Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Stereochemical analysis of the antigenic tip of the V3 loop peptide of HIV-1 gp120

A novel multiple turn conformation has been observed for a segment GPGRAFY in the crystal structure of a complex of HIV-1 gp120 V3 loop peptide with the Fab fragment of a neutralizing antibody [Ghiara ct al. (1994) Science 264, 82-85]. A structural motif has been defined for the peptide segment, employing idealized backbone conformations characterized by ranges of virtual C-alpha torsion angles and bond angles. A search of 122 high-resolution protein crystal structures has permitted identification of 24 examples of similar structural motifs. Two major conformational families have been identified, which differ primarily in the conformation at residue 3. The observed conformation at residue 3 in family 1 is left-handed helical (alpha(L)) and that in family 2 is right-handed helical (alpha(R)). Of the 10 examples in family 1, 9 examples have Gly residues at position 3. Of the 12 examples in family 2, 7 examples have Asn/Asp at position 3. Computer modeling of the V3 loop tip sequence using the two backbone conformational families as starting points leads to minimum-energy conformations in which antigenically important side-chains occupy similar spatial arrangements. This stereochemical analysis of the V3 loop tip sequence suggests a rational basis for the design of synthetic analog peptides for use as viral antagonists or synthetic antigens. (C) Munksgaard 1995.

Advanced transmission electron microscope triboprobe with automated closed-loop nanopositioning

Here the design and operation of a novel transmission electron microscope (TEM) triboprobe instrument with real-time vision control for advanced in situ electron microscopy is demonstrated. The NanoLAB triboprobe incorporates a new high stiffness coarse slider design for increased stability and positioning performance. This is linked with an advanced software control system which introduces both new and flexible in situ experimental functional testing modes, plus an automated vision control feedback system. This advancement in instrumentation design unlocks new possibilities of performing a range of new dynamical nanoscale materials tests, including novel friction and fatigue experiments inside the electron microscope.

The heat kernel on AdS(3) and its applications

We derive the heat kernel for arbitrary tensor fields on S-3 and (Euclidean) AdS(3) using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS(3). We apply this to the calculation of the one loop partition function of N = 1 supergravity on AdS(3). We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.

Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms

This paper presents a study of kinematic and force singularities in parallel manipulators and closed-loop mechanisms and their relationship to accessibility and controllability of such manipulators and closed-loop mechanisms, Parallel manipulators and closed-loop mechanisms are classified according to their degrees of freedom, number of output Cartesian variables used to describe their motion and the number of actuated joint inputs. The singularities in the workspace are obtained by considering the force transformation matrix which maps the forces and torques in joint space to output forces and torques ill Cartesian space. The regions in the workspace which violate the small time local controllability (STLC) and small time local accessibility (STLA) condition are obtained by deriving the equations of motion in terms of Cartesian variables and by using techniques from Lie algebra.We show that for fully actuated manipulators when the number ofactuated joint inputs is equal to the number of output Cartesian variables, and the force transformation matrix loses rank, the parallel manipulator does not meet the STLC requirement. For the case where the number of joint inputs is less than the number of output Cartesian variables, if the constraint forces and torques (represented by the Lagrange multipliers) become infinite, the force transformation matrix loses rank. Finally, we show that the singular and non-STLC regions in the workspace of a parallel manipulator and closed-loop mechanism can be reduced by adding redundant joint actuators and links. The results are illustrated with the help of numerical examples where we plot the singular and non-STLC/non-STLA regions of parallel manipulators and closed-loop mechanisms belonging to the above mentioned classes. (C) 2000 Elsevier Science Ltd. All rights reserved.

Support theorems on R-n and non-compact symmetric spaces

We consider convolution equations of the type f * T = g, where f, g is an element of L-P (R-n) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T, we show that f is compactly supported, provided g is. Similar results are proved for non-compact symmetric spaces as well. (C) 2010 Elsevier Inc. All rights reserved.

