Kinetics zero-order/saturation,

Interestingly, at very low concentrations of micellised Qi(DS)2, the rate of the reaction of 5.1a with 5.2 was observed to be zero-order in 5.1 a and only depending on the concentration of Cu(DS)2 and 5.2. This is akin to the turn-over and saturation kinetics exhibited by enzymes. The acceleration relative to the reaction in organic media in the absence of catalyst, also approaches enzyme-like magnitudes compared to the process in acetonitrile (Chapter 2), Cu(DS)2 micelles accelerate the Diels-Alder reaction between 5.1a and 5.2 by a factor of 1.8710 . This extremely high catalytic efficiency shows how a combination of a beneficial aqueous solvent effect, Lewis-acid catalysis and micellar catalysis can lead to tremendous accelerations. 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

FIGURE 14.7 Substrate saturation curve for au euzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v= Fnax- That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H9O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme. 

Case 1 When [S] is large compared to K , the enzyme is saturated with S and the kinetics are zero-order in S. 

AClAt = Umax C/(Km + C) n/2 = 0.693 (Km + C)fVmax With high concentration values (C Km), the metabolism capacity is saturated and zero-order kinetics result (-AClAt = Umax). 

Zero-order kinetics describe the time course of disappearance of drugs from the plasma, which do not follow an exponential pattern, but are initially linear (i.e. the drug is removed at a constant rate that is independent of its concentration in the plasma). This rare time course of elimination is most often caused by saturation of the elimination processes (e.g. a metabolizing enzyme), which occurs even at low drug concentrations. Ethanol or phenytoin are examples of drugs, which are eliminated in a time-dependent manner which follows a zero-order kinetic. 

The speed of autoxidation was compared for different carotenoids in an aqueous model system in which the carotenoids were adsorbed onto a C-18 solid phase and exposed to a continnons flow of water saturated with oxygen at 30°C. Major products of P-carotene were identified as (Z)-isomers, 13-(Z), 9-(Z), and a di-(Z) isomer cleavage prodncts were P-apo-13-carotenone and p-apo-14 -carotenal, and also P-carotene 5,8-epoxide and P-carotene 5,8-endoperoxide. The degradation of all the carotenoids followed zero-order reaction kinetics with the following relative rates lycopene > P-cryptoxanthin > (E)-P-carotene > 9-(Z)-p-carotene. 

In this case, most of the catalyst is in the form of M A and the reaction is zero order with respect to A. Thus, the kinetics move from first order at low cA toward zero order as cA increases. This feature of the rate saturating or reaching a plateau is common to many catalytic reactions, including surface catalysis (Section 8.4) and enzyme catalysis (Chapter 10). 

Saturation kinetics The rate is first order with respect to A at low concentrations of A (such that KAcA 1 + MBcB), but becomes zero order at higher concentrations when KAcA 1 + AfgCg.In the high-concentration limit, all the catalytic sites are saturated with A(8a = 1), and the rate is given by the number of catalytic sites times the rate constant, k. 

Silverman has pointed out that several criteria must be met to demonstrate that a compound is a true suicide substrate 1101 (1) Loss of enzyme activity must be time-dependent, and it must be first-order in [inactivator] at low concentrations and zero-order at higher concentrations (saturation kinetics), (2) substrate must protect the enzyme from inactivation (by blocking the active site), (3) the enzyme must be irreversibly inactivated and be shown to have a 11 stoichiometry of suicide substrate active site (dialysis of enzyme previously treated with radiolabeled suicide substrate must not release radiolabel into the buffer), (4) the enzyme must unmask the suicide substrate s potent electrophile via a catalytic step,1121 and (5) the enzyme must not be covalently labeled with the activated form of the suicide substrate following its escape from the active site (the presence of bulky scavenging thiol nucleophiles in the buffer must not decrease the observed rate of inactivation). 

