A coarse-grained normal mode approach for macromolecules: an efficient implementation and application to Ca(2+)-ATPase

Robust Heterogeneous Anisotropic Elastic Network Model Precisely Reproduces the Experimental B-factors of Biomolecules

A computational method called the progressive fluctuation matching (PFM) is developed for constructing robust heterogeneous anisotropic network models (HANMs) for biomolecular systems. An HANM derived through the PFM approach consists of harmonic springs with realistic positive force constants, and yields the calculated B-factors that are basically identical to the experimental ones. For the four tested protein systems including crambin, trypsin inhibitor, HIV-1 protease, and lysozyme, the root-mean-square deviations between the experimental and the computed B-factors are only 0.060, 0.095, 0.247, and 0.049 Å(2), respectively, and the correlation coefficients are 0.99 for all. By comparing the HANM/ANM normal modes to their counterparts derived from both an atomistic force field and an NMR structure ensemble, it is found that HANM may provide more accurate results on protein dynamics.

ΔΔPT: a comprehensive toolbox for the analysis of protein motion

Background

Normal Mode Analysis is one of the most successful techniques for studying motions in proteins and macromolecules. It can provide information on the mechanism of protein functions, used to aid crystallography and NMR data reconstruction, and calculate protein free energies.

Results

ΔΔPT is a toolbox allowing calculation of elastic network models and principle component analysis. It allows the analysis of pdb files or trajectories taken from; Gromacs, Amber, and DL_POLY. As well as calculation of the normal modes it also allows comparison of the modes with experimental protein motion, variation of modes with mutation or ligand binding, and calculation of molecular dynamic entropies.

Conclusions

This toolbox makes the respective tools available to a wide community of potential NMA users, and allows them unrivalled ability to analyse normal modes using a variety of techniques and current software.

Theory and simulations of adhesion receptor dimerization on membrane surfaces

The equilibrium constants of trans and cis dimerization of membrane bound (2D) and freely moving (3D) adhesion receptors are expressed and compared using elementary statistical-thermodynamics. Both processes are mediated by the binding of extracellular subdomains whose range of motion in the 2D environment is reduced upon dimerization, defining a thin reaction shell where dimer formation and dissociation take place. We show that the ratio between the 2D and 3D equilibrium constants can be expressed as a product of individual factors describing, respectively, the spatial ranges of motions of the adhesive domains, and their rotational freedom within the reaction shell. The results predicted by the theory are compared to those obtained from a novel, to our knowledge, dynamical simulations methodology, whereby pairs of receptors perform realistic translational, internal, and rotational motions in 2D and 3D. We use cadherins as our model system. The theory and simulations explain how the strength of cis and trans interactions of adhesive receptors are affected both by their presence in the constrained intermembrane space and by the 2D environment of membrane surfaces. Our work provides fundamental insights as to the mechanism of lateral clustering of adhesion receptors after cell-cell contact and, more generally, to the formation of lateral microclusters of proteins on cell surfaces.

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).

Coarse grained normal mode analysis vs. refined Gaussian Network Model for protein residue-level structural fluctuations

We investigate several approaches to coarse grained normal mode analysis on protein residual-level structural fluctuations by choosing different ways of representing the residues and the forces among them. Single-atom representations using the backbone atoms C(α), C, N, and C(β) are considered. Combinations of some of these atoms are also tested. The force constants between the representative atoms are extracted from the Hessian matrix of the energy function and served as the force constants between the corresponding residues. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The results are compared with all-atom normal mode analysis and the residue-level Gaussian Network Model. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, while their B-factor correlations are also higher. Their B-factor correlations are comparable with those estimated by the Gaussian Network Model and in many cases better. The extracted force constants are surveyed for different pairs of residues with different numbers of separation residues in sequence. The statistical averages are used to build a refined Gaussian Network Model, which is able to predict residue-level structural fluctuations significantly better than the conventional Gaussian Network Model in many test cases.

Response of rotation-translation blocked proteins using Langevin dynamics on a locally harmonic landscape

Langevin dynamics is used to compute the time evolution of the nonequilibrium motion of the atomic coordinates of a protein in response to ligand dissociation. The protein potential energy surface (PES) is approximated by a harmonic basin about the minimum of the unliganded state. Upon ligand dissociation, the protein undergoes relaxation from the bound to the unbound state. A coarse graining scheme based on rotation translation blocks (RTB) is applied to the relaxation of the two domain iron transport protein, ferric binding protein. This scheme provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment, thereby allowing for the number of dynamical degrees of freedom to be reduced. The results obtained from all flexible atom (constraint free) dynamics are compared to those obtained using RTB-Langevin dynamics. To assess the impact of the assumed rigid fragment clustering on the temporal relaxation dynamics of the protein molecule, three distinct rigid block decompositions were generated and their responses compared. Each of the decompositions was a variant of the one-block-per-residue grouping, with their force and friction matrices being derived from their fully flexible counterpart. Monitoring the time evolution of the distance separating a selected pair of amino acids, the response curves of the blocked decompositions were similar in shape to each other and to the control system in which all atomic degrees of freedom are fully independent. The similar shape of the blocked responses showed that the variations in grouping had only a minor impact on the kinematics. Compared with the all atom responses, however, the blocked responses were faster as a result of the instantaneous transmission of force throughout each rigid block. This occurred because rigid blocking does not permit any intrablock deformation that could store or divert energy. It was found, however, that this accelerated response could be successfully corrected by scaling each eigenvalue in the appropriate propagation matrix by the least-squares fitted slope of the blocked vs nonblocked eigenvalue spectra. The RTB responses for each test system were dominated by small eigenvalue overdamped Langevin modes. The large eigenvalue members of each response dissipated within the first 5 ps, after which the long time response was dominated by a modest set of low energy, overdamped normal modes, that were characterized by highly cooperative, functionally relevant displacements. The response assuming that the system is in the overdamped limit was compared to the full phase space Langevin dynamics results. The responses after the first 5 ps were nearly identical, confirming that the inertial components were significant only in the initial stages of the relaxation. Since the propagator matrix in the overdamped formulation is real-symmetric and does not require the inertial component in the propagator, the computation time and memory footprint was reduced by 1 order of magnitude.

