Self-organized criticality in dynamics without branching

We demonstrate the phenomenon of self-organized criticality (SOC) in a simple random walk model described by a random walk of a myopic ant, i.e., a walker who can see only nearest neighbors. The ant acts on the underlying lattice aiming at uniform digging, i.e., reduction of the height profile of the surface but is unaffected by the underlying lattice. In one, two, and three dimensions we have explored this model and have obtained power laws in the time intervals between consecutive events of "digging." Being a simple random walk, the power laws in space translate to power laws in time. We also study the finite size scaling of asymptotic scale invariant process as well as dynamic scaling in this system. This model differs qualitatively from the cascade models of SOC.

Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

Infinite Dimensional Slow Modulations In A Delayed Model For Orthogonal Cutting Vibrations

We apply the method of multiple scales (MMS) to a well known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the time scale of typical cutting tool oscillations. The MMS upto second order for such systems has been developed recently, and is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy. The main advantage of the present analysis is that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space. Lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS. Finally, the strong sensitivity of the dynamics to small changes in parameter values is seen clearly.

PocketMatch: A new algorithm to compare binding sites in protein structures

Recognizing similarities and deriving relationships among protein molecules is a fundamental requirement in present-day biology. Similarities can be present at various levels which can be detected through comparison of protein sequences or their structural folds. In some cases similarities obscure at these levels could be present merely in the substructures at their binding sites. Inferring functional similarities between protein molecules by comparing their binding sites is still largely exploratory and not as yet a routine protocol. One of the main reasons for this is the limitation in the choice of appropriate analytical tools that can compare binding sites with high sensitivity. To benefit from the enormous amount of structural data that is being rapidly accumulated, it is essential to have high throughput tools that enable large scale binding site comparison. Results: Here we present a new algorithm PocketMatch for comparison of binding sites in a frame invariant manner. Each binding site is represented by 90 lists of sorted distances capturing shape and chemical nature of the site. The sorted arrays are then aligned using an incremental alignment method and scored to obtain PMScores for pairs of sites. A comprehensive sensitivity analysis and an extensive validation of the algorithm have been carried out. A comparison with other site matching algorithms is also presented. Perturbation studies where the geometry of a given site was retained but the residue types were changed randomly, indicated that chance similarities were virtually non-existent. Our analysis also demonstrates that shape information alone is insufficient to discriminate between diverse binding sites, unless combined with chemical nature of amino acids. Conclusion: A new algorithm has been developed to compare binding sites in accurate, efficient and high-throughput manner. Though the representation used is conceptually simplistic, we demonstrate that along with the new alignment strategy used, it is sufficient to enable binding comparison with high sensitivity. Novel methodology has also been presented for validating the algorithm for accuracy and sensitivity with respect to geometry and chemical nature of the site. The method is also fast and takes about 1/250(th) second for one comparison on a single processor. A parallel version on BlueGene has also been implemented.

Localisation of Plasmodium falciparum uroporphyrinogen III decarboxylase of the heme-biosynthetic pathway in the apicoplast and characterisation of its catalytic properties

Uroporphyrinogen decarboxylase (UROD) is a key enzyme in the heme-biosynthetic pathway and in Plasmodium falciparum it occupies a strategic position in the proposed hybrid pathway for heme biosynthesis involving shuttling of intermediates between different subcellular compartments in the parasite. In the present study, we demonstrate that an N-terminally truncated recombinant P. falciparum UROD (r(Δ)PfUROD) over-expressed and purified from Escherichia coli cells, as well as the native enzyme from the parasite were catalytically less efficient compared with the host enzyme, although they were similar in other enzyme parameters. Molecular modeling of PfUROD based on the known crystal structure of the human enzyme indicated that the protein manifests a distorted triose phosphate isomerase (TIM) barrel fold which is conserved in all the known structures of UROD. The parasite enzyme shares all the conserved or invariant amino acid residues at the active and substrate binding sites, but is rich in lysine residues compared with the host enzyme. Mutation of specific lysine residues corresponding to residues at the dimer interface in human UROD enhanced the catalytic efficiency of the enzyme and dimer stability indicating that the lysine rich nature and weak dimer interface of the wild-type PfUROD could be responsible for its low catalytic efficiency. PfUROD was localised to the apicoplast, indicating the requirement of additional mechanisms for transport of the product coproporphyrinogen to other subcellular sites for its further conversion and ultimate heme formation.

Relativistic particle models with separable interactions

We present relativistic, classical particle models that possess Poincaré invariance, invariant world lines, particle interaction, and separability.

Separability in relativistic Hamiltonian particle dynamics

The problem of separability in recent models of classical relativistic interacting particles is examined. This physical requirement is shown to be more subtle than naive separability of all the constraints defining the system: it is adequate to be able to canonically transform the time-fixing constraints from an unseparated to a separated form when clusters emerge. Viewing separability in this way, and within a specific framework, we are led to a new no-interaction theorem which states the incompatibility of nontrivial interaction with relativistic invariance, separability, and invariant world lines for more than two particles.

Structure and interactions of aspirin-like drugs

A pre-requisite for the elucidation of the mechanism of action of aspirin-like drugs, which are believed to exert their pharmacological effects through the inhibition of prostaglandin biosynthesis, is an understanding of their molecular geometry, the non-covalent interactions they are likely to be involved in, and the geometrical and the electronic consequences of such interactions. This has been sought to be achieved through the x-ray analysis of these drug molecules and their crystalline complexes with other suitable molecules. The results obtained from such studies have been discussed in terms of specific typical examples. For instance, antipyrine can form metal and hydrogen-bonded complexes; phenylbutazone can form ionic complexes with basic molecules. Complex formation is accompanied by characteristic changes in the molecular geometry and the electronic structure in both the cases. The results obtained so far appear to indicate that the important common invariant structural features of the fenamates, deduced from crystal structures, are retained even when complexation takes place.

