Zero-order process

Fig. 11 Semilogarithmic plot of observed plasma concentrations (crosses) versus time for an orally administered drug absorbed by a zero-order process. (Data shown in Table 6.)... 

Acceleration of rate by temperature was very small. Conversions at varying space velocities resembled that of a zero-order reaction. If this were really a zero-order process, the energy of activation would be only 4.4 kcal/mole. 

Alcohol is metabolized by alcohol dehydrogenase (a zero-order process except at very high and very low concentrations) to acetaldehyde, which is metabolize to carbon dioxide and water by aldehyde dehydrogenase. Catalase and the microsomal alcohol oxidase system are also involved. 

Mislow and co-workers (258) and Hammond (259) have shown that optically active diaryl sulfoxides, which are configurationally stable in the dark at 200°C, lose their optical activity after 1 hr at room temperature on irradiation with ultraviolet light. Similarly, an easy conversion of the trans isomer of thianthrene-5,10-oxide 206a into the thermodynamically more stable cis isomer takes place upon irradiation in dioxane for 2 hr. However, the behavior of a-naphthylethyl p-tolyl sulfoxide under comparable irradiation conditions is different, namely, it is completely decomposed after 4 min. These differences are not surprising because the photochemical racemization of diaryl sulfoxides occurs by way of the pyramidal inversion mechanism whereas decomposition of the latter sulfoxide occurs via a radical mechanism with the cleavage of the sulfur-carbon bond. It is interesting to note that photoracemization may be a zero-order process in which the rate depends only on the intensity of the radiation and on the quantum yield. 

In a biochemical pathway there will be one reaction that is non-eqnilibrinm and for which the enzyme approaches satnration with its snbstrate (pathway snbstrate). That is, the enzyme catalyses a zero order process (Fignre 3.7). 

The kinetics of this relationship are straightforward the effector system (enzyme activity) is a zero order process (i.e. the substrate S saturates the enzyme Ej whereas the inactivation reaction E2 is a first order process. The consequences of the kinetics of this system is that the magnitude of the change in Ei results in precisely the same quantitative change in the concentration of X. For example a fivefold increase in Ei produces a fivefold increase in the concentration of X. This relationship is shown in Box 12.2. Three examples are given. 

Box 12.2 Theoretical analysis of the quantitative changes in the steady-state concentration of a messenger molecule that are the result of changes in the activity of a zero order process... 

Ei is a zero order process whose activity can be changed. X is the messenger molecule. Reaction (E2) is catalysed by an enzyme that obeys Michaelis Menten kinetics, the ATn of which for X is assumed to be 0.1 arbitrary units. 

Similarly, cychc GMP is generated from GTP by the enzyme guanyl cyclase and is converted (inactivated) by a phosphodiesterase to GMP and the same principle applies, since the cyclase catalyses a zero order process and phosphodiesterase a first order process. 

Enzyme Ei is the phospholipase A, for which there is an excess of substrate in the plasma membrane i.e. a zero order process. (Eor details of this process, see Chapter 11). E, is a phosphatase, which catalyses a first order process. In fact, IP2 can be hydrolysed to produce IPi which is further hydrolysed to produce free inositol. The latter is salvaged by using it to re-form phosphatidylinositol in the phospholipid synthetic pathway and then phosphorylated to prodnce PIP2 (Chapter 11, Eigure 11.21). These reactions are not jnst of biochemical interest bnt are involved in the treatment of bipolar disease a mental disorder. 

Figure 14.14 Quantitative biochemical similarities between the concentrations of precursors for messenger formation, the concentrations of messengers and the concentration of degradation products. These are represented by ions, cyclic AMP and a neurotransmitter. The precise concentrations of neurotransmitter in the presynaptic neurone terminal are not known if it were not localised in vesicles, it would be approximately 10 M/L so that within the vesicle it is estimated to be about 10 M/L. Similarly the precise concentration in the synaptic cleft is also a guesstimate. On the basis of the activity of exocytosis and the K , of the degradation process, it would be possible to calculate the concentration within the synaptic cleft (see Chapter 12 considerable for an example). There is Box 12.2 similarity between the substrate concentration for the zero order processes, the concentrations of messenger and the breakdown products for each process.

Cyclical synthesis/degradation of proteins in cells. Schimke treated the rate of protein synthesis as a zero-order process and the rate of protein degradation as a first-order reaction ... 

Aldrin is a pesticide used mainly on crops of feed corn. We will first mix a few grams of aldrin into the octanol. Then, we will pour the octanol/aldrin mixture slowly into some water in a container and seal the container, as shown in Figure E8.3.1. While gently shaking the container, we will extract samples of the water over time to perform our analysis. The sample data will be fit to the equation for a first-order and zero-order process ... 

The drug ALP has m.p. 305 °C and sublimes in a zero-order process. Activation energy for the process was calculated using zero-order kinetics. An Arrhenius plot showed an activation energy of 132.6 kj mol for this process <2001MI15>. 