Insight into the structure, dynamics and the unfolding property of amylosucrases: implications of rational engineering on thermostability

Amylosucrase (AS) is a kind of glucosyltransferases (E.C. 2.4.1.4) belonging to the Glycoside Hydrolase (GH) Family 13. In the presence of an activator polymer, in vitro, AS is able to catalyze the synthesis of an amylose-like polysaccharide composed of only α-1,4-linkages using sucrose as the only energy source. Unlike AS, other enzymes responsible for the synthesis of such amylose-like polymers require the addition of expensive nucleotide-activated sugars. These properties make AS an interesting enzyme for industrial applications. In this work, the structures and topology of the two AS were thoroughly investigated for the sake of explaining the reason why Deinococcus geothermalis amylosucrase (DgAS) is more stable than Neisseria polysaccharea amylosucrase (NpAS). Based on our results, there are two main factors that contribute to the superior thermostability of DgAS. On the one hand, DgAS holds some good structural features that may make positive contributions to the thermostability. On the other hand, the contacts among residues of DgAS are thought to be topologically more compact than those of NpAS. Furthermore, the dynamics and unfolding properties of the two AS were also explored by the gauss network model (GNM) and the anisotropic network model (ANM). According to the results of GNM and ANM, we have found that the two AS could exhibit a shear-like motion, which is probably associated with their functions. What is more, with the discovery of the unfolding pathway of the two AS, we can focus on the weak regions, and hence designing more appropriate mutations for the sake of thermostability engineering. Taking the results on structure, dynamics and unfolding properties of the two AS into consideration, we have predicted some novel mutants whose thermostability is possibly elevated, and hopefully these discoveries can be used as guides for our future work on rational design.

KOSMOS: a universal morph server for nucleic acids, proteins and their complexes

KOSMOS is the first online morph server to be able to address the structural dynamics of DNA/RNA, proteins and even their complexes, such as ribosomes. The key functions of KOSMOS are the harmonic and anharmonic analyses of macromolecules. In the harmonic analysis, normal mode analysis (NMA) based on an elastic network model (ENM) is performed, yielding vibrational modes and B-factor calculations, which provide insight into the potential biological functions of macromolecules based on their structural features. Anharmonic analysis involving elastic network interpolation (ENI) is used to generate plausible transition pathways between two given conformations by optimizing a topology-oriented cost function that guarantees a smooth transition without steric clashes. The quality of the computed pathways is evaluated based on their various facets, including topology, energy cost and compatibility with the NMA results. There are also two unique features of KOSMOS that distinguish it from other morph servers: (i) the versatility in the coarse-graining methods and (ii) the various connection rules in the ENM. The models enable us to analyze macromolecular dynamics with the maximum degrees of freedom by combining a variety of ENMs from full-atom to coarse-grained, backbone and hybrid models with one connection rule, such as distance-cutoff, number-cutoff or chemical-cutoff. KOSMOS is available at http://bioengineering.skku.ac.kr/kosmos.

Density-cluster NMA: A new protein decomposition technique for coarse-grained normal mode analysis

Normal mode analysis has emerged as a useful technique for investigating protein motions on long time scales. This is largely due to the advent of coarse-graining techniques, particularly Hooke's Law-based potentials and the rotational-translational blocking (RTB) method for reducing the size of the force-constant matrix, the Hessian. Here we present a new method for domain decomposition for use in RTB that is based on hierarchical clustering of atomic density gradients, which we call Density-Cluster RTB (DCRTB). The method reduces the number of degrees of freedom by 85-90% compared with the standard blocking approaches. We compared the normal modes from DCRTB against standard RTB using 1-4 residues in sequence in a single block, with good agreement between the two methods. We also show that Density-Cluster RTB and standard RTB perform well in capturing the experimentally determined direction of conformational change. Significantly, we report superior correlation of DCRTB with B-factors compared with 1-4 residue per block RTB. Finally, we show significant reduction in computational cost for Density-Cluster RTB that is nearly 100-fold for many examples.

fSUB: normal mode analysis with flexible substructures

In this paper, we report a novel normal-mode analysis for supramolecular complexes, named fSUB. The method models a complex as a group of flexible substructures. The low-frequency substructure modes are first determined with substructures in isolation, and the motions of the whole complex are then calculated on the basis of substructure modes and substructure-substructure interactions. The calculation of modes in fSUB requires modal analysis without initial energy minimization, which is essential for maintaining energetic and structural consistency between substructures and whole complex. Compared with other coarse-grained methods, such as the RTB method, fSUB delivers much more accurate modes for the complex and allows for the choice of much larger substructures. The method can also accommodate any type of substructure arrangement including covalent bonds across the interface. In tests on molecular chaperonin GroEL (7350 residues) and HK97 capsid complex (118,092 residues), fSUB was shown to be much more efficient in terms of combined accuracy and demand of computing resources. Our results clearly demonstrated the vital importance of including substructure flexibility in complex modal analysis, as the deformational patterns of substructures were found to play an important role even in the lowest frequency modes of the whole complex.

Constraints imposed by the membrane selectively guide the alternating access dynamics of the glutamate transporter GltPh

Substrate transport in sodium-coupled amino acid symporters involves a large-scale conformational change that shifts the access to the substrate-binding site from one side of the membrane to the other. The structural change is particularly substantial and entails a unique piston-like quaternary rearrangement in glutamate transporters, as evidenced by the difference between the outward-facing and inward-facing structures resolved for the archaeal aspartate transporter Glt(Ph). These structural changes occur over time and length scales that extend beyond the reach of current fully atomic models, but are regularly explored with the use of elastic network models (ENMs). Despite their success with other membrane proteins, ENM-based approaches for exploring the collective dynamics of Glt(Ph) have fallen short of providing a plausible mechanism. This deficiency is attributed here to the anisotropic constraints imposed by the membrane, which are not incorporated into conventional ENMs. Here we employ two novel (to our knowledge) ENMs to demonstrate that one can largely capture the experimentally observed structural change using only the few lowest-energy modes of motion that are intrinsically accessible to the transporter, provided that the surrounding lipid molecules are incorporated into the ENM. The presence of the membrane reduces the overall energy of the transition compared with conventional models, showing that the membrane not only guides the selected mechanism but also acts as a facilitator. Finally, we show that the dynamics of Glt(Ph) is biased toward transitions of individual subunits of the trimer rather than cooperative transitions of all three subunits simultaneously, suggesting a mechanism of transport that exploits the intrinsic dynamics of individual subunits. Our software is available online at http://www.membranm.csb.pitt.edu.

