Linear response theory in dihedral angle space for protein structural change upon ligand binding

A Retrospective on the Development of Methods for the Analysis of Protein Conformational Ensembles

Analysing protein conformational ensembles whether from molecular dynamics (MD) simulation or other sources for functionally relevant conformational changes can be very challenging. In the nineteen nineties dimensional reduction methods were developed primarily for analysing MD trajectories to determine dominant motions with the aim of understanding their relationship to function. Coarse-graining methods were also developed so the conformational change between two structures could be described in terms of the relative motion of a small number of quasi-rigid regions rather than in terms of a large number of atoms. When these methods are combined, they can characterize the large-scale motions inherent in a conformational ensemble providing insight into possible functional mechanism. The dimensional reduction methods first applied to protein conformational ensembles were referred to as Quasi-Harmonic Analysis, Principal Component Analysis and Essential Dynamics Analysis. A retrospective on the origin of these methods is presented, the relationships between them explained, and more recent developments reviewed.

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.

Exploring the conformational dynamics and flexibility of intrinsically disordered HIV-1 Nef protein using molecular dynamic network approaches

Intrinsically disordered proteins represent a class of proteins that lack fixed and well-defined three-dimensional structures in solution. HIV-1 Nef is an intrinsically disordered peripheral membrane protein involved in the replication and pathogenesis of HIV-1 infection. Nef controls expression levels of cell surface CD4 molecules that are essential for adaptive immunity. Despite the lack of fixed and stable structures, Nef physically interacts with the host cellular proteins (AP-1/MHC-I) and modulates intracellular trafficking pathways. Therefore, it is essential to understand how this dynamic conformational flexibility affects Nef structures and function. In this study, we combined all-atom molecular dynamics (MD) simulations and dynamic network approaches to better understand the structure and dynamics of Nef in two different forms, the free unbound and the bound state. Using the MD simulation approach, we show that the intrinsically disordered Nef exhibit a large dynamic field with more atomic fluctuations and lesser thermodynamic stability in the unbound conditions. The conformations of Nef change over time, and this protein remains more compact, folded, and stable in the bound form. The dynamic network analysis revealed regions of the protein capable of modulating the conformational behavior of the disordered Nef. The average betweenness centrality (BC) unveiled residues that are critical for mediating protein-protein interactions. The average shortest path length (L) and the perturbation response scanning exposed residues that are likely to be important in steering protein conformational changes. Overall, the study demonstrates how all-atom MD simulations combined with the dynamic network approach can be used to gain further insights into the structure and dynamics-function relationship of intrinsically disordered HIV-1 Nef.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s13205-021-02698-8.

Computational investigations on the dynamic binding effect of molecular tweezer CLR01 toward intrinsically disordered HIV-1 Nef

Intrinsically disordered proteins (IDPs) are highly flexible molecules that undergo disorder to order transition through their interaction with other molecules. IDPs play a vital role in several biological processes ranging from molecular recognition to several human diseases through the protein-protein interaction. The dynamic flexibility of IDPs and their implications in several human diseases enable these molecules to serve as novel therapeutic targets. However, the challenging task is to develop novel drugs against IDPs because of their lack of stable structures and the nature of high conformational flexibility. In this study, we have calculated the dynamic binding effect of the supramolecular tweezer CLR01 against the intrinsically disordered HIV-1 Nef by employing molecular docking and dynamics simulation approaches. From docking results, we predicted the strong binding affinity of the tweezer with the target residues of Nef. The docking results were further validated from the molecular dynamics simulation studies confirming the conformational stability of Nef upon tweezer binding. These findings provide useful insights into the development of potent inhibitors for targeting Nef protein functions.

