer is composed of five dynamical domains. The central domain is formed upon dimerization and composed of helix five of each monomer, in addition to proximal and distal domains of each monomer. Dimerization reduces the mobility of the central domains and increases the mobility of the distal domains, in particular the binding site within them. The three slowest ANM modes of the dimer assist the protease in ligand binding, motion of the conserved Arg142 and Arg143 toward the oxyanion, and reducing the activation barrier for the tetrahedral transition state by stretching the bond that is cleaved by the protease. In addition, we show that ligand binding reduces the motion of helices α1 and α5 at the interface and explain how ligand binding can stabilize the dimer.

Computation of the Protein Conformational Transition Pathway on Ligand Binding by Linear Response-Driven Molecular Dynamics

While extremely important for relating the protein structure to its biological function, determination of the protein conformational transition pathway upon ligand binding is made difficult due to the transient nature of intermediates, a large and rugged conformational space, and coupling between protein dynamics and ligand-protein interactions. Existing methods that rely on prior knowledge of the bound (holo) state structure are restrictive. A second concern relates to the correspondence of intermediates obtained to the metastable states on the apo → holo transition pathway. Here, we have taken the protein apo structure and ligand-binding site as only inputs and combined an elastic network model (ENM) representation of the protein Hamiltonian with linear response theory (LRT) for protein-ligand interactions to identify the set of slow normal modes of protein vibrations that have a high overlap with the direction of the protein conformational change. The structural displacement along the chosen direction was performed using excited normal modes molecular dynamics (MDeNM) simulations rather than by the direct use of LRT. Herein, the MDeNM excitation velocity was optimized on-the-fly on the basis of its coupling to protein dynamics and ligand-protein interactions. Thus, a determined set of structures was validated against crystallographic and simulation data on four protein-ligand systems, namely, adenylate kinase-di(adenosine-5')pentaphosphate, ribose binding protein-β-d-ribopyranose, DNA β-glucosyltransferase-uridine-5'-diphosphate, and G-protein α subunit-guanosine-5'-triphosphate, which present important differences in protein conformational heterogeneity, ligand binding mechanism, viz. induced-fit or conformational selection, extent, and nonlinearity in protein conformational changes upon ligand binding, and presence of allosteric effects. The obtained set of intermediates was used as an input to path metadynamics simulations to obtain the free energy profile for the apo → holo transition.

Plus and minus ends of microtubules respond asymmetrically to kinesin binding by a long-range directionally driven allosteric mechanism

Although it is known that majority of kinesin motors walk predominantly toward the plus end of microtubules (MTs) in a hand-over-hand manner, the structural origin of the stepping directionality is not understood. To resolve this issue, we modeled the structures of kinesin-1 (Kin1), MT, and the Kin1-MT complex using the elastic network model and calculated the residue-dependent responses to a local perturbation in the constructs. Kin1 binding elicits an asymmetric response that is pronounced in α/β-tubulin dimers in the plus end of the MT. Kin1 opens the clefts of multiple plus end α/β-tubulin dimers, creating binding-competent conformations, which is required for processivity. Reciprocally, MT induces correlations between switches I and II in the motor and enhances fluctuations in adenosine 5'-diphosphate and the residues in the binding pocket. Our findings explain both the directionality of stepping and MT effects on a key step in the catalytic cycle of kinesin.

Computational normal mode analysis accurately replicates the activity and specificity profiles of CRISPR-Cas9 and high-fidelity variants

The CRISPR-Cas system has transformed the field of gene-editing and created opportunities for novel genome engineering therapeutics. The field has significantly progressed, and recently, CRISPR-Cas9 was utilized in clinical trials to target disease-causing mutations. Existing tools aim to predict the on-target efficacy and potential genome-wide off-targets by scoring a particular gRNA according to an array of gRNA design principles or machine learning algorithms based on empirical results of large numbers of gRNAs. However, such tools are unable to predict the editing outcome by variant Cas enzymes and can only assess potential off-targets related to reference genomes. Here, we employ normal mode analysis (NMA) to investigate the structure of the Cas9 protein complexed with its gRNA and target DNA and explore the function of the protein. Our results demonstrate the feasibility and validity of NMA to predict the activity and specificity of SpyCas9 in the presence of mismatches by comparison to empirical data. Furthermore, despite the absence of their exact structures, this method accurately predicts the enzymatic activity of known high-fidelity engineered Cas9 variants.