On the applicability of elastic network normal modes in small-molecule docking

Incorporating backbone flexibility into protein-ligand docking is still a challenging problem. In protein-protein docking, normal mode analysis (NMA) has become increasingly popular as it can be used to describe the collective motions of a biological system, but the question of whether NMA can also be useful in predicting the conformational changes observed upon small-molecule binding has only been addressed in a few case studies. Here, we describe a large-scale study on the applicability of NMA for protein-ligand docking using 433 apo/holo pairs of the Astex data sets. On the basis of sets of the first normal modes from the apo structure, we first generated for each paired holo structure a set of conformations that optimally reproduce its C(α) trace with respect to the underlying normal mode subspace. Using AutoDock, GOLD, and FlexX we then docked the original ligands into these conformations to assess how the docking performance depends on the number of modes used to reproduce the holo structure. The results of our study indicate that, even for such a best-case scenario, the use of normal mode analysis in small-molecule docking is restricted and that a general rule on how many modes to use does not seem to exist or at least is not easy to find.

Evaluation of coupling terms between intra- and intermolecular vibrations in coarse-grained normal-mode analysis: does a stronger acid make a stiffer hydrogen bond?

Using theory of harmonic normal-mode vibration analysis, we developed a procedure for evaluating the anisotropic stiffness of intermolecular forces. Our scheme for coarse-graining of molecular motions is modified so as to account for intramolecular vibrations in addition to relative translational/rotational displacement. We applied this new analytical scheme to four carboxylic acid dimers, for which coupling between intra- and intermolecular vibrations is crucial for determining the apparent stiffness of the intermolecular double hydrogen bond. The apparent stiffness constant was analyzed on the basis of a conjunct spring model, which defines contributions from true intermolecular stiffness and molecular internal stiffness. Consequently, the true intermolecular stiffness was in the range of 43-48 N m(-1) for all carboxylic acids studied, regardless of the molecules' acidity. We concluded that the difference in the apparent stiffness can be attributed to differences in the internal stiffness of the respective molecules.

Optimal number of coarse-grained sites in different components of large biomolecular complexes

The computational study of large biomolecular complexes (molecular machines, cytoskeletal filaments, etc.) is a formidable challenge facing computational biophysics and biology. To achieve biologically relevant length and time scales, coarse-grained (CG) models of such complexes usually must be built and employed. One of the important early stages in this approach is to determine an optimal number of CG sites in different constituents of a complex. This work presents a systematic approach to this problem. First, a universal scaling law is derived and numerically corroborated for the intensity of the intrasite (intradomain) thermal fluctuations as a function of the number of CG sites. Second, this result is used for derivation of the criterion for the optimal number of CG sites in different parts of a large multibiomolecule complex. In the zeroth-order approximation, this approach validates the empirical rule of taking one CG site per fixed number of atoms or residues in each biomolecule, previously widely used for smaller systems (e.g., individual biomolecules). The first-order corrections to this rule are derived and numerically checked by the case studies of the Escherichia coli ribosome and Arp2/3 actin filament junction. In different ribosomal proteins, the optimal number of amino acids per CG site is shown to differ by a factor of 3.5, and an even wider spread may exist in other large biomolecular complexes. Therefore, the method proposed in this paper is valuable for the optimal construction of CG models of such complexes.

Virtual interface substructure synthesis method for normal mode analysis of super-large molecular complexes at atomic resolution

Normal mode analysis of large biomolecular complexes at atomic resolution remains challenging in computational structure biology due to the requirement of large amount of memory space and central processing unit time. In this paper, we present a method called virtual interface substructure synthesis method or VISSM to calculate approximate normal modes of large biomolecular complexes at atomic resolution. VISSM introduces the subunit interfaces as independent substructures that join contacting molecules so as to keep the integrity of the system. Compared with other approximate methods, VISSM delivers atomic modes with no need of a coarse-graining-then-projection procedure. The method was examined for 54 protein-complexes with the conventional all-atom normal mode analysis using CHARMM simulation program and the overlap of the first 100 low-frequency modes is greater than 0.7 for 49 complexes, indicating its accuracy and reliability. We then applied VISSM to the satellite panicum mosaic virus (SPMV, 78,300 atoms) and to F-actin filament structures of up to 39-mer, 228,813 atoms and found that VISSM calculations capture functionally important conformational changes accessible to these structures at atomic resolution. Our results support the idea that the dynamics of a large biomolecular complex might be understood based on the motions of its component subunits and the way in which subunits bind one another.

Changes in dynamics upon oligomerization regulate substrate binding and allostery in amino acid kinase family members

Oligomerization is a functional requirement for many proteins. The interfacial interactions and the overall packing geometry of the individual monomers are viewed as important determinants of the thermodynamic stability and allosteric regulation of oligomers. The present study focuses on the role of the interfacial interactions and overall contact topology in the dynamic features acquired in the oligomeric state. To this aim, the collective dynamics of enzymes belonging to the amino acid kinase family both in dimeric and hexameric forms are examined by means of an elastic network model, and the softest collective motions (i.e., lowest frequency or global modes of motions) favored by the overall architecture are analyzed. Notably, the lowest-frequency modes accessible to the individual subunits in the absence of multimerization are conserved to a large extent in the oligomer, suggesting that the oligomer takes advantage of the intrinsic dynamics of the individual monomers. At the same time, oligomerization stiffens the interfacial regions of the monomers and confers new cooperative modes that exploit the rigid-body translational and rotational degrees of freedom of the intact monomers. The present study sheds light on the mechanism of cooperative inhibition of hexameric N-acetyl-L-glutamate kinase by arginine and on the allosteric regulation of UMP kinases. It also highlights the significance of the particular quaternary design in selectively determining the oligomer dynamics congruent with required ligand-binding and allosteric activities.

