Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Structural Modes of Stabilization of Permissive Phosphorylation Sites in Protein Kinases: Distinct Strategies in Ser/Thr and Tyr Kinases

Protein kinases phosphorylate several cellular proteins providing control mechanisms for various signalling processes. Their activity is impeded in a number of ways and restored by alteration in their structural properties leading to a catalytically active state. Most protein kinases are subjected to positive and negative regulation by phosphorylation of Ser/Thr/Tyr residues at specific sites within and outside the catalytic core. The current review describes the analysis on 3D structures of protein kinases that revealed features distinct to active states of Ser/Thr and Tyr kinases. The nature and extent of interactions among well-conserved residues surrounding the permissive phosphorylation sites differ among the two classes of enzymes. The network of interactions of highly conserved Arg preceding the catalytic base that mediates stabilization of the activation segment exemplifies such diverse interactions in the two groups of kinases. The N-terminal and the C-terminal lobes of various groups of protein kinases further show variations in their extent of coupling as suggested from the extent of interactions between key functional residues in activation segment and the N-terminal αC-helix. We observe higher similarity in the conformations of ATP bound to active forms of protein kinases compared to ATP conformations in the inactive forms of kinases. The extent of structural variations accompanying phosphorylation of protein kinases is widely varied. The comparison of their crystal structures and the distinct features observed are hoped to aid in the understanding of mechanisms underlying the control of the catalytic activity of distinct subgroups of protein kinases.

A study of interaction in the lowest singlet and triplet states of H2

The potential energy curves of the ground state and the first excited state of H2 are examined in terms of the electronic force acting on each nucleus. The results reveal the detailed course of events that occur when two hydrogen atoms with parallel and antiparallel electron spins approach one another from a large internuclear separation.

Soft gluon k(t)-resummation and the Froissart bound

We study soft gluon k(t)-resurnmation and the relevance of InfraRed (IR) gluons for the energy dependence of total hadronic cross-sections. In our model, consistency with the Froissart bound is directly related to the ansatz that the IR behaviour of the QCD coupling constant follows an inverse power law.

Nonspecifically bound proteins spin while diffusing along DNA

It is known that DNA-binding proteins can slide along the DNA helix while searching for specific binding sites, but their path of motion remains obscure. Do these proteins undergo simple one-dimensional (1D) translational diffusion, or do they rotate to maintain a specific orientation with respect to the DNA helix? We measured 1D diffusion constants as a function of protein size while maintaining the DNA-protein interface. Using bootstrap analysis of single-molecule diffusion data, we compared the results to theoretical predictions for pure translational motion and rotation-coupled sliding along the DNA. The data indicate that DNA-binding proteins undergo rotation-coupled sliding along the DNA helix and can be described by a model of diffusion along the DNA helix on a rugged free-energy landscape. A similar analysis including the 1D diffusion constants of eight proteins of varying size shows that rotation-coupled sliding is a general phenomenon. The average free-energy barrier for sliding along the DNA was 1.1 +/- 0.2 k(B)T. Such small barriers facilitate rapid search for binding sites.

The Mycobacterial MsDps2 Protein Is a Nucleoid-Forming DNA Binding Protein Regulated by Sigma Factors sigma(A) and sigma(B)

The Dps (DNA-binding protein from starved cells) proteins from Mycobacterium smegmatis MsDps1 and MsDps2 are both DNA-binding proteins with some differences. While MsDps1 has two oligomeric states, with one of them responsible for DNA binding, MsDps2 has only one DNA-binding oligomeric state. Both the proteins however, show iron-binding activity. The MsDps1 protein has been shown previously to be induced under conditions of starvation and osmotic stress and is regulated by the extra cellular sigma factors sigma(H) and sigma(F). We show here, that the second Dps homologue in M. smegmatis, namely MsDps2, is purified in a DNA-bound form and exhibits nucleoid-like structures under the atomic force microscope. It appears that the N-terminal sequence of Dps2 plays a role in nucleoid formation. MsDps2, unlike MsDps1, does not show elevated expression in nutritionally starved or stationary phase conditions; rather its promoter is recognized by RNA polymerase containing sigma(A) or sigma(B), under in vitro conditions. We propose that due to the nucleoid-condensing ability, the expression of MsDps2 is tightly regulated inside the cells.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Free and ATP-bound structures of Ap(4)A hydrolase from Aquifex aeolicus V5