Synthetic peptide models for the redox-active disulfide loop of glutaredoxin. Conformational studies

Two cyclic peptide disulfides Boc-Cys-Pro-X-Cys-NHMe (X = L-Tyr or L-Phe) have been synthesized as models for the 14-membered redox-active disulfide loop of glutaredoxin. 'H NMR studies at 270 MHz in chloroform solutions establish a type I 0-turn conformation for the Pro-X segment in both peptides, stabilized by a 4-1 hydrogen bond between the Cys(1) CO and Cys(4) NH groups. Nuclear Overhauser effects establish that the aromatic ring in the X = Phe peptide is oriented over the central peptide unit. In dimethyl sulfoxide solutions two conformational species are observed in slow exchange on the NMR time scale, for both peptides. These are assigned to type I and type I1 p-turn structures with -Pro-Tyr(Phe)-as the corner residues. The structural assignments are based on correlation of NMR parameters with model 14-membered cyclic cystine peptides with Pro-X spacers. Circular dichroism studies based on the -S-Sn- u* transition suggest a structural change in the disulfide bridge with changing solvent polarity, establishing conformational coupling between the peptide backbone and the disulfide linkage in these systems.

Theoretical and Experimental Studies on an Ammonia-Based Loop Heat Pipe With a Flat Evaporator

An ammonia loop heat pipe (LHP) with a flat plate evaporator is developed and tested. The device uses a nickel wick encased in an aluminum-stainless steel casing. The loop is tested for various heat loads and different sink temperatures, and it demonstrated reliable startup characteristics. Results with the analysis of the experimental observation indicate that the conductance between the compensation chamber and the heater plate can significantly influence the operating temperatures of the LHP. A mathematical model is also presented which is validated against the experimental observations.

Chemistry in Confined Spaces: High-Energy Conformer of a Piperidine Derivative is Favored Within a Water-Soluble Capsuleplex

Propyloxy-substituted piperidine in solution adopts a conformation in which its alkoxy group is equatorially positioned Surprisingly, two conformers of it that do not interconvert in the NMR time scale at room temperature have been found within an octa-acid capsule The serendipitous finding of the axial conformer of propyloxy-substituted piperidine within a supramolecular capsule highlights the value of confined spaces in physical organic chemistry.

On the relation between rotation increments in different tangent spaces

In computational mechanics, finite rotations are often represented by rotation vectors. Rotation vector increments corresponding to different tangent: spaces are generally related by a linear operator, known as the tangential transformation T. In this note, we derive the higher order terms that are usually left out in linear relation. The exact nonlinear relation is also presented. Errors via the linearized T are numerically estimated. While the concept of T arises out of the nonlinear characteristics of the rotation manifold, it has been derived via tensor analysis in the context of computational mechanics (Cardona and Geradin, 1988). We investigate the operator T from a Lie group perspective, which provides a better insight and a 1-1 correspondence between approaches based on tensor analysis and the standard matrix Lie group theory. (C) 2010 Elsevier Ltd. All rights reserved.

Conformational Polymorphism in Telomeric Structures: Loop Orientation and Interloop Pairing in d(G4TnG4),

Sequence repeats constituting the telomeric regions of chromosomes are known to adopt a variety of unusual structures, consisting of a G tetraplex stem and short stretches of thymines or thymines and adenines forming loops over the stem. Detailed model building and molecular mechanics studies have been carried out for these telomeric sequences to elucidate different types of loop orientations and possible conformations of thymines in the loop. The model building studies indicate that a minimum of two thymines have to be interspersed between guanine stretches to form folded-back structures with loops across adjacent strands in a G tetraplex (both over the small as well as large groove), while the minimum number of thymines required to build a loop across the diagonal strands in a G tetraplex is three. For two repeat sequences, these hairpins, resulting from different types of folding, can dimerize in three distinct ways-i.e., with loops across adjacent strands and on same side, with loops across adjacent strands and on opposite sides, and with loops across diagonal strands and on opposite sides-to form hairpin dimer structures. Energy minimization studies indicate that all possible hairpin dimers have very similar total energy values, though different structures are stabilized by different types of interactions. When the two loops are on the same side, in the hairpin dimer structures of d(G(4)T(n)G(4)), the thymines form favorably stacked tetrads in the loop region and there is interloop hydrogen bonding involving two hydrogen bonds for each thymine-thymine pair. Our molecular mechanics calculations on various folded-back as well as parallel tetraplex structures of these telomeric sequences provide a theoretical rationale for the experimentally observed feature that the presence of intervening thymine stretches stabilizes folded-back structures, while isolated stretches of guanines adopt a parallel tetraplex structure

