Delineation of the Native Basin in Continuum Models of Proteins

We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the basin size can be determined by monitoring random distortions in the shape of the protein around the native state. Both techniques yield the similar results. As a byproduct, a simple method to determine the folding temperature is obtained.Comment: REVTeX, 6 pages, 5 EPS figure

Von Neumann's Quantization of General Relativity

Von Neumann's procedure is applied for quantization of General Relativity. We quantize the initial data of dynamical variables at the Planck epoch, where the Hubble parameter coincides with the Planck mass. These initial data are defined via the Fock simplex in the tangent Minkowskian space-time and the Dirac conformal interval. The Einstein cosmological principle is applied for the average of the spatial metric determinant logarithm over the spatial volume of the visible Universe. We derive the splitting of the general coordinate transformations into the diffeomorphisms (as the object of the second N\"other theorem) and the initial data transformations (as objects of the first N\"other theorem). Following von Neumann, we suppose that the vacuum state is a quantum ensemble. The vacuum state is degenerated with respect to quantum numbers of non-vacuum states with the distribution function that yields the Casimir effect in gravidynamics in analogy to the one in electrodynamics. The generation functional of the perturbation theory in gravidynamics is given as a solution of the quantum energy constraint. We discuss the region of applicability of gravidynamics and its possible predictions for explanation of the modern observational and experimental data.Comment: 14 pages, updated version with extended discussio

Laser tattoo removal comparison between 1064 and 532 NM of a Q-switched ND:YAG laser treatment

Invention of the Q-switch advanced laser method is the most effective methods of tattoo removal compared to other methods of i.e. chemical, mechanical and surgical. In this study, we are reporting black pigment tattoo removal by comparing two wavelengths 532 nm and 1064 nm of Q-switched Nd-YAG laser. Using a single-pulse laser at 1064 nm wavelength, the maximum laser fluence for skin damage is 3.04 J/cm2 with pulse energy 0.55 J. While, at 532 nm wavelength, maximum laser fluence is 0.5 J/cm2 with pulse energy 0.42 J at 8-10 ns for tattooed skins. Moreover, after 1064 nm and 532 nm laser irradiations, skin biopsy of black tattooed rat’s skin demonstrates the ink granules local redistribution. Microscopic study indicates that black ink particles become smaller and vanished from the skins after 1064 nm laser treatment. The findings of this study indicate that 1064 nm wavelengths of Q-switched Nd-YAG laser treatment with 0.55 J pulse energy, is one of the significant methods of black tattoo removal with remarkable differences

Universal geometrical factor of protein conformations as a consequence of energy minimization

The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/(A)) of the van der Waals volume V to the surface area A and average atomic radius of the folded structures, calculated with atomic radii setting used in SMMP [Eisenmenger F., et. al., Comput. Phys. Commun., 138 (2001) 192], approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures show that the ratio for real and well-designed proteins is universal and equal to 0.491\pm0.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disordered proteins, while it ceases to be universal for polypeptides with bad folding properties.Comment: 6 pages, 1 table, 4 figure

A Quadratic Spinor Lagrangian for General Relativity

We present a new finite action for Einstein gravity in which the Lagrangian is quadratic in the covariant derivative of a spinor field. Via a new spinor-curvature identity, it is related to the standard Einstein-Hilbert Lagrangian by a total differential term. The corresponding Hamiltonian, like the one associated with the Witten positive energy proof is fully four-covariant. It defines quasi-local energy-momentum and can be reduced to the one in our recent positive energy proof. (Fourth Prize, 1994 Gravity Research Foundation Essay.)Comment: 5 pages (Plain TeX), NCU-GR-94-QSL

Finite size effects on thermal denaturation of globular proteins

Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Omega, scales as N^zeta, where N is the number of amino acids. Surprisingly, we find that zeta is universal with zeta = 1 + gamma, where the exponent gamma characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires the folding transition temperature to be close to the collapse temperature.Comment: 3 figures. Physical Review Letters (in press

Collective Dynamics of One-Dimensional Charge Density Waves

The effect of disorder on the static and dynamic behaviour of one-dimensional charge density waves at low temperatures is studied by analytical and numerical approaches. In the low temperature region the spatial behaviour of the phase-phase correlation function is dominated by disorder but the roughness exponent remains the same as in the pure case. Contrary to high dimensional systems the dependence of the creep velocity on the electric field is described by an analytic function.Comment: 4 pages, 4 figure

Softer Junctions Can Result In Stiffer Gels: Associative Polymer Gels With Crystalline And Semicrystalline Domains

The ability to create synthetic materials that mimic the structural and mechanical properties of soft biological tissues remains a significant challenge. In this presentation, we discuss rheology and structural studies of poly(lactide)-poly(ethylene oxide)-poly(lactide) (PLA-PEO-PLA) triblock copolymer gels with various ratios of L-lactide and D-lactide in the PLA blocks (Figure 1). These materials form associative micellar gels in water, and previous work has shown that stereoregular triblocks with a L/D ratio of 100/0 form much stiffer gels than triblocks with a 50/50 L/D ratio. Our systems display an unexpected maximum in the storage modulus, G’, of the hydrogels at intermediate L/D ratio. The impact of stereochemistry on the rheology is very striking; gels with an L/D ratio of 85/15 have storage moduli that are ~1-2 orders of magnitude higher than hydrogels with L/D ratios of 100/0. No stereocomplexation is observed in the gels, although PLLA crystals are found for gels with L/D ratios of 95/5 and 90/10, and SANS results show a decrease in the intermicellar spacing for intermediate L/D ratios. We expect the dominant contribution to the elasticity of the gels to be intermicellar brdging chains and attribute the rheology to a competition between an increase in the time for PLA endblocks to pull out of micelles as the L/D ratio is increased and PLLA crystallization occurs, and a decrease in the number of bridging chains for micelles with crystalline PLA domains, as formation of bridges may be hindered by crowded crystalline PLA domains. Ultra-small angle neutron scattering (USANS) and confocal microscopy shows evidence of larger structures in these gels, reminiscent of the hierarchical structures observed in biological gels. These results provide a new strategy for controlling the rheology of PLA-based hydrogels for potential applications in biomaterials, as well as fundamental insights into how intermicellar interactions can be tuned via stereochemistry. Collectively, our work shows that stereochemistry can be used in unexpected ways to access novel structures and properties in relatively simple synthetic polymers, giving insight into new routes for creating complex soft materials. Please click Additional Files below to see the full abstract

Another positivity proof and gravitational energy localizations

Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the Hamiltonian and thereby a localization of gravitational energy and positive energy proof. These new results provide a link between the other two methods. Localization and prospects for quasi-localization are discussed.Comment: 14 pages REVTe

Multivariate Binomial Approximations for Asset Prices with Non-Stationary Variance and Covariance Characteristics

In this paper, we suggest an efficient method of approximating a general, multivariate lognormal distribution by a multivariate binomial process. There are two important features of such multivariate distributions. First, the state variables may have volatilities that change over time. Second, the two or more relevant state variables involved may covary with each other in a specified manner, with a time-varying covariance structure. We discuss the asymptotic properties of the resulting processes and show how the methodology can be used to value a complex, multiple-exercisable option whose payoff depends on the prices of two assets