Dynamically driven correlations in elastic net models reveal sequence of events and causality in proteins.

An explicit analytic solution is given for the Langevin equation applied to the Gaussian Network Model of a protein subjected to both a random and a deterministic periodic force. Synchronous and asynchronous components of time correlation functions are derived and an expression for phase differences in the time correlations of residue pairs is obtained. The synchronous component enables the determination of dynamic communities within the protein structure. The asynchronous component reveals causality, where the time correlation function between residues i and j differs depending on whether i is observed before j or vice versa, resulting in directional information flow. Driver and driven residues in the allosteric process of cyclophilin A and human NAD-dependent isocitrate dehydrogenase are determined by a perturbation-scanning technique. Factors affecting phase differences between fluctuations of residues, such as network topology, connectivity, and residue centrality, are identified. Within the constraints of the isotropic Gaussian Network Model, our results show that asynchronicity increases with viscosity and distance between residues, decreases with increasing connectivity, and decreases with increasing levels of eigenvector centrality.

Revealing Allosteric Mechanism of Amino Acid Binding Proteins from Open to Closed State.

Amino acid binding proteins (AABPs) undergo significant conformational closure in the periplasmic space of Gram-negative bacteria, tightly binding specific amino acid substrates and then initiating transmembrane transport of nutrients. Nevertheless, the possible closure mechanisms after substrate binding, especially long-range signaling, remain unknown. Taking three typical AABPs-glutamine binding protein (GlnBP), histidine binding protein (HisJ) and lysine/arginine/ornithine binding protein (LAOBP) in Escherichia coli (E. coli)-as research subjects, a series of theoretical studies including sequence alignment, Gaussian network model (GNM), anisotropic network model (ANM), conventional molecular dynamics (cMD) and neural relational inference molecular dynamics (NRI-MD) simulations were carried out. Sequence alignment showed that GlnBP, HisJ and LAOBP have high structural similarity. According to the results of the GNM and ANM, AABPs' Index Finger and Thumb domains exhibit closed motion tendencies that contribute to substrate capture and stable binding. Based on cMD trajectories, the Index Finger domain, especially the I-Loop region, exhibits high molecular flexibility, with residues 11 and 117 both being potentially key residues for receptor-ligand recognition and initiation of receptor allostery. Finally, the signaling pathway of AABPs' conformational closure was revealed by NRI-MD training and trajectory reconstruction. This work not only provides a complete picture of AABPs' recognition mechanism and possible conformational closure, but also aids subsequent structure-based design of small-molecule oncology drugs.

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.

Gaussian network model revisited: effects of mutation and ligand binding on protein behavior.

The coarse-grained Gaussian network model (GNM), considers only the alpha carbons of the folded protein. Therefore it is not directly applicable to the study of mutation or ligand binding problems where atomic detail is required. This shortcoming is improved by including all atom pairs within the coordination shell of each other into the Kirchoff adjacency matrix. Counting all contacts rather than only alpha carbon contacts diminishes the magnitude of fluctuations in the system. But more importantly, it changes the graph-like connectivity structure, i.e., the Kirchoff adjacency matrix of the protein. This change depends on amino acid type which introduces amino acid specific and position specific information into the classical coarse-grained GNM which was originally modeled in analogy with the phantom network model of rubber elasticity. With this modification, it is now possible to explain the consequences of mutation and ligand binding on residue fluctuations, their pair-correlations and mutual information shared by each pair. We refer to the new model as 'all-atom GNM'. Using examples from published data we show that the all-atom GNM givesB-factors that are in better agreement with experiment, can explain effects of mutation on long range communication in PDZ domains and can predict effects of GDP and GTP binding on the dimerization of KRAS.

Study on functional sites in human multidrug resistance protein 1 (hMRP1).

Human multidrug resistance protein 1 (hMRP1) is an important member of the ATP-binding cassette (ABC) transporter superfamily. It can extrude a variety of anticancer drugs and physiological organic anions across the plasma membrane, which is activated by substrate binding, and is accompanied by large-scale cooperative movements between different domains. Currently, it remains unclear completely about how the specific interactions between hMRP1 and its substrate are and which critical residues are responsible for allosteric signal transduction. To the end, we first construct an inward-facing state of hMRP1 using homology modeling method, and then dock substrate proinflammatory agent leukotriene C4 (LTC4) to hMRP1 pocket. The result manifests LTC4 interacts with two parts of hMRP1 pocket, namely the positively charged pocket (P pocket) and hydrophobic pocket (H pocket), similar to its binding mode with bMRP1 (bovine MRP1). Additionally, we use the Gaussian network model (GNM)-based thermodynamic method proposed by us to identify the key residues whose perturbations markedly alter their binding free energy. Here the conventional GNM is improved with covalent/non-covalent interactions and secondary structure information considered (denoted as sscGNM). In the result, sscGNM improves the flexibility prediction, especially for the nucleotide binding domains with rich kinds of secondary structures. The 46 key residue clusters located in different subdomains are identified which are highly consistent with experimental observations. Furtherly, we explore the long-range cooperation within the transporter. This study is helpful for strengthening the understanding of the work mechanism in ABC exporters and can provide important information to scientists in drug design studies.

