Kinetics, saturation

Most mechanisms that have rate laws with concentrations of a reactant in both the numerator and the denominator will show saturation kinetics. It is always indicative of a pre-equilibrium in the mechanism, where the step involving this reactant (B in this case) is after the equilibrium. For example, the mechanism given in Eq. 7.43 will also show saturation kinetics in [B] (convince yourself by examining Eq. 7.47), whereas the mechanism given in Eq. 7.48 will not (convince yourself by examining Eq. 7.52). 

The variation in Cbs as a function of the starting concentration of B for a reaction mechanism that shows saturation in B. 

Saturation Kinetics That We Take for Granted—SnI Reactions 

In introductory organic chemistry we often teach that the substitution of a tertiary alkyl halide with a nucleophile in ionizing solvents proceeds via a first order process (an SnI pathway). The reaction rate has no dejjendence upon the concentration of nucleophile. Does this really make sense If we add no nucleophile there would be no product formation, so how can the rate really have no dependence upon nucleophile The answer lies in the fact that under most exjjerimental conditions for SnI reactions, the kinetics of the reaction are already in the saturation region. 

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Reversibly fonned micelles have long been of interest as models for enzymes, since tliey provide an amphipatliic environment attractive to many substrates. Substrate binding (non-covalent), saturation kinetics and competitive inliibition are kinetic factors common to botli enzyme reaction mechanism analysis and micellar binding kinetics. 

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. 

The often fast binding step of the inhibitor I to the enzyme E, forming the enzyme inhibitor complex E-I, is followed by a rate-determining inactivation step to form a covalent bond. The evaluation of affinity labels is based on the fulfillment of the following criteria (/) irreversible, active site-directed inactivation of the enzyme upon the formation of a stable covalent linkage with the activated form of the inhibitor, (2) time- and concentration-dependent inactivation showing saturation kinetics, and (3) a binding stoichiometry of 1 1 of inhibitor to the enzyme s active site (34). 

Time Dependence—The Transient Approach to Steady-State and Saturation Kinetics... 

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 5a indicates the effect of the CTAB concentration on the rate constants of the complexes of 38b and 38c. In the case of the water soluble 38b ligand, the rate increases with increasing CTAB concentration up to a saturation level. This type of saturation kinetics is usually interpreted to show the incorporation of a ligand-metal ion complex into a micellar phase from a bulk aqueous phase, and the catalytic activity of the complex is higher in the micellar phase than in the aqueous phase. In the case of lipophilic 38c, a very similar curve as in Fig. 4 is obtained. At a first glance, there appears to be a big difference between these two curves. However, they are rather common in micellar reactions and obey the same reaction mechanism 27). 

We also found the saturation kinetics for alkaline hydrolyses of 44 (PNPA), 3-nitro-4-acetoxybenzoic acid 56 (NABA), and 3-nitro-4-acetoxybenzenearsonie acid 57 (NABAA) in the presence of QPVP1025. If ester-polymer complex formation occurs prior to the attack of OH-, Eq. (5) holds, according to Bunton etal. 103 where K is the equilibrium association constant of polyelectrolyte (PE) and ester (S), and kt the first-order rate coefficients1035, PE, S, and P indicate the poly-... 

We recently synthesized cationic polymers containing imidazole (e g. 68 (SZ811) and 69 (SZ11—3—3)] by reacting poly [N-(2,4-dinitrophenyl)-4-vinyl-pyridinium chloride] with histamine or histamine mixed with other amino derivatives ll8 The hydrolyses of neutral and anionic esters with the models followed saturation kinetics in alkaline media. 

However, saturable kinetics can also be described by a 1 -exp function. This function indeed has an integrated solution for the concentration. 

The dependence of v on [5] follows saturation kinetics, as shown in Fig. 5.1. The asymptotic value i>max provides a convenient estimate of cat by... 

Figure 8-6. Representation of sigmoid substrate saturation kinetics.

To refer to the kinetics of allosteric inhibition as competitive or noncompetitive with substrate carries misleading mechanistic implications. We refer instead to two classes of regulated enzymes K-series and V-se-ries enzymes. For K-series allosteric enzymes, the substrate saturation kinetics are competitive in the sense that is raised without an effect on V. For V-series allosteric enzymes, the allosteric inhibitor lowers... 

