Domain movements in human fatty acid synthase by quantized elastic deformational model

Coarse-Grained Models for Vault Normal Model Analysis

Recent experiments have shown that the molecular complex of vault has large conformational changes at its shoulder and cap regions in solution. From the comparison of two configuration structures, it has been found that the shoulder region can twist and move outward, while the cap region will rotate and push upward correspondingly. To further understand these experimental results, in this paper, we study the vault dynamics for the first time. Since vault has an extremely large-sized structure with around 63,336 Cα atoms, traditional normal mode method with the Cα coarse-grained representation will fall short. We employ a newly invented multiscale virtual particle-based anisotropic network model (MVP-ANM). To reduce the complexity, the 39-folder vault structure is coarse-grained to about 6000 virtual particles, which significantly reduces the computational cost while still maintaining the basic structure information. Among the 14 low frequency eigenmodes from Mode 7 to Mode 20, two eigenmodes, i.e., Mode 9 and Mode 20, are found to be directly associated with the experimental observations. In Mode 9, shoulder region undergoes a significant expansion while the cap part is lifted upward. In Mode 20, a clear rotation of both shoulder and cap regions is well observed. Our results are consistent with the experimental observations. More importantly, these low frequency eigenmodes indicate that the vault waist, shoulder and lower cap regions are the most likely regions for the opening of the vault particle. And the opening mechanism is highly likely to be rotation and expansion at these regions. As far as we know, this is the first work to provide the normal mode analysis for the vault complex.

Protein dynamics developments for the large scale and cryoEM: case study of ProDy 2.0

Cryo-electron microscopy (cryoEM) has become a well established technique with the potential to produce structures of large and dynamic supramolecular complexes that are not amenable to traditional approaches for studying structure and dynamics. The size and low resolution of such molecular systems often make structural modelling and molecular dynamics simulations challenging and computationally expensive. This, together with the growing wealth of structural data arising from cryoEM and other structural biology methods, has driven a trend in the computational biophysics community towards the development of new pipelines for analysing global dynamics using coarse-grained models and methods. At the centre of this trend has been a return to elastic network models, normal mode analysis (NMA) and ensemble analyses such as principal component analysis, and the growth of hybrid simulation methodologies that make use of them. Here, this field is reviewed with a focus on ProDy, the Python application programming interface for protein dynamics, which has been developed over the last decade. Two key developments in this area are highlighted: (i) ensemble NMA towards extracting and comparing the signature dynamics of homologous structures, aided by the recent SignDy pipeline, and (ii) pseudoatom fitting for more efficient global dynamics analyses of large and low-resolution supramolecular assemblies from cryoEM, revisited in the CryoDy pipeline. It is believed that such a renewal and extension of old models and methods in new pipelines will be critical for driving the field forward into the next cryoEM revolution.

State-dependent sequential allostery exhibited by chaperonin TRiC/CCT revealed by network analysis of Cryo-EM maps

The eukaryotic chaperonin TRiC/CCT plays a major role in assisting the folding of many proteins through an ATP-driven allosteric cycle. Recent structures elucidated by cryo-electron microscopy provide a broad view of the conformations visited at various stages of the chaperonin cycle, including a sequential activation of its subunits in response to nucleotide binding. But we lack a thorough mechanistic understanding of the structure-based dynamics and communication properties that underlie the TRiC/CCT machinery. In this study, we present a computational methodology based on elastic network models adapted to cryo-EM density maps to gain a deeper understanding of the structure-encoded allosteric dynamics of this hexadecameric machine. We have analysed several structures of the chaperonin resolved in different states toward mapping its conformational landscape. Our study indicates that the overall architecture intrinsically favours cooperative movements that comply with the structural variabilities observed in experiments. Furthermore, the individual subunits CCT1-CCT8 exhibit state-dependent sequential events at different states of the allosteric cycle. For example, in the ATP-bound state, subunits CCT5 and CCT4 selectively initiate the lid closure motions favoured by the overall architecture; whereas in the apo form of the heteromer, the subunit CCT7 exhibits the highest predisposition to structural change. The changes then propagate through parallel fluxes of allosteric signals to neighbours on both rings. The predicted state-dependent mechanisms of sequential activation provide new insights into TRiC/CCT intra- and inter-ring signal transduction events.

A complex multiscale virtual particle model based elastic network model (CMVP-ENM) for the normal mode analysis of biomolecular complexes

The CMVP-ENM for virus normal mode analysis. With a special ratio parameter, CMVP-ENM can characterize the multi-material properties of biomolecular complexes and systematically enhance or suppress the modes for different components.

Gaussian-input Gaussian mixture model for representing density maps and atomic models

A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm.

