Collective Motions Of Proteins Research Articles

Introduction to diffuse scattering and data collection.

A long-standing goal in X-ray crystallography has been to extract information about the collective motions of proteins from diffuse scattering: the weak, textured signal that is found in the background of diffraction images. In the past few years, the field of macromolecular diffuse scattering has seen dramatic progress, and many of the past challenges in measurement and interpretation are now considered tractable. However, the concept of diffuse scattering is still new to many researchers, and a general set of procedures needed to collect a high-quality dataset has never been described in detail. Here, we provide the first guidelines for performing diffuse scattering experiments, which can be performed at any macromolecular crystallography beamline that supports room-temperature studies with a direct detector. We begin with a brief introduction to the theory of diffuse scattering and then walk the reader through the decision-making processes involved in preparing for and conducting a successful diffuse scattering experiment. Finally, we define quality metrics and describe ways to assess data quality both at the beamline and at home. Data obtained in this way can be processed independently by crystallographic software and diffuse scattering software to produce both a crystal structure, which represents the average atomic coordinates, and a three-dimensional diffuse scattering map that can then be interpreted in terms of models for protein motions.

Dynamic Connection between Enzymatic Catalysis and Collective Protein Motions.

Enzymes employ a wide range of protein motions to achieve efficient catalysis of chemical reactions. While the role of collective protein motions in substrate binding, product release, and regulation of enzymatic activity is generally understood, their roles in catalytic steps per se remain uncertain. Here, molecular dynamics simulations, enzyme kinetics, X-ray crystallography, and nuclear magnetic resonance spectroscopy are combined to elucidate the catalytic mechanism of adenylate kinase and to delineate the roles of catalytic residues in catalysis and the conformational change in the enzyme. This study reveals that the motions in the active site, which occur on a time scale of picoseconds to nanoseconds, link the catalytic reaction to the slow conformational dynamics of the enzyme by modulating the free energy landscapes of subdomain motions. In particular, substantial conformational rearrangement occurs in the active site following the catalytic reaction. This rearrangement not only affects the reaction barrier but also promotes a more open conformation of the enzyme after the reaction, which then results in an accelerated opening of the enzyme compared to that of the reactant state. The results illustrate a linkage between enzymatic catalysis and collective protein motions, whereby the disparate time scales between the two processes are bridged by a cascade of intermediate-scale motion of catalytic residues modulating the free energy landscapes of the catalytic and conformational change processes.

Virtual Screening for the Identification of Potential Candidate Molecules Against Envelope (E) and Membrane (M) Proteins of SARS-CoV-2

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) causes COVID-19, a disease currently spreading around the world. Some drugs are underway or being used to combat this disease. Several proteins of the virus can be targeted in therapeutic approaches. Two structural proteins, membrane (M), envelope (E) have critical roles in virus life cycle, such as assembly, budding, envelope formation and pathogenesis. Here, we employed the in silico strategies to identify and evaluate the selected potential compounds against M and E proteins. For this, the structures of proteins were modeled and then several groups of compounds as FDA approved, natural products or under clinical trials were screened from DrugBank and ZINC databases. The selected dockings were analyzed and the ligands with best binding affinity scores were subjected to evaluate drug-likeness and medicinal chemistry friendliness through prediction of ADMET properties. Normal mode analyses were also performed for six selected complexes to explore the collective motions of proteins. Molecular dynamic (MD) simulation was also performed to calculate the stability of two docked protein–ligand complexes. The results revealed that several compounds had high affinity to the proteins along with some acceptable profiles of mobility and deformability, especially, for M protein.

Erratum: "Edge expansion parallel cascade selection molecular dynamics simulation for investigating large-amplitude collective motions of proteins" [J. Chem. Phys. 152, 225101 (2020)

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Efficient Conformational Sampling of Collective Motions of Proteins with Principal Component Analysis-Based Parallel Cascade Selection Molecular Dynamics.