Molecular Modeling is an Enabling Approach to Complement and Enhance Channelopathy Research

Hundreds of human membrane proteins form channels that transport necessary ions and compounds, including drugs and metabolites, yet details of their normal function or how function is altered by genetic variants to cause diseases are often unknown. Without this knowledge, researchers are less equipped to develop approaches to diagnose and treat channelopathies. High-resolution computational approaches such as molecular modeling enable researchers to investigate channelopathy protein function, facilitate detailed hypothesis generation, and produce data that is difficult to gather experimentally. Molecular modeling can be tailored to each physiologic context that a protein may act within, some of which may currently be difficult or impossible to assay experimentally. Because many genomic variants are observed in channelopathy proteins from high-throughput sequencing studies, methods with mechanistic value are needed to interpret their effects. The eminent field of structural bioinformatics integrates techniques from multiple disciplines including molecular modeling, computational chemistry, biophysics, and biochemistry, to develop mechanistic hypotheses and enhance the information available for understanding function. Molecular modeling and simulation access 3D and time-dependent information, not currently predictable from sequence. Thus, molecular modeling is valuable for increasing the resolution with which the natural function of protein channels can be investigated, and for interpreting how genomic variants alter them to produce physiologic changes that manifest as channelopathies. © 2022 American Physiological Society. Compr Physiol 12:3141-3166, 2022.

Response of Terahertz Protein Vibrations to Ligand Binding: Calmodulin-Peptide Complexes as a Case Study

Terahertz vibrations are sensitive reporters of the structure and interactions of proteins. Ligand binding alters the nature and distribution of these collective vibrations. The ligand-induced changes in the terahertz protein vibrations contribute to the binding entropy and to the overall thermodynamic stability of the resultant protein-ligand complexes. Here, we have examined the response of the low-frequency (below 6 terahertz) collective vibrations of the calcium-loaded calmodulin (CaM) to binding to five different ligands, both in the presence and absence of water, using normal-mode analysis and molecular dynamics simulations. A comparison of the vibrational spectra of hydrated and dry systems reveals that protein-solvent interactions stiffen the terahertz protein vibrations and that these solvent-coupled collective vibrations contribute significantly to the hydration-sensitive variation in the vibrational entropy of CaM. In the absence of water, the low-frequency vibrations of CaM are stiffened by ligand binding. On the contrary, the number and the cumulative vibrational entropy of low-frequency vibrational modes (ω < 200 cm^-1) of the hydrated CaM are increased noticeably after binding to the peptides, indicating binding-induced softening of collective vibrations of the protein. Although the calculated and experimental binding affinities of the chosen complexes correlated reasonably well, no systematic correlation was observed between the protein vibrational entropy and the binding affinity. The results underscored the importance of the interplay of protein-ligand and solvent interactions in modulating the low-frequency vibrations of proteins.

Optimized Elastic Network Models With Direct Characterization of Inter-Residue Cooperativity for Protein Dynamics

The elastic network models (ENMs)are known as representative coarse-grained models to capture essential dynamics of proteins. Due to simple designs of the force constants as a decay with spatial distances of residue pairs in many previous studies, there is still much room for the improvement of ENMs. In this article, we directly computed the force constants with the inverse covariance estimation using a ridge-type operater for the precision matrix estimation (ROPE)on a large-scale set of NMR ensembles. Distance-dependent statistical analyses on the force constants were further comprehensively performed in terms of several paired types of sequence and structural information, including secondary structure, relative solvent accessibility, sequence distance and terminal. Various distinguished distributions of the mean force constants highlight the structural and sequential characteristics coupled with the inter-residue cooperativity beyond the spatial distances. We finally integrated these structural and sequential characteristics to build novel ENM variations using the particle swarm optimization for the parameter estimation. The considerable improvements on the correlation coefficient of the mean-square fluctuation and the mode overlap were achieved by the proposed variations when compared with traditional ENMs. This study opens a novel way to develop more accurate elastic network models for protein dynamics.