Multiscale virtual particle based elastic network model (MVP-ENM) for normal mode analysis of large-sized biomolecules

In this paper, a multiscale virtual particle based elastic network model (MVP-ENM) is proposed for the normal mode analysis of large-sized biomolecules. The multiscale virtual particle (MVP) model is proposed for the discretization of biomolecular density data. With this model, large-sized biomolecular structures can be coarse-grained into virtual particles such that a balance between model accuracy and computational cost can be achieved. An elastic network is constructed by assuming "connections" between virtual particles. The connection is described by a special harmonic potential function, which considers the influence from both the mass distributions and distance relations of the virtual particles. Two independent models, i.e., the multiscale virtual particle based Gaussian network model (MVP-GNM) and the multiscale virtual particle based anisotropic network model (MVP-ANM), are proposed. It has been found that in the Debye-Waller factor (B-factor) prediction, the results from our MVP-GNM with a high resolution are as good as the ones from GNM. Even with low resolutions, our MVP-GNM can still capture the global behavior of the B-factor very well with mismatches predominantly from the regions with large B-factor values. Further, it has been demonstrated that the low-frequency eigenmodes from our MVP-ANM are highly consistent with the ones from ANM even with very low resolutions and a coarse grid. Finally, the great advantage of MVP-ANM model for large-sized biomolecules has been demonstrated by using two poliovirus virus structures. The paper ends with a conclusion.

Analytical Approaches to Improve Accuracy in Solving the Protein Topology Problem

To take advantage of recent advances in genomics and proteomics it is critical that the three-dimensional physical structure of biological macromolecules be determined. Cryo-Electron Microscopy (cryo-EM) is a promising and improving method for obtaining this data, however resolution is often not sufficient to directly determine the atomic scale structure. Despite this, information for secondary structure locations is detectable. De novo modeling is a computational approach to modeling these macromolecular structures based on cryo-EM derived data. During de novo modeling a mapping between detected secondary structures and the underlying amino acid sequence must be identified. DP-TOSS (Dynamic Programming for determining the Topology Of Secondary Structures) is one tool that attempts to automate the creation of this mapping. By treating the correspondence between the detected structures and the structures predicted from sequence data as a constraint graph problem DP-TOSS achieved good accuracy in its original iteration. In this paper, we propose modifications to the scoring methodology of DP-TOSS to improve its accuracy. Three scoring schemes were applied to DP-TOSS and tested: (i) a skeleton-based scoring function; (ii) a geometry-based analytical function; and (iii) a multi-well potential energy-based function. A test of 25 proteins shows that a combination of these schemes can improve the performance of DP-TOSS to solve the topology determination problem for macromolecule proteins.

PEM-fitter: A Coarse-Grained Method to Validate Protein Candidate Models

The volumetric images produced by Cryo-Electron Microscopy (cryo-EM) technique are used to model macromolecular assemblies and machines. De novo protein modeling uses these images to computationally model the structure of the molecules. Many candidate conformations are usually generated during the intermediate step. Conventionally, each of these candidates is evaluated by time-consuming approaches such as potential energy. We introduce an initial version of a geometrical screening method that uses the skeleton of the cryo-EM images to evaluate candidate structures. The aim of this method is to reduce the number of native-like candidate conformations and, therefore, reduce the time required for structural evaluation by energy calculations. A test of two datasets was performed. The first dataset contains 10 proteins and shows that our method can successfully detect the correct native structure for the given skeleton among a set of different protein structures. The second dataset contains 12 proteins and shows that our method can filter slightly modified decoy conformations of the same protein. The efficiency of the method is also reported.

PIM: phase integrated method for normal mode analysis of biomolecules in a crystalline environment

In this study, a normal mode analysis, named phase integrated method (PIM), is developed for computing modes of biomolecules in a crystalline environment. PIM can calculate low-frequency modes on one or a few asymmetric units (AUs) and generate exact modes of a whole unit cell according to space group symmetry, while the translational symmetry between unit cells is maintained via the periodic boundary condition. Therefore, the method can dramatically reduce computational cost in mode calculation in the presence of crystal symmetry. PIM also has an option to map modes onto a single AU to form an orthonormalized mode set, which can be directly applied to normal-mode-based thermal parameter refinement in X-ray crystallography. The performance of PIM was tested on all 65 space groups available in protein crystals (one protein for each space group) and on another set of 83 ultra-high-resolution X-ray structures. The results showed that considering space group symmetry in mode calculation is crucial for accurately describing vibrational motion in a crystalline environment. Moreover, the optimal inter-AU packing stiffness was found to be about 60% of that of intra-AU interactions (non-bonded interaction only).

Single-particle electron microscopy of animal fatty acid synthase describing macromolecular rearrangements that enable catalysis

We have used macromolecular electron microscopy (EM) to characterize the conformational flexibility of the animal fatty acid synthase (FAS). Here we describe in detail methods employed for image collection and analysis. We also provide an account of how EM results were interpreted by considering a high-resolution static FAS X-ray structure and functional data to arrive at a molecular understanding of the way in which conformational pliability enables fatty acid synthesis.

Coarse-Grained Representations of Large Biomolecular Complexes from Low-Resolution Structural Data

High-resolution atomistic structures of many large biomolecular complexes have not yet been solved by experiments, such as X-ray crystallography or NMR. Often however low-resolution information is obtained by alternative techniques, such as cryo-electron microscopy or small-angle X-ray scattering. Coarse-grained (CG) models are an appropriate choice to computationally study these complexes given the limited resolution experimental data. One of the important questions therefore is how to define CG representations from these low-resolution density maps. This work provides a space-based essential dynamics coarse-graining (ED-CG) method to define a CG representation from a density map without detailed knowledge of its underlying atomistic structure and primary sequence information. This method is demonstrated on G-actin (both the atomic structure and its density map). It is then applied to the density maps of the Escherichia coli 70S ribosome and the microtubule. The results indicate that the method can define highly CG models that still preserve functionally important dynamics of large biomolecular complexes.

