Kinetic mechanism of acetyl-CoA synthase: steady-state synthesis at variable Co/Co2 pressures.

Steady-state initial rates of acetyl-CoA synthesis (upsilon/[E(tot)]) catalyzed by acetyl-CoA synthase from Clostridium thermoaceticum (ACS) were determined at various partial pressures of CO and CO2. When [CO] was varied from 0 to 100 microM in a balance of Ar, rates increased sharply from 0.3 to 100 min(-1). At [CO] > 100 microM, rates declined sharply and eventually stabilized at 10 min(-1) at 980 microM CO. Equivalent experiments carried out in CO2 revealed similar inhibitory behavior and residual activity under saturating [CO]. Plots of upsilon/[E(tot)] vs [CO2] at different fixed inhibitory [CO] revealed that Vmax/[E(tot)] (kcat) decreased with increasing [CO]. Plots of upsilon/[E(tot)] vs [CO2] at different fixed noninhibitory [CO] showed that Vmax/[E(tot)] was insensitive to changes in [CO]. Of eleven candidate mechanisms, the simplest one that fit the data best had the following key features: (a) either CO or CO2 (at a designated reductant level and pH) activate the enzyme (E' + CO right arrow over left arrow E, E' + CO2/2e-/2H+ right arrow over left arrow E); (b) CO and CO2 are both substrates that compete for the same enzyme form (E + CO right arrow over left arrow ECO, E + CO2/2e-/2H+ right arrow over left arrow ECO, and ECO --> E + P); (c) between 3 and 5 molecules of CO bind cooperatively to an enzyme form different from that to which CO2 and substrate CO bind (nCO + ECO right arrow over left arrow (CO)nECO), and this inhibits catalysis; and (d) the residual activity arises from either the (CO)nECO state or a heterogeneous form of the enzyme. Implications of these results, focusing on the roles of CO and CO2 in catalysis, are discussed.     

Binary integer programs with two variables per inequality

Several recent papers have shown that some properties of the maximum weight stable set problem hold true in the more general setting of binary integer programs with two variables per inequality. In this paper, we show that in fact the two problems are equivalent by using the transitive closure of the binary integer program and (possibly) reducing the number of variables by fixing, complementing, or identifying them. We use this equivalence to prove two conjectures made by Johnson and Padberg regarding the perfection of bidirected graphs.     

Product integrals in strongly differentiable power associative groupoids

The existence of product integrals in differentiable semigroups with neighborhood of 1 homeomorphic to a Banach space and with multiplication strongly differentiable at (1,1) was shown by Garrett Birkhoff in 1938. This result was then used to transform the multiplication into canonical parameters. We show here a sufficient condition to guarantee the existence of product integrals in differentiable power associative groupoids with multiplication strongly differentiable at (1,1).     

On configuration-dependent loading

Summary A general investigation of the mathematical properties of configuration-dependent loading is described. This is loading which acts on the surface of an arbitrary body and which changes in a known way depending on the displacement of the neighbourhood of its point of application. Exact definitions of many possible kinds of such loading are given. Criteria for conservative loading are derived and applied. A virtual work principle for a sequence of perturbation problems is given. Suggestions are made for further research.     

Quantum fields on manifolds: PCT and gravitationally induced thermal states

We formulate an axiomatic scheme, designed to provide a framework for a general, rigorous theory of relativistic quantum fields on a class of manifolds, that includes Kruskal's extension of Schwarzschild space-time, as well as Minkowski space-time. The scheme is an adaptation of Wightman's to this class of manifolds. We infer from it that, given an arbitrary field (in general, interacting) on a manifold X, the restriction of the field to a certain open submanifold X⁽⁺⁾, whose boundaries are event horizons, satisfies the Kubo-Martin-Schwinger (KMS) thermal equilibrium conditions. This amounts to a rigorous, model-independent proof of a generalised Hawking-Unruh effect. Further, in cases where the field enjoys a certain PCT symmetry, the conjugation governing the KMS condition is just the PCT operator. The key to these results is an analogue, that we prove, of the Bisognano-Wichmann theorem. [J. Math. Phys.17 (1976), Theorem 1]. We also construct an alternative scheme by replacing a regularity condition at an event horizon by the assumption that the field in X⁽⁺⁾ is in a ground, rather than a thermal, state. We show that, in this case, the observables in X⁽⁺⁾ are uncorrelated to those in its causal complement, X^(?), and thus that the event horizons act as physical barriers. Finally, we argue that the choice between the two schemes must be dictated by the prevailing conditions governing the state of the field.     

Efficient broadband simulations for thin optical structures

The thickness of the layers comprising optical structures is usually very thin. When modelling such thin features using a traditional numerical method, for instance the transmission-line modelling (TLM) method, a very small space step is often used to properly discretize the material geometry. This consequently results in large memory storage and longer run time. In this paper a new technique embedding thin structures between TLM nodes is investigated. The key features of this technique are the acquisition of the formulations in the frequency domain and the utilisation of digital filter theory and an inverse Z transform to change the formulations to the time domain. This technique has been successfully applied to calculate the reflection and transmission coefficients of optical structures incorporating thin layers, including antireflection coatings and fibre Bragg grating structures.