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

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

Dynamical comparison between myoglobin and hemoglobin.

Myoglobin and hemoglobin are globular hemeproteins, when the former is a monomer and the latter a heterotetramer. Despite the structural similarity of myoglobin to α and ß subunits of hemoglobin, there is a functional difference between the two proteins, owing to the quaternary structure of hemoglobin. The effect of the quaternary structure of hemoglobin on the intrinsic dynamics of its subunits is explored by dynamical comparison of the two proteins. Anisotropic Network Model modes of motion were calculated for hemoglobin and myoglobin. Dynamical comparison between the proteins was performed using global and local Anisotropic Network Model mode alignment algorithms based on the algorithms of Smith-Waterman and Needleman-Wunsch for sequence comparison. The results indicate that the quaternary structure of hemoglobin substantially alters the intrinsic dynamics of its subunits, an effect that may contribute to the functional difference between the two proteins. Local dynamics similarity between the proteins is still observed at the major exit route of the ligand.

Causality, transfer entropy, and allosteric communication landscapes in proteins with harmonic interactions.

A fast and approximate method of generating allosteric communication landscapes in proteins is presented by using Schreiber's entropy transfer concept in combination with the Gaussian Network Model of proteins. Predictions of the model and the allosteric communication landscapes generated show that information transfer in proteins does not necessarily take place along a single path, but an ensemble of pathways is possible. The model emphasizes that knowledge of entropy only is not sufficient for determining allosteric communication and additional information based on time delayed correlations should be introduced, which leads to the presence of causality in proteins. The model provides a simple tool for mapping entropy sink-source relations into pairs of residues. By this approach, residues that should be manipulated to control protein activity may be determined. This should be of great importance for allosteric drug design and for understanding the effects of mutations on function. The model is applied to determine allosteric communication in three proteins, Ubiquitin, Pyruvate Kinase, and the PDZ domain. Predictions are in agreement with molecular dynamics simulations and experimental evidence. Proteins 2017; 85:1056-1064. © 2017 Wiley Periodicals, Inc.

Intrinsic Dynamics Analysis of a DNA Octahedron by Elastic Network Model.

DNA is a fundamental component of living systems where it plays a crucial role at both functional and structural level. The programmable properties of DNA make it an interesting building block for the construction of nanostructures. However, molecular mechanisms for the arrangement of these well-defined DNA assemblies are not fully understood. In this paper, the intrinsic dynamics of a DNA octahedron has been investigated by using two types of Elastic Network Models (ENMs). The application of ENMs to DNA nanocages include the analysis of the intrinsic flexibilities of DNA double-helices and hinge sites through the calculation of the square fluctuations, as well as the intrinsic collective dynamics in terms of cross-collective map calculation coupled with global motions analysis. The dynamics profiles derived from ENMs have then been evaluated and compared with previous classical molecular dynamics simulation trajectories. The results presented here revealed that ENMs can provide useful insights into the intrinsic dynamics of large DNA nanocages and represent a useful tool in the field of structural DNA nanotechnology.

Dynamics and allostery of the ionotropic glutamate receptors and the ligand binding domain.

The dynamics of the ligand-binding domain (LBD) and the intact ionotropic glutamate receptor (iGluR) were studied using Gaussian Network Model (GNM) analysis. The dynamics of LBDs with various allosteric modulators is compared using a novel method of multiple alignment of GNM modes of motion. The analysis reveals that allosteric effectors change the dynamics of amino acids at the upper lobe interface of the LBD dimer as well as at the hinge region between the upper- and lower- lobes. For the intact glutamate receptor the analysis show that the clamshell-like movement of the LBD upper and lower lobes is coupled to the bending of the trans-membrane domain (TMD) helices which may open the channel pore. The results offer a new insight on the mechanism of action of allosteric modulators on the iGluR and support the notion of TMD helices bending as a possible mechanism for channel opening. In addition, the study validates the methodology of multiple GNM modes alignment as a useful tool to study allosteric effect and its relation to proteins dynamics.

Universal features of fluctuations in globular proteins.