Molecular dynamics (MD) simulation has become a powerful tool because it provides a time series of protein dynamics at high temporal-spatial resolution. However, the accessible timescales of MD simulation are shorter than those of the biologically rare events. Generally, long-time MD simulations over microseconds are required to detect the rare events. Therefore, it is desirable to develop rare-event-sampling methods. For a rare-event-sampling method, we have developed parallel cascade selection MD (PaCS-MD). PaCS-MD generates transition pathways from a given source structure to a target structure by repeating short-time MD simulations. The key point in PaCS-MD is how to select reasonable candidates (protein configurations) with high potentials to make transitions toward the target structure. In the present study, based on principal component analysis (PCA), we propose PCA-based PaCS-MD to detect rare events of collective motions of a given protein. Here, the PCA-based PaCS-MD is composed of the following two steps. At first, as a preliminary run, PCA is performed using an MD trajectory from the target structure to define a principal coordinate (PC) subspace for describing the collective motions of interest. PCA provides principal modes as eigenvectors to project a protein configuration onto the PC subspace. Then, as a production run, all the snapshots of short-time MD simulations are ranked by inner products (IPs), where an IP is defined between a snapshot and the target structure. Then, snapshots with higher values of the IP are selected as reasonable candidates, and short-time MD simulations are independently restarted from them. By referring to the values of the IP, the PCA-based PaCS-MD repeats the short-time MD simulations from the reasonable candidates that are highly correlated with the target structure. As a demonstration, we applied the PCA-based PaCS-MD to adenylate kinase and detected its large-amplitude (open-closed) transition with a nanosecond-order computational cost.

Edge expansion parallel cascade selection molecular dynamics simulation for investigating large-amplitude collective motions of proteins.

We propose edge expansion parallel cascade selection molecular dynamics (eePaCS-MD) as an efficient adaptive conformational sampling method to investigate the large-amplitude motions of proteins without prior knowledge of the conformational transitions. In this method, multiple independent MD simulations are iteratively conducted from initial structures randomly selected from the vertices of a multi-dimensional principal component subspace. This subspace is defined by an ensemble of protein conformations sampled during previous cycles of eePaCS-MD. The edges and vertices of the conformational subspace are determined by solving the "convex hull problem." The sampling efficiency of eePaCS-MD is achieved by intensively repeating MD simulations from the vertex structures, which increases the probability of rare event occurrence to explore new large-amplitude collective motions. The conformational sampling efficiency of eePaCS-MD was assessed by investigating the open-close transitions of glutamine binding protein, maltose/maltodextrin binding protein, and adenylate kinase and comparing the results to those obtained using related methods. In all cases, the open-close transitions were simulated in ∼10 ns of simulation time or less, offering 1-3 orders of magnitude shorter simulation time compared to conventional MD. Furthermore, we show that the combination of eePaCS-MD and accelerated MD can further enhance conformational sampling efficiency, which reduced the total computational cost of observing the open-close transitions by at most 36%.

High-Precision Megahertz-to-Terahertz Dielectric Spectroscopy of Protein Collective Motions and Hydration Dynamics.

The low-frequency collective vibrational modes in proteins as well as the protein-water interface have been suggested as dominant factors controlling the efficiency of biochemical reactions and biological energy transport. It is thus crucial to uncover the mystery of the hydration structure and dynamics as well as their coupling to collective motions of proteins in aqueous solutions. Here, we report dielectric properties of aqueous bovine serum albumin protein solutions as a model system using an extremely sensitive dielectric spectrometer with frequencies spanning from megahertz to terahertz. The dielectric relaxation spectra reveal several polarization mechanisms at the molecular level with different time constants and dielectric strengths, reflecting the complexity of protein-water interactions. Combining the effective-medium approximation and molecular dynamics simulations, we have determined collective vibrational modes at terahertz frequencies and the number of water molecules in the tightly bound and loosely bound hydration layers. High-precision measurements of the number of hydration water molecules indicate that the dynamical influence of proteins extends beyond the first solvation layer, to around 7 Å distance from the protein surface, with the largest slowdown arising from water molecules directly hydrogen-bonded to the protein. Our results reveal critical information of protein dynamics and protein-water interfaces, which determine biochemical functions and reactivity of proteins.

Probing collective Motions of Proteins and Hydration Dynamics in Aqueous Solutions by a Wide Range Dielectric Spectroscopy

Conformational dynamics of proteins affect how biological molecules exert their function and regulate their biological processes. Studying the dynamics of proteins and their hydration allows us to analyze their functions in aqueous solutions. However, the strong absorption of water makes tracking collective mode changes challenging. Thus, we have developed a very sensitive dielectric megahertz-to-terahertz frequency-domain spectroscopy system to probe the hydration shells as well as large-scale dynamics of these biomolecules. Using this system, we explore the real and imaginary dielectric response of solvated biomolecules over a range of 50 MHz to 2 THz. We have chosen several proteins to provide a model system including bovine serum albumin (BSA), lysozyme, cytochome_c, and myoglobin proteins. We have compared the dynamics of proteins as well as their hydration water. We have deduced the dynamics and the hydration water of these proteins by comparing their real and imaginary dielectric response and hydration water relaxation times. Comparing these assets of various proteins in different classes helps us shed light on the macromolecular dynamics in a biologically relevant water environment.