The values of x = 0.5 and = 1 for the kinetic orders in acetone [1] and aldehyde [2] are not trae kinetic orders for this reaction. Rather, these values represent the power-law compromise for a catalytic reaction with a more complex catalytic rate law that corresponds to the proposed steady-state catalytic cycle shown in Scheme 50.3. In the generally accepted mechanism for the intermolecular direct aldol reaction, proline reacts with the ketone substrate to form an enamine, which then attacks the aldehyde substrate." A reaction exhibiting saturation kinetics in [1] and rate-limiting addition of [2] can show apparent power law kinetics with both x and y exhibiting orders between zero and one. 

A kinetic model describing the HRP-catalyzed oxidation of PCP by H202 should account for the effects of the concentrations of HRP, PCP, and H202 on the reaction rate. To derive such an equation, a reaction mechanism involving saturation kinetics is proposed. Based on the reaction scheme described in Section 17.3.1, which implies that the catalytic cycle is irreversible, the three distinct reactions steps (Equations 17.2 to 17.4) are modified to include the formation of Michaelis-Menten complexes ... 

As a simple model for the enzyme penicillinase, Tutt and Schwartz (1970, 1971) investigated the effect of cycloheptaamylose on the hydrolysis of a series of penicillins. As illustrated in Scheme III, the alkaline hydrolysis of penicillins is first-order in both substrate and hydroxide ion and proceeds with cleavage of the /3-lactam ring to produce penicilloic acid. In the presence of an excess of cycloheptaamylose, the rate of disappearance of penicillin follows saturation kinetics as the cycloheptaamylose concentration is varied. By analogy to the hydrolysis of the phenyl acetates, this saturation behavior may be explained by inclusion of the penicillin side chain (the R group) within the cycloheptaamylose cavity prior to nucleophilic attack by a cycloheptaamylose alkoxide ion at the /3-lactam carbonyl. The presence of a covalent intermediate on the reaction pathway, although not isolated, was implicated by the observation that the rate of disappearance of penicillin is always greater than the rate of appearance of free penicilloic acid. 

The results presented in Table XVIII imply that rate enhancements are derived from association of the catalyst and substrate prior to reaction. In accord with this idea, the release of p-nitrophenol from p-nitrophenyl butyrate follows saturation kinetics in the presence of 16. The dissociation constant of the complex is reported to be 9.9 X 10-4 M, indicating that binding is very strong. Unfortunately, dissociation constants of the complexes of 16 with the other substrates have not yet been obtained. 

Rousselle C, Smirnova M, Clair P, Le-fauconnier JM, Chavanieu A, Calas B et al. Enhanced delivery of doxombicin into the brain via a peptide-vector-mediated strategy saturation kinetics and specificity. J Pharmacol Exp Ther 2001 296 124-131. 

Most of enzyme kinetics (and mechanism) revolves around the active site. As we ll see later, saturation kinetics is one of the direct consequences of an active site. 

Mathematically, the Michaelis-Menten equation is the equation of a rectangular hyperbola. Sometimes you ll here reference to hyperbolic kinetics, this means it follows the Michaelis-Menten equation. A number of other names also imply that a particular enzyme obeys the Michaelis-Menten equation Michaelis-Menten behavior, saturation kinetics, and hyperbolic kinetics. 

Reinhoudt at al. have recently reported [48] the preparation of a calix[4]arene functionalized with two Zn(II) centers 25, which is highly efficient on transesterification of HPNP. The dimer complex is reported to be 50 times more active (in 50 (v/v)% acetonitrile-water at pH = 7.4 and I = 298 K) than the corresponding monomer (26) which is itself 6 times more active than 27, implying the contribution of the calix[4]arene moiety in the mechanism. The saturation kinetic experiments showed high association constant for the catalyst-substrate complex (K -... 

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. 

Although we have never observed evidence of saturation kinetics in any of the metal-catalyzed reactions of the neutral phosphorus esters,17 it is difficult to envision... 

The TOF data from the table were corrected to 20 °C by assuming that every 10° rise doubled the rate. The TOF data were corrected to 1 atm each of H2 and C02 by assuming that the rates were first order with respect to both H2 and C02, but switched to 0 order above 80 atm due to saturation kinetics. The same sequence was obtained if saturation kinetics were not assumed. 

Abstract This chapter updates but mostly supplements the author s Ange-wandte Review,111 setting in context recent advances based on protein and nucleic acid engineering. Systems qualify as a true enzyme mimics if there is experimental evidence for both the initial binding interaction and catalysis with turnover, generally in the shape of saturation kinetics. They are discussed under five broad headings mimics based on natural enzymes, on other proteins, on other biopolymers, on synthetic macromolecules and on small-molecule host-guest interactions. 

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