Using data from 2000 non-homologous protein crystal structures, we show that the distribution of residue B factors of proteins collapses onto a single master curve. We show by maximum entropy arguments that this curve is a Gamma function whose order and dispersion are obtained from experimental data. The distribution for any given specific protein can be generated from the master curve by a linear transformation. Any perturbation of the B factor distribution of a protein, imposed at constant energy, causes a decrease in the entropy of the protein relative to that of the reference state. Proteins 2016; 84:721-725. © 2016 Wiley Periodicals, Inc.

Effects of ligand binding upon flexibility of proteins.

Binding of a ligand on a protein changes the flexibility of certain parts of the protein, which directly affects its function. These changes are not the same at each point, some parts become more flexible and some others become stiffer. Here, an equation is derived that gives the stiffness map for proteins. The model is based on correlations of fluctuations of pairs of points in proteins, which may be evaluated at different levels of refinement, ranging from all atom molecular dynamics to general elastic network models, including the simplest case of isotropic Gaussian Network Model. The latter is used, as an example, to evaluate the changes of stiffness upon dimerization of ACK1.

The Intrinsic Dynamics and Unfolding Process of an Antibody Fab Fragment Revealed by Elastic Network Model.

Antibodies have been increasingly used as pharmaceuticals in clinical treatment. Thermal stability and unfolding process are important properties that must be considered in antibody design. In this paper, the structure-encoded dynamical properties and the unfolding process of the Fab fragment of the phosphocholine-binding antibody McPC603 are investigated by use of the normal mode analysis of Gaussian network model (GNM). Firstly, the temperature factors for the residues of the protein were calculated with GNM and then compared with the experimental measurements. A good result was obtained, which provides the validity for the use of GNM to study the dynamical properties of the protein. Then, with this approach, the mean-square fluctuation (MSF) of the residues, as well as the MSF in the internal distance (MSFID) between all pairwise residues, was calculated to investigate the mobility and flexibility of the protein, respectively. It is found that the mobility and flexibility of the constant regions are higher than those of the variable regions, and the six complementarity-determining regions (CDRs) in the variable regions also exhibit relative large mobility and flexibility. The large amplitude motions of the CDRs are considered to be associated with the immune function of the antibody. In addition, the unfolding process of the protein was simulated by iterative use of the GNM. In our method, only the topology of protein native structure is taken into account, and the protein unfolding process is simulated through breaking the native contacts one by one according to the MSFID values between the residues. It is found that the flexible regions tend to unfold earlier. The sequence of the unfolding events obtained by our method is consistent with the hydrogen-deuterium exchange experimental results. Our studies imply that the unfolding behavior of the Fab fragment of antibody McPc603 is largely determined by the intrinsic dynamics of the protein.

Domain Motions and Functionally-Key Residues of L-Alanine Dehydrogenase Revealed by an Elastic Network Model.

Mycobacterium tuberculosis L-alanine dehydrogenase (L-MtAlaDH) plays an important role in catalyzing L-alanine to ammonia and pyruvate, which has been considered to be a potential target for tuberculosis treatment. In the present work, the functional domain motions encoded in the structure of L-MtAlaDH were investigated by using the Gaussian network model (GNM) and the anisotropy network model (ANM). The slowest modes for the open-apo and closed-holo structures of the enzyme show that the domain motions have a common hinge axis centered in residues Met133 and Met301. Accompanying the conformational transition, both the 1,4-dihydronicotinamide adenine dinucleotide (NAD)-binding domain (NBD) and the substrate-binding domain (SBD) move in a highly coupled way. The first three slowest modes of ANM exhibit the open-closed, rotation and twist motions of L-MtAlaDH, respectively. The calculation of the fast modes reveals the residues responsible for the stability of the protein, and some of them are involved in the interaction with the ligand. Then, the functionally-important residues relevant to the binding of the ligand were identified by using a thermodynamic method. Our computational results are consistent with the experimental data, which will help us to understand the physical mechanism for the function of L-MtAlaDH.

Multiple Gaussian network modes alignment reveals dynamically variable regions: the hemoglobin case.

Gaussian network model (GNM) modes of motion are calculated to a dataset of hemoglobin (Hb) structures and modes with dynamics similarity to the T state are multiply aligned. The sole criterion for the alignment is the mode shape itself and not sequence or structural similarity. Standard deviation (SD) of the GNM value score along the alignment is calculated, regions with high SD are defined as dynamically variable. The analysis shows that the α1ß1/α2ß2 interface is a dynamically variable region but not the α1ß2/α2ß1 and the α1α2/ß1ß2 interfaces. The results are in accordance with the T→R2 transition of Hb. We suggest that dynamically variable regions are regions that are likely to undergo structural change in the protein upon binding, conformational transition, or any other relevant chemical event. The represented technique of multiple dynamics-based alignment of modes is novel and may offer a new insight in proteins' dynamics to function relation.