A framework of finite element procedures for the analysis of proteins

Large-scale, functional collective motions of proteins and their supra-molecular assemblies occur in a physiological solvent environment at finite temperatures. The solution of these motions with standard molecular dynamics algorithms is computationally hardly possible when considering macromolecules. Much research has focused on alternative approaches that use coarse-graining to model proteins, but mostly in vacuum. In this paper, we incorporate realistically the physical effects of solvent damping into the finite element model of proteins. The proposed framework is based on Brownian dynamics and shown to be effective. An important advantage of the approach is that the computational cost is not dependent on the molecular size, which makes the long-time simulation of macromolecules possible. Using the proposed procedure, we demonstrate the analysis of a macromolecule in solvent—an analysis that has not been achieved before and could not be performed with a molecular dynamics algorithm.

A better prediction of conformational changes of proteins using minimally connected network models

Elastic network models have recently been used for studying low-frequency collective motions of proteins. These models simplify the complexity that arises from normal mode analysis by considering a simplified potential involving a few parameters. Two common parameters in most of the elastic network models are cutoff radius and force constant. Although the latter has been studied extensively and even elaborate new models were introduced, for the former usually an ad-hoc cutoff radius is considered. Moreover, the quality of the network models is usually assessed by evaluating their prediction against experimental B-factors. In this work, we consider various common elastic network models with different cutoff radii and assess them by their ability to predict conformational changes of proteins in complexes from unbound to bound state. This prediction is performed by perturbing the unbound structure using a number of low-frequency normal modes of its network model to optimally fit the bound structure. We evaluated a dataset of 30 proteins with distinct unbound and bound structures using this criterion. The results showed that, opposed to the common calibration process based on B-factors, a meaningful relationship exists between the quality of the prediction and model parameters. It was shown that the cutoff radius has a major role in this prediction and minimally connected network models, which use the shortest cutoff radius for which the network is stable, give the best results. It was also shown that by considering the first ten normal modes, the conformational changes can be predicted by about 25 percent. Hence, the evaluation process was extended to the case of considering the contribution of all normal modes in the prediction. The results indicated that minimally connected network models are superior, despite their simplicity, when any number of modes are considered in the prediction.

Collective Variable Approaches for Single Molecule Flexible Fitting and Enhanced Sampling

It is now well established that proteins and nucleic acids undergo local and global conformational fluctuations to perform a variety of cellular functions such as signal transduction, transport, and catalysis.1 Many experimental techniques such as X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, small-angle X-ray scattering (SAXS), and single-particle electron microscopy (EM) have indeed provided structural evidence at different resolutions to support the view of multiple functional states of biomolecules. Yet it remains difficult to characterize the vast conformational repertoire of biomolecules via experimental methods alone. Therefore, biophysical theory, modeling, and simulation techniques rooted in statistical mechanics are often useful for a detailed molecular understanding of biomolecular structures.2−5 Despite the limitations of molecular mechanics interaction potentials, computational methods can now be combined with low-resolution structural data to generate experimentally consistent conformational ensembles as well as to probe underlying mechanistic questions. Analyses of structural data for different functional states of biomolecules have revealed large-scale conformational rearrangements on the scales of entire domains. This means that a large group of atoms collectively move in a concerted way to facilitate functional movements. Traditionally, one relatively less expensive computational method to analyze collective motions in proteins has been to carry out normal-mode analysis (NMA) of equilibrium structures, because low-frequency modes are typically indicative of high-amplitude/large-scale motions.6−8 Such global and collective modes are robust, independent of sequence detail, and are intrinsically accessible to each biomolecule because they are encoded in their global shape.9−13 Given that the total number of degrees-of-freedom (DOF) in biomolecules is very large, NMA provides an efficient way to describe biomolecular dynamics in a reduced number of variables. As was originally pointed out by Hayward and Go,6 this reduction in dimensionality has led to the concept of an important subspace of variables, “collective variables (CVs)”, that are well-suited to characterize the dynamics of biomolecules. Interestingly, the concept of CVs as reaction coordinates has been recently extended to atomistic molecular dynamics (MD) simulations,14 which has significantly increased their capability in capturing long time-scale motions. This is chiefly possible because sampling in these CVs can be carried out more extensively in comparison to all possible DOF. Such methods are typically referred to as enhanced sampling techniques because they increase the likelihood of observation of a rare biomolecular event. The range of studies in which NMA and MD simulations have played a central role is immense, and it is not possible to do justice to all such studies in this focused Review. However, we refer the reader to pertinent comprehensive literature on those subjects along the way. Therefore, we have limited the scope of this Review to some specific applications of NMA, and enhanced sampling via temperature-acceleration in the context of flexible fitting to low-resolution EM data on macromolecular complexes. Particularly, we concentrate on two methods in this Review: (a) normal mode flexible fitting (NMFF)15,16 for structural refinement into EM maps; and (b) temperature-accelerated molecular dynamics (TAMD)17,18 for conformational exploration and flexible fitting. We first discuss theoretical underpinnings of all-atom and coarse-grained NMA of protein structures, which is followed by highlights of various successful applications. The theory and applications of NMA for flexible fitting of protein structures into EM maps are described thereafter. This is immediately followed by a discussion of the importance of enhanced sampling in biomolecular simulations, and how dynamics in these systems can be explored by evolving CVs via temperature acceleration, for example. Specifically, we discuss in detail various aspects of TAMD. During these discussions, we further highlight a few of the many cases where NMA and TAMD have alleviated difficulties faced by other methods in understanding large-scale functional excursions in biomolecules. This Review concludes with a brief overview and future outlook for these methods.