Defining coarse-grained representations of large biomolecules and biomolecular complexes from elastic network models

Coarse-grained (CG) models of large biomolecular complexes enable simulations of these systems over long timescales that are not accessible for atomistic molecular dynamics (MD) simulations. A systematic methodology, called essential dynamics coarse-graining (ED-CG), has been developed for defining coarse-grained sites in a large biomolecule. The method variationally determines the CG sites so that key dynamic domains in the protein are preserved in the CG representation. The original ED-CG method relies on a principal component analysis (PCA) of a MD trajectory. However, for many large proteins and multi-protein complexes such an analysis may not converge or even be possible. This work develops a new ED-CG scheme using an elastic network model (ENM) of the protein structure. In this procedure, the low-frequency normal modes obtained by ENM are used to define dynamic domains and to define the CG representation accordingly. The method is then applied to several proteins, such as the HIV-1 CA protein dimer, ATP-bound G-actin, and the Arp2/3 complex. Numerical results show that ED-CG with ENM (ENM-ED-CG) is much faster than ED-CG with PCA because no MD is necessary. The ENM-ED-CG models also capture functional essential dynamics of the proteins almost as well as those using full MD with PCA. Therefore, the ENM-ED-CG method may be better suited to coarse-grain a very large biomolecule or biomolecular complex that is too computationally expensive to be simulated by conventional MD, or when a high resolution atomic structure is not even available.

Vibrational dynamics of icosahedrally symmetric biomolecular assemblies compared with predictions based on continuum elasticity

Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the true atomistic molecular structure. We solve the elastic wave equations analytically for the case of spherical symmetry, yielding a symmetry-based classification of molecular motions together with explicit predictions for their vibrational frequencies. We address the case of icosahedral symmetry as a perturbation to the spherical case. Applications to lumazine synthase, satellite tobacco mosaic virus, and brome mosaic virus show that the spherical elastic model efficiently provides insights on collective motions that are otherwise obtained by detailed elastic network models. A major utility of the continuum models is the possibility of estimating macroscopic material properties such as the Young's modulus or Poisson's ratio for different types of viruses.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Effects of protein subunits removal on the computed motions of partial 30S structures of the ribosome

The Anisotropic Network Model (ANM) is used to study motions of the 30S small ribosomal subunit. The effect of the absence of certain subunits on the motions of the remaining partial structures was investigated by removing one protein, pairs of proteins and selected sets of proteins at a time. Our results show that the removal of some proteins doesn't change the large-scale dynamics of the partial structures, but the removal of certain subunits does cause significant changes in motion of the remaining structure, and these changes can be reverted by the removal of other subunits, which indicates interdependence between motions of various parts of the 30S ribosomal structure. We further found that the subunits showing such interdependence have strong positive correlation of their motions, which indicates that these subunits function as a unit block in the 30S small ribosomal subunit. Dynamically interdependent subunit pairs identified in this paper are consistent with previous experimental observations that suggested dimerization of those subunits.

On the relationship between the protein structure and protein dynamics

Recently, we have developed a method (Shih et al., Proteins: Structure, Function, and Bioinformatics 2007;68: 34-38) to compute correlation of fluctuations of proteins. This method, referred to as the protein fixed-point (PFP) model, is based on the positional vectors of atoms issuing from the fixed point, which is the point of the least fluctuations in proteins. One corollary from this model is that atoms lying on the same shell centered at the fixed point will have the same thermal fluctuations. In practice, this model provides a convenient way to compute the average dynamical properties of proteins directly from the geometrical shapes of proteins without the need of any mechanical models, and hence no trajectory integration or sophisticated matrix operations are needed. As a result, it is more efficient than molecular dynamics simulation or normal mode analysis. Though in the previous study the PFP model has been successfully applied to a number of proteins of various folds, it is not clear to what extent this model will be applied. In this article, we have carried out the comprehensive analysis of the PFP model for a dataset comprising 972 high-resolution X-ray structures with pairwise sequence identity <or=25%. We found that in most cases the PFP model works well. However, in case of proteins comprising multiple domains, each domain should be treated separately as an independent dynamical module with its own fixed point; and in case of the protein complex comprising a number of subunits, if functioning as a biological unit, the whole complex should be considered as one single dynamical module with one fixed point. Under such considerations, the resultant correlation coefficient between the computed and the X-ray structural B-factors for the data set is 0.59 and 75% (727/972) of proteins with a correlation coefficient >or=0.5. Our result shows that the fixed-point model is indeed quite general and will be a useful tool for high throughput analysis of dynamical properties of proteins.