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.

Large-scale analysis of the dynamics of enzymes.

Protein enzymes enable the cell to execute chemical reactions in short time by accelerating the rate of the reactions in a selective manner. The motions or dynamics of the enzymes are essential for their function. Comparison of the dynamics of a set of 1247 nonhomologous enzymes was performed. For each enzyme, the slowest modes of motion are calculated using the Gaussian network model (GNM) and they are globally aligned. Alignment is done using the dynamic programming algorithm of Needleman and Wunsch, commonly used for sequence alignment. Only 96 pairs of proteins were identified to have three similar GNM slow modes with 63 of them having a similar structure. The most frequent slowest mode of motion describes a two domains anticorrelated motion that characterizes at least 23% of the enzymes. Therefore, dynamics uniqueness cannot be accounted for by the slowest mode itself but rather by the combination of several slow modes. Different quaternary structure packing can restrain the motion of enzyme subunits differently and may serve as another mechanism that increases the dynamics uniqueness.

Ligand Binding Introduces Significant Allosteric Shifts in the Locations of Protein Fluctuations.

Allostery is usually considered to be a mechanism for transmission of signals associated with physical or dynamic changes in some part of a protein. Here, we investigate the changes in fluctuations across the protein upon ligand binding based on the fluctuations computed with elastic network models. These results suggest that binding reduces the fluctuations at the binding site but increases fluctuations at remote sites, but not to fully compensating extents. If there were complete conservation of entropy, then only the enthalpies of binding would matter and not the entropies; however this does not appear to be the case. Experimental evidence also suggests that energies and entropies of binding can compensate but that the extent of compensation varies widely from case to case. Our results do however always show transmission of an allosteric signal to distant locations where the fluctuations are increased. These fluctuations could be used to compute entropies to improve evaluations of the thermodynamics of binding. We also show the allosteric relationship between peptide binding in the GroEL trans-ring that leads directly to the release of GroES from the GroEL-GroES cis-ring. This finding provides an example of how calculating these changes to protein dynamics induced by the binding of an allosteric ligand can regulate protein function and mechanism.

Stability and folding behavior analysis of zinc-finger using simple models.

Zinc-fingers play crucial roles in regulating gene expression and mediating protein-protein interactions. In this article, two different proteins (Sp1f2 and FSD-1) are investigated using the Gaussian network model and anisotropy elastic network model. By using these simple coarse-grained methods, we analyze the structural stabilization and establish the unfolding pathway of the two different proteins, in good agreement with related experimental and molecular dynamics simulation data. From the analysis, it is also found that the folding process of the zinc-finger motif is predominated by several factors. Both the zinc ion and C-terminal loop affect the folding pathway of the zinc-finger motif. Knowledge about the stability and folding behavior of zinc-fingers may help in understanding the folding mechanisms of the zinc-finger motif and in designing new zinc-fingers. Meanwhile, these simple coarse-grained analyses can be used as a general and quick method for mechanistic studies of metalloproteins.

A study on allosteric communication in U1A-snRNA binding interactions: network analysis combined with molecular dynamics data.

The allosteric regulation during the binding interactions between small nuclear RNAs (snRNAs) and the associated protein factors is critical to the function of spliceosomes in alternative RNA splicing. Although network models combined with molecular dynamics simulations have shown to be powerful tools for the analysis of protein allostery, the atomic-level simulations are, however, too expensive and with limited accuracy for the large-size systems. In this work, we use a residual network model combined with a coarse-grained Gaussian network model (GNM) to investigate the binding interactions between the snRNA and the human U1A protein which is a major component of the spliceosomal U1 small nuclear ribonucleoprotein particle, and to identify the residues that play an important role in the allosteric communication in U1A during this process. We also utilize the Girvan-Newman method to detect the structural organization in U1A-snRNA recognition and interactions. Our results reveal that: (Ι) not only the residues at the binding sites that are traditionally considered to play a major role in U1A-snRNA association, but those residues that are far away from the RNA binding interface participate in the U1A's allosteric signal transmission induced by the RNA binding; (Π) the structure of U1A protein is well organized with different communities acting different roles for its RNA binding and allosteric regulation. The study demonstrates that the combination of the residual network and elastic network models is an effective and efficient method which can be readily extended to the investigation of the allosteric communication for other macromolecular interaction systems.