Cooperative allostery and structural dynamics of streptavidin at cryogenic- and ambient-temperature

Multimeric protein assemblies are abundant in nature. Streptavidin is an attractive protein that provides a paradigm system to investigate the intra- and intermolecular interactions of multimeric protein complexes. Also, it offers a versatile tool for biotechnological applications. Here, we present two apo-streptavidin structures, the first one is an ambient temperature Serial Femtosecond X-ray crystal (Apo-SFX) structure at 1.7 Å resolution and the second one is a cryogenic crystal structure (Apo-Cryo) at 1.1 Å resolution. These structures are mostly in agreement with previous structural data. Combined with computational analysis, these structures provide invaluable information about structural dynamics of apo streptavidin. Collectively, these data further reveal a novel cooperative allostery of streptavidin which binds to substrate via water molecules that provide a polar interaction network and mimics the substrate biotin which displays one of the strongest affinities found in nature.

Correlated Motions and Dynamics in Different Domains of Epidermal Growth Factor Receptor With L858R and T790M Mutations

Non-small cell lung cancer with an activating epidermal growth factor receptor (EGFR) mutation responds well to targeted drugs. In most cases, drug resistance appears after about a year. Several studies have been conducted on the kinase domain of EGFR to understand the drug resistance mechanism. Since EGFR is a multi-domain protein, mutation in the kinase domain may affect the other domains as well. In this study, we examine the complete structure of the multi-domain EGFR protein and its mutants. We performed molecular dynamics simulations for wildtype EGFR, EGFR with L858R mutation, and EGFR with L858R and T790M mutations. We applied normal mode analysis and complex network analysis to extract the correlated motions in the domains of EGFR. The normal modes are used to construct the dynamic cross-correlation map (DCCM). Simulation results show different patterns of correlated motions in each domain of EGFR mutants compared to the wildtype. In Domains 1 and 3 of the extracellular region, a small number of weak positively correlated motions are extracted. Domains 2 and 4 show large numbers of both positive and negative motions. However, the negatively correlated motions are stronger in mutant structures compared to the wildtype. In Domain 7, some residues showed a positive correlation around the main diagonal. We also identified different communities, nodes and crucial residues in the domains of the structures, which can be important for the function of EGFR. Moreover, hydrogen bond analysis is performed for the stability analysis. The mutant structures have fewer hydrogen bonds compared to the wildtype. Overall, these findings are useful for understanding the dynamics and communications in EGFR domains.

Why are large conformational changes well described by harmonic normal modes?

Low-frequency normal modes generated by elastic network models tend to correlate strongly with large conformational changes of proteins, despite their reliance on the harmonic approximation, which is only valid in close proximity of the native structure. We consider 12 variants of the torsional network model (TNM), an elastic network model in torsion angle space, that adopt different sets of torsion angles as degrees of freedom and reproduce with similar quality the thermal fluctuations of proteins but present drastic differences in their agreement with conformational changes. We show that these differences are related to the extent of the deviations from the harmonic approximation, assessed through an anharmonic energy function whose harmonic approximation coincides with the TNM. Our results indicate that mode anharmonicity is more strongly related to its collectivity, i.e., the number of atoms displaced by the mode, than to its amplitude; low-frequency modes can remain harmonic even at large amplitudes, provided they are sufficiently collective. Finally, we assess the potential benefits of different strategies to minimize the impact of anharmonicity. The reduction of the number of degrees of freedom or their regularization by a torsional harmonic potential significantly improves the collectivity and harmonicity of normal modes and the agreement with conformational changes. In contrast, the correction of normal mode frequencies to partially account for anharmonicity does not yield substantial benefits. The TNM program is freely available at https://github.com/ugobas/tnm.

