Ivet Bahar

Anisotropy of Fluctuation Dynamics of Proteins with an Elastic Network Model

Fluctuations about the native conformation of proteins have proven to be suitably reproduced with a simple elastic network model, which has shown excellent agreement with a number of different properties for a wide variety of proteins. This scalar model simply investigates the magnitudes of motion of individual residues in the structure. To use the elastic model approach further for developing the details of protein mechanisms, it becomes essential to expand this model to include the added details of the directions of individual residue fluctuations. In this paper a new tool is presented for this purpose and applied to the retinol-binding protein, which indicates enhanced flexibility in the region of entry to the ligand binding site and for the portion of the protein binding to its carrier protein.

Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential

BACKGROUND An elastic network model is proposed for the interactions between closely (< or = 7.0 A) located alpha-carbon pairs in folded proteins. A single-parameter harmonic potential is adopted for the fluctuations of residues about their mean positions in the crystal structure. The model is based on writing the Kirchhoff adjacency matrix for a protein defining the proximity of residues in space. The elements of the inverse of the Kirchhoff matrix give directly the auto-correlations or cross-correlations of atomic fluctuations. RESULTS The temperature factors of the C alpha atoms of 12 X-ray structures, ranging from a 41 residue subunit to a 633 residue dimer, are accurately predicted. Cross-correlations are also efficiently characterized, in close agreement with results obtained with a normal mode analysis coupled with energy minimization. CONCLUSIONS The simple model and method proposed here provide a satisfactory description of the correlations between atomic fluctuations. Furthermore, this is achieved within computation times at least one order of magnitude shorter than commonly used molecular approaches.

Global Dynamics of Proteins: Bridging Between Structure and Function

Biomolecular systems possess unique, structure-encoded dynamic properties that underlie their biological functions. Recent studies indicate that these dynamic properties are determined to a large extent by the topology of native contacts. In recent years, elastic network models used in conjunction with normal mode analyses have proven to be useful for elucidating the collective dynamics intrinsically accessible under native state conditions, including in particular the global modes of motions that are robustly defined by the overall architecture. With increasing availability of structural data for well-studied proteins in different forms (liganded, complexed, or free), there is increasing evidence in support of the correspondence between functional changes in structures observed in experiments and the global motions predicted by these coarse-grained analyses. These observed correlations suggest that computational methods may be advantageously employed for assessing functional changes in structure and allosteric mechanisms intrinsically favored by the native fold.

ProDy: protein dynamics inferred from theory and experiments.

Summary: We developed a Python package, ProDy, for structure-based analysis of protein dynamics. ProDy allows for quantitative characterization of structural variations in heterogeneous datasets of structures experimentally resolved for a given biomolecular system, and for comparison of these variations with the theoretically predicted equilibrium dynamics. Datasets include structural ensembles for a given family or subfamily of proteins, their mutants and sequence homologues, in the presence/absence of their substrates, ligands or inhibitors. Numerous helper functions enable comparative analysis of experimental and theoretical data, and visualization of the principal changes in conformations that are accessible in different functional states. ProDy application programming interface (API) has been designed so that users can easily extend the software and implement new methods. Availability: ProDy is open source and freely available under GNU General Public License from http://www.csb.pitt.edu/ProDy/. Contact: ahb12@pitt.edu; bahar@pitt.edu

Cardiolipin externalization to the outer mitochondrial membrane acts as an elimination signal for mitophagy in neuronal cells

Recognition of injured mitochondria for degradation by macroautophagy is essential for cellular health, but the mechanisms remain poorly understood. Cardiolipin is an inner mitochondrial membrane phospholipid. We found that rotenone, staurosporine, 6-hydroxydopamine and other pro-mitophagy stimuli caused externalization of cardiolipin to the mitochondrial surface in primary cortical neurons and SH-SY5Y cells. RNAi knockdown of cardiolipin synthase or of phospholipid scramblase-3, which transports cardiolipin to the outer mitochondrial membrane, decreased the delivery of mitochondria to autophagosomes. Furthermore, we found that the autophagy protein microtubule-associated-protein-1 light chain 3 (LC3), which mediates both autophagosome formation and cargo recognition, contains cardiolipin-binding sites important for the engulfment of mitochondria by the autophagic system. Mutation of LC3 residues predicted as cardiolipin-interaction sites by computational modelling inhibited its participation in mitophagy. These data indicate that redistribution of cardiolipin serves as an ‘eat-me’ signal for the elimination of damaged mitochondria from neuronal cells.

Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins

1.1. Protein Dynamics and Allostery 1.1.1. Dynamic Equilibrium between Pre-existing Conformations The ability of macromolecules to sample an ensemble of conformations has been evident for decades, starting from the statistical mechanical theory and simulations of polymers.1–3 A polymer chain of N atoms enjoys 3N – 6 internal degrees of freedom, which gives rise to infinitely many conformations. Even a simple model of N = 100 atoms where bond lengths and bond angles are fixed, and dihedral angles are restricted to discrete isomeric states—say three states per bond—has access to 3N–3 = 1.9 × 1046 conformations. Proteins, too, are polymers, and have access to ensembles of conformations. The main structural difference between proteins and other chain molecules is that, under physiological conditions, proteins sample a significantly narrower distribution of conformations compared to disordered polymers. Their conformational variations are confined to the neighborhood of a global energy minimum that defines their “native state”. While the native state has been traditionally viewed as a “unique structure” selected or encoded by the particular amino acid sequence, it is now established by theory, computations, and experiments, after the work of pioneering scientists in the field,4–15 that the native state actually represents an ensemble of microstates: these microstates maintain the overall “fold” and usually share common secondary structure, but they differ in their detailed atomic coordinates. Differences are manifested by variations in bond lengths, bond angles, dihedral angles, loop conformations, substructure packing, or even entire domain or subunit positions and orientations. Importantly, these microstates are not static: there is a dynamic equilibrium which allows for continual interconversions between them while maintaining their probability distribution. These “jigglings and wigglings of atoms” as expressed by Feynman,16 and clearly observed in molecular dynamics (MD) simulations, were originally viewed as random events, or stochastic properties, hardly relevant to biological function. They essentially account for local relaxation phenomena in the nanoseconds regime, which may facilitate, for example, the diffusion of oxygen into the heme cavity of myoglobin17 or the permeation of ions across selectivity filters in ion channels.18–20 However, recent studies indicate that these thermal fluctuations may not only passively facilitate but also actively drive concerted domain movements and/or allosteric interactions, such as those required for substrate binding, ion channel gating, or catalytic function.15,21–34 Figure 1 provides an overview of the broad range of equilibrium motions accessible under native state conditions, ranging from bond length vibrations, of the order of femtoseconds, to coupled movements of multimeric substructures, of the order of milliseconds or seconds. Figure 1 Equilibrium motions of proteins. Motions accessible near native state conditions range from femtoseconds (bond length vibrations) to milliseconds or slower (concerted movements of multiple subunits; passages between equilibrium substates). X-ray crystallographic ... 1.1.2. Functional Significance of Collective Motions In the last two decades, there has been a surge in the number of studies based on principal components analysis (PCA)36 of biomolecular structures and dynamics. These studies have proven useful in unraveling the collective modes, and in particular those at the low frequency end of the mode spectrum, that underlie the equilibrium dynamics of proteins.37 Normal mode analysis (NMA) of equilibrium structures,38,39 essential dynamics analysis (EDA) of the covariance matrices retrieved from MD runs,40 and singular value decomposition (SVD) of MD or Monte Carlo (MC) trajectories41–43 all fall in this category of PCA-based methods. Recently, a server has been developed to efficiently perform such calculations using a variety of input structures.44 PCA-based studies provide increasing support to the view that the apparently random fluctuations of proteins under native state conditions conceal contributions from highly cooperative movements (e.g., concerted opening and closing of domains) that are directly relevant to biological function. Functional movements indeed involve passages between collections of microstates or substates that coexist in a dynamic equilibrium (Figure 2). The most cooperative motions usually occur at the low frequency end of the mode spectrum. These modes engage large substructures, if not the entire structure, hence their designation as global or essential modes. They are intrinsically accessible to biomolecules, arising solely from structure. In a sense, in the same way as sequence encodes structure, structure encodes the equilibrium dynamics. We refer to these global movements that are collectively encoded by the 3-dimensional (3D) structure as intrinsic motions of the examined protein, intrinsic to the protein fold or topology of native contacts. Biomolecular structures conceivably evolved to favor the global modes that help them achieve their biological or allosteric functions.21 Briefly, the emerging paradigm is structure-encodes-dynamics-encodes-function, and an evolutionary pressure originating from functional dynamics requirements may have selected the relatively small space of functional structures. Figure 2 Energy profile of the native state modeled at different resolutions. N denotes the native state, modeled at a coarse-grained scale as a single energy minimum. A more detailed examination of the structure and energetics reveals two or more substates (S1, ... The predisposition of proteins to undergo functional changes in structure is now supported by numerous experimental and computational studies, and an increasing amount of data demonstrates that allosteric responses are driven by intrinsically accessible motions.15,23,24,45–51 These studies have brought a new understanding to the role of collective dynamics in protein functions, demonstrating in particular how the functions of membrane proteins such as signal transduction, pore opening, ion gating, or substrate translocation are enabled by the cooperative movements of symmetrically arranged subunits. These findings are in support of the original Monod–Wyman–Changeux (MWC) view of allosteric effects,52,53 the main tenets of which are predisposition of the structure to access alternative conformations via cooperative changes in structure (simultaneously engaging all subunits) and selection from this pool of accessible conformation to achieve biological function in the presence of ligand/substrate binding. Recent findings on the relevance of global modes to functional dynamics are presented below for select, widely studied membrane proteins. The goal here is to review NMA-based computational methods and their applications to membrane proteins. We will also discuss recent developments for improving the methodology and its implementation in structure refinement and drug discovery methods.

