Evaluation of dipolar shifts and paramagnetic anisotropy in penta coordinated cobalt(II) complexes

The isotropic proton shifts for the pyridine N-oxide and γ-picoline N-oxide protons have been observed in the penta coordinated adducts of these bases with bis[di(p-tolyl)dithiophosphinato] cobalt(II). The contribution to the observed shifts due to dipolar interaction has been calculated. From the dipolar shifts, it was ascertained that the pyridine N-oxide complexes have a bent structure in solution with a Co-O-N angle of 125°. An estimate of the paramagnetic anisotropy of the cobalt complex yields K_?-K_⊥ = 4244 × 10^?6 cm³/mole.     

A large volume pressure cell for high temperatures

Abstract

Studies of matter under very high pressure at synchrotron radiation sources are mostly done using pressure cells with single-crystal diamond anvils. In some cases the available volume (≤ 10^?3mm³)in such cells causes problems especially at high temperature and for crystal synthesis. To ensure sufficient homogeneity of pressure and temperature, the use of cells with large sample volumes (≥ 1 mm³) is necessary.

Existing devices for such measurements are compared with a novel setup which consists of a toroidal anvil arrangement and a lightweight (50 kg) press with 250 tonnes (2.5 MN) capacity. Preliminary tests of this instrument with synchrotron radiation are reported.

Presented at the IUCr Workshop on ‘Synchrotron Radiation Instrumentation for HighPressure Crystallography’. Daresbury Laboratory 20-21 July 1991     

Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô–Isoda function

In this paper, we extend the literature by adapting the Nikaidô–Isoda function as an indicator function termed as regularized indicator Nikaidô–Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations.     

Well-setness and scalarization in set optimization

In this paper, we consider a notion of global well-setness for a set optimization problem using the excess function. We give sufficient conditions for well-setness and establish Dontchev–Zolezzi type measure for well-setness. Moreover, we relate this notion with well-setness notion for a scalar problem obtained by using generalized Gerstewitz’s function.     

Enhanced podophyllotoxin production from Agrobacterium rhizogenes transformed cultures of Podophyllum hexandrum

Podophyllotoxin, a potent chemotherapeutic agent is obtained from Podophyllum hexandrum Royle. Embryos of P. hexandrum were transformed using different strains of Agrobacterium rhizogenes viz. A4, 15834, K599. Transformed nature of the calli was ascertained and the cultures were further maintained as individual clones. HPLG analysis of transformed cultures depicted a three-fold increase in podophyllotoxin content in comparison to controls.     

Stochastic theory of large-scale enzyme-reaction networks: finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.     

Approximate solutions and scalarization in set-valued optimization

Abstract

Certain notions of approximate weak efficient solutions are considered for a set-valued optimization problem based on vector and set criteria approaches. For approximate solutions based on the vector approach, a characterization is provided in terms of an extended Gerstewitz’s function. For the set approach case, two notions of approximate weak efficient solutions are introduced using a lower and an upper quasi order relations for sets and further compactness and stability aspects are discussed for these approximate solutions. Existence and scalarization using a generalized Gerstewitz’s function are also established for approximate solutions, based on the lower set order relation.     

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order Ω(-3∕2) for reaction systems which do not obey detailed balance and at least accurate to order Ω(-2) for systems obeying detailed balance, where Ω is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order Ω(-1∕2) and variance estimates accurate to order Ω(-3∕2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.     

Proton magnetic resonance studies of the association of amino methyl pyridines

Proton magnetic resonance studies of the solutions of (a) 2-amino, 3-methyl pyridine and (b) 2-amino, 6-methyl pyridine in carbontetrachloride show that in these molecules there is an equilibrium between monomers and hydrogen-bonded dimers. The equilibrium constants for the two cases have been obtained. Evidence has also been obtained to show that chloroform forms hydrogen bond with the ring nitrogen of these compounds. These NMR results have been compared with those obtained earlier from infra-red studies.