Mixed-solvent molecular dynamics simulation-based discovery of a putative allosteric site on regulator of G protein signaling 4

Regulator of G protein signaling 4 (RGS4) is an intracellular protein that binds to the G_α subunit ofheterotrimeric G proteins and aids in terminating G protein coupled receptor signaling. RGS4 has been implicated in pain, schizophrenia, and the control of cardiac contractility. Inhibitors of RGS4 have been developed but bind covalently to cysteine residues on the protein. Therefore, we sought to identify alternative druggable sites on RGS4 using mixed-solvent molecular dynamics simulations, which employ low concentrations of organic probes to identify druggable hotspots on the protein. Pseudo-ligands were placed in consensus hotspots, and perturbation with normal mode analysis led to the identification and characterization of a putative allosteric site, which would be invaluable for structure-based drug design of non-covalent, small molecule inhibitors. Future studies on the mechanism of this allostery will aid in the development of novel therapeutics targeting RGS4.

Pseudokinases repurpose flexibility signatures associated with the protein kinase fold for noncatalytic roles

The bilobal protein kinase-like fold in pseudokinases lack one or more catalytic residues, conserved in canonical protein kinases, and are considered enzymatically deficient. Tertiary structures of pseudokinases reveal that their loops topologically equivalent to activation segments of kinases adopt contracted configurations, which is typically extended in active conformation of kinases. Herein, anisotropic network model based normal mode analysis (NMA) was conducted on 51 active conformation structures of protein kinases and 26 crystal structures of pseudokinases. Our observations indicate that although backbone fluctuation profiles are similar for individual kinase-pseudokinase families, low intensity mean square fluctuations in pseudo-activation segment and other sub-structures impart rigidity to pseudokinases. Analyses of collective motions from functional modes reveal that pseudokinases, compared to active kinases, undergo distinct conformational transitions using the same structural fold. All-atom NMA of protein kinase-pseudokinase pairs from each family, sharing high amino acid sequence identities, yielded distinct community clusters, partitioned by residues exhibiting highly correlated fluctuations. It appears that atomic fluctuations from equivalent activation segments guide community membership and network topologies for respective kinase and pseudokinase. Our findings indicate that such adaptations in backbone and side-chain fluctuations render pseudokinases competent for catalysis-independent roles.

Computing the Structural Dynamics of RVFV L Protein Domain in Aqueous Glycerol Solutions

Many biological and biotechnological processes are controlled by protein–protein and protein–solvent interactions. In order to understand, predict, and optimize such processes, it is important to understand how solvents affect protein structure during protein–solvent interactions. In this study, all-atom molecular dynamics are used to investigate the structural dynamics and energetic properties of a C-terminal domain of the Rift Valley Fever Virus L protein solvated in glycerol and aqueous glycerol solutions in different concentrations by molecular weight. The Generalized Amber Force Field is modified by including restrained electrostatic potential atomic charges for the glycerol molecules. The peptide is considered in detail by monitoring properties like the root-mean-squared deviation, root-mean-squared fluctuation, radius of gyration, hydrodynamic radius, end-to-end distance, solvent-accessible surface area, intra-potential energy, and solvent–peptide interaction energies for hundreds of nanoseconds. Secondary structure analysis is also performed to examine the extent of conformational drift for the individual helices and sheets. We predict that the peptide helices and sheets are maintained only when the modeling strategy considers the solvent with lower glycerol concentration. We also find that the solvent-peptide becomes more cohesive with decreasing glycerol concentrations. The density and radial distribution function of glycerol solvent calculated when modeled with the modified atomic charges show a very good agreement with experimental results and other simulations at 298.15K.

RNA Flexibility Prediction With Sequence Profile and Predicted Solvent Accessibility

Structural flexibility plays an essential role in many biological processes. B-factor is an important indicator to measure the flexibility of protein or RNA structures. Many methods were developed to predict protein B-factors, but few studies have been done for RNA B-factor prediction. In this paper, we proposed a new method RNAbval to predict RNA B-factors using random forest. The method was developed using a comprehensive set of features, including the sequence profile and predicted solvent accessibility. RNAbval achieved an improvement of 9.2-20.5 percent over the state-of-the-art method on two benchmark test datasets. The proposed method is available at http://yanglab.nankai.edu.cn/RNAbval/.