Structure-derived potentials and protein simulations

There has recently been an explosion in the number of structure-derived potential functions that are based on the increasing number of high-resolution protein crystal structures. These functions differ principally in their reference states; the usual two classes correspond either to initial solvent exposure or to residue exposure of residues. Reference states are critically important for applications of these potentials functions. Inspection of the potential functions and their derivation can tell us not only about protein interaction strengths themselves, but can also provide suggestions for the design of better folding simulations. An appropriate goal in this field is achieving self-consistency between the details in the derivation of potentials and the applied simulations.

Anisotropic network model: systematic evaluation and a new web interface

MOTIVATION The Anisotropic Network Model (ANM) is a simple yet powerful model for normal mode analysis of proteins. Despite its broad use for exploring biomolecular collective motions, ANM has not been systematically evaluated to date. A lack of a convenient interface has been an additional obstacle for easy usage. RESULTS ANM has been evaluated on a large set of proteins to establish the optimal model parameters that achieve the highest correlation with experimental data and its limits of accuracy and applicability. Residue fluctuations in globular proteins are shown to be more accurately predicted than those in nonglobular proteins, and core residues are more accurately described than solvent-exposed ones. Significant improvement in agreement with experiments is observed with increase in the resolution of the examined structure. A new server for ANM calculations is presented, which offers flexible options for controlling model parameters and output formats, interactive animation of collective modes and advanced graphical features. AVAILABILITY ANM server (http://www.ccbb.pitt.edu/anm)

Dynamics of proteins predicted by molecular dynamics simulations and analytical approaches: Application to α-amylase inhibitor

The dynamics of α‐amylase inhibitors has been investigated using molecular dynamics (MD) simulations and two analytical approaches, the Gaussian network model (GNM) and anisotropic network model (ANM). MD simulations use a full atomic approach with empirical force fields, while the analytical approaches are based on a coarse‐grained single‐site‐per‐residue model with a single‐parameter harmonic potential between sufficiently close (r ≤ 7 Å) residue pairs. The major difference between the GNM and the ANM is that no directional preferences can be obtained in the GNM, all residue fluctuations being theoretically isotropic, while ANM does incorporate directional preferences. The dominant modes of motions are identified by (i) the singular value decomposition (SVD) of the MD trajectory matrices, and (ii) the similarity transformation of the Kirchhoff matrices of inter‐residue contacts in the GNM or ANM. The mean‐square fluctuations of individual residues and the cross‐correlations between domain movements retain the same characteristics, in all approaches—although the dispersion of modes and detailed amplitudes of motion obtained in the ANM conform more closely with MD results. The major weakness of the analytical approaches appears, on the other hand, to be their inadequacy to account for the anharmonic motions or multimeric transitions driven by the slowest collective mode observed in MD. Such motions usually suffer, however, from MD sampling inefficiencies, and multiple independent runs should be tested before making conclusions about their validity and detailed mechanisms. Overall this study invites attention to (i) the robustness of the average properties (mean‐square fluctuations, cross‐correlations) controlled by the low frequency motions, which are invariably reproduced in all approaches, and (ii) the utility and efficiency of the ANM, the computational time cost of which is of the order of “minutes” (real time), as opposed to “days” for MD simulations. Proteins 2000;40:512–524.

Normal mode analysis : theory and applications to biological and chemical systems

Normal mode theory and harmonic potential approximations Konrad Hinsen All-atom normal mode calculations of large molecular systems using iterative methods Liliane Mouawad and David Perahia The Gaussian network model: Theory and applications A.J. Radar, Chakra Chennubhotla, Lee-Wei Yang, Ivet Bahar Normal mode analysis of macromolecules: from enzyme activity site to molecular machines Guohui Li, Adam Van Wynsbergh, Omar N.A. Demerdash, Qiang Cui Functional information from slow mode shapes Yves-Henri Sanejouand Unveiling molecular mechanisms of biological functions in large macromolecular assemblies using elastic network normal mode analysis Florence Tama, Charles L. Brooks III Applications of normal mode analysis in structural refinement of supramolecular complexes Jianpeng Ma Normal mode analysis in studying protein motions with x-ray crystallography George N. Phillips, Jr. Optimizing the parameters of the Gaussian network model for ATP-binding proteins Taner Z. Sen, Robert L. Jernigan Effects of sequence, cyclization, and superhelical stress on the internet motions of DNA Atsushi Matsumoto, Wilma K. Olson Symmetry in normal mode analysis of icosahedral viruses Herman W.T. van Vlijmen Extension of the normal mode concept: Principal component analysis, jumping-among-minima model, and their applications to experimental data analysis Akio Kitao Imaginary-frequency, unstable instantaneous normal modes, the potential energy landscape, and diffusion in liquids T.Keyes Driven molecular dynamics for normal modes of biomolecules without the Hessian, and beyond Martina Kaledin, Alexey L. Kaledin, Alex Brown, and Joel Bowman Probing vibrational energy relaxation in proteins using normal modes Hiroshi Fujisaki, Lintao Bu, and John E. Straub Anharmonic decay of vibrational state in proteins Xin Yu, David M. Leitner Collective coordinate approaches to extended conformational sampling Michael Nilges, Rogher Abseher Using collective coordinates to guide conformational sampling in atomic simulations Haiyan Liu, Zhiyong Zhang, Jianbin He, Yunyu Shi