Asymmetric diadenosine tetraphosphate (Ap(4)A) hydrolases degrade the metabolite Ap(4)A back into ATP and AMP. The three-dimensional crystal structure of Ap(4)A hydrolase (16 kDa) from Aquifex aeolicus has been determined in free and ATP-bound forms at 1.8 and 1.95 angstrom resolution, respectively. The overall three-dimensional crystal structure of the enzyme shows an alpha beta alpha-sandwich architecture with a characteristic loop adjacent to the catalytic site of the protein molecule. The ATP molecule is bound in the primary active site and the adenine moiety of the nucleotide binds in a ring-stacking arrangement equivalent to that observed in the X-ray structure of Ap(4)A hydrolase from Caenorhabditis elegans. Binding of ATP in the active site induces local conformational changes which may have important implications in the mechanism of substrate recognition in this class of enzymes. Furthermore, two invariant water molecules have been identified and their possible structural and/or functional roles are discussed. In addition, modelling of the substrate molecule at the primary active site of the enzyme suggests a possible path for entry and/or exit of the substrate and/or product molecule.

Low-lying states of transverse substituted trans-polyacetylene and trans-polyacetylene: A comparative DMRG study

The density-matrix renormalization group (DMRG) method is used for a comparative study of low-lying excitations in trans-polyacetylene (t-PA) and transversely substituted t-PA (TS-t-PA). We have employed the Pariser-Parr-Pople model Hamiltonian which incorporates long-range electronic correlations to model these systems. We find some fundamental differences in the excited states of the t-PA and TS-t-PA. We find that the lowest two-photon allowed excited state in TS-t-PA is not made up of two triplet excitons and the gap to this state is nonzero even for undimerized chains in the thermodynamic limit. Contrary to earlier results for the Hubbard model, we find that the lowest two-photon state is always below the first optically allowed state in all the systems studied here making TS-t-PA systems only weakly fluorescent materials. Nonresonant tumbling averaged linear and third harmonic generation optic coefficients of TS-t-PA systems are also much smaller than that of t-PA.

Critical test for Altshuler-Aronov theory: Evolution of the density of states singularity in double perovskite Sr2FeMoO6 with controlled disorder

With high-resolution photoemission spectroscopy measurements, the density of states (DOS) near the Fermi level (E-F) of double perovskite Sr2FeMoO6 having different degrees of Fe/Mo antisite disorder has been investigated with varying temperature. The DOS near E-F showed a systematic depletion with increasing degree of disorder, and recovered with increasing temperature. Altshuler-Aronov (AA) theory of disordered metals well explains the dependences of the experimental results. Scaling analysis of the spectra provides experimental indication for the functional form of the AA DOS singularity.

Detection of alpha(2u)-globulin and its bound putative pheromones in the preputial gland of the Indian commensal rat (Rattus rattus) using mass spectrometry

The role of pheromones and pheromone-binding proteins in the laboratory rat has been extensively investigated. However, we have previously reported that the preputial gland of the Indian commensal rat produces a variety of pheromonal molecules and preputial glands would seem to be the predominant source for pheromonal communication. The presence of pheromone-binding proteins has not yet been identified in the preputial gland of the Indian commensal rat; therefore, the experiments were designed to unravel the alpha(2u)-globulin (alpha 2u) and its bound volatiles in the commensal rat. Total preputial glandular proteins were first fractionated by sodium dodecyl sulfate/polyacrylamide gel electrophoresis (SDS-PAGE) and subsequently analyzed by mass spectrometry. Further, we purified alpha 2u and screened for the presence of bound pheromonal molecules with the aid of gas chromatography/mass spectrometry (GC/MS). A novel alpha 2u was identified with a high score and this protein has not been previously described as present in the preputial gland of Indian commensal rats.This novel alpha 2u was then characterized by tandem mass spectrometry (MS/MS). Peptides with m/z values of 969, 1192, 1303 and 1876 were further fragmented with the aid of MS/MS and generated de novo sequences which provided additional evidence for the presence of alpha 2u in the preputial gland. Finally, we identified the presence of farnesol 1 and 2 bound to alpha 2u. The present investigation confirms the presence of alpha 2u (18.54 kDa) in the preputial gland of the Indian commensal rat and identifies farnesol 1 and 2 as probably involved in chemo-communication by the Indian commensal rat.Copyright (C) 2010 John Wiley & Sons, Ltd.

Novel peptides of therapeutic promise from Indian Conidae

Highly structured small peptides are the major toxic constituents of the venom of cone snails, a family of widely distributed predatory marine molluscs. These animals use the venom for rapid prey immobilization. The peptide components in the venom target a wide variety of membrane-bound ion channels and receptors. Many have been found to be highly selective for a diverse range of mammalian ion channels and receptors associated with pain-signaling pathways. Their small size, structural stability, and target specificity make them attractive pharmacologic agents. A select number of laboratories mainly from the United States, Europe, Australia, Israel, and China have been engaged in intense drug discovery programs based on peptides from a few snail species. Coastal India has an estimated 20-30% of the known cone species; however, few serious studies have been reported so far. We have begun a comprehensive program for the identification and characterization of peptides from cone snails found in Indian Coastal waters. This presentation reviews our progress over the last 2 years. As expected from the evolutionary history of these venom components, our search has yielded novel peptides of therapeutic promise from the new species that we have studied.

Multiple conformational states in crystals and in solution in alpha gamma hybrid peptides. Fragility of the C-12 helix in short sequences

The conformational properties of foldamers generated from alpha gamma hybrid peptide sequences have been probed in the model sequence Boc-Aib-Gpn-Aib-Gpn-NHMe. The choice of alpha-aminoisobutyryl (Aib) and gabapentin (Gpn) residues greatly restricts sterically accessible coil formational space. This model sequence was anticipated to be a short segment of the alpha gamma C-12 helix, stabilized by three successive 4 -> 1 hydrogen bonds, corresponding to a backbone-expanded analogue of the alpha polypeptide 3(10)-helix. Unexpectedly, three distinct crystalline polymorphs were characterized in the solid state by X-ray diffraction. In one form, two successive C-12 hydrogen bonds were obtained at the N-terminus, while a novel C-17 hydrogen-bonded gamma alpha gamma turn was observed at the C-terminus. In the other two polymorphs, isolated C-9 and C-7 hydrogen-bonded turns were observed at Gpn (2) and Gpn (4). Isolated C-12 and C-9 turns were also crystallographically established in the peptides Boc-Aib-Gpn-Aib-OMe and Boc-Gpn-Aib-NHMe, respectively. Selective line broadening of NH resonances and the observation of medium range NH(i)<-> NH(i+2) NOEs established the presence of conformational heterogeneity for the tetrapeptide in CDCl3 solution. The NMR results are consistent with the limited population of the continuous C-12 helix conformation. Lengthening of the (alpha gamma)(n) sequences in the nonapeptides Boc-Aib-Gpn-Aib-Gpn-Aib-Gpn-Aib-Gpn-Xxx (Xxx = Aib, Leu) resulted in the observation of all of the sequential NOEs characteristic of an alpha gamma C-12 helix. These results establish that conformational fragility is manifested in short hybrid alpha gamma sequences despite the choice of conformationally constrained residues, while stable helices are formed on chain extension.

Structural Ordering of Disordered Ligand-Binding Loops of Biotin Protein Ligase into Active Conformations as a Consequence of Dehydration

Mycobacterium tuberculosis (Mtb), a dreaded pathogen, has a unique cell envelope composed of high fatty acid content that plays a crucial role in its pathogenesis. Acetyl Coenzyme A Carboxylase (ACC), an important enzyme that catalyzes the first reaction of fatty acid biosynthesis, is biotinylated by biotin acetyl-CoA carboxylase ligase (BirA). The ligand-binding loops in all known apo BirAs to date are disordered and attain an ordered structure only after undergoing a conformational change upon ligand-binding. Here, we report that dehydration of Mtb-BirA crystals traps both the apo and active conformations in its asymmetric unit, and for the first time provides structural evidence of such transformation. Recombinant Mtb-BirA was crystallized at room temperature, and diffraction data was collected at 295 K as well as at 120 K. Transfer of crystals to paraffin and paratone-N oil (cryoprotectants) prior to flash-freezing induced lattice shrinkage and enhancement in the resolution of the X-ray diffraction data. Intriguingly, the crystal lattice rearrangement due to shrinkage in the dehydrated Mtb-BirA crystals ensued structural order of otherwise flexible ligand-binding loops L4 and L8 in apo BirA. In addition, crystal dehydration resulted in a shift of similar to 3.5 angstrom in the flexible loop L6, a proline-rich loop unique to Mtb complex as well as around the L11 region. The shift in loop L11 in the C-terminal domain on dehydration emulates the action responsible for the complex formation with its protein ligand biotin carboxyl carrier protein (BCCP) domain of ACCA3. This is contrary to the involvement of loop L14 observed in Pyrococcus horikoshii BirA-BCCP complex. Another interesting feature that emerges from this dehydrated structure is that the two subunits A and B, though related by a noncrystallographic twofold symmetry, assemble into an asymmetric dimer representing the ligand-bound and ligand-free states of the protein, respectively. In-depth analyses of the sequence and the structure also provide answers to the reported lower affinities of Mtb-BirA toward ATP and biotin substrates. This dehydrated crystal structure not only provides key leads to the understanding of the structure/function relationships in the protein in the absence of any ligand-bound structure, but also demonstrates the merit of dehydration of crystals as an inimitable technique to have a glance at proteins in action.