Katz model

In the del Castillo and Katz model it is important to notice that the fraction of receptors occupied is the sum of both active (AR ) and occupied, but inactive (AR) receptors ... 

We assume here that the del Castillo-Katz model applies. Using the Gaddum equation, based on the simpler scheme explored by Hill and by Clark, leads to exactly the same conclusion, as the reader can easily show by following the same steps but starting with Eq. (1.48). 

Analysis based on the del Castillo-Katz model of receptor activation (see Sections 1.2.3 and 1.4.4) The fraction of receptors in the active state is defined by ... 

This linear current-voltage relationship can be compared to the Goldman-Hodgkin-Katz model of Equation (3.64), which in terms of current density is... 

J.R. Norris, H. Scheer, and J.J. Katz, Models for antenna and reaction center chlorophylls,... 

Katz, R.J. Role of serotonergic mechanisms in animal models of predation. Prog Neuropsychopharmacol 4 219-231, 1980. 

Miller CW, Benson LV (1983) Simulation of solute transport in a chemically reactive heterogeneous system model development and application. Water Resourc Res 19 381-391 Moise X, Starinsky A, Katz A, Kolodny Y (2000) Ra isotopes and Rn in brines and ground waters of the Jordan-Dead Sea Rift Valley enrichment, retardation, and mixing. Geochim Cosmochim Acta 64 2371-2388... 

The pore geometry described in the above section plays a dominant role in the fluid transport through the media. For example, Katz and Thompson [64] reported a strong correlation between permeability and the size of the pore throat determined from Hg intrusion experiments. This is often understood in terms of a capillary model for porous media in which the main contribution to the single phase flow is the smallest restriction in the pore network, i.e., the pore throat. On the other hand, understanding multiphase flow in porous media requires a more complete picture of the pore network, including pore body and pore throat. For example, in a capillary model, complete displacement of both phases can be achieved. However, in real porous media, one finds that displacement of one or both phases can be hindered, giving rise to the concept of residue saturation. In the production of crude oil, this often dictates the fraction of oil that will not flow. 

Just a year after Stephenson s classical paper of 1956, J. del Castillo and B. Katz published an electrophysiological study of the interactions that occurred when pairs of agonists with related structures were applied simultaneously to the nicotinic receptors at the endplate region of skeletal muscle. Their findings could be best explained in terms of a model for receptor activation that has already been briefly introduced in Section 1.2.3 (see particularly Eq. (1.7)). In this scheme, the occupied receptor can isomerize between an active and an inactive state. This is very different from the classical model of Hill, Clark, and Gaddum in which no clear distinction was made between the occupation and activation of a receptor by an agonist. 

The next question to consider is the interpretation of efficacy (both in the particular sense introduced by Stephenson and in more general terms) in the context of the model proposed by del Castillo and Katz. 

The term state rather than condition is often used in this context. However, the latter seems preferable in an introductory account. This is because the del Castillo-Katz mechanism is often described as a two-state model of receptor action, meaning here that the occupied receptor exists in two distinct (albeit interconvertible) forms, AR and AR, whereas three conditions of the receptor (R, AR, and AR ) have to be identified when applying the law of mass action to the binding of the ligand, A. 

L Herbette, AM Katz, JM Sturtevant. Comparisons of the interaction of propranolol and timolol with model biological membrane systems. Molec Pharmacol 24 259-269, 1983. 

Weber W, McGinley P, Katz L (1992) A distributed reactivity model for sorption by soils and sediments. 1. Conceptual basis and equilibrium assessments. Environ Sci Technol 26 1955-1962... 

The primary donor in Photosystem I P700 is thought to be a special pair of chlorophyll a molecules. Katz and Hindman (18) have reviewed a number of systems designed to mimic the properties of P700 ranging from chlorophyll a in certain solvents under special conditions where dimers form spontaneously (19) to covalently linked chlorophylls (20). Using these models it has been possible to mimic many of the optical, EPR and redox properties of the in vivo P700 entity. 

Cram and co-workers have been successful in modifying certain of their cavitands such that reactions with a bound substrate are promoted. Such systems provide a first step towards the synthesis of rudimentary enzymes (Cram, Katz, Dicker, 1984). One example of this type, involving a binding step followed by a fast acylation step, is illustrated by Figure 5.1. This sequence resembles part of the mechanism used by chymo-trypsin to cleave a peptide bond. Thus, the enzymic process entails several stages but, like the model system, begins with a binding step followed by a crucial transacylation step. 

Falkowski PG, Katz ME, Knoll AH, Quigg A, Raven JA, Schofield O, Taylor FJR (2004) The evolution of modem eukaryotic phytoplankton. Science 305 354-360 Flynn KJ (2005) Castles built on sand dysfunctionality in plankton models and the inadequacy of dialogue between biologists and modellers. J Plankton Res 27 205-210 Fontana A (2007) Chemistry of oxylipin pathways in marine diatoms. Pure Appl Chem 79 481 490... 

Katz JL, Higgins ST (2003) The validity of the reinstatement model of craving and relapse to drug use. Psychopharmacology 168 21-30... 

Katz, B. A., and H. Leith. Seasonality of decomposers, pp. 163-184. In H. Leith, Ed. Phenology and Seasonality Modeling (Ecological Studies Analysis and Synthesis, Vol. 8). New Yoilc Springer-Verlag, 1974. 

Hoffman, B.T., Kopajtic, T., Katz, J.L., and Newman, A.H. 2D QSAR Modeling and preliminary database searching for dopamine transporter inhibitors using genetic algorithm variable selection of Molconn Z descriptors./. Med. Chem. 

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