Modelling multiple disulphide loop containing polypeptides by random conformation generation. The test cases of α-conotoxin GI and edothelin I

A general procedure for arriving at 3-D models of disulphiderich olypeptide systems based on the covalent cross-link constraints has been developed. The procedure, which has been coded as a computer program, RANMOD, assigns a large number of random, permitted backbone conformations to the polypeptide and identifies stereochemically acceptable structures as plausible models based on strainless disulphide bridge modelling. Disulphide bond modelling is performed using the procedure MODIP developed earlier, in connection with the choice of suitable sites where disulphide bonds could be engineered in proteins (Sowdhamini,R., Srinivasan,N., Shoichet,B., Santi,D.V., Ramakrishnan,C. and Balaram,P. (1989) Protein Engng, 3, 95-103). The method RANMOD has been tested on small disulphide loops and the structures compared against preferred backbone conformations derived from an analysis of putative disulphide subdatabase and model calculations. RANMOD has been applied to disulphiderich peptides and found to give rise to several stereochemically acceptable structures. The results obtained on the modelling of two test cases, a-conotoxin GI and endothelin I, are presented. Available NMR data suggest that such small systems exhibit conformational heterogeneity in solution. Hence, this approach for obtaining several distinct models is particularly attractive for the study of conformational excursions.

Relationship between the controllability grammian and closed-loop eigenvalues: the single input case

The controllability grammian is important in many control applications. Given a set of closed-loop eigenvalues the corresponding controllability grammian can be obtained by computing the controller which assigns the eigenvalues and then by solving the Lyapunov equation that defines the grammian. The relationship between the controllability grammian, resulting from state feedback, and the closed-loop eigenvalues of a single input linear time invariant (LTI) system is obtained. The proposed methodology does not require the computation of the controller that assigns the specified eigenvalues. The closed-loop system matrix is obtained from the knowledge of the open-loop system matrix, control influence matrix and the specified closed-loop eigenvalues. Knowing the closed-loop system matrix, the grammian is then obtained from the solution of the Lyapunov equation that defines it. Finally the proposed idea is extended to find the state covariance matrix for a specified set of closed-loop eigenvalues (without computing the controller), due to impulsive input in the disturbance channel and to solve the eigenvalue assignment problem for the single input case.

Analogues of the Wiener-Tauberian and Schwartz theorems for radial functions on symmetric spaces

We prove a Wiener Tauberian theorem for the L-1 spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz-type theorem for complex groups. As a corollary we obtain a Wiener Tauberian type result for compactly supported distributions.

Effect of Substrate Binding Loop Mutations on the Structure, Kinetics, and Inhibition of Enoyl Acyl Carrier Protein Reductase from Plasmodium falciparum

Enoyl acyl carrier protein reductase (ENR), which catalyzes the final and rate limiting step of fatty acid elongation, has been validated as a potential drug target. Triclosan is known to be an effective inhibitor for this enzyme. We mutated the substrate binding site residue Ala372 of the ENR of Plasmodium falciparum (PfENR) to Methionine and Valine which increased the affinity of the enzyme towards triclosan to almost double, close to that of Escherichia coli ENR (EcENR) which has a Methionine at the structurally similar position of Ala372 of PfENR. Kinetic studies of the mutants of PfENR and the crystal structure analysis of the A372M mutant revealed that a more hydrophobic environment enhances the affinity of the enzyme for the inhibitor. A triclosan derivative showed a threefold increase in the affinity towards the mutants compared to the wild type, due to additional interactions with the A372M mutant as revealed by the crystal structure. The enzyme has a conserved salt bridge which stabilizes the substrate binding loop and appears to be important for the active conformation of the enzyme. We generated a second set of mutants to check this hypothesis. These mutants showed loss of function, except in one case, where the crystal structure showed that the substrate binding loop is stabilized by a water bridge network. (C) 2011 IUBMB mum Life, 63(1): 30-41,2011