Sigmoid kinetics

The feedback mechanisms are mediated via mineralocorticoid and glucocorticoid receptors (MR, GR), which means overlapping of nonlinear positive and negative feedback loops with nonlinear dependencies on cortisol (Michaelis-Menten kinetics, sigmoidal activation curves of corticoid receptors). 

Compared to the hydrolysis reactions of NHS ester model compoimds in solution, [ 136] we observe a decrease in the apparent rate constants by 2-3 orders of magnitude for NHS - C2 and NHS - C10. More strikingly, the reaction of the NHS esters in the highly ordered SAM NHS - Cl5 shows a different overall kinetic profile. Instead of the expected pseudo first order (exponential) kinetics, sigmoid kinetics with a pronoimced induction period are found. 

A kinetic sigmoidal wave (curve 3 in Fig. 12B) indicates low values of 2 at high values of electron transfer parameter A). The current tends towards the limiting value given by the equation... 

Keywords— Species specific nanobiosensor, hybrid nanobioprobe, hybridization kinetics, sigmoidal relationship, synthetic oligo-targets. 

For those pesticides which are utilized as microbial growth substrates, sigmoidal rates of biodegradation are frequentiy observed (see Fig. 2). Sigmoidal data are more difficult to summarize than exponential (first-order) data because of their inherent nonlinearity. Sigmoidal rates of pesticide metabohsm can be described using microbial growth kinetics (Monod) however, four kinetics constants are required. Consequentiy, it is more difficult to predict the persistence of these pesticides in the environment. 

The kinetic analysis of the sigmoid pH-rate profile will yield numerical estimates of the pH-independent parameters K, k, and k". With these estimates the apparent constant k is calculated using the theoretical equation over the pH range that was explored experimentally. Quantitative agreement between the calculated line and the experimental points indicates that the model is a good one. A further easy, and very pertinent, test is a comparison of the kinetically determined value with the value obtained by conventional methods under the same conditions. 

FIGURE 15.8 Sigmoid versus [S] plot. The dotted line represents the hyperbolic plot characteristic of normal Michaelis-Men ten-type enzyme kinetics. 

There have been few satisfactory demonstrations that decompositions of hydrides, carbides and nitrides proceed by interface reactions, i.e. either nucleation and growth or contracting volume mechanisms. Kinetic studies have not usually been supplemented by microscopic observations and this approach is not easily applied to carbides, where the product is not volatile. The existence of a sigmoid a—time relation is not, by itself, a proof of the occurrence of a nucleation and growth process since an initial slow, or very slow, process may represent the generation of an active surface, e.g. poison removal, or the production of an equilibrium concentration of adsorbed intermediate. The reactions included below are, therefore, tentative classifications based on kinetic indications of interface-type processes, though in most instances this mechanistic interpretation would benefit from more direct experimental support. 

It is appropriate to start with BaN6 since this compound has been studied particularly intensively and has been regarded as a model in the development of the theory of kinetics of decompositions of solids. The sigmoid a—time curves for BaN6 pyrolyses, Fig. 15, are typical examples of solid state autocatalytic behaviour. 

Isothermal a—time curves were sigmoid [1024] for the anhydrous Ca and Ba salts and also for Sr formate, providing that nucleation during dehydration was prevented by refluxing in 100% formic acid. From the observed obedience to the Avrami—Erofe ev equation [eqn. (6), n = 4], the values of E calculated were 199, 228 and 270 kJ mole"1 for the Ca, Sr and Ba salts, respectively. The value for calcium formate is in good agreement with that obtained [292] for the decomposition of this solid dispersed in a pressed KBr disc. Under the latter conditions, concentrations of both reactant (HCOJ) and product (CO3") were determined by infrared measurements and their variation followed first-order kinetics. 

The a—time curves for the vacuum decomposition at 593—693 K of lanthanum oxalate [1098] are sigmoid. Following a short induction period (E = 164 kJ mole-1), the inflexion point occurred at a 0.15 and the Prout—Tompkins equation [eqn. (9)] was applied (E = 133 kJ mole-1). Young [29] has suggested, however, that a more appropriate analysis is that exponential behaviour [eqn. (8)] is followed by obedience to the contracting volume equation [eqn. (7), n = 3]. Similar kinetic characteristics were found [1098] for several other lanthanide oxalates and the sequence of relative stabilities established was Gd > Sm > Nd > La > Pr > Ce. The behaviour of europium(III) oxalate [1100] is exceptional in that Eu3+ is readily reduced... 