Protein function requires a three-dimensional structure with specific dynamic features for catalytic and binding events, and, in many cases, the structure results from the assembly of more than one polypeptide chain (also called monomer or subunit) to form an oligomer or multimer. Proteins such as hemoglobin or chaperonin GroEL are oligomers formed by 2 and 14 subunits, respectively, whereas virus capsids are multimers composed of hundreds of monomers. In these cases, the architecture of the interface between the subunits and the overall assembly geometry are essential in determining the functional motions that these sophisticated structures are able to perform under physiological conditions. Here we present results from our computational study of the large-amplitude motions of dimeric and hexameric proteins that belong to the Amino Acid Kinase family. Our study reveals that the monomers in these oligomeric proteins are arranged in such a way that the oligomer inherits the intrinsic dynamic features of its components. The packing geometry additionally confers the ability to perform highly cooperative conformational changes that involve all monomers and enable the biological activity of the multimer. The study highlights the significance of the quaternary design in favoring the oligomer dynamics that enables ligand-binding and allosteric regulation functions.

Transforming binding affinities from three dimensions to two with application to cadherin clustering

Membrane-bound receptors often form large assemblies resulting from binding to soluble ligands, cell-surface molecules on other cells and extracellular matrix proteins. For example, the association of membrane proteins with proteins on different cells (trans-interactions) can drive the oligomerization of proteins on the same cell (cis-interactions). A central problem in understanding the molecular basis of such phenomena is that equilibrium constants are generally measured in three-dimensional solution and are thus difficult to relate to the two-dimensional environment of a membrane surface. Here we present a theoretical treatment that converts three-dimensional affinities to two dimensions, accounting directly for the structure and dynamics of the membrane-bound molecules. Using a multiscale simulation approach, we apply the theory to explain the formation of ordered, junction-like clusters by classical cadherin adhesion proteins. The approach features atomic-scale molecular dynamics simulations to determine interdomain flexibility, Monte Carlo simulations of multidomain motion and lattice simulations of junction formation. A finding of general relevance is that changes in interdomain motion on trans-binding have a crucial role in driving the lateral, cis-, clustering of adhesion receptors.

ReplicOpter: a replicate optimizer for flexible docking

We present a computationally efficient method for flexible refinement of docking predictions that reflects observed motions within a protein's structural class. Using structural homologs, we derive deformation models that capture likely motions. The models or "replicates" typically align along a rigid core, with a handful of flexible loops, linkers and tails. A few replicates can generate a much larger number of conformers, by exchanging each flexible region independently of the others. In this way, 10 replicates of a protein having 6 flexible regions can be used to generate a million conformations of a molecule. While this has obvious advantages in terms of sampling, the cost of assessing energies at every conformer is prohibitive, particularly when both molecules are flexible. Our approach addresses this combinatorial explosion, using key assumptions to compress the sampling by many orders of magnitude. ReplicOpter can perform hierarchical clustering from a list of rigid docking predictions and find nearby structures to any promising cluster representatives. These predicted complexes can then be refined and rescored. ReplicOpter's scoring function includes a Lennard-Jones potential softened using the Anderson-Chandler-Weeks decomposition, a desolvation term derived from the Atomic Contact Energy function, Coulombic electrostatics, hydrogen bonding, and terms to model pi-pi and pi-cation interactions. ReplicOpter has performed well on several recent CAPRI systems. We are presently benchmarking ReplicOpter on the complete docking benchmark set to fully establish its utility in refining rigid docking predictions and identifying near-native solutions.

Large-scale comparison of protein essential dynamics from molecular dynamics simulations and coarse-grained normal mode analyses

A large-scale comparison of essential dynamics (ED) modes from molecular dynamic simulations and normal modes from coarse-grained normal mode methods (CGNM) was performed on a dataset of 335 proteins. As CGNM methods, the elastic network model (ENM) and the rigid cluster normal mode analysis (RCNMA) were used. Low-frequency normal modes from ENM correlate very well with ED modes in terms of directions of motions and relative amplitudes of motions. Notably, a similar performance was found if normal modes from RCNMA were used, despite a higher level of coarse graining. On average, the space spanned by the first quarter of ENM modes describes 84% of the space spanned by the five ED modes. Furthermore, no prominent differences for ED and CGNM modes among different protein structure classes (CATH classification) were found. This demonstrates the general potential of CGNM approaches for describing intrinsic motions of proteins with little computational cost. For selected cases, CGNM modes were found to be more robust among proteins that have the same topology or are of the same homologous superfamily than ED modes. In view of recent evidence regarding evolutionary conservation of vibrational dynamics, this suggests that ED modes, in some cases, might not be representative of the underlying dynamics that are characteristic of a whole family, probably due to insufficient sampling of some of the family members by MD.

Evaluating elastic network models of crystalline biological molecules with temperature factors, correlated motions, and diffuse x-ray scattering

In this study, the variance-covariance matrix of protein motions is used to compare several elastic network models within the theoretical framework of x-ray scattering from crystals. A set of 33 ultra-high resolution structures is used to characterize the average scaling behavior of the vibrational density of states and make comparisons between experimental and theoretical temperature factors. Detailed investigations of the vibrational density of states, correlations, and predicted diffuse x-ray scatter are carried out for crystalline Staphylococcal nuclease; correlations and diffuse x-ray scatter are also compared to predictions from the translation, libration, screw model and a liquid-like dynamics model. We show that elastic network models developed to best predict temperature factors without regard for the crystal environment have relatively strong long-range interactions that yield very short-ranged atom-atom correlations. Further, we find that the low-frequency modes dominate the variance-covariance matrix only for those models with a physically reasonable vibrational density of states, and the fraction of modes required to converge the correlations is higher than that typically used for elastic network model studies. The practical implications are explored using computed diffuse x-ray scatter, which can be measured experimentally.

