Multifractality, Levinthal paradox, and energy hypersurface

Fully relativistic rovibrational energies and spectroscopic constants of the lowest X:(1)0(+)g, A':(1)2( u ), A:(1)1 ( u ), B':(1)0(-)u and B:(1)0(+)u states of molecular chlorine

The main goal of this paper is to present the rovibrational energies and spectroscopic constants of the Cl(2) molecular system in the relativistic states [Formula: see text], A':(1)2( u ), A:(1)1( u ), [Formula: see text] and [Formula: see text]. More precisely, we have evaluated the Cl(2) ω ( e ), ω ( e ) x ( e ), ω ( e ) y ( e ), α ( e ), γ ( e ) and B ( e ) rovibrational spectroscopic constants using two different procedures. The first was obtained by combining the rovibrational energies, calculated through solving Schrödinger's nuclear equation and the diatomic rovibrational energy equation. The second was obtained by using the Dunham method. The calculated properties are in good agreement with available experimental data.

Nonextensivity and self-affinity in the mammalian neuromuscular junction

We study time series and the spontaneous miniature end-plate potentials (MEPPs) of mammals recorded at neuromuscular junctions using two different approaches: generalized thermostatistics and detrended fluctuation analysis (DFA). Classical concepts establish that the magnitude of these potentials is characterized by Gaussian statistics and that their intervals are randomly displayed. First we show that MEPP distributions adequately satisfy the q-Gaussian distributions that maximize the Tsallis entropy, indicating their nonextensive and nonequilibrium behavior. We then examine the intervals between the miniature potentials via DFA, where the profile of the intervals between events configures a deviation from the expected random behavior. Some possible physiological substrates for these findings are discussed.

Self-similarity and protein compactness

The hydrophobic effect is the major factor that drives a protein toward collapse and folding. As a consequence of the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We analyze the solvent-accessible surface area of 1825 nonhomolog protein chains deposited in the Brookhaven Protein Data Bank. This solvent-accessible surface area presents an intrinsic self-similarity behavior. The comparison between the accessible surface area as function of the number of amino acids and the accessible surface area as function of gyration radius supplies a measure of the scaling exponent close to the one observed by volume as function of radius of gyration or by mass-size exponent. The present finding indicates that the fractal analysis describes the protein compactness as an object packing between random spheres in percolation threshold and crumpled wires.

Amino acid hydrophobicity and accessible surface area

It is well known that the hydrophobic effect is the major factor that drives a protein toward collapse and folding. We analyze the variation of the solvent-accessible surface area of amino acids in small fragments of protein (3N45) . In this way, we look into 5526 protein chains deposited in the Brookhaven Protein Data Bank. The accessible surface area behaves as a power law for N9 . The comparison between the loss of accessible area and the self-similar behavior gives us a measure of the possibility of an amino acid to have apolar or polar side chain. It is therefore possible to infer about amino acid hydrophobicity, i.e., if one amino acid has a hydrophobic side chain or if it has a hydrophilic one. Furthermore, the present findings indicate that the variation of the accessible surface area describes an alternative hydrophobicity scale.

Self-similarity and protein chains

Fractal properties of 5526 different protein chains are investigated. Characteristic fractal behavior for different molecular systems is obtained from the fractal dimension analysis, which shows that the dimension is delta=2.47 . This dimension gives a measure of the protein compactness. The present finding indicates that the fractal analysis describes some structural properties of proteins and corroborates the explanation about multifractality in the energy hypersurface.

New stochastic strategy to analyze helix folding

We propose an alternative stochastic strategy to search secondary structures based on the generalized simulated annealing (GSA) algorithm, by using conformational preferences based on the Ramachandran map. We optimize the search for polypeptide conformational space and apply to peptides considered to be good alpha-helix promoters above a critical number of residues. Our strategy to obtain conformational energies consist in coupling a classical force field (THOR package) with the GSA procedure, biasing the Phi x Psi backbone angles to the allowed regions in the Ramachandran map. For polyalanines we obtained stable alpha-helix structures when the number of residues were equal or exceeded 13 amino acids residues. We also observed that the energy gap between the global minimum and the first local minimum tends to increase with the polypeptide size. These conformations were generated by performing 2880 stochastic molecular optimizations with a continuum medium approach. When compared with molecular dynamics or Monte Carlo methods, GSA can be considered the fastest.