Allosteric response to ligand binding: Molecular dynamics study of the N-terminal domains in IP receptor

Inositol 1,4,5-trisphosphate (IP₃) receptor (IP₃R) is a huge tetrameric intracellular Ca²⁺ channel that mediates cytoplasmic Ca²⁺ signaling. The structural basis of the gating in IP₃R has been studied by X-ray crystallography and cryo-electron microscopy, focusing on the domain rearrangements triggered by IP₃ binding. Here, we conducted molecular dynamics (MD) simulations of the three N-terminal domains of IP₃R responsible for IP₃ binding (IBC/SD; two domains of the IP₃ binding core, IBCβ and IBCα, and suppressor domain, SD) as a model system to study the initial gating stage. The response upon removal of IP₃ from the IP₃-bound form of IBC/SD was traced in MD trajectories. The two IBC domains showed an immediate response of opening after removal of IP₃, and SD showed a simultaneous opening motion indicating a tight dynamic coupling with IBC. However, when IBC remained in a more closed form, the dynamic coupling broke and SD exhibited a more amplified closing motion independently of IBC. This amplified SD motion was caused by the break of connection between SD and IBCβ at the hinge region, but was suppressed in the native tetrameric state. The analyses using Motion Tree and the linear response theory clarified that in the open form, SD and IBCα moved collectively relative to IBCβ with a response upon IP₃ binding within the linear regime, whereas in the closed form, such collectiveness disappeared. These results suggest that the regulation of dynamics via the domain arrangement and multimerization is requisite for large-scale allosteric communication in IP₃R gating machinery.

A computational model for controlling conformational cooperativity and function in proteins

We present a computational model that allows for rapid prediction of correlations among a set of residue pairs when the fluctuations of another set of residues are perturbed. The simple theory presented here is based on the knowledge of the fluctuation covariance matrix only. In this sense, the theory is model independent and therefore universal. Perturbation of any set of fluctuations and the resulting response of the remaining set are calculated using conditional probabilities of a multivariate normal distribution. The model is expected to rapidly and accurately map the consequences of mutations in proteins, as well as allosteric activity and ligand binding. Knowledge of triple correlations of fluctuations of residues i, j, and k, 〈 Δ R i Δ R j Δ R k 〉 emerges as the necessary source of information for controlling residue pairs by perturbing a distant residue. Triple correlations have not received wide attention in literature. Perturbation-response-function relations for ubiquitin (UBQ) are discussed as an example. Covariance matrix for UBQ obtained from the Gaussian Network Model combined with the present computational algorithm is able to reflect the millisecond molecular dynamics correlations and observed NMR results. © 2018 Wiley Periodicals, Inc.

Computational approaches for deciphering the equilibrium and kinetic properties of iron transport proteins

With the advances in three-dimensional structure determination techniques, high quality structures of the iron transport proteins transferrin and the bacterial ferric binding protein (FbpA) have been deposited in the past decade. These are proteins of relatively large size, and developments in hardware and software have only recently made it possible to study their dynamics using standard computational resources. We review computational techniques towards understanding the equilibrium and kinetic properties of iron transport proteins under different environmental conditions. At the level of detail that requires quantum chemical treatments, the octahedral geometry around iron has been scrutinized and it has been established that the iron coordinating tyrosines are in an unusual deprotonated state. At the atomistic level, both the N-lobe and the full bilobal structure of transferrin have been studied under varying conditions of pH, ionic strength and binding of other metal ions by molecular dynamics (MD) simulations. These studies have allowed questions to be answered, among others, on the function of second shell residues in iron release, the role of synergistic anions in preparing the active site for iron binding, and the differences between the kinetics of the N- and the C-lobe. MD simulations on FbpA have led to the detailed observation of the binding kinetics of phosphate to the apo form, and to the conformational preferences of the holo form under conditions mimicking the environmental niches provided by the periplasmic space. To study the dynamics of these proteins with their receptors, one must resort to coarse-grained methodologies, since these systems are prohibitively large for atomistic simulations. A study of the complex of human transferrin (hTf) with its pathogenic receptor by such methods has revealed a potential mechanistic explanation for the defense mechanism that arises in evolutionary warfare. Meanwhile, the motions in the transferrin receptor bound hTf have been shown to disfavor apo hTf dissociation, explaining why the two proteins remain in complex during the recycling process from the endosome to the cell surface. Open problems and possible technological applications related to metal ion binding-release in iron transport proteins that may be handled by hybrid use of quantum mechanical, MD and coarse-grained approaches are discussed.