Fasteners in Composite Plates - Effects of Interfacial Friction

The effects of tangential friction at pin—hole interfaces are appropriately modelled for the analysis of fasteners in large composite (orthotropic) plate loaded along its edges. The pin—hole contact could be of interference, clearance or neat fit. When the plate load is monotonically increased, interference fits give rise to receding contact, whereas clearance fits result in advancing contact. In either case, the changing contact situations lead to non-linear moving boundary value problems. The neat fit comes out as a special case in which the contact and separation regions are invariant with the applied load level and so the problem remains linear. The description of boundary conditions in the presence of tangential friction, will depend on whether the problem is one of advancing or receding contact, advancing contact presenting a special problem. A model is developed for the limiting case of a rigid pin and an ideally rough interface (infinitely large friction coefficient). The non-linearity resulting from the continuously varying proportions of contact and separation at the interface, is handled by an “Inverse Formulation” which was successfully applied earlier by the authors for smooth (zero friction) interfacial conditions. The additional difficulty introduced by advancing contact is handled by adopting a “Marching Solution”. The modelling and the procedure are illustrated in respect of symmetric plate load cases. Numerical results are presented bringing out the effects of interfacial friction and plate orthotropy on load-contact relations and plate stresses.

Structural studies of analgesics and their interactions .10. A hydrated 1-1 complex between niflumic acid and ethanolamine, c13h8f3n2o-2.c2h8no+.h2o.

Mr= 361.3, triclinic, P1, a = 6-239 (2), b=11.280(2), c=12-451(2)A, a=101.2 (1), B= 92.3 (1), 7=99.9(1)°, V=844.123 A3, Z=2, Dx= 1.42, D m = 1.42 (1) Mg m -3, n(Cu Ka) = 1.5418 ,A., g = 1-102 mm -1, F(000) = 376, T= 293 K. Final R = 0.064 for 2150 observed reflections. The niflumic acid anions consist essentially of three planar groupings, namely, two six-membered rings and a carboxylate group attached to one of them. The invariant common structural features observed in the crystal structures of fenamates, namely, the coplanarity of the carboxyl group and the six-membered ring bearing it, and the internal hydrogen bond between the carboxyl group and the imino N atom that bridges the two sixmembered rings, are retained in the complex. The amino N atom is gauche with respect to the terminal hydroxyl group in the ethanolamine cation. The complexation between the two molecules is achieved through ionic and hydrogen-bonded interactions involving the carboxylate group in niflumic acid.

The carbon dioxide hydration activity of the sulfonamide-resistant carbonic anhydrase from the liver of male rat: pH independence of the steady-state kinetics

The steady-state kinetic constants for the catalysis of CO2 hydration by the sulfonamide-resistant and testosterone-induced carbonic anhydrase from the liver of the male rat has been determined by stopped-flow spectrophotometry. The turnover number was 2.6 ± 0.6 × 103 s− at 25 °C, and was invariant with pH ranging from 6.2 to 8.2 within experimental error. The Km at 25 °C was 5 ± 1 mImage , and was also pH independent. These data are in quantitative agreement with earlier findings of pH-independent CO2 hydration activity for the mammalian skeletal muscle carbonic anhydrase isozyme III. The turnover numbers for higher-activity isozymes I and II are strongly pH dependent in this pH range. Thus, the kinetic status of the male rat liver enzyme is that of carbonic anhydrase III. This finding is consistent with preliminary structural and immunologic data from other laboratories.

The sputtering temperature of a cooling cylindrical rod with an insulated core

By a standard application of Jones's method associated with the Wiener-Hopf technique an explicit solution is obtained for the temperature distribution inside a cylindrical rod with an insulated inner core when the rod is allowed to enter into a fluid of large extent with a uniform speed, and a simple integral expression is derived for the value of the sputtering temperature of the rod at the points of entry. Numerical results under certain special circumstances are also obtained and presented in the form of a table.

Watson-Crick pairing, the Heisenberg group and Milnor invariants

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

The sputtering temperature of a cooling cylindrical rod with an insulated core

By a standard application of Jones's method associated with the Wiener-Hopf technique an explicit solution is obtained for the temperature distribution inside a cylindrical rod with an insulated inner core when the rod is allowed to enter into a fluid of large extent with a uniform speed, and a simple integral expression is derived for the value of the sputtering temperature of the rod at the points of entry. Numerical results under certain special circumstances are also obtained and presented in the form of a table.

Conserved water-mediated H-bonding dynamics of catalytic Asn 175 in plant thiol protease

The role of invariant water molecules in the activity of plant cysteine protease is ubiquitous in nature. On analysing the 11 different Protein DataBank (PDB) structures of plant thiol proteases, the two invariant water molecules W I and W2 (W220 and W222 in the template 1PPN structure) were observed to form H-bonds with the Ob atom of Asn 175. Extensive energy minimization and molecular dynamics simulation studies up to 2 ns on all the PDB and solvated structures clearly revealed the involvement of the H-bonding association of the two water molecules in fixing the orientation of the asparagine residue of the catalytic triad. From this study, it is suggested that H-bonding of the water molecule at the W1 invariant site better stabilizes the Asn residue at the active site of the catalytic triad.