Discrete breathers in nonlinear network models of proteins.

We introduce a topology-based nonlinear network model of protein dynamics with the aim of investigating the interplay of spatial disorder and nonlinearity. We show that spontaneous localization of energy occurs generically and is a site-dependent process. Localized modes of nonlinear origin form spontaneously in the stiffest parts of the structure and display site-dependent activation energies. Our results provide a straightforward way for understanding the recently discovered link between protein local stiffness and enzymatic activity. They strongly suggest that nonlinear phenomena may play an important role in enzyme function, allowing for energy storage during the catalytic process.

Functional modes of proteins are among the most robust.

It is shown that a small subset of modes which are likely to be involved in protein functional motions of large amplitude can be determined by retaining the most robust normal modes obtained using different protein models. This result should prove helpful in the context of several applications proposed recently, like for solving difficult molecular replacement problems or for fitting atomic structures into low-resolution electron density maps. It may also pave the way for the development of methods allowing us to predict such motions accurately.

Slow energy relaxation of macromolecules and nanoclusters in solution.

Many systems in the realm of nanophysics from both the living and the inorganic world display slow relaxation kinetics of energy fluctuations. In this Letter we propose a general explanation for such a phenomenon, based on the effects of interactions with the solvent. Within a simple harmonic model of the system fluctuations, we demonstrate that the inhomogeneity of coupling to the solvent of the bulk and surface atoms suffices to generate a complex spectrum of decay rates. We show for myoglobin and for a metal nanocluster that the result is a complex, nonexponential relaxation dynamics.

Dynamical properties of the MscL of Escherichia coli: a normal mode analysis.

The mechanosensitive channel (MscL) is an integral membrane protein which gates in response to membrane tension. Physiological data have shown that the gating transition involves a very large change in the conformation, and that the open state of the channel forms a large non-specific pore with a high conductance. The Escherichia coli channel structure was first modeled by homology modeling, starting with the X-ray structure of the homologous from Mycobacterium tuberculosis. Then, the dynamical and conformational properties of the channel were explored, using normal mode analysis. Such an analysis was also performed with the different structures proposed recently by Sukharev and co-workers. Similar dynamical behaviors are observed, which are characteristic of the channel architecture, subtle differences being due to the different relative positioning of the structural elements. The ability of particular regions of the channel to deform is discussed with respect to the functional and structural properties, implied in the gating process. Our results show that the first step of the gating mechanism can be described with three low-frequency modes only. The movement associated to these modes is clearly an iris-like movement involving both tilt and twist rotation.

Exploring the natural conformational changes of the C-terminal domain of calmodulin.

Several experimental results suggest that the Ca2+-loaded C-terminal domain of calmodulin (or some of its mutants) exhibits conformational changes triggered solely by thermal fluctuations. The time scales involved are in the 10(-6)-10(-3) s range. Here we develop a theoretical method to explore this type of motions based on a modified version of molecular dynamics algorithm where the secondary structure motifs are held fixed. In this version, increasing the temperature enhances the sampling of conformations with locally fixed secondary structures. From the temperature dependence of the transition rate between various conformational states, we obtain characteristic times that are consistent with those observed experimentally.

Simplified normal mode analysis of conformational transitions in DNA-dependent polymerases: the elastic network model.

The Elastic Network Model is used to investigate the open/closed transition in all DNA-dependent polymerases whose structure is known in both forms. For each structure the model accounts well for experimental crystallographic B-factors. It is found in all cases that the transition can be well described with just a handful of the normal modes. Usually, only the lowest and/or the second lowest frequency normal modes deduced from the open form give rise to calculated displacement vectors that have a correlation coefficient larger than 0.50 with the observed difference vectors between the two forms. This is true for every structural class of DNA-dependent polymerases where a direct comparison with experimental structural data is available. In cases where only one form has been observed by X-ray crystallography, it is possible to make predictions concerning the possible existence of another form in solution by carefully examining the vector displacements predicted for the lowest frequency normal modes. This simple model, which has the advantage to be computationally inexpensive, could be used to design novel kind of drugs directed against polymerases, namely drugs preventing the open/closed transition from occurring in bacterial or viral DNA-dependent polymerases.

Conformational change of proteins arising from normal mode calculations.