Using THz time-scale infrared spectroscopy to examine the role of collective, thermal fluctuations in the formation of myoglobin allosteric communication pathways and ligand specificity.

In this investigation we use THz time-scale spectroscopy to conduct an initial set of studies on myoglobin with the aim of providing further insight into the global, collective thermal fluctuations in the protein that have been hypothesized to play a prominent role in the dynamic formation of transient ligand channels as well as in shaping the molecular level basis for ligand discrimination. Using the two ligands O2 and CO, we have determined that the perturbation from the heme-ligand complex has a strong influence on the characteristics of the myoglobin collective dynamics that are excited upon binding. Further, the differences detected in the collective protein motions in Mb-O2 compared with those in Mb-CO appear to be intimately tied with the pathways of long-range allosteric communication in the protein, which ultimately determine the trajectories selected by the respective ligands on the path to and from the heme-binding cavity.

Spatio-temporal hierarchy in the dynamics of a minimalist protein model

A method for time series analysis of molecular dynamics simulation of a protein is presented. In this approach, wavelet analysis and principal component analysis are combined to decompose the spatio-temporal protein dynamics into contributions from a hierarchy of different time and space scales. Unlike the conventional Fourier-based approaches, the time-localized wavelet basis captures the vibrational energy transfers among the collective motions of proteins. As an illustrative vehicle, we have applied our method to a coarse-grained minimalist protein model. During the folding and unfolding transitions of the protein, vibrational energy transfers between the fast and slow time scales were observed among the large-amplitude collective coordinates while the other small-amplitude motions are regarded as thermal noise. Analysis employing a Gaussian-based measure revealed that the time scales of the energy redistribution in the subspace spanned by such large-amplitude collective coordinates are slow compared to the other small-amplitude coordinates. Future prospects of the method are discussed in detail.

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions.

Elastic network models (ENMs) are valuable tools for investigating collective motions of proteins, and a rich variety of simple models have been proposed over the past decade. A good representation of the collective motions requires a good approximation of the covariances between the fluctuations of the individual atoms. Nevertheless, most studies have validated such models only by the magnitudes of the single-atom fluctuations they predict. In the present study, we have quantified the agreement between the covariance structure predicted by molecular dynamics (MD) simulations and those predicted by a representative selection of proposed coarse-grained ENMs. We then contrast this approach with the comparison to MD-predicted atomic fluctuations and comparison to crystallographic B-factors. While all the ENMs yield approximations to the MD-predicted covariance structure, we report large and consistent differences between proposed models. We also find that the ability of the ENMs to predict atomic fluctuations is correlated with their ability to capture the covariance structure. In contrast, we find that the models that agree best with B-factors model collective motions less reliably and recommend against using B-factors as a benchmark.

QM/MM Calculations Suggest a Novel Intermediate Following the Proton Abstraction Catalyzed by Thymidylate Synthase

The cleavage of covalent C-H bonds is one of the most energetically demanding, yet biologically essential, chemical transformations. Two C-H bond cleavages are involved in the reaction catalyzed by thymidylate synthase (TSase), which provides the sole de novo source of thymidylate (i.e., the DNA base T) for most organisms. Our QM/MM free energy calculations show that the C-H → O proton transfer has three transition states that are energetically similar but structurally diverse. These characteristics are different from our previous calculation results on the C-H → C hydride transfer, providing an explanation for differences in temperature dependences of KIEs on these two C-H bond activation steps. The calculations also suggest that the traditionally proposed covalent bond between the protein and substrate (the C6-S bond) is very labile during the multistep catalytic reaction. Collective protein motions not only assist cleavage of the C6-S bond to stabilize the transition state of the proton transfer step but also rearrange the H-bond network at the end of this step to prepare the active site for subsequent chemical steps. These computational results illustrate functionalities of specific protein residues that reconcile many previous experimental observations and provide guidance for future experiments to examine the proposed mechanisms. The synchronized conformational changes in the protein and ligands observed in our simulations demonstrate participation of protein motions in the reaction coordinate of enzymatic reactions. Our computational findings suggest the existence of new reaction intermediates not covalently bound to TSase, which may lead to a new class of drugs targeting DNA biosynthesis.