Anisotropic elastic network modeling of entire microtubules

Microtubules are supramolecular structures that make up the cytoskeleton and strongly affect the mechanical properties of the cell. Within the cytoskeleton filaments, the microtubule (MT) exhibits by far the highest bending stiffness. Bending stiffness depends on the mechanical properties and intermolecular interactions of the tubulin dimers (the MT building blocks). Computational molecular modeling has the potential for obtaining quantitative insights into this area. However, to our knowledge, standard molecular modeling techniques, such as molecular dynamics (MD) and normal mode analysis (NMA), are not yet able to simulate large molecular structures like the MTs; in fact, their possibilities are normally limited to much smaller protein complexes. In this work, we developed a multiscale approach by merging the modeling contribution from MD and NMA. In particular, MD simulations were used to refine the molecular conformation and arrangement of the tubulin dimers inside the MT lattice. Subsequently, NMA was used to investigate the vibrational properties of MTs modeled as an elastic network. The coarse-grain model here developed can describe systems of hundreds of interacting tubulin monomers (corresponding to up to 1,000,000 atoms). In particular, we were able to simulate coarse-grain models of entire MTs, with lengths up to 350 nm. A quantitative mechanical investigation was performed; from the bending and stretching modes, we estimated MT macroscopic properties such as bending stiffness, Young modulus, and persistence length, thus allowing a direct comparison with experimental data.

SwarmDock and the use of normal modes in protein-protein docking

Here is presented an investigation of the use of normal modes in protein-protein docking, both in theory and in practice. Upper limits of the ability of normal modes to capture the unbound to bound conformational change are calculated on a large test set, with particular focus on the binding interface, the subset of residues from which the binding energy is calculated. Further, the SwarmDock algorithm is presented, to demonstrate that the modelling of conformational change as a linear combination of normal modes is an effective method of modelling flexibility in protein-protein docking.

Prediction of protein motions from amino acid sequence and its application to protein-protein interaction

BACKGROUND

Structural flexibility is an important characteristic of proteins because it is often associated with their function. The movement of a polypeptide segment in a protein can be broken down into two types of motions: internal and external ones. The former is deformation of the segment itself, but the latter involves only rotational and translational motions as a rigid body. Normal Model Analysis (NMA) can derive these two motions, but its application remains limited because it necessitates the gathering of complete structural information.

RESULTS

In this work, we present a novel method for predicting two kinds of protein motions in ordered structures. The prediction uses only information from the amino acid sequence. We prepared a dataset of the internal and external motions of segments in many proteins by application of NMA. Subsequently, we analyzed the relation between thermal motion assessed from X-ray crystallographic B-factor and internal/external motions calculated by NMA. Results show that attributes of amino acids related to the internal motion have different features from those related to the B-factors, although those related to the external motion are correlated strongly with the B-factors. Next, we developed a method to predict internal and external motions from amino acid sequences based on the Random Forest algorithm. The proposed method uses information associated with adjacent amino acid residues and secondary structures predicted from the amino acid sequence. The proposed method exhibited moderate correlation between predicted internal and external motions with those calculated by NMA. It has the highest prediction accuracy compared to a naïve model and three published predictors.

CONCLUSIONS

Finally, we applied the proposed method predicting the internal motion to a set of 20 proteins that undergo large conformational change upon protein-protein interaction. Results show significant overlaps between the predicted high internal motion regions and the observed conformational change regions.

Molecular recognition of RNA: challenges for modelling interactions and plasticity

There is growing interest in molecular recognition processes of RNA because of RNA's widespread involvement in biological processes. Computational approaches are increasingly used for analysing and predicting binding to RNA, fuelled by encouraging progress in developing simulation, free energy and docking methods for nucleic acids. These developments take into account challenges regarding the energetics of RNA-ligand binding, RNA plasticity, and the presence of water molecules and ions in the binding interface. Accordingly, we will detail advances in force field and scoring function development for molecular dynamics (MD) simulations, free energy computations and docking calculations of nucleic acid complexes. Furthermore, we present methods that can detect moving parts within RNA structures based on graph-theoretical approaches or normal mode analysis (NMA). As an example of the successful use of these developments, we will discuss recent structure-based drug design approaches that focus on the bacterial ribosomal A-site RNA as a drug target.

Structure, evolutionary conservation, and conformational dynamics of Homo sapiens fascin-1, an F-actin crosslinking protein

Eukaryotes have several highly conserved actin-binding proteins that crosslink filamentous actin into compact ordered bundles present in distinct cytoskeletal processes, including microvilli, stereocilia and filopodia. Fascin is an actin-binding protein that is present predominantly in filopodia, which are believed to play a central role in normal and aberrant cell migration. An important outstanding question regards the molecular basis for the unique localization and functional properties of fascin compared with other actin crosslinking proteins. Here, we present the crystal structure of full-length Homo sapiens fascin-1, and examine its packing, conformational flexibility, and evolutionary sequence conservation. The structure reveals a novel arrangement of four tandem beta-trefoil domains that form a bi-lobed structure with approximate pseudo 2-fold symmetry. Each lobe has internal approximate pseudo 2-fold and pseudo 3-fold symmetry axes that are approximately perpendicular, with beta-hairpin triplets located symmetrically on opposite sides of each lobe that mutational data suggest are actin-binding domains. Sequence conservation analysis confirms the importance of hydrophobic core residues that stabilize the beta-trefoil fold, as well as interfacial residues that are likely to stabilize the overall fascin molecule. Sequence conservation also indicates highly conserved surface patches near the putative actin-binding domains of fascin, which conformational dynamics analysis suggests to be coupled via an allosteric mechanism that might have important functional implications for F-actin crosslinking by fascin.

On the conservation of the slow conformational dynamics within the amino acid kinase family: NAGK the paradigm

N-Acetyl-L-Glutamate Kinase (NAGK) is the structural paradigm for examining the catalytic mechanisms and dynamics of amino acid kinase family members. Given that the slow conformational dynamics of the NAGK (at the microseconds time scale or slower) may be rate-limiting, it is of importance to assess the mechanisms of the most cooperative modes of motion intrinsically accessible to this enzyme. Here, we present the results from normal mode analysis using an elastic network model representation, which shows that the conformational mechanisms for substrate binding by NAGK strongly correlate with the intrinsic dynamics of the enzyme in the unbound form. We further analyzed the potential mechanisms of allosteric signalling within NAGK using a Markov model for network communication. Comparative analysis of the dynamics of family members strongly suggests that the low-frequency modes of motion and the associated intramolecular couplings that establish signal transduction are highly conserved among family members, in support of the paradigm sequence→structure→dynamics→function.