Atomic torsional modal analysis for high-resolution proteins

We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier one-parameter formulation [M. M. Tirion, Phys. Rev. Lett. 77, 1905 (1996)] that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function that is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states in the 0 to 300cm-1 frequency range, not merely the slow modes. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface side chains and helps fix the spectrum thin tail frequencies (100-300cm-1). Second, we take into account the atomic identities and the distance of separation of all pairwise interactions, improving the spectrum distribution in the 20 to 300cm-1 range. With these modifications, not only does the spectrum reproduce that of full atomic potentials, but we obtain stable reliable eigenmodes for the slow modes and over a wide range of frequencies.

Characterizing conformation changes in proteins through the torsional elastic response

The relationship between functional conformation changes and thermal dynamics of proteins is investigated with the help of the torsional network model (TNM), an elastic network model in torsion angle space that we recently introduced. We propose and test a null-model of "random" conformation changes that assumes that the contributions of normal modes to conformation changes are proportional to their contributions to thermal fluctuations. Deviations from this null model are generally small. When they are large and significant, they consist in conformation changes that are represented by very few low frequency normal modes and overcome small energy barriers. We interpret these features as the result of natural selection favoring the intrinsic protein dynamics consistent with functional conformation changes. These "selected" conformation changes are more frequently associated to ligand binding, and in particular phosphorylation, than to pairs of conformations with the same ligands. This deep relationship between the thermal dynamics of a protein, represented by its normal modes, and its functional dynamics can reconcile in a unique framework the two models of conformation changes, conformational selection and induced fit. The program TNM that computes torsional normal modes and analyzes conformation changes is available upon request. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Long-distance correlations of rhinovirus capsid dynamics contribute to uncoating and antiviral activity

Human rhinovirus (HRV) and other members of the enterovirus genus bind small-molecule antiviral compounds in a cavity buried within the viral capsid protein VP1. These compounds block the release of the viral protein VP4 and RNA from inside the capsid during the uncoating process. In addition, the antiviral compounds prevent "breathing" motions, the transient externalization of the N-terminal regions of VP1 and VP4 from the inside of intact viral capsid. The site for externalization of VP1/VP4 or release of RNA is likely between protomers, distant to the binding cavity for antiviral compounds. Molecular dynamics simulations were conducted to explore how the antiviral compound, WIN 52084, alters properties of the HRV 14 capsid through long-distance effect. We developed an approach to analyze capsid dynamics in terms of correlated radial motion and the shortest paths of correlated motions. In the absence of WIN, correlated radial motion is observed between residues separated by as much as 85 Å, a remarkably long distance. The most frequently populated path segments of the network were localized near the fivefold symmetry axis and included those connecting the N termini of VP1 and VP4 with other regions, in particular near twofold symmetry axes, of the capsid. The results provide evidence that the virus capsid exhibits concerted long-range dynamics, which have not been previously recognized. Moreover, the presence of WIN destroys this radial correlation network, suggesting that the underlying motions contribute to a mechanistic basis for the initial steps of VP1 and VP4 externalization and uncoating.

Comparative molecular dynamics simulation study of crystal environment effect on protein structure

Crystal structures of proteins are under the influence from the crystal environment. In this study, we used molecular dynamics (MD) simulations to explore the possibility of eliminating the effect of the crystal packing and recovering the structure in solution. Ten representative proteins were chosen from the Protein Structural Change Database as the target systems, and 50 ns MD stimulations starting from two crystal structures having different domain arrangements were performed for each. The MD trajectories of the relaxation processes upon the release from the crystal environment revealed that the behaviors of the proteins were classified into three groups: "single domain linker", "harmonic motion", and "large barrier". We discuss the structural features common to the proteins in each group.

