Sigmoidal type

Enzymatic reactions frequently undergo a phenomenon referred to as substrate inhibition. Here, the reaction rate reaches a maximum and subsequently falls as shown in Eigure 11-lb. Enzymatic reactions can also exhibit substrate activation as depicted by the sigmoidal type rate dependence in Eigure 11-lc. Biochemical reactions are limited by mass transfer where a substrate has to cross cell walls. Enzymatic reactions that depend on temperature are modeled with the Arrhenius equation. Most enzymes deactivate rapidly at temperatures of 50°C-100°C, and deactivation is an irreversible process. 

In this type, the response is quantal or all or none type. If dose-response curve is plotted, no significant response is observed till a certain steady or threshold level is attained. The dose with which it is obtained is called ceiling dose. Beyond this point, there is no further increase in the therapeutic effect which remains unchanged even after increasing the dose of the drug. This type of response gives a sigmoid type dose-response curve. 

The number of receptor sites and the position of the equilibrium (Eq. 1) as reflected in KT, will clearly influence the nature of the dose response, although the curve will always be of the familiar sigmoid type (Fig. 2.4). If the equilibrium lies far to the right (Eq. 1), the initial part of the curve may be short and steep. Thus, the shape of the dose-response curve depends on the type of toxic effect measured and the mechanism underlying it. For example, as already mentioned, cyanide binds very strongly to cytochrome a3 and curtails the function of the electron transport chain in the mitochondria and hence stops cellular respiration. As this is a function vital to the life of the cell, the dose-response curve for lethality is very steep for cyanide. The intensity of the response may also depend on the number of receptors available. In some cases, a proportion of receptors may have to be occupied before a response occurs. Thus, there is a threshold for toxicity. With carbon monoxide, for example, there are no toxic effects below a carboxyhemoglobin concentration of about 20%, although there may be... 

Equations (6.132) or (6.133) for the converted charge are valid for any electrochemical technique, i.e., the charge/potential response for a reversible process is universal. The Q-E curves given in these equations present a sigmoidal-type feature which allows us to obtain the QP value and, therefore, the total surface excess I, , at sufficiently negative potentials of the cathodic response. 

When the selectivity changes, that is, when ota changes with the composition, the ion-exchange isotherms show a sigmoid-type form (Figure 7.4c and e) [23],... 

The adsorption of nonionic cellulose derivatives (HPMC 2910, HEC, and HPC) and their stabilizing effect on suspensions of polystyrene latices and of the antirheumatismal ibuprofen have been examined by Law and Kayes [117, 118]. Adsorption isotherms (see Fig. 20 for HPMC and ibuprofen) are of a sigmoidal type rapid initial adsorption, then a plateau corresponding to monolayer adsorption and finally a further increase in adsorption. At the same time, a gradual reduction in the sedimentation volume (decreased flocculation) is observable, while the redispersibility tends to be optimum (minimum number of revolutions necessary) at values of HPMC corresponding to a monolayer surface coverage. 

The requirements to describe population outbreaks with a predator-prey model (15.5) are the following (i) sigmoidal (type-III) functional response ... 

The network consists of two input neurons for presentation of the two v-values as well as four output neurons, y, which represent the four classes (cf Figure 8.15). In addition, a hidden layer was added with up to 20 neurons and the intercepts of the surfaces are modeled by bias neurons to both the hidden and output layers. The transfer function in the neurons of the hidden layer was of sigmoid type, and aggregation of the neurons in the output layer was carried out by calculating the normalized exponentials (softmax criterion). 

The optimization procedure could have been further refined when computerized instruments are used. The sigmoid type current curves in the Isv technique would certainly give a better selectivity if the first derivative of the current would be used. 

The kinetic evolution is usually represented by a sigmoid-type curve. Such a typical curve is given in Figure 9 for the case of displacement reaction, Ni + CuO Cu -F NiO realized in planetary ball mill [58]. Author of this overview analyzed these experimental results by one of the most frequently used kinetic model applied to various solid-state reactions, namely Johnson-Mehl-Avrami equation ... 

Figure 5.13. Basic biokinetic models including simple hyperbolic saturation type (e.g., Monod with K ) and sigmoidal type (e.g., allosteric Hill with Kj ).

These sigmoid-type curves can be identified with thermal decomposition of a single solid in an autocatalytic-type reaction having an initial (a<0.2) induction period and an intermediate (0.2normal growth stage with the final (a>0.9) decay or deceleratory stage absent [8,9]. 

Since the diffusion layer is of constant thickness, the concentration gradient becomes steeper. Consequently, the electrolysis current increases with potential shifting in the negative direction. The maximum current is reached when the surface concentration approaches zero. This maximum current is called the diffusion-limited current It>. With appUed potential beyond this point, Csurf cannot become less than zero, the gradient does not increase, and consequently Id remains constant and independent of further potential change. These interrelations are typical for current-potential curves of the sigmoidal type (Fig. 2.26). 

Considering the CS2 example, several assays were made considering four different kernels linear, polynomial (with different degrees), radial basis functions (RBF) and a sigmoid type. The RMSEC and the RMSEP errors for calibration and validation were considered in order to select a model and a satisfactory trade-off searched for. As expected, some good fits yielded nonuseful predictions for the unknowns. 

By plotting M/M = f (F ) (Pignre 2), for Fickean sorption kinetics the slope of the linear portion of the obtained curve provides direct access to the diffusion coefficient. But no direct access to the diffusion coefficient is possible for sigmoid-type and two-steps sorption kinetics. The diffusion coefficient can be determined by fitting the experimental curves. 

For the amyl acetate/PP system considered here, we have found that the sorption kinetics is of sigmoidal-type. This indicates an asymptotic behavior of the sorption kinetics at the polymer surface. 

The block copolymers with cylindrical microdomains also show confined and breakout crystallization and the expected crystallization kinetics. There is, however, an intermediate region for this class of copolymer. In this region small-angle x-ray scattering patterns indicated that the crystallization was confined to the cylindrical domains, yet sigmoidal type kinetics resulted.(65) This intermediate rate region is defined approximately by 1.5 < (xM)c/(xM)odt- Here, so-called templated... 

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