Definition of kinetic constants in terms

Definition of kinetic constants in terms of rate constants... 

If the interconversion of central complexes is taken into account (rate constants kg and fcio are present), the definition of kinetic constants in terms of rate constants becomes more complex (Plapp, 1973) ... 

Definition of Kinetic Constants in Terms of Rate Constants Ordered Ter Bi mechanism... 

Definition of Rate Constants in Terms of Kinetic Constants... 

Reaction kinetics represented by the general form of Equation 1 have been employed in a number of quantitative chemical models of natural systems. Under ideal conditions, the four parameters, total mass transfer, kinetic rate constants, time, and the reactive surface area can be determined independently, permitting the unique definition of the model. In most cases, at least one of the variables, most often surface area, is treated as a dependent term. This nonuniqueness arises when the reactive surface area of a natural system cannot be estimated, or because such estimates made either from geometric or BET measurements do not produce reasonable fits to the other parameters. Most often the calculated total mass transfer significantly exceeds the observed transfer based on measured aqueous concentrations. 

Various experimental observations, obtained by studies of diverse nature, indirectly suggest that micellar pseudophase is not homogeneous in terms of micropolarity, water concentration, dielectric constant, and ionic strength (for ionic micelles). " This fact has not been considered in the classical pseudophase kinetic model hrst suggested by Berezin et al. " and Martinek et al. It is therefore logical for Davies et al. to suggest that the micellar pseudophase should be divided up into an arbitrary number of pseudophases, each with a different mean partition coefficient for the reactant or reactants and each with a different mean rate constant. This generalization of the classical (Berezin s) pseudophase model is referred to as the multiple micellar pseudophase (MMPP) model and leads to a kinetic equation similar to Equation 3.61 or Equation 3.11 with modified definitions of kinetic parameters such as kM (= (kMW]y,)KRKs) = E(kM iA Mr)KR iKs i with i = 1, 2, 3,. .., q Kr = S Kr, with i = 1, 2, 3,. .., q and Kg = X K i with i = 1,2, 3,..., q, where q represents an arbitrary number of micelle pseudophases. 

In this chapter, we study networks of linear reactions. For any ordering of reaction rate constants we look for the dominant kinetic system. The dominant system is, by definition, the system that gives us the main asymptotic terms of the stationary state and relaxation in the limit for well-separated rate constants. In this limit any two constants are connected by the relation or... 

Scheme 6.1 The multiple mass transport equations used to describe microdialysis sampling. D is the diffusion coefficient through the dialysate, Dd, membrane, Dm, and sample, Ds. L is the membrane length. T (cm) is a composite function A ep(r), km(r), and kc(r) are kinetic rate constants as a function of radial position (/) from the microdialysis probe. Additional term definitions can be found in Ref. 42.

It should be noted that the mechanism depicted in Scheme 1 is the simplest that is consistent with mechanism-based inhibition. The mechanism for a given inhibitor and enzyme may be considerably more complex due to (a) multiple intermediates [e.g., MIC formation often involves four or more intermediates (29)], (b) detectable metabolite that may be produced from more than one intermediate, and (c) the fact that enzyme-inhibitor complex may produce a metabolite that is mechanistically unrelated to the inactivation pathway. Events such as these will necessitate alternate definitions for Z inact, Kh and r in terms of the microrate constants of the appropriate model. The hyperbolic relationship between rate of inactivation and inhibitor concentration will, however, remain, unless nonhyperbolic kinetics characterize this interaction. Silverman discussed this possibility from the perspective of an allosteric interaction between inhibitor and enzyme (5). Nonhyperbolic kinetics has been observed for the interaction of several drugs with members of the CYPs (30). 

For the experimental determination of the 0, it is necessary to quantify the light output of the direct chemiluminescent process. The experimental definition of the direct chemiluminescence quantum yield is given in Eq. 36, that is, the initial rate of photon production (/q ) per initial rate of dioxetane decomposition k )[D]o). Alternatively, the total or integrated light intensity per total dioxetane decomposed can be used. The /t )[Z)]o term is readily assessed by following the kinetics of the chemiluminescence decay, which is usually first order. Thus, from a semilogarithmic plot of the emission intensity vs. time, the dioxetane decomposition rate constant kjj is obtained and the initial dioxetane concentration [Z)]o is known,especially if the dioxetanes have been isolated and purified. In those cases in which the dioxetanes are too labile for isolation and purification, [/)]o is determined by quantitative spectroscopic measurements or iodometric titration. 

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