Determination of Kinetic Parameters Using Data Linearization

Determination of Kinetic Parameters Using Data Linearization... 

Experimental determination of kinetic parameters for inhibition mechanisms follows the same pattern as in simple Michaelis-Menten kinetics (section 3.2.2). Linearization methods are particularly useful to determine the mechanism of inhibition as a previous step to the quantification of the kinetic parameters. Experimental design consists now in a matrix in which initial rate data are gathered at different substrate and inhibitor concentrations (s and i respectively) as depicted in Table 3.3. Inhibitor is here considered in general terms as any substance exerting enzyme inhibition, be it a product of reaction, as previously considered, or catalytically inert. Of course inhibition by products and/or substrate is more technologically relevant, since catalytically inert inhibitors can be simply kept out from the reaction medium. 

Kinetic analysis usually employs concentration as the independent variable in equations that express the relationships between the parameter being measured and initial concentrations of the components. Such is the case with simultaneous determinations based on the use of the classical least-squares method but not for nonlinear multicomponent analyses. However, the problem is simplified if the measured parameter is used as the independent variable also, this method resolves for the concentration of the components of interest being measured as a function of a measurable quantity. This model, which can be used to fit data that are far from linear, has been used for the resolution of mixtures of protocatechuic... 

We again consider a network crosslinked by actin binding protein. The number of crosslinks that are formed. A, is given by Equation 10, and a plot of G vs (the total amount of added ABP) is shown, schematically, in Figure 3. Both the slope and the intercept provide information about the kinetic parameters of network formation. Elasticity determinations clearly can be used to assess the amount of crosslinking protein in an assembly if all other conditions are kept constant, G varies linearly with consequently, after appropriate calibration (in principle with only two data points), elasticity measurements could be used for quantitative assessment of the efficacy of biochemical purification procedures. Parenthetically, we note that if conditions can be arranged such that K S 1, gives a direct measure of the number of nuclei iIq. 

To effectively determine the start-of-cycle reforming kinetics, a set of experimental isothermal data which covers a wide range of feed compositions and process conditions is needed. From these data, selectivity kinetics can be determined from Eq. (12). With the selectivity kinetics known, Eqs. (17) and (18a)-(18c) are used to determine the activity parameters. It is important to emphasize that the original definition of pseudomonomolecular kinetics allowed the transformation of a highly nonlinear problem [Eq. (5)] into two linear problems [Eqs. (12) and (15)]. Not only are the linear problems easier to solve, the results are more accurate since confounding between kinetic parameters is reduced. 

In Figure 2, a double-reciprocal plot is shown Figure 1 is a nonlinear plot of v as a function of [5]. It can be seen how the least accurately measured data at low [5] make the determination of the slope in the double-reciprocal plot difficult. The kinetic parameters obtained in this example by making linear regression on the double-reciprocal data are vm = 1.15 and Km = 0.25 (arbitrary units). The same kinetic parameters obtained by software using nonlinear regression are umax = 1.00 and Km = 0.20 (arbitrary units). 

For the determination of the initial rate constants and the kinetic parameters, the experimental data can be fitted using non-linear regression programs such as Origin 7.5SR6 (OriginLab Corporation, Northampton, Massachusetts). 

Toxicokinetics is a term used for describing kinetic studies conducted in conjunction with toxicology evaluations (Di Carlo 1982) that deal with absorption, distribution, and elimination processes of chemicals present at concentrations that produce toxic effects. By monitoring the blood concentrations of the chemical and/or metabolites over time after administration by different routes, the test chemical s bioavailability and kinetic characteristics can be readily obtained. The data also permit the determination of the so-called linear dose range based on area under the plasma versus time curve and clearance or other related toxicokinetic parameters, as well as the prediction of possible bioaccumulation after multiple doses. Changes in kinetic parameters after multiple exposures... 

FIGURE 13.2 Biochemical plots for the enz5me kinetic characterizations of biotransformation, (a) Direct concentration-rate or Michaelis-Menten plot (b), Eadie-Hofstee plot (c), double-reciprocal or Lineweaver-Burk plot. The Michaelis-Menten plot (a), typically exhibiting hyperbolic saturation, is fundamental to the demonstration of the effects of substrate concentration on the rates of metabolism, or metabolite formation. Here, the rates at 1 mM were excluded for the parameter estimation because of the potential for substrate inhibition. Eadie-Hofstee (b) and Lineweaver-Burk (c) plots are frequently used to analyze kinetic data. Eadie-Hofstee plots are preferred for determining the apparent values of and Umax- The data points in Lineweaver-Burk plots tend to be unevenly distributed and thus potentially lead to unreliable reciprocals of lower metabolic rates (1 /V) these lower rates, however, dictate the linear regression curves. In contrast, the data points in Eadie-Hofstee plot are usually homogeneously distributed, and thus tend to be more accurate. 

Eq. 6.2.6 was solved analytically to obtain the operation curve of the reactor (X vs t). Lumped kinetic parameters were determined by non-linear regression of experimental data using the numerical method of Newton-Raphson with first-order Taylor series expansion. Lumped parameters were smooth functions of temperature all parameters were adequately fitted to second order polynomials except for D that required a fourth order polynomial. The model can be used for reactor temperature optimization and can be extended to prolonged sequential batch operation provided that a sound model for enzyme inactivation is validated (Illanes et al. 2005b). 

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