A normal mode analysis of 20 proteins in 'open' or 'closed' forms was performed using simple potential and protein models. The quality of the results was found to depend upon the form of the protein studied, normal modes obtained with the open form of a given protein comparing better with the conformational change than those obtained with the closed form. Moreover, when the motion of the protein is a highly collective one, then, in all cases considered, there is a single low-frequency normal mode whose direction compares well with the conformational change. When it is not, in most cases there is still a single low-frequency normal mode giving a good description of the pattern of the atomic displacements, as they are observed experimentally during the conformational change. Hence a lot of information on the nature of the conformational change of a protein is often found in a single low-frequency normal mode of its open form. Since this information can be obtained through the normal mode analysis of a model as simple as that used in the present study, it is likely that the property captured by such an analysis is for the most part a property of the shape of the protein itself. One of the points that has to be clarified now is whether or not amino acid sequences have been selected in order to allow proteins to follow a single normal mode direction, as least at the very beginning of their conformational change.

Building-block approach for determining low-frequency normal modes of macromolecules.

Normal mode analysis of proteins of various sizes, ranging from 46 (crambin) up to 858 residues (dimeric citrate synthase) were performed, by using standard approaches, as well as a recently proposed method that rests on the hypothesis that low-frequency normal modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino-acid residues. Such a hypothesis is strongly supported by our results, because we show that the latter method, named RTB, yields very accurate approximations for the low-frequency normal modes of all proteins considered. Moreover, the quality of the normal modes thus obtained depends very little on the way the polypeptidic chain is split into blocks. Noteworthy, with six amino-acids per block, the normal modes are almost as accurate as with a single amino-acid per block. In this case, for a protein of n residues and N atoms, the RTB method requires the diagonalization of an n x n matrix, whereas standard procedures require the diagonalization of a 3N x 3N matrix. Being a fast method, our approach can be useful for normal mode analyses of large systems, paving the way for further developments and applications in contexts for which the normal modes are needed frequently, as for example during molecular dynamics calculations.

Ca2+/Mg2+ exchange in parvalbumin and other EF-hand proteins. A theoretical study.

A remarkable conformational rearrangement occurs upon Ca2+/Mg2+ exchange in the C-terminal EF-hand site (labelled site EF or EF-4) of parvalbumin, as initially established by X-ray crystallography. Such a conformational rearrangement is characterised as follows: (i) the co-ordination number decreases from seven oxygen atoms in the Ca-loaded form to six oxygen atoms in the Mg-loaded form, the heptaco-ordination of Ca2+ corresponding with a skewed pentagonal bipyramid configuration of the seven oxygen atoms, whereas the hexaco-ordination of Mg2+ corresponds with a regular octahedral configuration of the six oxygen atoms; and (ii) Glu101, at the relative position 12 in the EF-hand loop sequence (labelled "Glu12"), acts as a bidentate ligand in the Ca-loaded form and as a monodentate ligand in the Mg-loaded form. As part of the conformational rearrangement, the chi1 dihedral angle undergoes a gauche(+) to gauche(-) transition upon substitution of Ca2+ by Mg2+, whereas the chi2 angle remains practically unchanged and the chi3 angles in both forms adopt a nearly mirror image relationship. In order to understand the molecular mechanisms underlying such a conformational rearrangement, we undertook a theoretical study using the free energy perturbation (FEP) method, starting from high-resolution crystal structures of the same parvalbumin (pike 4. 10 isoform) differing by the substitution of their two cationic sites EF-3 (or CD) and EF-4 (or EF), i.e. the 1pal structure with EF-3(Ca2+) and EF-4(Ca2+), the 4pal structure with EF-3(Ca2+) and EF-4(Mg2+). When Mg2+ is "alchemically" transformed into Ca2+ within the EF-4 site of 4pal, the conformational rearrangement of Glu12 is correctly predicted by the FEP calculation. When Ca2+ is transformed into Mg2+ within the EF-3 site of 4pal, the FEP calculation predicts the topology of the fully Mg-loaded form for which no crystallographic data is presently available. As expected, Glu62 (at the relative position 12 in EF-3 loop) is predicted to be a monodentate residue within a regular octahedral arrangement of six oxygen atoms around Mg2+. We also investigated the behaviour during Ca2+/Mg2+ exchange of two other typical EF-hand proteins, troponin C (TnC) and calmodulin (CaM), for which no three-dimensional structure of their Mg-loaded forms is available so far. It is also predicted that the EF-3 site of TnC and the EF-1 site of CaM have their invariant Glu12 residues switching from the bidentate to the monodentate configuration when Ca2+ is substituted by Mg2+, with six oxygen atoms being observed in the co-ordination sphere of the alchemically generated Mg2+ cation.

Modeling large-scale dynamics of proteins.

We study a dynamical model for the large-scale motions of bovine pancreatic trypsin inhibitor in vacuum. The model is obtained by projecting Newton equations onto some set of anharmonic modes. We compare the statistics of the so-obtained trajectories with those obtained by standard techniques, and conclude that our dynamical model is able to reproduce fairly well the average properties of the large-scale motions of this protein. Moreover, it allows for time steps one order of magnitude larger than the standard ones.