During the last 20 years both the experimental and computational communities have provided strong evidence that proteins cannot be regarded as static entities, but as intrinsically flexible molecules that exploit their fluctuation dynamics for catalytic and ligand-binding events, as well as for allosteric regulation. This intrinsic dynamics is encoded in the protein structure and, therefore, those proteins with similar folding should share dynamic features essential to their biological function. In this work, we have applied an Elastic Network Model to predict the large-amplitude dynamics of different enzymes belonging to the same protein family (Amino Acid Kinase family). Subsequent comparison of the dynamics of these proteins reveals that this protein family follows the same dynamic pattern. The present results are strongly supported by experimental data and provide new insights into the performance of biological function by these enzymes. The investigation presented here provides us with a useful framework to identify dynamic fingerprints among proteins with structural similarities.

RNA polymerase II flexibility during translocation from normal mode analysis

The structural dynamics in eukaryotic RNA polymerase II (RNAPII) is described from computational normal mode analysis based on a series of crystal structures of pre- and post-translocated states with open and closed trigger loops. Conserved modes are identified that involve translocation of the nucleic acid complex coupled to motions of the enzyme, in particular in the clamp and jaw domains of RNAPII. A combination of these modes is hypothesized to be involved during active transcription. The NMA modes indicate furthermore that downstream DNA translocation may occur separately from DNA:RNA hybrid translocation. A comparison of the modes between different states of RNAPII suggests that productive translocation requires an open trigger loop and is inhibited by the presence of an NTP in the active site. This conclusion is also supported by a comparison of the overall flexibility in terms of root mean square fluctuations.

The subspace iteration method in protein normal mode analysis

Normal mode analysis plays an important role in relating the conformational dynamics of proteins to their biological function. The subspace iteration method is a numerical procedure for normal mode analysis that has enjoyed widespread success in the structural mechanics community due to its numerical stability and computational efficiency in calculating the lowest normal modes of large systems. Here, we apply the subspace iteration method to proteins to demonstrate its advantageous properties in this area of computational protein science. An effective algorithm for choosing the number of iteration vectors in the method is established, offering a considerable improvement over the original implementation. In the present application, computational time scales linearly with the number of normal modes computed. Additionally, the method lends itself naturally to normal mode analyses of multiple neighboring macromolecular conformations, as demonstrated in a conformational change pathway analysis of adenylate kinase. These properties, together with its computational robustness and intrinsic scalability to multiple processors, render the subspace iteration method an effective and reliable computational approach to protein normal mode analysis.

Conformational preference of ChaK1 binding peptides: a molecular dynamics study

TRPM7/ChaK1 is a recently discovered atypical protein kinase that has been suggested to selectively phosphorylate the substrate residues located in α-helices. However, the actual structure of kinase-substrate complex has not been determined experimentally and the recognition mechanism remains unknown. In this work we explored possible kinase-substrate binding modes and the likelihood of an α-helix docking interaction, within a kinase active site, using molecular modeling. Specifically kinase ChaK1 and its two peptide substrates were examined; one was an 11-residue segment from the N-terminal domain of annexin-1, a putative endogenous substrate for ChaK1, and the other was an engineered 16-mer peptide substrate determined via peptide library screening. Simulated annealing (SA), replica-exchange molecular dynamics (REMD) and steered molecular dynamics (SMD) simulations were performed on the two peptide substrates and the ChaK1-substrate complex in solution. The simulations indicate that the two substrate peptides are unlikely to bind and react with the ChaK1 kinase in a stable α-helical conformation overall. The key structural elements, sequence motifs, and amino acid residues in the ChaK1 and their possible functions involved in the substrate recognition are discussed.

PACS Codes: 87.15.A-

Structure-based predictive models for allosteric hot spots

In allostery, a binding event at one site in a protein modulates the behavior of a distant site. Identifying residues that relay the signal between sites remains a challenge. We have developed predictive models using support-vector machines, a widely used machine-learning method. The training data set consisted of residues classified as either hotspots or non-hotspots based on experimental characterization of point mutations from a diverse set of allosteric proteins. Each residue had an associated set of calculated features. Two sets of features were used, one consisting of dynamical, structural, network, and informatic measures, and another of structural measures defined by Daily and Gray [1]. The resulting models performed well on an independent data set consisting of hotspots and non-hotspots from five allosteric proteins. For the independent data set, our top 10 models using Feature Set 1 recalled 68–81% of known hotspots, and among total hotspot predictions, 58–67% were actual hotspots. Hence, these models have precision P = 58–67% and recall R = 68–81%. The corresponding models for Feature Set 2 had P = 55–59% and R = 81–92%. We combined the features from each set that produced models with optimal predictive performance. The top 10 models using this hybrid feature set had R = 73–81% and P = 64–71%, the best overall performance of any of the sets of models. Our methods identified hotspots in structural regions of known allosteric significance. Moreover, our predicted hotspots form a network of contiguous residues in the interior of the structures, in agreement with previous work. In conclusion, we have developed models that discriminate between known allosteric hotspots and non-hotspots with high accuracy and sensitivity. Moreover, the pattern of predicted hotspots corresponds to known functional motifs implicated in allostery, and is consistent with previous work describing sparse networks of allosterically important residues.

Allostery is the process whereby a molecule binds to one site in a protein and alters the function of a distant site. This phenomenon is ubiquitous, as proteins frequently must adapt their behavior to changes in the cellular milieu. The mechanism(s) underlying allostery remains incompletely understood. In particular, predictive models are needed that distinguish amino-acid residues that are critical to allostery, or “hotspots”, from non-hotspots. Here we have used data-mining approaches to infer rules that distinguish hotspots from non-hotspots. Starting with a data set of known hotspot and non-hotspot residues from a diverse set of allosteric proteins, the training data set, we applied machine learning to this data to “learn” models, or sets of rules, for distinguishing hotspots and non-hotspots by inferring associations between the classification (hotspot or non-hotspot) and an associated set of calculated attributes. Many models that showed the highest predictive power on the training data also exhibited high accuracy and sensitivity when applied to an independent data set. Moreover, the pattern of predicted hotspots in the proteins we studied was consistent with known structure/function relationships and previous work suggesting that a network of essential residues mediates the allosteric transition.

