Rigid and flexible region in lysozyme and the invariant features in its hydration shell

Water-mediated transformations provide a useful handle for exploring the flexibility in protein molecules and the invariant features in their hydration shells. Low-humidity monoclinic hen egg white lysozyme, resulting from such a transformation, has perhaps the lowest solvent content observed in any protein crystal so far and has a well-ordered structure. A detailed comparison involving this structure, low-humidity tetragonal lysozyme, and the other available refined crystal structures of the enzyme permits the delineation of the relatively rigid, moderately flexible and highly flexible regions of the molecule. The relatively rigid region forms a contiguous structural unit close to the molecular centroid and encompasses parts of of the main beta-structure and three alpha-helices. The hydration shell of the protein contains 30 invariant water molecules. Many of them are involved in holding different parts of the molecule together or in stabilizing local structure. Five of the six invariant water molecules attached to the substrate-binding region form part of a water cluster contiguous with the side-chains of the catalytic residues Glu-35 and Asp-52.

Gauge-invariant reformulation of theories with second-class constraints

Given a classical dynamical theory with second-class constraints, it is sometimes possible to construct another theory with first-class constraints, i.e., a gauge-invariant one, which is physically equivalent to the first theory. We identify some conditions under which this may be done, explaining the general principles and working out several examples. Field theoretic applications include the chiral Schwinger model and the non-linear sigma model. An interesting connection with the work of Faddeev and Shatashvili is pointed out.

Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

A low power, process invariant keeper design for high speed dynamic logic circuits

A low power keeper circuit using the concept of rate sensing has been proposed. The proposed technique reduces the amount of short circuit power dissipation in the domino gate by 70% compared to the conventional keeper technique. Also the total power-delay product is 26% lower compared to the previously reported techniques. The process tracking capability of the design enables the domino gate to achieve uniform delay across different process corners. This reduces the amount of short circuit power dissipation that occurs in the cascaded domino gates by 90%. The use of the proposed technique in the read path of a register file reduces the energy requirement by 26% as compared to the other keeper techniques. The proposed technique has been prototyped in 130nm CMOS technology.

Conjugacy invariant pseudo-norms, representability and RNA secondary structures

To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases: We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms. We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.

An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Poincare invariant quantum field theories with twisted internal symmetries

Following up the work of 1] on deformed algebras, we present a class of Poincare invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can provide a natural-framework for the discussion of the marginal deformations (beta-deformations) of the N = 4 SUSY theories.

Role of invariant water molecules and water-mediated ionic interactions in D-xylose isomerase from Streptomyces rubiginosus

The enzyme, D-xylose isomerase (D-xylose keto-isomerase; EC 5.3.1.5) is a soluble enzyme that catalyzes the conversion of the aldo-sugar D-xylose to the keto-sugar D-xylulose. A total of 27 subunits of D-xylose isomerase from Streptomyces rubiginosus were analyzed in order to identify the invariant water molecules and their water-mediated ionic interactions. A total of 70 water molecules were found to be invariant. The structural and/or functional roles of these water molecules have been discussed. These invariant water molecules and their ionic interactions may be involved in maintaining the structural stability of the enzyme D-xylose isomerase. Fifty-eight of the 70 invariant water molecules (83%) have at least one interaction with the main chain polar atom.