Discovery of GSK837149A, an inhibitor of human fatty acid synthase targeting the beta-ketoacyl reductase reaction

GSK837149A has been identified as a selective inhibitor of human fatty acid synthase (FAS). The compound was first isolated as a minor impurity in a sample found to be active against the enzyme in a high-throughput screening campaign. The structure of this compound was confirmed by NMR and MS studies, and evaluation of the newly synthesized molecule confirmed its activity against FAS. The compound and other analogs synthesized, all being symmetrical structures containing a bisulfonamide urea, act by inhibiting the beta-ketoacyl reductase activity of the enzyme. GSK837149A inhibits FAS in a reversible mode, with a K(i) value of approximately 30 nm, and it possibly binds to the enzyme-ketoacyl-ACP complex. Although initial results suggest that cell penetration for these compounds is impaired, they still can be regarded as useful tools with which to probe and explore the beta-ketoacyl reductase active site in FAS, helping in the design of new inhibitors.

Protein structure fitting and refinement guided by cryo-EM density

For many macromolecular assemblies, both a cryo-electron microscopy map and atomic structures of its component proteins are available. Here we describe a method for fitting and refining a component structure within its map at intermediate resolution (<15 A). The atomic positions are optimized with respect to a scoring function that includes the crosscorrelation coefficient between the structure and the map as well as stereochemical and nonbonded interaction terms. A heuristic optimization that relies on a Monte Carlo search, a conjugate-gradients minimization, and simulated annealing molecular dynamics is applied to a series of subdivisions of the structure into progressively smaller rigid bodies. The method was tested on 15 proteins of known structure with 13 simulated maps and 3 experimentally determined maps. At approximately 10 A resolution, Calpha rmsd between the initial and final structures was reduced on average by approximately 53%. The method is automated and can refine both experimental and predicted atomic structures.

Normal-mode flexible fitting of high-resolution structure of biological molecules toward one-dimensional low-resolution data

We present a method for reconstructing a 3D structure from a pair distribution function by flexibly fitting known x-ray structures toward a conformation that agrees with the low-resolution data. This method uses a linear combination of low-frequency normal modes from elastic-network description of the molecule in an iterative manner to deform the structure optimally to conform to the target pair distribution function. A simple function, pair distance distribution function between atoms, is chosen as a test model to establish computational algorithms-optimization algorithm and scoring function-that can utilize low-resolution 1D data. To select a correct structural model based on less information, we developed a scoring function that takes into account a characteristic of pair distribution functions. In addition, we employ a new optimization algorithm, the trusted region method, that relies on both first and second derivatives of the scoring function. Illustrative results of our studies on simulated 1D data from five different proteins, for which large conformational changes are known to occur, are presented.

Packing regularities in biological structures relate to their dynamics

The high packing density inside proteins leads to certain geometric regularities and also is one of the most important contributors to the high extent of cooperativity manifested by proteins in their cohesive domain motions. The orientations between neighboring nonbonded residues in proteins substantially follow the similar geometric regularities, regardless of whether the residues are on the surface or buried, a direct result of hydrophobicity forces. These orientations are relatively fixed and correspond closely to small deformations from those of the face-centered cubic lattice, which is the way in which identical spheres pack at the highest density. Packing density also is related to the extent of conservation of residues, and we show this relationship for residue packing densities by averaging over a large sample or residue packings. There are three regimes: (1) over a broad range of packing densities the relationship between sequence entropy and inverse packing density is nearly linear, (2) over a limited range of low packing densities the sequence entropy is nearly constant, and (3) at extremely low packing densities the sequence entropy is highly variable. These packing results provide important justification for the simple elastic network models that have been shown for a large number of proteins to represent protein dynamics so successfully, even when the models are extremely coarse grained. Elastic network models for polymeric chains are simple and could be combined with these protein elastic networks to represent partially denatured parts of proteins. Finally, we show results of applications of the elastic network model to study the functional motions of the ribosome, based on its known structure. These results indicate expected correlations among its components for the step-wise processing steps in protein synthesis, and suggest ways to use these elastic network models to develop more detailed mechanisms, an important possibility because most experiments yield only static structures.

SYMMETRY, FORM, AND SHAPE: Guiding Principles for Robustness in Macromolecular Machines

Computational studies of large macromolecular assemblages have come a long way during the past 10 years. With the explosion of computer power and parallel computing, timescales of molecular dynamics simulations have been extended far beyond the hundreds of picoseconds timescale. However, limitations remain for studies of large-scale conformational changes occurring on timescales beyond nanoseconds, especially for large macromolecules. In this review, we describe recent methods based on normal mode analysis that have enabled us to study dynamics on the microsecond timescale for large macromolecules using different levels of coarse graining, from atomically detailed models to those employing only low-resolution structural information. Emerging from such studies is a control principle for robustness in Nature's machines. We discuss this idea in the context of large-scale functional reorganization of the ribosome, virus particles, and the muscle protein myosin.

Mammalian fatty acid synthase: X-ray structure of a molecular assembly line

Mammalian fatty acid synthase (FAS) is a homodimeric, multifunctional polypeptide which comprises two full sets of catalytic subunits that carry out fatty acid synthesis. A recently published X-ray structure of FAS reveals, for the first time, the organization of all active sites involved in acyl chain elongation and provides a structural framework for interpretation of extensive functional studies. Further analysis with techniques capable of providing information about single molecule conformations will eventually provide a more complete understanding of FAS.