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.

Combining an Elastic Network With a Coarse-Grained Molecular Force Field: Structure, Dynamics, and Intermolecular Recognition

Structure-based and physics-based coarse-grained molecular force fields have become attractive approaches to gain mechanistic insight into the function of large biomolecular assemblies. Here, we study how both approaches can be combined into a single representation, that we term ELNEDIN. In this representation an elastic network is used as a structural scaffold to describe and maintain the overall shape of a protein and a physics-based coarse-grained model (MARTINI-2.1) is used to describe both inter- and intramolecular interactions in the system. The results show that when used in molecular dynamics simulations ELNEDIN models can be built so that the resulting structural and dynamical properties of a protein, including its collective motions, are comparable to those obtained using atomistic protein models. We then evaluate the behavior of such models in (1) long, microsecond time-scale, simulations, (2) the modeling of very large macromolecular assemblies, a viral capsid, and (3) the study of a protein-protein association process, the reassembly of the ROP homodimer. The results for this series of tests indicate that ELNEDIN models allow microsecond time-scale molecular dynamics simulations to be carried out readily, that large biological entities such as the viral capsid of the cowpea mosaic virus can be stably modeled as assemblies of independent ELNEDIN models, and that ELNEDIN models show significant promise for modeling protein-protein association processes.

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.

Approximate normal mode analysis based on vibrational subsystem analysis with high accuracy and efficiency

Normal mode analysis (NMA) has been proven valuable in modeling slow conformational dynamics of biomolecular structures beyond the reach of direct molecular simulations. However, it remains computationally expensive to directly solve normal modes for large biomolecular systems. In this study, we have evaluated the accuracy and efficiency of two approximate NMA protocols-one based on our recently proposed vibrational subsystem analysis (VSA), the other based on the rotation translation block (RTB), in comparison with standard NMA that directly solves a full Hessian matrix. By properly accounting for flexibility within blocks of residues or atoms based on a subsystem-environment partition, VSA-based NMA has attained a much higher accuracy than RTB and much lower computing cost than standard NMA. Therefore, VSA enables accurate and efficient calculations of normal modes from all-atom or coarse-grained potential functions, which promise to improve conformational sampling driven by low-frequency normal modes.

Deciphering the mismatch recognition cycle in MutS and MSH2-MSH6 using normal-mode analysis

Postreplication DNA mismatch repair is essential for maintaining the integrity of genomic information in prokaryotes and eukaryotes. The first step in mismatch repair is the recognition of base-base mismatches and insertions/deletions by bacterial MutS or eukaryotic MSH2-MSH6. Crystal structures of both proteins bound to mismatch DNA reveal a similar molecular architecture but provide limited insight into the detailed molecular mechanism of long-range allostery involved in mismatch recognition and repair initiation. This study describes normal-mode calculations of MutS and MSH2-MSH6 with and without DNA. The results reveal similar protein flexibilities and suggest common dynamic and functional characteristics. A strongly correlated motion is present between the lever domain and ATPase domains, which suggests a pathway for long-range allostery from the N-terminal DNA binding domain to the C-terminal ATPase domains, as indicated by experimental studies. A detailed analysis of individual low-frequency modes of both MutS and MSH2-MSH6 shows changes in the DNA-binding domains coupled to the ATPase sites, which are interpreted in the context of experimental data to arrive at a complete molecular-level mismatch recognition cycle. Distinct conformational states are proposed for DNA scanning, mismatch recognition, repair initiation, and sliding along DNA after mismatch recognition. Hypotheses based on the results presented here form the basis for further experimental and computational studies.

Normal modes for large molecules with arbitrary link constraints in the mobile block Hessian approach

In a previous paper [Ghysels et al., J. Chem. Phys. 126, 224102 (2007)] the mobile block Hessian (MBH) approach was presented. The method was designed to accurately compute vibrational modes of partially optimized molecular structures. The key concept was the introduction of several blocks of atoms, which can move as rigid bodies with respect to a local, fully optimized subsystem. The choice of the blocks was restricted in the sense that none of them could be connected, and also linear blocks were not taken into consideration. In this paper an extended version of the MBH method is presented that is generally applicable and allows blocks to be adjoined by one or two common atoms. This extension to all possible block partitions of the molecule provides a structural flexibility varying from very rigid to extremely relaxed. The general MBH method is very well suited to study selected normal modes of large macromolecules (such as proteins and polymers) because the number of degrees of freedom can be greatly reduced while still keeping the essential motions of the molecular system. The reduction in the number of degrees of freedom due to the block linkages is imposed here directly using a constraint method, in contrast to restraint methods where stiff harmonic couplings are introduced to restrain the relative motion of the blocks. The computational cost of this constraint method is less than that of an implementation using a restraint method. This is illustrated for the alpha-helix conformation of an alanine-20-polypeptide.

Application of elastic network models to proteins in the crystalline state

Normal mode analysis using elastic network models has grown popular for probing the low-frequency collective dynamics of proteins and other biomolecular assemblies. In most previous studies, these models were validated by comparing calculated atomic fluctuations for isolated proteins with experimental temperature factors determined in the crystalline state, although there were also hints that including crystal contacts in the calculations has an impact on the comparison. In this study, a set of 83 ultra-high resolution crystal structures with experimentally determined anisotropic displacement parameters is used to evaluate several C(alpha)-based elastic network models that either ignore or treat the crystal environment in different ways; the latter include using periodic boundary conditions defined with respect to the asymmetric unit or the primitive unit cell as well as using the Born-von Kármán boundary condition that accounts for lattice vibrations. For all elastic network models, treating the crystal environment leads to better agreement with experimental anisotropic displacement parameters with the Born-von Kármán boundary condition giving the best agreement. Atomic correlations over the entire protein are clearly affected by the presence of the crystal contacts and fairly sensitive to the way that the crystal environment is treated. These observations highlight the importance of properly treating the protein system in an environment consistent with experiment when either evaluating approximate protein models or using approximate dynamic models in structural refinement application types. Finally, investigation of the scaling behaviors of the cumulative density of states and the heat capacity indicates that there are still gaps between simplified elastic models and all-atom models for proteins.