Normal Mode Analysis of KRas4B Reveals Partner Specific Dynamics

Ras GTPase interacts with its regulators and downstream effectors for its critical function in cellular signaling. Targeting the disrupted mechanisms in Ras-related human cancers requires understanding the distinct dynamics of these protein-protein interactions. We performed normal mode analysis (NMA) of KRas4B in wild-type or mutant monomeric and neurofibromin-1 (NF1), Son of Sevenless 1 (SOS1) or Raf-1 bound dimeric conformational states to reveal partner-specific dynamics of the protein. Gaussian network model (GNM) analysis showed that the known KRas4B lobes further partition into subdomains upon binding to its partners. Furthermore, KRas4B interactions with different partners suppress the flexibility in not only their binding sites but also distant residues in the allosteric lobe in a partner-specific way. The conformational changes can be driven by intrinsic residue fluctuations of the open state KRas4B-GDP, as we illustrated with anisotropic network model (ANM) analysis. The allosteric paths connecting the nucleotide binding residues to the allosteric site at α3-L7 portray differences in the inactive and active states. These findings help in understanding the partner-specific KRas4B dynamics, which could be utilized for therapeutic targeting.

Computational Ways to Enhance Protein Inhibitor Design

Two new computational approaches are described to aid in the design of new peptide-based drugs by evaluating ensembles of protein structures from their dynamics and through the assessing of structures using empirical contact potential. These approaches build on the concept that conformational variability can aid in the binding process and, for disordered proteins, can even facilitate the binding of more diverse ligands. This latter consideration indicates that such a design process should be less restrictive so that multiple inhibitors might be effective. The example chosen here focuses on proteins/peptides that bind to hemagglutinin (HA) to block the large-scale conformational change for activation. Variability in the conformations is considered from sets of experimental structures, or as an alternative, from their simple computed dynamics; the set of designe peptides/small proteins from the David Baker lab designed to bind to hemagglutinin, is the large set considered and is assessed with the new empirical contact potentials.

Equally Weighted Multiscale Elastic Network Model and Its Comparison with Traditional and Parameter-Free Models

Dynamical properties of proteins play an essential role in their function exertion. The elastic network model (ENM) is an effective and efficient tool in characterizing the intrinsic dynamical properties encoded in biomacromolecule structures. The Gaussian network model (GNM) and anisotropic network model (ANM) are the two often-used ENM models. Here, we introduce an equally weighted multiscale ENM (equally weighted mENM) based on the original mENM (denoted as mENM), in which fitting weights of Kirchhoff/Hessian matrixes in mENM are removed since they neglect the details of pairwise interactions. Then, we perform its comparison with the mENM, traditional ENM, and parameter-free ENM (pfENM) in reproducing dynamical properties for the six representative proteins whose molecular dynamics (MD) trajectories are available in http://mmb.pcb.ub.es/MoDEL/. In the results, for B-factor prediction, mENM performs best, while the equally weighted mENM performs also well, better than the traditional ENM and pfENM models. As to the dynamical cross-correlation map calculation, mENM performs worst, while the results produced from the equally weighted mENM and pfENM models are close to those from MD trajectories with the latter a little better than the former. Furthermore, encouragingly, the equally weighted mANM displays the best performance in capturing the functional motional modes, followed by pfANM and traditional ANM models, while the mANM fails in all the cases. This work is helpful for strengthening the understanding of the elastic network model and provides a valuable guide for researchers to utilize the model to explore protein dynamics.