Which effective property of amino acids is best preserved by the genetic code?

Simple procedures are proposed to quantify how much an effective property embodied in a given ranking of the twenty amino acids can be affected by random point mutations at nucleotide bases. As expected, of the various orderings tested, rankings based on most hydrophobicity scales exhibit low scores, thus offering better immunity towards such single-base mutations. This, however, occurs to different extents and the method allows sharp discriminations between the scales. Hydrophobicity scales based on global properties such as spatial environment data of proteins residues, or mutation matrices of amino acid replacements, generally behave better than those based on pure physicochemical properties of isolated residues. An averaged scale built from the available hydrophobicity scales exhibits one of the most favorable scores. A systematic search for the best amino acid order has been carried out across all possible scales. Optimized scales are characterized by the existence of a clustering scheme into three zones, within which permutations are more or less tolerated, depending on the zone and on the summation procedure used in the score calculation. The first cluster corresponds to the hydrophobic side, and includes the ten amino acids WMCFILVGRS. Next follows the ATP triad. The third cluster coincides with the hydrophilic side and includes, in the last seven positions, the amino acids EDKNQHY. Interpretation of these optimized scales in terms of codon positions in the genetic code further suggests a clustering scheme composed of four groups, WMCFILV-GRS-ATP-EDKNQHY, emphasizing the role of the second base as the main driving parameter. As a consequence, the conserved character of the genetic code is better reflected when it is displayed in UGCA ordering rather than in the commonly used UCAG ordering. The present a priori classification of the amino acids could find potential use in protein sequence homology and structure prediction.

Yeast hexokinase inhibitors designed from the 3-D enzyme structure rebuilding.

This work describes a search for hexokinase inhibitors based on the interactions analysis at the active site of the X-ray resolved o-tolulyl-glucosamine-hexokinase (OTG-HK) complex structure. As the actual enzyme sequence was unknown when the X-ray structure was made (only 30% homology), the structure of the complex was rebuilt by modelling on the X-ray structure frame which allowed residues in close vicinity to the inhibitor to be defined, particularly Glu249 and Gln278. Compounds with inhibitor-bearing groups able to interact with these residues were synthesized and assayed. Some of them revealed strong affinities, in the Km range for glucose. Kinetic analysis of their behaviour towards glucose and ATP together with spectroscopic studies using NMR, allowed the determination of the corresponding inhibition patterns and provided complementary information on HK.

[Role of the conformation changement of CD4 in the HIV-cell fusion]. / Rôle du changement de conformation du CD4 lors de la fusion VIH/cellule.

It is well known that the gp120-gp41 complex undergoes a conformational change after CD4 binding. It is likely that CD4 undergoes a conformational change as well. Recently, a calculation of the normal modes of the two N-terminal domains of CD4 has shown that a hinge-bending motion of one of these domains with respect to the other may occur. In the present study, results obtained previously are verified with two other normal mode calculations, starting from crystallographic structures of different origin. A scheme describing the first steps of the process leading to cell infection by human immunodeficiency virus (HIV) is then proposed. It rests upon the idea that CD4 and gp120-gp41 conformational changes allow for bringing the cell and virus membranes closer to each other.

Normal-mode analysis suggests important flexibility between the two N-terminal domains of CD4 and supports the hypothesis of a conformational change in CD4 upon HIV binding.

Human CD4 is the receptor for human immunodeficiency virus (HIV). It is well established that the first domain of CD4 binds with high affinity to gp120, an envelope protein of HIV, but it has also been demonstrated that amino acids located in its second domain, within or close to residues 120-127 or 163-166 (lying 15 A away from the binding site), play a role in virus infectivity. We show here that these two stretches of amino acids happen to be important for the largest amplitude motion obtained with the normal-mode theory for the two N-terminal domains of human CD4: an overall rigid-body displacement of one domain with respect to the other. Such a 'hinge-bending' motion is unexpected since these two domains were found by crystallographers to be tightly abutting. On the other hand, since for several proteins the hinge-bending motion experimentally observed upon ligand binding was found to be similar to the largest amplitude motion obtained with the normal-mode theory for these proteins, our results suggest that CD4 may undergo such a kind of conformational change upon HIV binding.

Hinge-bending motion in citrate synthase arising from normal mode calculations.

A normal mode analysis of the closed form of dimeric citrate synthase has been performed. The largest-amplitude collective motion predicted by this method compares well with the crystallographically observed hinge-bending motion. Such a result supports those obtained previously in the case of hinge-bending motions of smaller systems, such as lysozyme or hexokinase. Taken together, all these results suggest that low-frequency normal modes may become useful for determining a first approximation of the conformational path between the closed and open forms of these proteins.