If tlie release characteristics of the formulation can be described by a zero-order process for some period of time (e.g., 5%/hr from 4 to 12 hours), and the dissolution profile appears to fit a linear function for that period of time, a release rate specification may be established to describe the dissolution characteristics of that formulation. A release rate specification may be an addition to the specifications established on the cumulative amount dissolved at the selected time points. Alternatively, a release the rate specification may be the only specification except for the specification for time when at least 80% of drug has dissolved. 

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. 

All internal transformations (chemical, photochemical, biological) in which the chemical is consumed, are described by first-order processes. The in situ production of the compound is described as a zero-order process, j. This includes the case in which the compound may be produced by (e.g., first-order) transformation of another compound, provided that the concentration of the latter is approximately constant. 

A carbocation is formed as shown in Eq. 12-11, which represents just one-half of the overall displacement reaction. In the common terminology of physical organic chemistry this is an SN1 reaction rather than an Sn2 reaction of the kind shown in Eqs. 12-3 and 12-5. This terminology is not quite appropriate for enzymes because the breakdown of ES complexes to product is usually a zero-order process and the numbers 1 and 2... 

Using Mossbauer spectroscopy to monitor the formation of p-hematin under in vitro reaction conditions, Adams et al. have demonstrated that the reaction is a psuedo-zero-order process [109]. Such a process is consistent with a mechanism whereby a small concentration of heme is kept soluble via acetate, functioning as a phase-transfer catalyst, in a heme-saturated solution. In the rate limiting step, the soluble heme aggregates to P-hematin, which in turn grows until it precipitates from solution. There are clearly complicated heterogeneous reaction equilibria involved in the aqueous chemical formation of p-hematin. Consequently, it should be emphasized that the detailed mechanistic analysis of the complex solubilization of the species involved in the chemical synthesis... 

A reaction order of 1/2 was determined by Malavasic et al.91) for the curing of epoxy resins with cyclic anhydrides over the conversion range 18-79 %. At 86-98.5 % conversion, the authors established a first-order curing reaction. Booss and Hau-schildt90) regard copolymerization and curing as a zero-order process with respect... 

Hydrolysis must appear in principle as a pseudo-zero-order process, except if the end-life conversion nf/E0 exceeds largely 10%, which seems unlikely. In linear polymers, the number of chain scissions n can be determined from molar mass measurements. In thermosets, it is considerably more difficult to determine. Some possible ways are discussed in the following section. 

Zero-order process The rate of the process is independent of the concentration of the substance (e.g., liver metabolism of ethyl alcohol). 

Suppose it is correct that 02 consumption is a zero-order process until its concentration is depleted to 15% of saturation (at sea level). Then 80-85% of the available oxygen was consumed by approximately 10% of the cells - the 10% with which the feed first came in contact. Clearly, the remainder of the cells was starved for oxygen. The resulting biochemical stress could have effected an increase in productivity of phenolics indeed, Hallsby concluded from batch ex-... 

For a zero-order process, the effectiveness factor (defined as the ratio of the actual consumption of reactant to that which would occur in the absence of mass transfer resistance) is equal to unity whenever the following inequality holds ... 

If 02 consumption were indeed zero order for a particular plant species, then it would appear that any phytoproduction process involving that species would require only that a minimum dissolved 02 concentration be maintained any concentration increase beyond that would be irrelevant. In the case of tobacco cells, any concentration greater than 15 % of air saturation would yield the same metabolic rate and, presumably, the same productivity of all metabolites. If, on the other hand, consumption is first order in the concentration range achievable in a practical bioreactor (equivalently, if Kf is comparable to working concentrations), then its concentration is an important control parameter in the bioreactor. However, Kobayashi et al. studied berberine production by suspended and immobilized cells of Thalictrum minus [50]. They assert that 02 uptake is a zero-order process but observed that berberine production depended on 02 availability. They controlled that availability by adjusting the speed of shaking of the culture flasks, thus varying the mass transfer coefficient for absorption of 02. 

The results for the second phase can also be interpreted in terms of the model shown in Scheme 3. Following the kY step, excess Ru(IV)02+ is present in solution, and Ru(II)OH22+ is bound to DNA. For continued oxidation of DNA to occur, inactive Ru(II)OH22+ must dissociate before another active Ru(IV)02+ complex can bind. Both oxidation states must have approximately the same binding constant, because they have the same charge and their structures differ only by two protons. We know from the analysis of the first phase that dissociation (kQg) is slower than oxidation (k2) or binding (fcon). Thus, the rate-limiting step becomes the dissociation of the reduced ruthenium complex so that another Ru(IV)02+ can bind. Because dissociation is a zero-order process, we would expect the rate to be concentration-independent, as is observed. 

If we assume that for every inversion taking place through rate determining 0 "Si dissociation there is also likely to be a retention (this is very likely as attack by NMI on the four coordinate salt is very fast on the NMR time scale, [9]) then the rate constant for retention by SiN cleavage, taking place through a zero order process in NMI (the first two clockwise steps in Scheme 8) is given by Eq. 2. 

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