A New Method for Coarse-Grained Elastic Normal-Mode Analysis

In this paper, we report a new method for coarse-grained elastic normal-mode analysis. The purpose is to overcome a long-standing problem in the conventional analysis called the tip effect that makes the motional patterns (eigenvectors) of some low-frequency modes irrational. The new method retains the merits of a conventional method such as not requiring lengthy initial energy minimization, which always distorts structures, and also delivers substantially more accurate low-frequency modes with no tip effect for proteins of any size. This improvement of modes is crucial for certain types of applications such as structural refinement or normal-mode-based sampling.

Reorientational contact-weighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation

A new model for the prediction of protein backbone motions is presented. The model, termed reorientational contact-weighted elastic network model, is based on a multidimensional reorientational harmonic potential of the backbone amide bond vector orientations and it is applied to the interpretation of dynamics parameters obtained from NMR relaxation data. The individual energy terms are weighted as a function of the intervector distances and by the contact strengths of each bond vector with respect to its local environment. Correlated reorientational motional properties of the bond vectors are obtained by means of normal mode analysis. Application to a set of proteins with known three-dimensional structures yields good to excellent agreement between predicted and experimental NMR order parameters presenting an improvement over the local contact model. The reorientational eigenmodes of the reorientational contact-weighted elastic network model method provide direct information on the collective nature of protein backbone motions. The dominant eigenmodes have a notably low collectivity, which is consistent with the behavior found for reorientational eigenmodes from molecular dynamics simulations.

Cloning and functional characterization of a fatty acid synthase component FAS2 gene from Saccharomyces kluyveri

A gene coding the alpha subunit of fatty acid synthase (FAS2) was isolated from the budding yeast Saccharomyces kluyveri. Nucleotide sequence analysis indicated that this gene, termed Sk-FAS2, coded a protein having an amino acid sequence 83% identical to the FAS2 protein of S. cerevisiae (Sc-FAS2). The Sk-FAS2 gene was able to functionally complement an S. cerevisiae fas2 disruptant. This Sk-FAS2-expressing strain was found to produce larger amounts of C18 than C16, in contrast to the Sc-FAS2-expressing fas2 strain. In addition, fusion genes of Sk-FAS2 and Sc-FAS2 were transformed into a fas2-disrupted strain of S. cerevisiae, and fatty acid analysis of these transformants suggested that the region containing the acyl carrier protein and beta-ketoacyl reductase domains of yeast FAS2 protein play an important role in determining carbon chain length of fatty acids.

The Allosteric Mechanism of Yeast Chorismate Mutase: A Dynamic Analysis

The effector-regulated allosteric mechanism of yeast chorismate mutase (YCM) was studied by normal mode analysis and targeted molecular dynamics. The normal mode analysis shows that the conformational change between YCM in the R state and in the T state can be represented by a relatively small number of low-frequency modes. This suggests that the transition is coded in the structure and is likely to have a low energetic barrier. Quantitative comparisons (i.e. frequencies) between the low-frequency modes of YCM with and without effectors (modeled structures) reveal that the binding of Trp increases the global flexibility, whereas Tyr decreases global flexibility. The targeted molecular dynamics simulation of substrate analog release from the YCM active site suggests that a series of residues are critical for orienting and "recruiting" the substrate. The simulation led to the switching of a series of substrate-release-coupled salt-bridge partners in the ligand-binding domain; similar changes occur in the transition between YCM R-state and T-state crystal structures. Thus, the normal mode analysis and targeted molecular dynamics results provide evidence that the effectors regulate YCM activity by influencing the global flexibility. The change in flexibility is coupled to the binding of substrate to the T state and release of the product from the R state, respectively.

Escherichia coli adenylate kinase dynamics: comparison of elastic network model modes with mode-coupling (15)N-NMR relaxation data

The dynamics of adenylate kinase of Escherichia coli (AKeco) and its complex with the inhibitor AP(5)A, are characterized by correlating the theoretical results obtained with the Gaussian Network Model (GNM) and the anisotropic network model (ANM) with the order parameters and correlation times obtained with Slowly Relaxing Local Structure (SRLS) analysis of (15)N-NMR relaxation data. The AMPbd and LID domains of AKeco execute in solution large amplitude motions associated with the catalytic reaction Mg(+2)*ATP + AMP --> Mg(+2)*ADP + ADP. Two sets of correlation times and order parameters were determined by NMR/SRLS for AKeco, attributed to slow (nanoseconds) motions with correlation time tau( perpendicular) and low order parameters, and fast (picoseconds) motions with correlation time tau( parallel) and high order parameters. The structural connotation of these patterns is examined herein by subjecting AKeco and AKeco*AP(5)A to GNM analysis, which yields the dynamic spectrum in terms of slow and fast modes. The low/high NMR order parameters correlate with the slow/fast modes of the backbone elucidated with GNM. Likewise, tau( parallel) and tau( perpendicular) are associated with fast and slow GNM modes, respectively. Catalysis-related domain motion of AMPbd and LID in AKeco, occurring per NMR with correlation time tau( perpendicular), is associated with the first and second collective slow (global) GNM modes. The ANM-predicted deformations of the unliganded enzyme conform to the functional reconfiguration induced by ligand-binding, indicating the structural disposition (or potential) of the enzyme to bind its substrates. It is shown that NMR/SRLS and GNM/ANM analyses can be advantageously synthesized to provide insights into the molecular mechanisms that control biological function.