In zone a of Figure 2.5, the kinetics are first order with respect to [S], that is to say that the rate is limited by the availability (concentration) of substrate so if [S] doubles the rate of reaction doubles. In zone c however, we see zero order kinetics with respect to [S], that is the increasing substrate concentration no longer has an effect as the enzyme is saturated zone b is a transition zone. In practice it is difficult to demonstrate the plateau in zone c unless very high concentrations of substrate are used in the experiment. Figure 2.5 is the basis of the Michaelis-Menten graph (Figure 2.6) from which two important kinetic parameters can be approximated ... 

Figure 11.1 illustrates the behavior of Equation 11.6. By the assumption of rapid equilibrium the rate determining step is the unimolecular decomposition. At high substrate composition [S] KM and the rate becomes zero-order in substrate, v = Vmax = k3 [E0], the rate depends only on the initial enzyme concentration, and is at its maximum. We are dealing with saturation kinetics. The most convenient way to test mechanism is to invert Equation 11.6... 

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. 

The best-known exception to exponential kinetics is the elimination of alcohol (ethanol), which obeys a linear time course (zero-order kinetics), at least at blood concentrations > 0.02 %. It does so because the rate-limiting enzyme, alcohol dehydrogenase, achieves half-saturation at very low substrate concentrations, i.e at about 80 mg/L (0.008 %). Thus, reaction velocity reaches a plateau at blood ethanol concentrations of about 0.02 %, and the amount of drug eliminated per unit of time remains constant at concentrations above this level. 

Referring to reactions in which the reaction velocity is independent of the reactant under consideration. For example, for the reaction A + B C, if the empirical rate expression is v = A [B], the reaction is first order with respect to B but zero order with respect to A. See Chemical Kinetics Rate Saturation Michaelis-Menten Equation... 

CHEMICAL KINETICS RATE SATURATION MICHAELIS-MENTEN EQUATION ZERO-ORDER REACTIONS ORDER OF REACTION MOLECULARITY... 

The presence of 4e as the predominant species during the catalysis is also in accord with the observed kinetic behavior of this catalyst with 1-octene and styrene as the substrates. The observation of this saturated acyl rhodium complex is in line with the positive dependence of the reaction rate on the hydrogen concentration and the zero order in alkene concentration. It was concluded previously that this saturated acyl complex is an unreactive resting state [18]. Before the final hydro-genolysis reaction step can occur, a CO molecule has to dissociate in order to form... 

B. Phenytoin is one of a handful of drugs that demonstrates zero-order (or saturation) kinetics. If a patient is showing signs of toxicity to phenytoin, it is important to measure blood levels, since the likelihood that phenytoin is demonstrating zero-order kinetics is very high. 

When only a fixed amount of drug is eliminated in a given interval of time, because enzymes for biotransformation and elimination are saturated, the kinetics of drug elimination are zero order (16). Alcohol is the classic example, where blood levels rise exponentially with increased amounts ingested, because elimination mechanisms are saturated and only a certain fraction of the total dose taken can be eliminated before the next dose is ingested. 

First order kinetics means that the amount eliminated per unit of time is directly proportional to the amount ingested, so there is a linear relationship between dose change and plasma level change (i.e., 1 1). In contrast, with zero order kinetics there is a larger than proportional increase in the plasma concentration for each dose increment because the elimination mechanism is saturated. 

Zero order kinetics Situation in which only a fixed amount of drug eliminated per unit of time regardless of plasma concentration because all mechanisms mediating elimination are saturated. 

Non-linear pharmacokinetics are much less common than linear kinetics. They occur when drug concentrations are sufficiently high to saturate the ability of the liver enzymes to metabolise the drug. This occurs with ethanol, therapeutic concentrations of phenytoin and salicylates, or when high doses of barbiturates are used for cerebral protection. The kinetics of conventional doses of thiopentone are linear. With non-linear pharmacokinetics, the amount of drug eliminated per unit time is constant rather than a constant fraction of the amount in the body, as is the case for the linear situation. Non-linear kinetics are also referred to as zero order or saturation kinetics. The rate of drug decline is governed by the Michaelis-Menton equation ... 

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