Iterative cluster-NMA: A tool for generating conformational transitions in proteins

Computational models provide insight into the structure-function relationship in proteins. These approaches, especially those based on normal mode analysis, can identify the accessible motion space around a given equilibrium structure. The large magnitude, collective motions identified by these methods are often well aligned with the general direction of the expected conformational transitions. However, these motions cannot realistically be extrapolated beyond the local neighborhood of the starting conformation. In this article, the iterative cluster-NMA (icNMA) method is presented for traversing the energy landscape from a starting conformation to a desired goal conformation. This is accomplished by allowing the evolving geometry of the intermediate structures to define the local accessible motion space, and thus produce an appropriate displacement. Following the derivation of the icNMA method, a set of sample simulations are performed to probe the robustness of the model. A detailed analysis of beta1,4-galactosyltransferase-T1 is also given, to highlight many of the capabilities of icNMA. Remarkably, during the transition, a helix is seen to be extended by an additional turn, emphasizing a new unknown role for secondary structures to absorb slack during transitions. The transition pathway for adenylate kinase, which has been frequently studied in the literature, is also discussed.

Theory of the low frequency mechanical modes and Raman spectra of the M13 bacteriophage capsid with atomic detail

We present a theoretical study of the low frequency vibrational modes of the M13 bacteriophage using a fully atomistic model. Using ideas from electronic structure theory, the few lowest vibrational modes of the M13 bacteriophage are determined using classical harmonic analysis. The relative Raman intensity is estimated for each of the mechanical modes using a bond polarizability model. Comparison of the atomic mechanical modes calculated here with modes derived from elastic continuum theory shows that a much richer spectrum emerges from an atomistic picture.

A minimalist network model for coarse-grained normal mode analysis and its application to biomolecular x-ray crystallography

In this article, we report a method for coarse-grained normal mode analysis called the minimalist network model. The main features of the method are that it can deliver accurate low-frequency modes on structures without undergoing initial energy minimization and that it also retains the details of molecular interactions. The method does not require any additional adjustable parameters after coarse graining and is computationally very fast. Tests on modeling the experimentally measured anisotropic displacement parameters in biomolecular x-ray crystallography demonstrate that the method can consistently perform better than other commonly used methods including our own one. We expect this method to be effective for applications such as structural refinement and conformational sampling.

Allosteric communication in myosin V: from small conformational changes to large directed movements

The rigor to post-rigor transition in myosin, a consequence of ATP binding, plays an essential role in the Lymn–Taylor functional cycle because it results in the dissociation of the actomyosin complex after the powerstroke. On the basis of the X-ray structures of myosin V, we have developed a new normal mode superposition model for the transition path between the two states. Rigid-body motions of the various subdomains and specific residues at the subdomain interfaces are key elements in the transition. The allosteric communication between the nucleotide binding site and the U50/L50 cleft is shown to result from local changes due to ATP binding, which induce large amplitude motions that are encoded in the structure of the protein. The triggering event is the change in the interaction of switch I and the P-loop, which is stabilized by ATP binding. The motion of switch I, which is a relatively rigid element of the U50 subdomain, leads directly to a partial opening of the U50/L50 cleft; the latter is expected to weaken the binding of myosin to actin. The calculated transition path demonstrates the nature of the subdomain coupling and offers an explanation for the mutual exclusion of ATP and actin binding. The mechanism of the uncoupling of the converter from the motor head, an essential part of the transition, is elucidated. The origin of the partial untwisting of the central β-sheet in the rigor to post-rigor transition is described.

Myosins are molecular motor proteins that interact with actin filaments to perform a wide range of cellular functions. They use the universal energy storage molecule adenosine triphosphate (ATP). The functional cycle involves myosin binding to actin, a “powerstroke” leading to directed movement, and myosin release in preparation for the next step. A fundamental question concerns the mechanism by which the local structural changes due to ATP binding, hydrolysis, and products release can generate the large myosin changes of conformation required for this cycle. Here, we focus on the rigor to post-rigor transition of myosin V, which results in the release of myosin from actin. Starting from the X-ray structures of the two states, we have used the optimal superposition of normal modes to determine the transition path. The path shows the allosteric mechanism by which ATP binding leads to the opening of the U50/L50 cleft, the essential step in the unbinding of myosin from actin. More generally, the new normal-mode superposition model can be useful for describing large-amplitude conformational transitions encoded in protein structures by evolution.

Large scale motions in a biosensor protein glucose oxidase: a combined approach by QENS, normal mode analysis, and molecular dynamics studies

The characteristics of the glucose oxidase were studied using a combination of experimental and theoretical techniques. Quasi elastic neutron scattering experiments were used to obtain the vibrational frequencies of the protein. These were compared to theoretical results obtained by normal mode analysis. Results indicate a good match between the experimental and theoretical values. Molecular dynamic simulation with covariant analysis was used to study the structure and dynamics of glucose oxidase. Various parameters like the radius of gyration, root mean square fluctuations, solvent accessibility were studied for evaluating the structural stability of the protein. The frequency of vibration calculated from the three methods is used to derive the large scale motions. Theses studies were used to predict the suitable lysine residues for linkage with carbon nanotubes.

Folding of small helical proteins assisted by small-angle X-ray scattering profiles

This paper reports a computational method for folding small helical proteins. The goal was to determine the overall topology of proteins given secondary structure assignment on sequence. In doing so, a Monte Carlo protocol, which combines coarse-grained normal modes and a Hamiltonian at a different scale, was developed to enhance sampling. In addition to the knowledge-based potential functions, a small-angle X-ray scattering (SAXS) profile was also used as a weak constraint for guiding the folding. The algorithm can deliver structural models with overall correct topology, which makes them similar to those of 5 approximately 6 A cryo-EM density maps. The success could contribute to make the SAXS technique a fast and inexpensive solution-phase experimental method for determining the overall topology of small, soluble, but noncrystallizable, helical proteins.