Stepwise association model

Ghosh and Mukerjee [230] have described the self-association of the cationic dye, methylene blue, using a stepwise association model in which all the equilibrium constants are assumed to be of equal value... 

The light-scattering plots of both of these drugs indicate a non-micellar association pattern. Analysis of the data reveals that the association can best be described by a stepwise association model similar to that of pavatrine in high electrolyte concentration with association constants increasing with aggregation number according to the relationship, K = K n — l)/n,... 

Many studies of the surface properties of hormones have appeared in the literature. These studies have been concerned with interaction of hormones with monomolecular films [124-128] and the properties of monolayers of the hormones themselves [129]. Very few studies of the association of hormones have, however, been reported, the notable exception being that of insulin. Lightscattering investigations by Doty and co-workers [130] showed that below pH 2.2 the association could be described in terms of a monomer-dimer equilibrium. At higher pH, tetramers and probably trimers exist in solution. The data were fitted to a stepwise association model [131] using an analytical technique developed by Steiner [132]. 

The theoretical aspects of the kinetics of two-component micelles based on the stepwise association model were later extended to high surfactant concentrations. - This model applies to binary mixtures of nonionic surfactants as well as to one ionic surfactant, the surfactant ion and its counterion then being the two components of the system. 

It is interesting to note that the stepwise association model or stepwise aggregation model for micelle formation, as shown in Scheme 3.2, leads to the expression = (C, - [S])/(C , - [S]), where represents the number-average micellar aggregation number, C, is the total analytical concentration of surfactant (i.e., C, = [Surflj), C i is the total concentration of osmotically active particles (i.e., monomers + micelles or CMC + [D ]), and [S] (= CMC) is the monomer concentration." Although the stepwise association model is not exactly similar to the phase-separation model, the basis of preequilibrium kinetic model of micelle (Scheme 3.1), the expression = (Ct - [S])/(Cni - [S]) is exactly similar to assumption (5) in the PEK model. The mass action model or multiequilibrium model. Equation 3.1, which is equivalent to Equation 1.20 in Chapter 1... 

The Noncooperative Model, (a = 7 = 1, c= 0). This model applies to assembhes that involve only intemiolecular interactions without any allosteric effect. The occupation of the various binding sites of the receptor is dictated only by statistics. This model is the reference for spotting the presence of allosteric effects in real systems. It also applies to the formation of a given ohgomer in isodesmic polymerizations. This process is exemplified by a monomer A—B that undergoes a reversible polymerization in which all of the stepwise association constants are identical and equal to K. The formation constant of each oligomer (A—B), is given by Eq. [51] in which a = y = 1, c = 0, = 1 and f) = 1 -... 

The Allosteric Cooperative Model, a 1, y = l, c = 0). This model is typical of cooperative systems involving only intermolecular interactions such as haemoglobin. It also apphes to the reversible formation of linear oligomers under the condition of different stepwise association constants, as in the case of nucleation-growth polymerizations. " ... 

B3LYP/6-31 l-i-i-G(d,p) calculations, AIM calculations, and NBO analyses in the gas phase and using the CPCM method in water, THF, and diethyl ether have shown that the P-N hydrolysis of tepa and thiotepa in the gas phase and in water, THF, and diethyl ether occurs by a an acid-catalysed concerted backside attack rather than a stepwise associative, a stepwise dissociative, or a concerted frontside attack. B3LYP/6-31-i-i-G(d,p) level calculations of the 5 reactions between diethyl p-nitrophenylphosphate and methoxide ion and methyl thiolate ion in the gas phase and using the PCM model for the reaction in water have shown that with one exception, the 5[ 2 P reaction displacing thep-nitrophenoxide ion is faster than the 5N2-type reaction at the ethyl carbon in both the gas phase and in solution. The reaction at phosphorus... 

Micellar colloids represent dynamic association-dissociation equilibria. However, the theoretical treatment of micelles depends on whether the micelle is regarded as a chemical species or as a separate phase. The mass action model which has been used ever since the discovery of micelles, takes the former point of view," " whereas the phase separation model regards micelles as a separate phase. To apply the mass action model strictly, one must know every association constant over the whole stepwise association from monomer to micelle, a requirement almost impossible to meet experimentally. Therefore, this model has the disadvantage that either monodispersity of the micelle aggregation number must be employed or numerical values of each association constant have to be assumed. " The phase separation model, on the other hand, is based on the assumption that the activity " of a surfactant molecule and/or the surface tension of a surfactant solution remain constant above the CMC. In... 

The currently accepted explanation for the effect of surfactant concentta-tion on micellar stability was proposed by Aniansson and coworkers in the 1970s and expanded by Kahlweit and coworkers in the early 1980s [13-16], Annianson s model [13-15] nicely predicts micelle kinetics at a low surfactant concentration based on stepwise association of surfactant monomers. Hence, the major parameters in this model are the critical micelle concentration (cmc) and the total concentration of the surfactant in solution. 

The formation of the PIC described above is based on the sequential addition of purified components in in vitro experiments. An essential feature of this model is that the assembly takes place on the DNA template. Accordingly, transcription activators, which have autonomous DNA binding and activation domains (see Chapter 39), are thought to function by stimulating either PIC formation or PIC function. The TAF coactivators are viewed as bridging factors that communicate between the upstream activators, the proteins associated with pol II, or the many other components of TFIID. This view, which assumes that there is stepwise assembly of the PIC—promoted by various interactions between activators, coactivators, and PIC components— is illustrated in panel A of Figure 37-10. This model was supported by observations that many of these proteins could indeed bind to one another in vitro. 

In order to show the inflation of q2, which results from the use of improper statistical methods, we have performed comparative studies involving stepwise regression and RR [68,70]. In these studies, comparative models were developed for the prediction of rat fat air and human blood air partitioning of chemicals. For the former, proper statistical methods yielded a model with a q2 value of 0.841, while the stepwise approach was associated with an inflated q2 of 0.934. Likewise, the rat fat air model derived using proper methods had a q2 value of 0.854, while the stepwise approach yielded a model with an inflated q2 of 0.955. 

Computer packages such as SAS can fit these models, provide estimates of the values of the b coefficients together with standard errors, and give p-values associated with the hypothesis tests of interest. These hypotheses will be exactly as Hqj, Hq2 and Hq3 in Section 6.3. Methods of stepwise regression are also available for the identification of a subset of the baseline variables/factors that are predictive of outcome. 

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