Multi-Step-Model

Xanthou G, Wilhams TJ, Pease JE (2003) Molecular characterization of the chemokine receptor CXCR3 evidence for the involvement of distinct extracellular domains in a multi-step model of ligand binding and receptor activation. Eur J Immunol 33 2927-2936 Xia MQ, Hyman BT (1999) Chemokines/chemokine receptors in the central nervous system and Alzheimer s disease. J Neurovirol 5 32-41... 

In thermolysis and photolysis of 3-chloro-3-benzyldiazirines 23, carbenes 24 are formed as indicated by reaction 2. In both electron-rich (tetramethylethylene) and electron-poor (diethyl fumarate) alkenes (as solvents), cyclopropanes (and chlorostyrenes) are obtained59. The probable reaction pathway is the multi-step model shown in Scheme 9. 

Multi-step models of biological sulfate and sulfite reduction. . . 329... 

As previously discussed, Harrison and Thode (1958) invoked a two-step model to account for the range of isotopic fractionation encountered during sulfate reduction by D. desulfuricans. Rees (1973) developed a steady-state multi-step model for isotope fractionation during bacterial reduction. His approach differed from previous attempts in that he included the possibility of zero-order kinetics for describing the uptake of sulfate. His reaction scheme is basically of the form... 

Therefore we attempted to simulate advanced pyrolysis using a multi-step model (MSM). This model was developed using TGA- and DSC-derived kinetic coefficients, determined for chemically and thermally treated oil shale samples by modelling particular reaction steps. The MSM is based on the reaction scheme shown in Fig. 4-116 which displays a series of parallel and consecutive first order reactions. K and B denote the kerogen and bitumen originally present in the oil shale B, B, and to /Jj are non-volatilized intermediates and products (solids and liquids) to are volatilized products (gases and vapors) and/j to/jg are the stoichiometric coefficients that fulfil the condition ... 

These differences in pyrolysis behavior of the oil shales can be explained by structural differences in the corresponding kerogen types. The kerogens of oil shales Aleksinac, Estonia, and Korea are associated with type I, which is of predominantly paraffinic nature. Oil shale Knjazevac is associated with kerogen type HI, which is of predominantly aromatic nature. Thus the multi-step model appears to be suitable for simulating the pyrolysis of oil shales with kerogen type I, but cannot be properly adjusted for the other kerogen types. 

Modeling of mass transfer has been carried out in the field of chemical engineering and environmental engineering (e.g., Takamatsu et al. 1977). Models commonly used are (1) batch model, (2) perfectly mixing model (Fig. 3.7), (3) piston flow model (Fig. 3.8), and (4) tank model (multi-step model). 

If, for example, the route from parent carcinogen to the actual biologically-active metabolite is considered as a multi-step pathway, the terms that appear in the model equation can be thought of as representing the rate-determining steps. 

Adsorption and Film Formation. Inhibition of HC1 corrosion by organic compounds is a complicated multi-step process. Nevertheless, the effect of an inhibitor on corrosion of a metal is often treated mathematically with an equilibrium adsorption model for displacement of water (19,20) ... 

Figure 7.22 Cytochrome P450 model compound reaction profile consistent with a multi-step catalytic mechanism. (Adapted with permission from Schemes 7 and 8 of reference 68. Copyright 1997, Society of Biological Inorganic Chemistry.)...

The suitability of this model, at least for a non-too-wide conversion range, has been confirmed by several authors. However, a correct description of the maleic anhydride production obviously demands splitting of kB into individual rate coefficients for maleic anhydride formation and for combustion, while in fact a separate equation should be added for maleic anhydride combustion. Such multi-step redox models have not been reported in the literature. Sets of first-order rate equations, however, are widely used,... 

It is not irrelevant whether the charge transfer proceeds via the adsorbed or via the non-adsorbed species, because a model is needed to give eqn. (166g) an explicit formulation. As we have seen in Sect. 4, a non-linear multi-step mechanism may lead eventually to rather complex expressions of v — f(E, cD, cR ). If the reaction is supposed to proceed via adsorbed O and R, similar or even heavier complexity can be expected, depending on the nature of the isotherms. In that case, the formulation in terms of surface excesses, i.e. v = f(E, rD, PR ) may be advantageous. 

The details of protonation of several alkyl-substituted phenanthrenes by superacids have been reported.73 The observed mono- and di-cations are usually in agreement with those predicted by AMI MO calculations. Molecular modelling studies have suggested a multi-step pathway for the sulfonation of toluene widi sulfur trioxide.74 Intermediate 71-complcx. Wheland intermediate and pyrosulfonate species (34) are suggested, the product (p-toluenesulfonic acid) arising from an exothermic reaction between toluene and the acid (35) fonned by a facile prototropic rearrangement of (34). The sulfur trioxide monosulfonation of isopyrene and some derivatives leads usually to sulfonated... 

Tufano, V., A multi-step kinetic model for phenol oxidation in high pressure water, Chem. Eng. Technol., 16, 186-190. 

Risk assessment (i.e., calculation of risk) is a complex, multi-step process, and the results usually have a significant degree of uncertainty because of limitations in data and in the models of environmental and biological systems. In addition, for purposes of generally classifying waste, risk assessment must be generic i.e., it is not intended to apply to disposition of a specific waste in a specific manner at a specific site. 

It must be admitted that 0-0 and a-n switch processes are of limited stereochemical interest. Given the prototypes (92) or (97), the reactions must be syw-stereospecific any other stereochemical result would in fact be used as a criterion of a multi-step mechanism. This is also true of the mixed types, (101)-(104). But these reactions are exceedingly useful as models for orbital-based calculations or estimates of free energies of activation, with the use of extended HMO theory. The four- or six-center process (92)-(104) does not appear to be more complex than the Diels-Alder reaction, which has been investigated theoretically (Herndon and Hall, 1967). 

Recently NOESY MAS was used to study molecular motions in technically relevant materials such as rubbers [46, 47]. For the evaluation of these parameters, it is necessary to understand the cross-relaxation process in the presence of anisotropic motions and under sample spinning. Such a treatment is provided in [47] and the cross-relaxation rates were found to weakly depend on fast motions in the Larmor-frequency range and strongly on slow motions of the order of the spinning frequency vR. Explicit expressions for the vR dependent cross-relaxation rates were derived for different motional models. Examples explicitly discussed were based on a heterogeneous distribution of correlation times [1,8,48] or on a multi-step process in the most simple case assuming a bimodal distribution of correlation times [49-51]. 

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