PSCDB: a database for protein structural change upon ligand binding

Proteins are flexible molecules that undergo structural changes to function. The Protein Data Bank contains multiple entries for identical proteins determined under different conditions, e.g. with and without a ligand molecule, which provides important information for understanding the structural changes related to protein functions. We gathered 839 protein structural pairs of ligand-free and ligand-bound states from monomeric or homo-dimeric proteins, and constructed the Protein Structural Change DataBase (PSCDB). In the database, we focused on whether the motions were coupled with ligand binding. As a result, the protein structural changes were classified into seven classes, i.e. coupled domain motion (59 structural changes), independent domain motion (70), coupled local motion (125), independent local motion (135), burying ligand motion (104), no significant motion (311) and other type motion (35). PSCDB provides lists of each class. On each entry page, users can view detailed information about the motion, accompanied by a morphing animation of the structural changes. PSCDB is available at http://idp1.force.cs.is.nagoya-u.ac.jp/pscdb/.

On the role of electrostatics in protein-protein interactions

The role of electrostatics in protein-protein interactions and binding is reviewed in this paper. A brief outline of the computational modeling, in the framework of continuum electrostatics, is presented and the basic electrostatic effects occurring upon the formation of the complex are discussed. The effect of the salt concentration and pH of the water phase on protein-protein binding free energy is demonstrated which indicates that the increase of the salt concentration tends to weaken the binding, an observation that is attributed to the optimization of the charge-charge interactions across the interface. It is pointed out that the pH-optimum (pH of optimal binding affinity) varies among the protein-protein complexes, and perhaps is a result of their adaptation to particular subcellular compartments. The similarities and differences between hetero- and homo-complexes are outlined and discussed with respect to the binding mode and charge complementarity.

Classification and annotation of the relationship between protein structural change and ligand binding

The causal relationship between protein structural change and ligand binding was classified and annotated for 839 nonredundant pairs of crystal structures in the Protein Data Bank-one with and the other without a bound low-molecular-weight ligand molecule. Protein structural changes were first classified into either domain or local motions depending on the size of the moving protein segments. Whether the protein motion was coupled with ligand binding was then evaluated based on the location of the ligand binding site and by application of the linear response theory of protein structural change. Protein motions coupled with ligand binding were further classified into either closure or opening motions. This classification revealed the following: (i) domain motions coupled with ligand binding are dominated by closure motions, which can be described by the linear response theory; (ii) local motions frequently accompany order-disorder or α-helix-coil conformational transitions; and (iii) transferase activity (Enzyme Commission number 2) is the predominant function among coupled domain closure motions. This could be explained by the closure motion acting to insulate the reaction site of these enzymes from environmental water.

An interpretation of positional displacement of the helix12 in nuclear receptors: preexistent swing-up motion triggered by ligand binding

Positional displacement of helix12 (H12) in the estrogen receptor alpha, which belongs to the nuclear receptor (NR) superfamily, is studied by the molecular dynamics (MD) simulation and the linear response theory. Tendency of the H12 to swing up upon ligand binding, which is consistent with X-ray structures and earlier MD simulations, is reproduced by the calculation of the conformational fluctuation in apo state and the response to the external perturbation. Our study thus provides an interpretation of the positional change of the H12 such that it is derived by the preexistent swing-up motion where the ligand binding works only as a trigger. Our finding, which illustrates underlying mechanism of the H12 motion, would contribute to finding a way to regulate the transcriptional activity by synthesized ligands because the transcriptional activity of the NR is governed by the position of the H12.

Torsional network model: normal modes in torsion angle space better correlate with conformation changes in proteins

We introduce the torsional network model (TNM), an elastic network model whose degrees of freedom are the torsion angles of the protein backbone. Normal modes of the TNM displace backbone atoms including C(β) maintaining their covalent geometry. For many proteins, low frequency TNM modes are localized in torsion space yet collective in Cartesian space, reminiscent of hinge motions. A smaller number of TNM modes than anisotropic network model modes are enough to represent experimentally observed conformation changes. We observed significant correlation between the contribution of each normal mode to equilibrium fluctuations and to conformation changes, and defined the excess correlation with respect to a simple neutral model. The stronger this excess correlation, the lower the predicted free energy barrier of the conformation change and the fewer modes contribute to the change.