Galactose oxidase models: solution chemistry, and phenoxyl radical generation mediated by the copper status

Galactose oxidase (GO) is an enzyme that catalyzes two-electron oxidations. Its active site contains a copper atom coordinated to a tyrosyl radical, the biogenesis of which requires copper and dioxygen. We have recently studied the properties of electrochemically generated mononuclear Cu(II)-phenoxyl radical systems as model compounds of GO. We present here the solution chemistry of these ligands under various copper and dioxygen statuses: N(3)O ligands first chelate Cu(II), leading, in the presence of base, to [Cu(II)(ligand)(CH(3)CN)](+) complexes (ortho-tert-butylated ligands) or [(Cu(II))(2)(ligand)(2)](2+) complexes (ortho-methoxylated ligands). Excess copper(II) then oxidizes the complex to the corresponding mononuclear Cu(II)-phenoxyl radical species. N(2)O(2) tripodal ligands, in the presence of copper(II), afford directly a copper(II)-phenoxyl radical species. Addition of more than two molar equivalents of copper(II) affords a Cu(II)-bis(phenoxyl) diradical species. The donor set of the ligand directs the reaction towards comproportionation for ligands possessing an N(3)O donor set, while disproportionation is observed for ligands possessing an N(2)O(2) donor set. These results are discussed in the light of recent results concerning the self-processing of GO. A path involving copper(II) disproportionation is proposed for oxidation of the cross-linked tyrosinate of GO, supporting the fact that both copper(I) and copper(II) activate the enzyme.     

Decay of correlations in surface models

A convergent low-temperature expansion for a variety of models of twodimensional surfaces is presented. It yields existence of the thermodynamic limit for the pressure and correlation functions as well as analyticity inz =e ^– In addition, the estimates give exponential decay of truncated correlations, which proves the existence of a gap in the spectrum of the transfer matrix below the ground state eigenvalue. Two particular examples included in the general framework are the solid-on-solid and discrete Gaussian models.Supported in part by the National Science Foundation under grant No. PHY 79-16812.     

Indirect detection in reversed-phase liquid chromatography: Ion-pair retention models for ionic compounds on μ Bondapak phenyl

Summary Retention models for ionic compounds in reversed-phase ion-pair chromatographic systems have been developed on the basis of the capacity ratios of solutes and ionic mobile phase components using indirect detection. The binding to the adsorbent, μBondapak Phenyl, has been expressed by ion-pair distribution constants and tested in the retention models by non-linear regression. All the ionic compounds followed adsorption models of the Langmuir type comprising two kinds of binding sites with widely different adsorption capacities and binding constants. The results indicate certain differences between the two sites regarding the binding of cationic and anionic components, respectively.     

Generalized nets in neurology: an example of mathematical modelling

The purpose of this paper is to explain the basic theory of generalized nets (GNs) and their applications in the context of the differential diagnosis of neurological diseases. We define formally the concepts of a GN and transitions of a GN and also outline some remarks on their theory. The work here constructs an example which aims to trace the process of diagnosing different signs and symptoms in neurology. This will enable the interested reader to see the scope of nets in general as tools for the modelling, simulation, optimization and control of real processes.     

A mathematical model for a distributed attack on targeted resources in a computer network

A mathematical model has been developed to analyze the spread of a distributed attack on critical targeted resources in a network. The model provides an epidemic framework with two sub-frameworks to consider the difference between the overall behavior of the attacking hosts and the targeted resources. The analysis focuses on obtaining threshold conditions that determine the success or failure of such attacks. Considering the criticality of the systems involved and the strength of the defence mechanism involved, a measure has been suggested that highlights the level of success that has been achieved by the attacker. To understand the overall dynamics of the system in the long run, its equilibrium points have been obtained and their stability has been analyzed, and conditions for their stability have been outlined.     

A Self-Assembled Cage with Endohedral Acid Groups both Catalyzes Substitution Reactions and Controls Their Molecularity

A self-assembled Fe₄L₆ cage complex internally decorated with acid functions is capable of accelerating the thioetherification of activated alcohols, ethers and amines by up to 1000-fold. No product inhibition is seen, and effective supramolecular catalysis can occur with as little as 5 % cage. The substrates are bound in the host with up to micromolar affinities, whereas the products show binding that is an order of magnitude weaker. Most importantly, the cage host alters the molecularity of the reaction: whereas the reaction catalyzed by simple acids is a unimolecular, S_N1-type substitution process, the rate of the host-mediated process is dependent on the concentration of nucleophile. The molecularity of the cage-catalyzed reaction is substrate-dependent, and can be up to bimolecular. In addition, the catalysis can be prevented by a large excess of nucleophile, where substrate inhibition dominates, and the use of tritylated anilines as substrates causes a negative feedback loop, whereby the liberated product destroys the catalyst and stops the reaction.     

The inventory models under conditional trade credit in a supply chain system

In several recent investigations dealing with the economic order quantity with permissible delay in payments, the following assumptions are made:     

Discrete filter operators for large‐eddy simulation using high‐order spectral difference methods

The combination of a high‐order unstructured spectral difference (SD) spatial discretization scheme with sub‐grid scale (SGS) modeling for large‐eddy simulation is investigated with particular focus on the consistent implementation of a structural mixed model based on the scale similarity hypothesis. The difficult task of deriving a consistent formulation for the discrete filter within the SD element of arbitrary order led to the development of a new class of three‐dimensional constrained discrete filters. The discrete filters satisfy a set of selected criteria and are completely local within the SD element. Their weights can be automatically computed at run time from the number of solution points within each element and the expected filter cutoff length scale. The novel discrete filters can be applied to any SGS model involving explicit filtering and to a broad class of high‐order discontinuous finite element numerical schemes. The code is applied to the computation of turbulent channel flows at three Reynolds numbers, namely Re_τ = 180, 395, and 590 (based on the friction velocity u_τ and channel half‐width δ). Results from computations with and without the SGS model are compared against results from direct numerical simulation. The numerical experiments suggest that the results are sensitive to the use of the SGS model, even when a high‐order numerical scheme is used, especially when the grid resolution is kept relatively low and mostly in terms of resolved Reynolds stresses. Results obtained using existing filters based on the projection of the solution over lower‐order polynomial bases are also shown and demonstrate that these filters are inadequate for SGS modeling purposes, mostly because of their inability to enforce the selected cutoff length scale with sufficient accuracy. The use of the similarity mixed formulation proved to be particularly accurate in reproducing SGS interactions, confirming that its well‐known potential can be realized in conjunction with state‐of‐the‐art high‐order numerical schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Uniform persistence for population interaction models with time delay

In this paper uniform persistence is establised for kolmogorov type Prey‐Predator and competion models with per capitals ent growth rates that are dependent on time‐lagged population densities.