First-order processes active transport

K0 is now the zero-order rate constant and is expressed in terms of mass/time. In an active carrier-mediated transport process following zero-order kinetics, the rate of drug transport is always equal to K once the system is fully loaded or saturated. At subsaturation levels, the rate is initially first order as the carriers become loaded with the toxicant, but at concentrations normally encountered in pharmacokinetics, the rate becomes constant. Thus, as dose increases, the rate of transport does not increase in proportion to dose as it does with the fractional rate constant seen in first-order process. This is illustrated in the Table 6.1 where it is assumed that the first-order rate constant is 0.1 (10% per minute) and the zero-order rate is 10 mg/min. 

When a short-lived radioactive isotope is introduced into a biological system, the observed decay in radioactivity results from a combination of normal radioactive decay and biological turnover (e.g., removal of the isotope from the bloodstream by excretion or transport into tissues). If the biological turnover is a first-order process, then Aapp, the apparent first-order rate constant, is the sum of Xr (radioactive)-H A (biological). This is quite understandable since A represents the fraction of the activity present that disappears per small increment of time. Fractions can be added. The observed radioactivity at any time is given by ... 

The kinetics described so far have been based on first-order processes, yet often in toxicology, the situation after large doses are administered has to be considered when such processes do not apply. This situation may arise when excretion or metabolism is saturated and hence the rate of elimination decreases. This is known as Michaelis-Menten or saturation kinetics. Excretion by active transport (see below) and enzyme-mediated metabolism are saturable processes. In some cases cofactors are required and their concentration may be limiting (see Chapter 7, salicylate poisoning). When the concentration of foreign compound in the relevant tissue is lower than the km then linear, first-order... 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

Chemical clastogenesis and mutagenesis both involve a complex series of processes, including pharmacokinetic mechanisms (uptake, transport, diffusion, excretion), metabolic activation and inactivation, production of DNA lesions and their incomplete repair or misrepair, and steps leading to the subsequent expression of mutations in surviving cells or individuals (Thble 7.1). Each of the steps in these processes might conceivably involve first order kinetics at low doses (e.g., diffusion, MichaeUs-Menten enzyme kinetics) and hence be linear. In principle, therefore, the overall process edso might be linear and without threshold. 

The half-life will be independent of the dose, provided that the elimination is first order and therefore should remain constant. Changes in the half-life, therefore, may indicate alteration of elimination processes due to toxic effects because the half-life of a compound reflects the ability of the animal to metabolize and excrete that compound. When this ability is impaired, for example, by saturation of enzymic or active transport processes, or if the liver or kidneys are damaged, the half-life may be prolonged. For example, after overdoses of paracetamol, the plasma half-life increases severalfold as the liver damage reduces the metabolic capacity, and in some cases, kidney damage may reduce excretion (see chap. 7). 

The statement is true. Passive diffusion is a first-order rate process as it is dependent on the concentration of the chemical. In contrast, active transport is a zero-order process as it is not dependent on the concentration. 

Factors analogous to those affecting gut absorption also can affect drug distribution and excretion. Any transporters or metabolizing enzymes can be taxed to capacity—which clearly would make the kinetic process nonlinear (see Linear versus Nonlinear Pharmacokinetics ). In order to have linear pharmacokinetics, all components (distribution, metabolism, filtration, active secretion, and active reabsorption) must be reasonably approximated by first-order kinetics for the valid design of controlled release delivery systems. 

Immediately on entering the body, a chemical begins changing location, concentration, or chemical identity. It may be transported independently by several components of the circulatory system, absorbed by various tissues, or stored the chemical may effect an action, be detoxified, or be activated the parent compound or its metabo-lite(s) may react with body constituents, be stored, or be eliminated—to name some of the more important actions. Each of these processes may be described by rate constants similar to those described earlier in our discussion of first-order rate processes that are associated with toxicant absorption, distribution, and elimination and occur... 

The temperature dependence of ki shows considerable variation (2.0 - 5.6 kcal/mole), and may also be a function of the hydrodynamic conditions of the experiment. Lund e al. (13) obtained an activation energy of 15 kcal/mol between -15.6 and +1.0°C under conditions where they concluded both surface reaction and transport processes influenced the rate. They found rate proportional to the 0.63 power of IT " rather than the first order reaction observed for conditions of transport control. 

The permeation of most drugs through cellular membranes is by the process of passive diffusion, a nonsaturable process that follows first-order kinetics. Concentration gradient and lipid solubility of the drug are important determinants of the rate of diffusion. Only a few drug molecules are substrates for active transport processes (eg, tubular secretion of beta-lactam antibiotics) these are saturable at high concentrations. Only very small ions (eg, Li+) or drugs (eg, ethanol) may penetrate biomembranes via aqueous pores. 

PROBABLE FATE photolysis, could be important, only identifiable transformation process if released to air is reaction with hydroxyl radicals with an estimated half-life of 8.4 months oxidation, has a possibility of occurring, photooxidation half-life in air 42.7 days-1.2 yrs hydroiysis too slow to be important, first-order hydrolytic half-life 275 yrs voiatilization likely to be a significant transport process, if released to water or soil, volatilization will be the dominant environmental fate process, volatilization half-life from rivers and streams 43 min-16.6 days with a typical half-life being 46 hrs sorption adsorption onto activated carbon has been demonstrated bioiogicai processes moderate potential for bioaccumulation, biodegradation occurs in some organisms, in aquatic media where volatilization is not possible, anaerobic degradation may be the major removal process other reactions/interactions may be formed from haloform reaction after chlorination of water if sufficient bromide is present... 

When all entities are active in the self-influence phenomenon, the well-known relationship between flow [often called in this case reaction rate or transport ( mass ) flux] and basic quantity for a first-order kinetic process is found from the activity definition (Equation 8.114). 

Dynamic properties of i.s.e.s. differ greatly for various electrode types and constructions. When the capacitance of analyte/active surface interface is the only cause of response delay, then relaxation time (or time constant of first-order step-response characteristic) is in the order of milliseconds. When the transport of ions across the dynamic Prandtl layer to the surface of the i.s.e. is the main factor (i.e., this transport is the slowest process of equilibrium reinstallation), for a mixing velocity of about lOcm/s a relaxation time of several seconds occurs. This is typical of solid-membrane electrodes with the exception of glass ones. On the other hand, the limited rate of the exchange process in the liquid membrane, the small diffusion flux of the tested ions into the membrane, the slow dynamics for the creation of diffusion potential and the solubility of the active component of the membrane in the testing solution are the main reasons for the slow response of liquid ion-exchanger electrodes (time constants 10-30 s or even more). 

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