Usefulness and limitations of normal mode analysis in modeling dynamics of biomolecular complexes

Various types of large-amplitude molecular deformation are ubiquitously involved in the functions of biological macromolecules, especially supramolecular complexes. They can be very effectively analyzed by normal mode analysis with well-established procedures. However, despite its enormous success in numerous applications, certain issues related to the applications of normal mode analysis require further discussion. In this review, the author addresses some common issues so as to raise the awareness of the usefulness and limitations of the method in the general community of structural biology.

The role of shape in determining molecular motions

We examined the role of molecular shape in determining the patterns of low-frequency deformational motions of biological macromolecules. The low-frequency subspace of eigenvectors in normal mode analysis was found to be robustly similar upon randomization of the Hessian matrix elements as long as the structure of the matrix is maintained, which indicates that the global shape of molecules plays a more dominant role in determining the highly anisotropic low-frequency motions than the absolute values of stiffness and directionality of local interactions. The results provided a quantitative foundation for the validity of elastic normal mode analysis.

The structure of mammalian fatty acid synthase turned back to front

On page 1667 of this issue, Stuart Smith and colleagues [1] demonstrate that the animal fatty acid synthase is a head-to-head dimer rather than the head-to-tail dimer depicted in textbooks. This has important ramifications for the mechanisms of other multifunctional enzymes such as polyketide synthases [2].

Coupling between catalytic site and collective dynamics: a requirement for mechanochemical activity of enzymes

Growing evidence supports the view that enzymatic activity results from a subtle interplay between chemical kinetics and molecular motions. A systematic analysis is performed here to delineate the type and level of coupling between catalysis and conformational mechanics. The dynamics of a set of 98 enzymes representative of different EC classes are analyzed with the Gaussian network model (GNM) and compared with experimental data. In more than 70% of the examined enzymes, the global hinge centers predicted by the GNM are found to be colocalized with the catalytic sites experimentally identified. Low translational mobility (< 7%) is observed for the catalytic residues, consistent with the fine-tuned design of enzymes to achieve precise mechanochemical activities. Ligand binding sites, while closely neighboring catalytic sites, enjoy a moderate flexibility to accommodate the ligand binding. These findings could serve as additional criteria for assessing drug binding residues and could lessen the computational burden of substrate docking searches.

Normal mode based flexible fitting of high-resolution structure into low-resolution experimental data from cryo-EM

A new method for the flexible fitting of high-resolution structures into low-resolution maps of macromolecular complexes from electron microscopy has been recently described in applications to simulated electron density maps. This method uses a linear combination of low-frequency normal modes in an iterative manner to deform the structure optimally to conform to the low-resolution electron density map. Gradient-following techniques in the coordinate space of collective normal modes are used to optimize the overall correlation coefficient between computed and measured electron densities. With this approach, multi-scale flexible fitting can be performed using all-atoms or Calpha atoms. In this paper, illustrative studies of normal mode based flexible fitting to experimental cryo-EM maps are presented for three different systems. Large, functionally relevant conformational changes for elongation factor G bound to the ribosome, Escherichia coli RNA polymerase and cowpea chlorotic mottle virus are elucidated as the result of the application of NMFF from high-resolution structures to cryo-electron microscopy maps.

A structural perspective on protein-protein interactions

Structures of macromolecular complexes are necessary for a mechanistic description of biochemical and cellular processes. They can be solved by experimental methods, such as X-ray crystallography, NMR spectroscopy and electron microscopy, as well as by computational protein structure prediction, docking and bioinformatics. Recent advances and applications of these methods emphasize the need for hybrid approaches that combine a variety of data to achieve better efficiency, accuracy, resolution and completeness.

Theoretical analysis of twist/bend ratio and mechanical moduli of bacterial flagellar hook and filament

Certain motile bacteria employ rotating flagella for propulsion. The relative flexibility of two key components of the flagellum, filament and hook, is partially responsible for the mechanistic workings of this motor. A new computational method, the quantized elastic deformational model, was employed in this article to calculate the dimensionless twist/bend ratio (EI/GJ) of the filament and hook, providing a quantitative means to compare their relative stiffness. Both ratios were much <1.0, an average of 0.0440 for the filament and 0.0512 for the hook, indicating that within each structure bending is favored over twisting. These two ratios, along with previous experimental measurements, allowed us to propose a theoretical Young's modulus (E) between 10(6) and 10(7) dyn/cm(2) for the hook. This value is orders of magnitude smaller than experimentally determined Young's moduli of the filament, hence in agreement with empirical evidence linking compliance in the flagellum mainly to the hook.

Structure and function of animal fatty acid synthase

Fatty acid synthase (FAS; EC 2.3.1.85) of animal tissues is a complex multifunctional enzyme consisting of two identical monomers. The FAS monomer (approximately 270 kDa) contains six catalytic activities and from the N-terminus the order is beta-ketoacyl synthase (KS), acetyl/malonyl transacylase (AT/MT), beta-hydroxyacyl dehydratase (DH), enoyl reductase (ER), beta-ketoacyl reductase (KR), acyl carrier protein (ACP), and thioesterase (TE). Although the FAS monomer contains all the activities needed for palmitate synthesis, only the dimer form of the synthase is functional. Both the biochemical analyses and the small-angle neutron-scattering analysis determined that in the dimer form of the enzyme the monomers are arranged in a head-to-tail manner generating two centers for palmitate synthesis. Further, these analyses also suggested that the component activities of the monomer are organized in three domains. Domain I contains KS, AT/MT, and DH, domain II contains ER, KR, and ACP, and domain III contains TE. Approximately one fourth of the monomer protein located between domains I and II contains no catalytic activities and is called the interdomain/core region. This region plays an important role in the dimer formation. Electron cryomicrographic analyses of FAS revealed a quaternary structure at approximately 19 A resolution, containing two monomers (180 x 130 x 75 A) that are separated by about 19 A, and arranged in an antiparallel fashion, which is consistent with biochemical and neutron-scattering data. The monomers are connected at the middle by a hinge generating two clefts that may be the two active centers of fatty acid synthesis. Normal mode analysis predicted that the intersubunit hinge region and the intrasubunit hinge located between domains II and III are highly flexible. Analysis of FAS particle images by using a simultaneous multiple model single particle refinement method confirmed that FAS structure exists in various conformational states. Attempts to get higher resolution of the structure are under way.

New advances in normal mode analysis of supermolecular complexes and applications to structural refinement

Normal mode analysis is an effective computational method for studying large-amplitude low-frequency molecular deformations that are ubiquitously involved in the functions of biological macromolecules, especially supermolecular complexes. The recent years have witnessed a substantial advance in methodology development in the field. This review is intended to summarize some of the important advances that enable one to simulate deformations of supermolecular complexes at expended resolution- and length-scales, with particular emphasis on the implications in structural refinement against low- to intermediate-resolution structural data such as those from electron cryomicroscopy and fibre diffraction.

The crystal structure of murine p97/VCP at 3.6A

p97/VCP is a member of the AAA ATPase family and has roles in both membrane fusion and ubiquitin dependent protein degradation. Here, we present a 3.6A crystal structure of murine p97 in which D2 domain has been modelled as poly-alanine and the remaining approximately 100 residues are absent. The resulting structure illustrates a head-to-tail packing arrangement of the two p97 AAA domains in a natural hexameric state with D1 ADP bound and D2 nucleotide free. The head-to-tail packing arrangement observed in this structure is in contrast to our previously predicted tail-to-tail packing model. The linker between the D1 and D2 domains is partially disordered, suggesting a flexible nature. Normal mode analysis of the crystal structure suggests anti-correlated motions and distinct conformational states of the two AAA domains.

Change in protein flexibility upon complex formation: Analysis of Ras-Raf using molecular dynamics and a molecular framework approach

Changes in flexibility upon protein-protein complex formation of H-Ras and the Ras-binding domain of C-Raf1 have been investigated using the molecular framework approach FIRST (Floppy Inclusion and Rigid Substructure Topology) and molecular dynamics simulations (MD) of in total approximately 35 ns length. In a computational time of about one second, FIRST identifies flexible and rigid regions in a single, static three-dimensional molecular framework, whose vertices represent protein atoms and whose edges represent covalent and non-covalent (hydrogen bond and hydrophobic) constraints and fixed bond angles within the protein. The two methods show a very good agreement with respect to the identification of changes in flexibility in both binding partners on a local scale. This implies that flexibility can be successfully predicted by identifying which bonds limit motion within a molecule and how they are coupled. In particular, as identified by MD, the beta-sheet in Raf shows considerably more pronounced orientational correlations in the bound state compared to the unbound state. Similarly, FIRST assigns the beta-sheet to the largest rigid cluster of the complex. Interestingly, FIRST allows us to identify that interactions across the interface (but not conformational changes upon complex formation) result in the observed rigidification. Since regions of the beta-sheet of Raf that do not interact directly with Ras become rigidified, this also demonstrates the long-range aspect to rigidity percolation. Possible implications of the change of flexibility of the Ras-binding domain of Raf on the activation of Raf upon complex formation are discussed. Finally, the sensitivity of FIRST results with respect to the representation of non-covalent interactions used as constraints is probed.

