The Universe With Bulk Viscosity

Exact solutions for a model with variable $G$, $\Lambda$ and bulk viscosity are obtained. Inflationary solutions with constant (de Sitter-type) and variable energy density are found. An expanding anisotropic universe is found to isotropize during its course of expansion but a static universe is not. The gravitational constant is found to increase with time and the cosmological constant decreases with time as $\Lambda \propto t^{-2}$.Comment: 7 LateX pages, no figure

The color of polarization in cuprate superconductors

A technique for the identification of individual anisotropic grains in a heterogeneous and opaque material involves the observation of grain color in reflected light through crossed polarizers (color of polarization). Such colors are generally characteristic of particular phases. When grains of many members of the class of hole carrier cuprate superconductors are so viewed, using a xenon light source (600 K color temperature), a characteristic color of polarization is observed. This color was studied in many of these cuprate superconductors and a strong correlation was found between color and the existence of superconductivity. One of the members of the electron carrier cuprate superconductors (Nd(1.85)Ce(.15)CuO(4-x) was examined and found that it possesses the same color of polarization as all the electron hole carrier cuprate superconductors so far examined. The commonality of the characteristic color in the cuprate superconductors indicated that the presence of this color is independent of the nature of charge carriers. The correlation of this color with existence of superconductivity suggests that the origin of the color relates to the origin of superconductivity in the cuprate superconductors. Photometric techniques are also discussed

Free Energy Self-Averaging in Protein-Sized Random Heteropolymers

Current theories of heteropolymers are inherently macrpscopic, but are applied to folding proteins which are only mesoscopic. In these theories, one computes the averaged free energy over sequences, always assuming that it is self-averaging -- a property well-established only if a system with quenched disorder is macroscopic. By enumerating the states and energies of compact 18, 27, and 36mers on a simplified lattice model with an ensemble of random sequences, we test the validity of the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is a valid approximation at the length scale of real proteins. These results validate certain sequence design methods which can exponentially speed up computational design and greatly simplify experimental realizations.Comment: 4 pages, 3 figure

Is Heteropolymer Freezing Well Described by the Random Energy Model?

It is widely held that the Random Energy Model (REM) describes the freezing transition of a variety of types of heteropolymers. We demonstrate that the hallmark property of REM, statistical independence of the energies of states over disorder, is violated in different ways for models commonly employed in heteropolymer freezing studies. The implications for proteins are also discussed.Comment: 4 pages, 3 eps figures To appear in Physical Review Letters, May 199

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

A Multicanonical Molecular Dynamics Study on a Simple Bead-Spring Model for Protein Folding

We have performed a multicanonical molecular dynamics simulation on a simple model protein.We have studied a model protein composed of charged, hydrophobic, and neutral spherical bead monomers.Since the hydrophobic interaction is considered to significantly affect protein folding, we particularly focus on the competition between effects of the Coulomb interaction and the hydrophobic interaction. We found that the transition which occurs upon decreasing the temperature is markedly affected by the change in both parameters and forms of the hydrophobic potential function, and the transition changes from first order to second order, when the Coulomb interaction becomes weaker.Comment: 7 pages, 6 postscript figures, To appear in J.Phys.Soc.Jpn. Vol.70 No.

Geometrically Reduced Number of Protein Ground State Candidates

Geometrical properties of protein ground states are studied using an algebraic approach. It is shown that independent from inter-monomer interactions, the collection of ground state candidates for any folded protein is unexpectedly small: For the case of a two-parameter Hydrophobic-Polar lattice model for $L$-mers, the number of these candidates grows only as $L^2$. Moreover, the space of the interaction parameters of the model breaks up into well-defined domains, each corresponding to one ground state candidate, which are separated by sharp boundaries. In addition, by exact enumeration, we show there are some sequences which have one absolute unique native state. These absolute ground states have perfect stability against change of inter-monomer interaction potential.Comment: 9 page, 4 ps figures are include

Origin of Native Driving Force in Protein Folding

We derive an expression with four adjustable parameters that reproduces well the 20x20 Miyazawa-Jernigan potential matrix extracted from known protein structures. The numerical values of the parameters can be approximately computed from the surface tension of water, water-screened dipole interactions between residues and water and among residues, and average exposures of residues in folded proteins.Comment: LaTeX file, Postscript file; 4 pages, 1 figure (mij.eps), 2 table