Metabolite excretion rates equations

At this point, it would appear that one can account for most of the observed effects of temperature and dilution rate on the macro-coefficients by simply assuming temperature dependencies such as those shown in Figure 3 for the micro-coefficients in eqtiatlons (20) - (27). These equations with the parameter values specified in Figure 3 will now be used to analyze the thermal sensitivity of the net biomass production and metabolite excretion rates. 

The rates of biomass production and metabolite excretion can be shown to saturate In substrate concentration If Bg Is assumed to adjust much more slowly to changes In S than B does. So, on the time scale of changes In Bg, B 0, and from equation (8) ... 

The maximum-velocity coefficient for metabolite excretion as given by equation (17b) is identically equal to e. As a result, it should generally rise exponentially with temperature and be insensitive to dilution rate. Thus, the maximum-velocity coefficient for metabolite excretion in batch culture should also be identical to that seen in continuous culture. 

The rate Isotherms for metabolite excretion (as specified by equations (11b) and (17) and Figures 3 and 4) show the same three thermal sensitivity patterns as the net biomass production rate Isotherms. Thus, the rate of metabolite excretion may also have an optimum temperature that shifts to higher values as substrate concentration rises. 

Figure 9. Predicted influence of temperature on the rate of metabolite excretion with substrate concentration as a parameter. Solid lines, curves generated from Equations Ilb and 17 with the parameter values given in Figures 3 and 4. Dashed line, locus of thermal rate maxima (O).

Table II shows renal excretion data. Calculated values were obtained from Equations 38, 44, 47, and 52. Here, the rate constants of acetosulfamine and sulfadimethoxine are as well correlated as those of the other compounds for rats and rabbits. This could be expected since the kEx value is directly determined by the proportion of the integrated amount of non-metabolized drug in the total urinary excreted materials whereas the kAc value is derived by assuming that metabolites, other than N-4-acetyl derivatives, are negligible in the urine. For humans, the rate constant of sulfadimethoxine is well correlated while that of acetosulfamine is not. The latter may be excreted by a different mechanism as mentioned.

Determination of exposure and toxic effects of chemicals also requires knowledge of toxicokinetics. Toxicokinetics is the study of changes in the levels of toxic chemicals and their metabolites over time in various fluids, tissues, and excreta of the body, and determines mathematical relationships to explain these processes. These processes depend upon uptake rates and doses, metabolism, excretion, internal transport, and tissue distribution. Methods for determining these processes include studies with laboratory animals, volunteer human subjects, persons accidentally exposed to high doses of chemicals, and experiments with tissue or organs cultured in the laboratory. Computer simulations of such processes are often formulated using complex mathematical equations. 

Other metabolite production. The rate of production of aromatic coumpounds - higher alcohols, esters, ethers, acids - is assumed proportional to the rate of yeast growth. Some, like diketones, are reassimilated or chemically transformed after excretion, so that the following general equation was used ... 

Pharmacokinetics is the study of the dynamics of absorption, distribution, biotransformation, and excretion of a chemical from the body. These processes can be described by a set of differential equations which comprise the pharmacokinetic model of the chemical. The types of rate processes incorporated in the model describe the qualitative behavior of the chemical and its metabolites, and quantitation of the rate processes (i.e., numerical values of the pharmacokinetic parameters) provides the means of predicting the concentration of the chemical as a function of time following single or repeated doses. Since most toxic responses (including carcinogenesis) appear to be dependent both on the concentration of the toxic entity at the sensitive site and on the length of time it resides there, the pharmacokinetic characteristics of a chemical are intricately linked to its toxic response. 

Once the absorption and elimination rate constants are known, calculation of peak time is possible by using the equations in Answer 4. Since 65% of the dose is excreted in urine as procainamide and 35% as N-acetylprocaina-mide (metabolite), for a 750 mg intravenous bolus dose, the amount excreted at time infinity is dose X % excreted. 

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