On the use of low-frequency normal modes to enforce collective movements in refining macromolecular structural models

As more and more structures of macromolecular complexes get solved in different conditions, it has become apparent that flexibility is an inherent part of their biological function. Normal mode analysis using simplified models of proteins such as the elastic network model has proved very effective in showing that many of the structural transitions derived from a survey of the Protein Data Bank can be explained by just a few of the lowest-frequency normal modes. In this work, normal modes are used to carry out medium- or low-resolution structural refinement, enforcing collective and large-amplitude movements that are beyond the reach of existing methods. Refinement is carried out in reciprocal space with respect to the normal mode amplitudes, by using standard conjugate-gradient minimization. Several tests on synthetic diffraction data whose mode concentration follows the one of real movements observed in the Protein Data Bank have shown that the radius of convergence is larger than the one of rigid-body refinement. Tests with experimental diffraction data for the same protein in different environments also led to refined structural models showing drastic reduction of the rms deviation with the target model. Because the structural transition is described by very few parameters, over-fitting of real experimental data is easily detected by using a cross-validation test. The method has also been applied to the refinement of atomic models into molecular envelopes and could readily be used to fit large macromolecular complex rearrangements into cryo-electron microscopy-reconstructed images as well as small-angle x-ray scattering-derived envelopes.

Flexible Multi-scale Fitting of Atomic Structures into Low-resolution Electron Density Maps with Elastic Network Normal Mode Analysis

A novel method is presented for the quantitative flexible docking of high-resolution structure into low-resolution maps of macromolecular complexes from electron microscopy. This method uses a linear combination of low-frequency normal modes from elastic network description of the molecular framework in an iterative manner to deform the structure optimally to conform to the low-resolution electron density map. The methodology utilizes gradient following techniques in collective normal modes to locally optimize the overall correlation coefficient between computed and measured electron density. To evaluate the performance of our approach, several proteins, which undergo large conformational changes, have been studied. We demonstrate that refinement based on normal mode analysis provides an accurate and fast alternative for the flexible fitting of high-resolution structure into a low-resolution density map. Additionally, we show that lower resolution (multi-scale) structural models can be used for the normal mode searching in lieu of fully atomic models with little loss of overall accuracy.

Experimental Verification of Conformational Variation of Human Fatty Acid Synthase as Predicted by Normal Mode Analysis

Fatty acid synthase (FAS) is a 550 kDa homodimeric enzyme with multiple functional and structural domains. Normal mode analysis of a previously determined 19 A structure of FAS suggested that this enzyme might assume different conformational states with several distinct hinge movements. We have used a simultaneous multiple-model refinement method to search for the presence of the structural conformers from the electron images of FAS. We have demonstrated that the resulting models observed in the electron images are consistent with the predicted conformational changes. This technique demonstrates the potential of the combination of normal mode analysis with multiple model refinement to elucidate the multiple conformations of flexible proteins. Since each of these structures is based on a more homogeneous particle set, this technique has the potential, provided that sufficient references are used, to improve the resolution of the final reconstructions of single particles from electron cryomicroscopy.

Visualization of DNA-induced conformational changes in the DNA repair kinase DNA-PKcs

The catalytic subunit of the DNA-dependent protein kinase (DNA-PKcs) is essential for the repair of double-stranded DNA breaks (DSBs) in non- homologous end joining (NHEJ) and during V(D)J recombination. DNA-PKcs binds single- and double-stranded DNA in vitro, and in vivo the Ku heterodimer probably helps recruit it to DSBs with high affinity. Once loaded onto DNA, DNA-PKcs acts as a scaffold for other repair factors to generate a multiprotein complex that brings the two DNA ends together. Human DNA-PKcs has been analysed by electron microscopy in the absence and presence of double-stranded DNA, and the three-dimensional reconstruction of DNA-bound DNA-PKcs displays large conformational changes when compared with the unbound protein. DNA-PKcs seems to use a palm-like domain to clip onto the DNA, and this new conformation correlates with the activation of the kinase. We suggest that the observed domain movements might help the binding and maintenance of DNA-PKcs' interaction with DNA at the sites of damage, and that these conformational changes activate the kinase.

FEMME database: topologic and geometric information of macromolecules

FEMME (Feature Extraction in a Multi-resolution Macromolecular Environment: http://www.biocomp.cnb.uam.es/FEMME/) database version 1.0 is a new bioinformatics data resource that collects topologic and geometric information obtained from macromolecular structures solved by three-dimensional electron microscopy (3D-EM). Although the FEMME database is focused on medium resolution data, the methodology employed (based on the so-called alpha-shape theory) is applicable to atomic resolution data as well. The alpha-shape representation allows the automatic extraction of structural features from 3D-EM volumes and their subsequent characterisation. FEMME is being populated with 3D-EM data stored in the electron microscopy database EMD-DB (http://www.ebi.ac.uk/msd/). However, and since the number of entries in EMD-DB is still relatively small, FEMME is also being populated in this initial phase with structural data from PDB and PQS databases (http://www.rcsb.org/pdb/ and pqs.ebi.ac.uk/, respectively) whose resolution has been lowered accordingly. Each FEMME entry contains macromolecular geometry and topology information with a detailed description of its structural features. Moreover, FEMME data have facilitated the study and development of a method to retrieve macromolecular structures by their structural content based on the combined use of spin images and neural networks with encouraging results. Therefore, the FEMME database constitutes a powerful tool that provides a uniform and automatic way of analysing volumes coming from 3D-EM that will hopefully help the scientific community to perform wide structural comparisons.