Slow energy relaxation of macromolecules and nano-clusters in solution

Many systems in the realm of nanophysics from both the living and inorganic world display slow relaxation kinetics of energy fluctuations. In this paper we propose a general explanation for such 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 nano-cluster that the result is a complex, non-exponential relaxation dynamics.Comment: 5 pages, 3 figure

Functional modes of proteins are among the most robust ones

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. Moreover, it may also pave the way for the development of methods allowing to predict such motions accurately.Comment: 4 pages, 5 figure

Energy transfer in nonlinear network models of proteins

We investigate how nonlinearity and topological disorder affect the energy relaxation of local kicks in coarse-grained network models of proteins. We find that nonlinearity promotes long-range, coherent transfer of substantial energy to specific, functional sites, while depressing transfer to generic locations. Remarkably, transfer can be mediated by the self-localization of discrete breathers at distant locations from the kick, acting as efficient energy-accumulating centers.Comment: 4 pages, 3 figure

Dimensionless cosmology

Although it is well known that any consideration of the variations of fundamental constants should be restricted to their dimensionless combinations, the literature on variations of the gravitational constant $G$ is entirely dimensionful. To illustrate applications of this to cosmology, we explicitly give a dimensionless version of the parameters of the standard cosmological model, and describe the physics of Big Bang Neucleosynthesis and recombination in a dimensionless manner. The issue that appears to have been missed in many studies is that in cosmology the strength of gravity is bound up in the cosmological equations, and the epoch at which we live is a crucial part of the model. We argue that it is useful to consider the hypothetical situation of communicating with another civilization (with entirely different units), comparing only dimensionless constants, in order to decide if we live in a Universe governed by precisely the same physical laws. In this thought experiment, we would also have to compare epochs, which can be defined by giving the value of any {\it one} of the evolving cosmological parameters. By setting things up carefully in this way one can avoid inconsistent results when considering variable constants, caused by effectively fixing more than one parameter today. We show examples of this effect by considering microwave background anisotropies, being careful to maintain dimensionlessness throughout. We present Fisher matrix calculations to estimate how well the fine structure constants for electromagnetism and gravity can be determined with future microwave background experiments. We highlight how one can be misled by simply adding $G$ to the usual cosmological parameter set

About some possible empirical evidences in favor of a cosmological time variation of the speed of light

Possible empirical evidences in favor of the hypothesis that the speed of light decreases by a few centimeters per second each year are examined. Lunar laser ranging data are found to be consistent with this hypothesis, which also provides a straightforward explanation for the so-called Pioneer anomaly, that is, a time-dependent blue-shift observed when analyzing radio tracking data from distant spacecrafts, as well as an alternative explanation for both the apparent time-dilation of remote events and the apparent acceleration of the Universe. The main argument against this hypothesis, namely, the constancy of fine-structure and Rydberg constants, is discussed. Both of them being combinations of several physical constants, their constancy implies that, if the speed of light is indeed time-dependent, then at least two other “fundamental constants” have to vary as well. This puts severe constraints on the development of any future varying–speed-of-light theory

Simplified Normal Mode Analysis of Conformational Transitions in DNA-dependent Polymerases: the Elastic Network Model

International audienceThe 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

Simple Two-Body Cation−Water Interaction Potentials Derived fromab Initio Calculations. Comparison to Results Obtained with an Empirical Approach

Ab initio calculations were performed on M(H2O)n systems, M being Li+, Na+, K+, Be2+, Mg2+, or Ca2+, with n = 1, 2, 4, or 6. For the most hydrated systems, parameters for the effective Lennard-Jones interaction between the cation and the water molecules were determined, so as to reproduce ab initio results. In order to compare our results to those obtained previously by J. Åqvist with a purely empirical approach, water−water interactions were assumed to be given by the TIP3P model. Different forms for the effective two-body interaction potential were tested. The best fits of ab initio data were obtained with a smooth r-7 repulsive and a classical r-4 attractive term, in addition to standard Coulombic interactions. Though better fits were obtained for alkaline cations than for alkaline-earth ones, only Be2+ obviously requires a more complicated form of the potential energy function.The corresponding parameters were tested with molecular dynamics simulations of cations in water solutions and with hydration free energy difference calculations, using the thermodynamic perturbation approach. Radial distribution functions consistent with experimental data were obtained for all cations. Free energy differences are obviously much more challenging. The most accurately reproduced value is the difference between the hydration free energies of Na+ and K+. This result is likely to be significant since effective interaction energies between Na+ or K+ and water molecules as obtained in Åqvist's and in the present work are found to be very similar, despite the fact that the corresponding sets of parameters were determined with completely different approaches

Parameterizing Elastic Network Models to Capture the Dynamics of Proteins

International audienceCoarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental Bfactors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes