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.

Specific requirement of lysophosphatidylcholine for palmitoyl-CoA synthetase of chicken intestine

The presence of palmitoyl-CoA synthetase (EC 6.2.1.3) in the brush borderfree particulate fraction of chicken intestinal mucosa is demonstrated. The enzyme was dependent on the simultaneous presence of lysophosphatidylcholine and Triton X-100 as well as ATP, CoA and Mg2+ for maximal activity. Lysophosphatidylcholine could not be replaced by other lipids. Enzyme preparations solubilized by Triton X-100 or lysophosphatidylcholine were still dependent on the presence of detergents for maximal activity.

State Minimization of Incompletely Specified Sequential Machines

A simple procedure for the state minimization of an incompletely specified sequential machine whose number of internal states is not very large is presented. It introduces the concept of a compatibility graph from which the set of maximal compatibles of the machine can be very conveniently derived. Primary and secondary implication trees associated with each maximal compatible are then constructed. The minimal state machine covering the incompletely specified machine is then obtained from these implication trees.

Succinate and malate improve development of hamster eight-cell embryos in vitro: Confirmation of viability by embryo transfer

The in vitro development of hamster preimplantation embryos is supported by non-glucose energy substrates. To investigate the importance of embryonic metabolism, influence of succinate and malate on the development of hamster 8-cell embryos to blastocysts was examined using a chemically defined protein-free modified hamster embryo culture medium-2 (HECM-2m). There was a dose-dependent influence of succinate on blastocyst development; 0.5 mM succinate was optimal (85.1% ± 3.9 vs. 54.5% ± 3.5). In succinate-supplemented HECM-2m, blastocyst development was reduced by omission of lactate (68.5% ± 7.2), but not pyruvate (85.8% ± 6.2) or glutamine (84.1% ± 2.1). Succinate along with either glutamine or lactate or pyruvate poorly supported blastocyst development (28%-58%). Malate also stimulated blastocyst development; 0.01 mM malate was optimal (86.3% ± 2.8). Supplementation of both succinate and malate to HECM-2m supported maximal (100%) blastocyst development, which was inhibited 4-fold by the addition of glucose/phosphate. The mean cell numbers (MCN) of blastocysts cultured in succinate-supplemented HECM-2m was higher (28.3 ± 1.1) than it was for those cultured in the absence of glutamine or pyruvate (range 20-24). The MCN was the highest (33.4 ± 1.6) for blastocysts cultured in succinate-malate-supplemented HECM-2m followed by those in succinate (28.3 ± 1.1) or malate (24.7 ± 0.5) supplemented HECM-2m. Embryo transfer experiments showed that 29.8% (±4.5) of transferred blastocysts cultured in succinate-malate-supplemented HECM-2m produced live births, similar (P > 0.1) to the control transfers of freshly recovered 8-cells (33.5% ± 2.0) or blastocysts (28.9% ± 3.0). These data show that supplementation of succinate and malate to HECM-2m supports 100% development of hamster 8-cell embryos to high quality viable blastocysts and that non-glucose oxidizable energy substrates are the most preferred components in hamster embryo culture medium. Mol. Reprod. Dev. 47:440-447, 1997. © 1997 Wiley-Liss, Inc.

Thermodynamic characterization of the reversible, two-state unfolding of maltose binding protein, a large two-domain protein

The folding and stability of maltose binding protein (MBP) have been investigated as a function of pH and temperature by intrinsic tryptophan fluorescence, far- and near-UV circular dichroism, and high-sensitivity differential scanning calorimetric measurements. MBP is a monomeric, two-domain protein containing 370 amino acids. The protein is stable in the pH range of 4-10.5 at 25 degrees C. The protein exhibits reversible, two-state, thermal and guanidine hydrochloride-mediated denaturation at neutral pH. The thermostability of MBP is maximal at pH 6, with a Tm of 64.9 degrees C and a deltaHm of 259.7 kcal mol(-1). The linear dependence of deltaHm on Tm was used to estimate a value of deltaCp of 7.9 kcal mol(-1) K(-1) or 21.3 cal (mol of residue)(-1) K(-1). These values are higher than the corresponding deltaCp's for most globular proteins studied to date. However, the extrapolated values of deltaH and deltaS (per mole of residue) at 110 degrees C are similar to those of other globular proteins. These data have been used to show that the temperature at which a protein undergoes cold denaturation depends primarily on the deltaCp (per mol of residue) and that this temperature increases with an increase in deltaCp. The predicted decrease in stability of MBP at low temperatures was experimentally confirmed by carrying out denaturant-mediated unfolding studies at neutral pH at 2 and 28 degrees C.

Strategies for efficient disruption of metabolism in Mycobacterium tuberculosis from network analysis

Tuberculosis continues to be a major health challenge, warranting the need for newer strategies for therapeutic intervention and newer approaches to discover them. Here, we report the identification of efficient metabolism disruption strategies by analysis of a reactome network. Protein-protein dependencies at a genome scale are derived from the curated metabolic network, from which insights into the nature and extent of inter-protein and inter-pathway dependencies have been obtained. A functional distance matrix and a subsequent nearness index derived from this information, helps in understanding how the influence of a given protein can pervade to the metabolic network. Thus, the nearness index can be viewed as a metabolic disruptability index, which suggests possible strategies for achieving maximal metabolic disruption by inhibition of the least number of proteins. A greedy approach has been used to identify the most influential singleton, and its combination with the other most pervasive proteins to obtain highly influential pairs, triplets and quadruplets. The effect of deletion of these combinations on cellular metabolism has been studied by flux balance analysis. An obvious outcome of this study is a rational identification of drug targets, to efficiently bring down mycobacterial metabolism.

A Novel Invertase from a Thermophilic FungusThermomyces lanuginosus:Its Requirement of Thiol and Protein for Activation

Unlike the invertases from the mesophilic fungi and yeasts, invertase from a thermophilic fungus,Thermomyces lanuginosus,was unusually unstable bothin vivoandin vitro.The following observations suggested that the unstable nature of the enzyme activity in the cell-free extracts was due to the oxidation of the cysteine residue(s) in the enzyme molecule: (a) the addition of dithiothreitol or reduced glutathione stabilized invertase activity during storage of the extracts and also revived enzyme activity in the extracts which had become inactive with time; (b)N-ethylmaleimide, iodoacetamide, oxidized glutathione, cystine, or oxidized coenzyme A-inactivated invertase; (c) invertase activity was low when the ratio reduced/oxidized glutathione was lower and high when this ratio was higher, suggesting regulation of the enzyme by thiol/disulfide exchange reaction. In contrast to the activation of invertase by the thiol compounds and its inactivation by the disulfides in the cell-free extracts, the purified enzyme did not respond to these compounds. Following its inactivation, the purified enzyme required a helper protein in addition to dithiothreitol for maximal activation. A cellular protein was identified that promoted activation of invertase by dithiothreitol and it was called “PRIA” for theprotein which helps inrestoringinvertaseactivity. The revival of enzyme activity was due to the conversion of the inactive invertase molecules into an active form. A model is presented to explain the modulation of invertase activity by the thiol compounds and the disulfides, both in the crude cell-free extracts and in the purified preparations. The requirement of free sulfhydryl group(s) for the enzyme activity and, furthermore, the reciprocal effects of the thiols and the disulfides on invertase activity have not been reported for invertase from any other source. The finding of a novel invertase which shows a distinct mode of regulation demonstrates the diversity in an enzyme that has figured prominently in the development of biochemistry.

Heat shock response in mulberry silkworm races with different thermotolerances

The thermal sensitivity and heat shock response of the different races of the mulberry silkworm Bombyx mori have been analysed. The multivoltine race, strains C. Nichi and Pure Mysore showed better survival rates than the bivoltine race, strain NB4D2 exposed to 41 degrees C and above. In general, the fifth instar larvae and the pupae exhibited maximum tolerance compared to the early larval instars, adult moths or the eggs. Exposure up to 39 degrees C for 1 or 2 h was tolerated equally whereas temperatures above 43 degrees C proved to be lethal for all. Treatment of larvae at 41 degrees C for Ih resulted in a variety of physiological alterations including increased heart beat rates, differential haemocyte counts, enlargement of granulocytes and the presence of additional protein species in the tissues and haemolymph. The appearance of a 93 kDa protein in the haemolymph, fat bodies and cuticle, following the heat shocking of larvae in vivo was a characteristic feature in all the three strains examined although the kinetics of their appearance itself was different. In haemolymph, the protein appeared immediately in response to heat shock in C. Nichi reaching the maximal levels in 2-4 h whereas its presence was noticeable only after 2-4 h recovery time in Pure Mysore and bivoltine races. The fat body from both C. Nichi and NB4D2 showed the presence of 93 kDa, 89 kDa and 70 kDa proteins on heat shock. The haemocytes, on the other hand, expressed only a 70 kDa protein consequent to heat shock. The 93 kDa protein in the haemolymph, therefore could have arisen from some other tissue, possibly the fat body. The 93 kDa protein was detected after heat shock in pupae and adult moths as well, although the presence of an additional (56 kDa) protein was also apparent in the adults. The presence of 46 kDa and 28 kDa bands in addition to the 93 kDa band in the cuticular proteins immediately following heat shock was clearly discernible. The 70 kDa band did not show much changes in the cuticular proteins on heat shock. In contrast to the changes in protein profiles seen in tissues and haemolymph following heat shock in vivo, the heat treatment of isolated fat body or haemolymph in vitro resulted in protein degradation.

Binding and regulatory properties of phosphofructokinase from swine kidney

The influence of fructose 2,6-bisphosphate on the activation of purified swine kidney phosphofructokinase as a function of the concentration of fructose 6P, ATP and citrate was investigated. The purified enzyme was nearly completely inhibited in the presence of 2 mM ATP. The addition of 20 nM fructose 2,6-P2 reversed the inhibition and restored more than 80% of the activity. In the absence of fructose 2,6-P2 the reaction showed a sigmoidal dependence on fructose-6-phosphate. The addition of 10 nM fructose 2,6-bisphosphate decreased the K0.5 for fructose 6-phosphate from 3 mM to 0.4 mM in the presence of 1.5 mM ATP. These results clearly show that fructose 2,6-bisphosphate increases the affinity of the enzyme for fructose 6-phosphate and decreases the inhibitory effect of ATP. The extent of inhibition by citrate was also significantly decreased in the presence of fructose 2,6-phosphate. The influence of various effectors of phosphofructokinase on the binding of ATP and fructose 6-P to the enzyme was examined in gel filtration studies. It was found that kidney phosphofructokinase binds 5.6 moles of fructose 6-P per mole of enzyme, which corresponds to about one site per subunit of tetrameric enzyme. The KD for fructose 6-P was 13 microM and in the presence of 0.5 mM ATP it increased to 27 microM. The addition of 0.3 mM citrate also increased the KD for fructose 6-P to about 40 microM. AMP, 10 microM, decreased the KD to 5 microM and the addition of fructose 2,6-phosphate decreased the KD for fructose 6-P to 0.9 microM. The addition of these compounds did not effect the maximal amount of fructose 6-P bound to the enzyme, which indicated that the binding site for these compounds might be near, but was not identical to the fructose 6-P binding site. The enzyme bound a maximum of about 12.5 moles of ATP per mole, which corresponds to 3 moles per subunit. The KD of the site with the highest affinity for ATP was 4 microM, and it increased to 15 microM in the presence of fructose 2,6-bisphosphate. The addition of 50 microM fructose 1,6-bisphosphate increased the KD for ATP to 5.9 microM. AMP increased the KD to 5.9 microM whereas 0.3 mM citrate decreased the KD for ATP to about 2 microM.(ABSTRACT TRUNCATED AT 400 WORDS).

Acyclic edge coloring of subcubic graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and it is denoted by a′(G). From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using five colors. This result is tight since there are 3-regular graphs which require five colors. In this paper we prove that any non-regular connected graph of maximum degree 3 is acyclically edge colorable using at most four colors. This result is tight since all edge maximal non-regular connected graphs of maximum degree 3 require four colors.

Conflict-Tolerant Features

We consider systems composed of a base system with multiple “features” or “controllers”, each of which independently advise the system on how to react to input events so as to conform to their individual specifications. We propose a methodology for developing such systems in a way that guarantees the “maximal” use of each feature. The methodology is based on the notion of “conflict-tolerant” features that are designed to continue offering advice even when their advice has been overridden in the past. We give a simple priority-based composition scheme for such features, which ensures that each feature is maximally utilized. We also provide a formal framework for specifying, verifying, and synthesizing such features. In particular we obtain a compositional technique for verifying systems developed in this framework.

Conflict-Tolerant Real-Time Features

This paper addresses the problem of detecting and resolving conflicts due to timing constraints imposed by features in real-time systems. We consider systems composed of a base system with multiple features or controllers, each of which independently advise the system on how to react to input events so as to conform to their individual specifications. We propose a methodology for developing such systems in a modular manner based on the notion of conflict tolerant features that are designed to continue offering advice even when their advice has been overridden in the past. We give a simple priority based scheme for composing such features. This guarantees the maximal use of each feature. We provide a formal framework for specifying such features, and a compositional technique for verifying systems developed in this framework.

Low-delay, high-rate, non-square STBCs from scaled complex orthogonal designs

Space-time block codes (STBCs) obtained from non-square complex orthogonal designs are bandwidth efficient compared to those from square real/complex orthogonal designs for colocated coherent MIMO systems and has other applications in (i) non-coherent MIMO systems with non-differential detection, (ii) Space-Time-Frequency codes for MIMO-OFDM systems and (iii) distributed space-time coding for relay channels. Liang (IEEE Trans. Inform. Theory, 2003) has constructed maximal rate non-square designs for any number of antennas, with rates given by [(a+1)/(2a)] when number of transmit antennas is 2a-1 or 2a. However, these designs have large delays. When large number of antennas are considered this rate is close to 1/2. Tarokh et al (IEEE Trans. Inform. Theory, 1999) have constructed rate 1/2 non-square CODs using the rate-1 real orthogonal designs for any number of antennas, where the decoding delay of these codes is less compared to the codes constructed by Liang for number of transmit antennas more than 5. In this paper, we construct a class of rate-1/2 codes for arbitrary number of antennas where the decoding delay is reduced by 50% when compared with the rate-1/2 codes given by Tarokh et al. It is also shown that even though scaling the variables helps to lower the delay it can not be used to increase the rate.

Single-Symbol ML Decodable Precoded DSTBCs for Cooperative Networks

Single-symbol maximum likelihood (ML) decodable distributed orthogonal space-time block codes (DOST- BCs) have been introduced recently for cooperative networks and an upper-bound on the maximal rate of such codes along with code constructions has been presented. In this paper, we introduce a new class of distributed space-time block codes (DSTBCs) called semi-orthogonal precoded distributed single-symbol decodable space-time block codes (Semi-SSD-PDSTBCs) wherein, the source performs preceding on the information symbols before transmitting it to all the relays. A set of necessary and sufficient conditions on the relay matrices for the existence of semi-SSD- PDSTBCs is proved. It is shown that the DOSTBCs are a special case of semi-SSD-PDSTBCs. A subset of semi-SSD-PDSTBCs having diagonal covariance matrix at the destination is studied and an upper bound on the maximal rate of such codes is derived. The bounds obtained are approximately twice larger than that of the DOSTBCs. A systematic construction of Semi- SSD-PDSTBCs is presented when the number of relays K ges 4 and the constructed codes are shown to have higher rates than that of DOSTBCs.

The generalized anomeric effect in the 1,3-thiazolidines: Evidence forboth sulphur and nitrogen as electron donors. Crystal structures of various N-acylthiazolidines including mercury(II) complexes. Possible relevance to penicillin action

Evidence for the generalized anomeric effect (GAE) in the N-acyl-1,3-thiazolidines, an important structural motif in the penicillins, was sought in the crystal structures of N-(4-nitrobenzoyl)-1,3-thiazolidine and its (2:1) complex with mercuric chloride, N-acetyl-2-phenyl-1,3-thiazolidine, and the (2:1) complex of N-benzoyl-1,3-thiazolidine with mercuric bromide. An inverse relationship was generally observed between the. C-2-N and C-2-S bond lengths of the thiazolidine ring, supporting the existence of the GAE. (Maximal bond length changes were similar to 0.04 angstrom for C-2-N-3, S-1-C-2, and similar to 0.08 angstrom for N-3-C-6.) Comparison with N-acylpyrrolidines and tetrahydrothiophenes indicates that both the nitrogen-to-sulphur and sulphur-to-nitrogen GAE's operate simultaneously in the 1,3-thiazolidines, the former being dominant. (This is analogous to the normal and exo-anomeric effects in pyranoses, and also leads to an interesting application of Baldwin's rules.) The nitrogen-to-sulphur GAE is generally enhanced in the mercury(II) complexes (presumably via coordination at the sulphur); a 'competition' between the GAE and the amide resonance of the N-acyl moiety is apparent. There is evidence for a 'push-pull' charge transfer between the thiazolidine moieties in the mercury(II) complexes, and for a 'back-donation' of charge from the bromine atoms to the thiazolidine moieties in the HgBr2 complex. (The sulphur atom appears to be sp(2) hybridised in the mercury(II) complexes, possibly for stereoelectronic reasons.) These results are apparently relevant to the mode of action of the penicillins. (c) 2006 Elsevier B.V. All rights reserved.