Modal Analysis of the Lysozyme Protein Considering All-Atom and Coarse-Grained Finite Element Models

Proteins are the fundamental entities of several organic activities. They are essential for a broad range of tasks in a way that their shapes and folding processes are crucial to achieving proper biological functions. Low-frequency modes, generally associated with collective movements at terahertz (THz) and sub-terahertz frequencies, have been appointed as critical for the conformational processes of many proteins. Dynamic simulations, such as molecular dynamics, are vastly applied by biochemical researchers in this field. However, in the last years, proposals that define the protein as a simplified elastic macrostructure have shown appealing results when dealing with this type of problem. In this context, modal analysis based on different modelization techniques, i.e., considering both an all-atom (AA) and coarse-grained (CG) representation, is proposed to analyze the hen egg-white lysozyme. This work presents new considerations and conclusions compared to previous analyses. Experimental values for the B-factor, considering all the heavy atoms or only one representative point per amino acid, are used to evaluate the validity of the numerical solutions. In general terms, this comparison allows the assessment of the regional flexibility of the protein. Besides, the low computational requirements make this approach a quick method to extract the protein’s dynamic properties under scrutiny.

Exploring the intrinsic dynamics of SARS-CoV-2, SARS-CoV and MERS-CoV spike glycoprotein through normal mode analysis using anisotropic network model

COVID-19 caused by SARS-CoV-2 have become a global pandemic with serious rate of fatalities. SARS-CoV and MERS-CoV have also caused serious outbreak previously but the intensity was much lower than the ongoing SARS-CoV-2. The main infectivity factor of all the three viruses is the spike glycoprotein. In this study we have examined the intrinsic dynamics of the prefusion, lying state of trimeric S protein of these viruses through Normal Mode Analysis using Anisotropic Network Model. The dynamic modes of the S proteins of the aforementioned viruses were compared by root mean square inner product (RMSIP), spectral overlap and cosine correlation matrix. S proteins show homogenous correlated or anticorrelated motions among their domains but direction of Cα atom among the spike proteins show less similarity. SARS-CoV-2 spike shows high vertically upward motion of the receptor binding motif implying its propensity for binding with the receptor even in the lying state. MERS-CoV spike shows unique dynamical motion compared to the other two S protein indicated by low RMSIP, spectral overlap and cosine correlation value. This study will guide in developing common potential inhibitor molecules against closed state of spike protein of these viruses to prevent conformational switching from lying to standing state.

Distinguishing Enzymes and Non-enzymes Based on Structural Information with an Alignment Free Approach

Background:

Knowledge of protein functions is very crucial for the understanding of biological processes. Experimental methods for protein function prediction are powerless to treat the growing amount of protein sequence and structure data.

Objective:

To develop some computational techniques for the protein function prediction.

Method:

Based on the residue interaction network features and the motion mode information, an SVM model was constructed and used as the predictor. The role of these features was analyzed and some interesting results were obtained.

Results:

An alignment-free method for the classification of enzyme and non-enzyme is developed in this work. There is not any single feature that occupies a dominant position in the prediction process. The topological and the information-theoretic residue interaction network features have a better performance. The combination of the fast mode and the slow mode can get a better explanation for the classification result.

Conclusion:

The method proposed in this paper can act as a classifier for the enzymes and nonenzymes.

Inferring functional units in ion channel pores via relative entropy

Coarse-grained protein models approximate the first-principle physical potentials. Among those modeling approaches, the relative entropy framework yields promising and physically sound results, in which a mapping from the target protein structure and dynamics to a model is defined and subsequently adjusted by an entropy minimization of the model parameters. Minimization of the relative entropy is equivalent to maximization of the likelihood of reproduction of (configurational ensemble) observations by the model. In this study, we extend the relative entropy minimization procedure beyond parameter fitting by a second optimization level, which identifies the optimal mapping to a (dimension-reduced) topology. We consider anisotropic network models of a diverse set of ion channels and assess our findings by comparison to experimental results.

Using normal mode analysis on protein structural models. How far can we go on our predictions?

Normal mode analysis (NMA) is a fast and inexpensive approach that is largely used to gain insight into functional protein motions, and more recently to create conformations for further computational studies. However, when the protein structure is unknown, the use of computational models is necessary. Here, we analyze the capacity of NMA in internal coordinate space to predict protein motion, its intrinsic flexibility, and atomic displacements, using protein models instead of native structures, and the possibility to use it for model refinement. Our results show that NMA is quite insensitive to modeling errors, but that calculations are strictly reliable only for very accurate models. Our study also suggests that internal NMA is a more suitable tool for the improvement of structural models, and for integrating them with experimental data or in other computational techniques, such as protein docking or more refined molecular dynamics simulations.