An increase in co from 400 to 1600rpm tints results in a twofold increase of the signal. A deviation from linearity of a plot of z) vs. col/1 suggests some kinetic limitations. In addition, at veiy low rotation speeds (0-100 rpm), a slight upward bend is observed due to contribution by natural convection. The voltammetric wave has a sigmoidal shape for reversible systems it is identical to that common in DC polarography (described in Section 3-2), and independent of to. 

The kinetics of propagation of this cyclic barium salt is described in their following paper 83). The conversion curves are sigmoidal indicating, as anticipated, the accelera-... 

Figure 8-6. Representation of sigmoid substrate saturation kinetics.

As a result of fliese temperature - programmed runs, additiond experiments were conducted isothermally at temperatures between 723 - 873 K. Based on tbe second phase peak (peak 2), the conversion - time profiles at different temperatures exhibited a characteristic Sigmoid shape and may therefore be used to interpret the solid carburization kinetics. As detailed in Brown [5], the transient convrasion data may be d cribed by... 

The more usual pattern found experimentally is that shown by B, which is called a sigmoid curve. Here the graph is indicative of a slow initial rate of kill, followed by a faster, approximately linear rate of kill where there is some adherence to first-order reaction kinetics this is followed again by a slower rate of kill. This behaviour is compatible with the idea of a population of bacteria which contains a portion of susceptible members which die quite rapidly, an aliquot of average resistance, and a residue of more resistant members which die at a slower rate. When high concentrations of disinfectant are used, i.e. when the rate of death is rapid, a curve ofthe type shown by C is obtained here the bacteria are dying more quickly than predicted by first-order kinetics and the rate constant diminishes in value continuously during the disinfection process. 

A, obtained if the disinfection process obeyed the first-order kinetic law. B, sigmoid curve. This shows a slow initial rate of kill, a steady rate and finally a slower rate of kill. This is the form of curve most usually encountered. C, obtained if bacteria are dying more quickly than first-order kinetics would predict. The constant, K, diminishes in value continuously during the process. 

The permanganate oxidation of oxalic acid has been studied exhaustively and has been reviewed by Ladbury and Cullis . It is characterised by an induction period and a sigmoid dependence of rate upon time. Addition of manganous ions eliminates the induction period and produces first-order decay kinetics . Addition of fluoride ions, however, practically eliminates reaction . ... 

For the amino-borane dehydrocoupling using [Rh(l,5-cod)(p-Cl)]2 as starting catalyst, an induction period and a sigmoid-shaped kinetic curve (plot of substrate conversion versus time) were also observed, consistent with metal-particle formation. But, for Ph2PH BH3... 

The kinetics of soybean lipoxygenase-1 in a biphasic medium is different from the kinetics in an aqueous system [Fig. 5(a),(b)]. The kinetic curve in the two-phase system has a sigmoid shape, which is due to surface active properties of LA and HP [25]. When initial LA concentration is small in the organic phase (0-5 mM) its transfer is poor and bioconversion in the aqueous phase is slow. 

Furthermore, in the system with coupled lipase and lipoxygenase, the production rate of HP is governed by the first enzymatic reaction and mass transfer. When TL,- is small (0 to 1 mM equiv. 3 mM LA), the kinetic curve has a sigmoid shape due to surface active properties of LA and HP [25]. Hydrolysis of TL and the increase of LA favor the transfer of LA. Such a transfer allows the lipoxygenase reaction to progress. Since lipox-ygenation consumes LA and produces HP, catalysis and transfer demonstrates a reciprocal influence. 

Hence the picture of the cathodic and anodic waves obtainable for a completely reversible redox couple by means of the RDE corresponds fully with that in Fig. 3.9 the value of i, i.e., the height of the sigmoidal waves, is linearly proportional to to1/2 and to C (see eqn. 3.89 and the Levich constant). If for a well chosen combination of C and E a plot of i against co1/2 deviates from a straight line passing through the origin, then in the kinetics of the electrode reaction we have to deal only with a rapid electron transfer (cf., Fig. 3.10) or even with a slow electron transfer (cf., Fig. 3.11), in which latter instance the transfer coefficient a plays an appreciable role (cf., eqns. 3.17 and 3.18). 

Cooperative enzymes show sigmoid or sigmoidal kinetics because the dependence of the initial velocity on the concentration of the substrate is not Michaelis-Menten-like but gives a sigmoid curve (Fig. 8-7). 

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