Pre-existing soft modes of motion uniquely defined by native contact topology facilitate ligand binding to proteins.

Modeling protein flexibility constitutes a major challenge in accurate prediction of protein-ligand and protein-protein interactions in docking simulations. The lack of a reliable method for predicting the conformational changes relevant to substrate binding prevents the productive application of computational docking to proteins that undergo large structural rearrangements. Here, we examine how coarse-grained normal mode analysis has been advantageously applied to modeling protein flexibility associated with ligand binding. First, we highlight recent studies that have shown that there is a close agreement between the large-scale collective motions of proteins predicted by elastic network models and the structural changes experimentally observed upon ligand binding. Then, we discuss studies that have exploited the predicted soft modes in docking simulations. Two general strategies are noted: pregeneration of conformational ensembles that are then utilized as input for standard fixed-backbone docking and protein structure deformation along normal modes concurrent to docking. These studies show that the structural changes apparently "induced" upon ligand binding occur selectively along the soft modes accessible to the protein prior to ligand binding. They further suggest that proteins offer suitable means of accommodating/facilitating the recognition and binding of their ligand, presumably acquired by evolutionary selection of the suitable three-dimensional structure.

Detecting coupled collective motions in protein by independent subspace analysis

Protein dynamics evolves in a high-dimensional space, comprising aharmonic, strongly correlated motional modes. Such correlation often plays an important role in analyzing protein function. In order to identify significantly correlated collective motions, here we employ independent subspace analysis based on the subspace joint approximate diagonalization of eigenmatrices algorithm for the analysis of molecular dynamics (MD) simulation trajectories. From the 100 ns MD simulation of T4 lysozyme, we extract several independent subspaces in each of which collective modes are significantly correlated, and identify the other modes as independent. This method successfully detects the modes along which long-tailed non-Gaussian probability distributions are obtained. Based on the time cross-correlation analysis, we identified a series of events among domain motions and more localized motions in the protein, indicating the connection between the functionally relevant phenomena which have been independently revealed by experiments.

Validating and improving elastic network models with molecular dynamics simulations

Elastic network models (ENMs) are a class of simple models intended to represent the collective motions of proteins. In contrast to all-atom molecular dynamics simulations, the low computational investment required to use an ENM makes them ideal for speculative hypothesis-testing situations. Historically, ENMs have been validated via comparison to crystallographic B-factors, but this comparison is relatively low-resolution and only tests the predictions of relative flexibility. In this work, we systematically validate and optimize a number of ENM-type models by quantitatively comparing their predictions to microsecond-scale all-atom simulations of three different G protein coupled receptors. We show that, despite their apparent simplicity, well-optimized ENMs perform remarkably well, reproducing the protein fluctuations with an accuracy comparable to what one would expect from all-atom simulations run for several hundred nanoseconds.

Effects of Disease Causing Mutations on the Essential Motions in Proteins

This study embodies a detailed comparative analysis of the essential motions of the Wild type and the eight different disease mutant forms of the Human CYPlbl. The mutations considered in this study have been implicated in Primary Congenital Glaucoma, an in-born, genetic disorder associated with eye-abnormality. The principal component analysis for Wild type and the Mutants was carried out using the stabilized molecular dynamics trajectories, which ranged from 35 to 45 nanoseconds. Investigations revealed the nature of the collective motions that characterize functionally relevant ‘essential motions’. The essential motions in Wild type are characterized by the collective motions of the Substrate Access Channel including the β-rich domain and the loops in the region of p450-reductase interaction. Comparative analysis of the essential motions of the Wild type and Mutants, especially those involving the functionally important regions indicated distinct differences in their magnitudes as well as the residue-wise distribution. The Mutants in general are associated with higher root mean square fluctuations, and involve some of the relatively intact core regions of the protein, in large collective motions. This study sheds light on the possible effects of disease causing mutations on the large functionally important collective motions in proteins.

Communication Breakdown: Protein Dynamics and Drug Design

Mauldin et al. (2009) use NMR to show that drug binding can break up collective protein motions necessary for function. We discuss their findings in the context of drug discovery in pharmaceutical research.