Transient association between proteins elicits alteration of dynamics at sites far away from interfaces

Proteins are known to undergo structural changes upon binding to partner proteins. However, the prevalence, extent, location, and function of change in protein dynamics due to transient protein-protein interactions is not well documented. Here, we have analyzed a dataset of 58 protein-protein complexes of known three-dimensional structure and structures of their corresponding unbound forms to evaluate dynamics changes induced by binding. Fifty-five percent of cases showed significant dynamics change away from the interfaces. This change is not always accompanied by an observed structural change. Binding of protein partner is found to alter inter-residue communication within the tertiary structure in about 90% of cases. Also, residue motions accessible to proteins in unbound form were not always maintained in the bound form. Further analyses revealed functional roles for the distant site where dynamics change was observed. Overall, the results presented here strongly suggest that alteration of protein dynamics due to binding of a partner protein commonly occurs.

A Time-Dependent Quantum Approach to Allostery and a Comparison With Light-Harvesting in Photosynthetic Phenomenon

The allosteric effect is one of the most important processes in regulating the function of proteins, and the elucidation of this phenomenon plays a significant role in understanding emergent behaviors in biological regulation. In this process, a perturbation, generated by a ligand in a part of the macromolecule (the allosteric site), moves along this system and reaches a specific (active) site, dozens of Ångströms away, with a great efficiency. The dynamics of this perturbation in the macromolecule can model precisely the allosteric process. In this article, we will be studying the general characteristics of allostery, using a time-dependent quantum approach to obtain rules that apply to this kind of process. Considering the perturbation as a wave that moves within the molecular system, we will characterize the allosteric process with three of the properties of this wave in the active site: (1) t_a, the characteristic time for reaching that site, (2) A_a, the amplitude of the wave in this site, and (3) B_a, its corresponding spectral broadening. These three parameters, together with the process mechanism and the perturbation efficiency in the process, can describe the phenomenon. One of the main purposes of this paper is to link the parameters t_a, A_a, and B_a and the perturbation efficiency to the characteristics of the system. There is another fundamental process for life that has some characteristics similar to allostery: the light-harvesting (LH) process in photosynthesis. Here, as in allostery, two distant macromolecular sites are involved—two sites dozens of Ångströms away. In both processes, it is particularly important that the perturbation is distributed efficiently without dissipating in the infinite degrees of freedom within the macromolecule. The importance of considering quantum effects in the LH process is well documented in literature, and the quantum coherences are experimentally proven by time-dependent spectroscopic techniques. Given the existing similarities between these two processes in macromolecules, in this work, we suggest using Quantum Mechanics (QM) to study allostery.

A New Protocol for Atomic-Level Protein Structure Modeling and Refinement Using Low-to-Medium Resolution Cryo-EM Density Maps

The rapid progress of cryo-electron microscopy (cryo-EM) in structural biology has raised an urgent need for robust methods to create and refine atomic-level structural models using low-resolution EM density maps. We propose a new protocol to create initial models using I-TASSER protein structure prediction, followed by EM density map-based rigid-body structure fitting, flexible fragment adjustment and atomic-level structure refinement simulations. The protocol was tested on a large set of 285 non-homologous proteins and generated structural models with correct folds for 260 proteins, where 28% had RMSDs below 2 Å. Compared to other state-of-the-art methods, the major advantage of the proposed pipeline lies in the uniform structure prediction and refinement protocol, as well as the extensive structural re-assembly simulations, which allow for low-to-medium resolution EM density map-guided structure modeling starting from amino acid sequences. Interestingly, the quality of both the image fitting and subsequent structure refinement was found to be strongly correlated with the correctness of the initial I-TASSER models; this is mainly due to the different correlation patterns observed between force field and structural quality for the models with template modeling score (or TM-score, a metric quantifying the similarity of models to the native) above and below a threshold of 0.5. Overall, the results demonstrate a new avenue that is ready to use for large-scale cryo-EM-based structure modeling and atomic-level density map-guided structure refinement.