Independent site model

A) or adding H2PO4" into host 4 solution at 0.69 mM (panel B). The lines represent the best fit to a two-independent-site-model. 

The Scatchard plots for the binding of tilorone to calf thymus DNA (Fig. 4a), Mic. lys. DNA (Fig. 4b), poly (dA-dT) -poly (dA-dT) (Fig. 4c), and poly (dG-dC) poly (dG-dC) (Fig. 4d) are shown in Fig. 4. As follows from the Scatchard plots for natural DNAs, (Fig. 4a and 4b), the independent site model does not fit for DNA-ligand interaction however, we employed the binding parameters of this model to analyse the Scatchard plots. The binding parameters, Kapp and Bapp derived from the Scatchard plots (Fig. 4a-d) are presented in Table 1. This table summarizes the results of several measurements. 

The Independent Site Model Describes the Principle of Adsorption Chromatography... 

From these data, make a Scatchard plot and evaluate the equilibrium constant, K, and total number of sites per DNA molecule. Is the identical and independent sites model for binding applicable ... 

The transmittance is a dimensionless function of energy, just like the transmission. By definition, for a single-site model it equals unity, and is independent of energy. Using our simple model, we shall now calculate it for arbitrarily long chains. 

Although reductive dechlorination is modelled either based on an empirical approach or a single site model, TCE dechlorination in the presence of cysteine apparently requires the use of a two-site model. The simulation as shown in Figure 3b indicates that quantitatively, the two-site model proposed here is sufficient for the interpretation of the experimental results. To enhance the predictive capability of the model, further research is needed to determine adsorption parameters independently. 

Wu and Gschwend (1986) reviewed and evaluated several kinetic models to investigate sorption kinetics of hydrophobic organic substances on sediments and soils. They evaluated a first-order model (one-box) where the reaction is evaluated with one rate coefficient (k) as well as a two-site model (two-box) whereby there are two classes of sorbing sites, two chemical reactions in series, or a sorbent with easily accessible sites and difficultly accessible sites. Unfortunately, the latter model has three independent fitting parameters kx, the exchange rate from the solution to the first (accessible sites) box k2, the exchange rate from the first box to the... 

For consistency with the experimental data, an equivalent site model requires that the absorption characteristics of each of the two type 3 copper ions be independent of their state of coupling. For a nonequivalent site model one has to assume that the absorption at 330 nm is entirely caused by the Cu(II) ion with the higher redox potential, so that the observed equilibrium can be assigned to the oxidation-reduction of this site. In both cases we take into account that the addition of four oxidizing equivalents restore the original absorption of the enzyme, and we assume... 

With modelling attempts of specific adsorption it is important to distinguish between s.a. ions that adsorb at the same adsorption sites as the protons, and s.a. ions that adsorb on independent sites. The first type of specific adsorption has been assumed in sections 4.5. to 4.7. Spectroscopic studies on metal ion adsorption [83-85] support this view. The description presented in sections 4.5. to 4.7. is adequate for monovalent ions. However, modelling of complexation of multivalent ions with surface groups is faced with several complications. 

Using independently measured parameters for Cr, Selim and Amacher (1988) showed fair agreement between the second-order, two-site model and experimental Cr BTC (Fig. 10-6). Adsorption isotherms obtained from batch studies were modeled with the two-site Langmuir expression to provide model parameters,/(fraction of type-1 sites) and Sj (maximum number of sites). 

Although the first-order model has met with widespread success, there are conditions under which this model may fail. For example, a more continuous distribution, rather than the extreme duality in reaction rates assumed by the bicontinuum models, may be a more accurate representation of true conditions. Accordingly, the separation of the sorbent into two parallel domains differing in reaction time may be extended to accommodate any number of domains, each with its own unique rate constant. For example, Boesten et al. (1989) have presented a three-site model. The limiting case would be a continuous distribution of domains and associated rate constants. A model describing this case has been developed by Villermaux (1974), where the site population is represented by the transfer-time distribution (i.e., the rate-constant distribution). However, the number of parameters associated with such a model greatly exceeds our present capability to independently evaluate the processes represented by those parameters. Such models would, therefore, be constrained to operation in a calibration mode. 

The distributed multipole analysis method of Stone and co-workers is similar in concept but is based on nonredundant spherical harmonic representation of the multipoles (recall that whereas there are six second moments, only five are independent). He initially places numerous site multipoles at centers of orbital overlap. The individual monopoles are spread out along the molecular axis, and are thought to represent the distribution of charge the site dipoles are also spread out along the bond axis. This very detailed description is simplified into a three-site model, which includes a site in the F—H bond. However, the multipole expansion does not converge well, especially for the bond center site. 

As mentioned before, essentially two molecular models have been put forward for explaining the water binding processes in hair a, water molecules bind to discrete, independent sites attached to the polypeptide chains or b, water is absorbed by a swelling process of the polymeric network as described by Flory s polymer theories (8 ). 

Bakaev et al. [77] employed a similar approach to study CO2 adsorption on glass surfaces. Their results confirm that CO2 molecule is sensitive to the structure of the surface while Ar does not show this characteristic. In another paper Bakeva et al. [78] studied CO2 adsorption on glass fibers in a wide temperature range. Employing the classical volumetric technique they have determined the adsorption isotherms and also calculated the isosteric heats of adsorption. They have also analyzed their data in terms of the independent adsorption sites model [74,79,80]. The most important equation of this model is... 

On the other hand, the binding site model mentioned in the preceding section assumes that counterions of type i bind independently to single sites at the membrane surface with an intrinsic binding constant X,. Then, the... 

One obvious distinction between these two theoretical models is that the ion condensation theory gives a fractional neutralization (cation concentration in the condensation layer) which is independent of cation concentration in the bulk solution, while the binding site model does not explicitly predict such a result. 

Because the binding process for our systems cannot be described by the independent single-site model as discussed above, we further examined our data by the expressions derived on the basis of the nearest-neighboring interaction model. 

While thermodynamics provides a starting point, kinetics is essential for providing any corrosion model of practical utility. The term electrode kinetics is often used as, in the electrochemical paradigm, the oxidation and reduction occur at independent sites, which can be considered as separate electrodes marking a solid/electrolyte interface at which the half-ceU reactions take place. In the case of chemical corrosion, these half-cell reactions can take place at the same location, in which case there is no external current flow between the half-reaction centers, but instead, direct charge transfer between the reactants via electronic contact at the same metal site. 

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