Intrinsic rate, substrate

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

The fact that the intrinsic rate constants for nucleophilic addition to Fischer carbene complexes are relatively low, for example, much lower than for most reactions with comparable vinylic substrates or carboxylic esters,188 constitutes strong evidence for the presence of substantial transition state imbalances. However, there have only been a few studies of substituent effects that demonstrate the imbalance directly by showing a uc > p uc or by providing an estimate of its magnitude from the difference a uc - p uc. One such study is the reactions of 76-Cr-Z and 76-W-Z with HC CCII20 and C.F3CH20, 183 It yielded a Llc 0.59 and p ]uc< 0.46 for 76-Cr-Z, and a[juc 0.56 and 0 42 for 76-W-Z, i.e., a ue > p uc as expected. 

In summary, ATP hydrolysis by P-gp correlates well with the intrinsic rate of substrate transport. A complete characterization of the interaction of a compound with P-gp is obtained by measuring the ATPase activity as a function of concentration. The rate of intrinsic substrate transport first increases with increasing concentration, reaches a maximum, and decreases again at high concentrations. The rate of intrinsic transport by P-gp depends not only on the substrate concentration but also on its affinity to the transporter substrates with high affinities for P-gp are transported more slowly than those with low affinities. 

Intrinsic Rate Constants as a Function of X and Y. The largest set of data obtained under comparable conditions refers to the addition of piperidine and morpholine to benzylidene-type substrates in 50% (CH3)2SO-50% water at 20 °C. 

Similar conclusions are reached when comparing the reactivity of ben-zylidene-type substrates, IV, with respect to attack by hydroxide ion. If adjustments for the dependence of the equilibrium constants on X and Y are made (18, 19), the relative intrinsic rate constants can be estimated (Table III). As with the amine reactions, the k0 values follow the same order as for... 

For an intrinsic rate-limited reaction in the organic phase, if the rate equation can be expressed as rate = ky[catalyst]oj.g[substrate]o g, then for a given substrate the rate of reaction depends mainly on the concentration of the active catalytic species in the organic phase and on the intrinsic rate coefficient, k . The distribution of catalyst in the organic phase can be determined by the extraction constant for the two-phase organic/aqueous system. If the transferred catalyst is in the form of a catalyst-anion pair, then it is important to take the extent of aggregation into account to obtain the effective concentration of the active catalytic species. 

The factors that affect the intrinsic rate coefficient include the nature of catalyst and substrate, the solvation of reactants, the transition state formed by the substrate and the activated reactant anion, and the temperature. If the transferred catalyst is in the form of catalyst-anion pair, then it is important to understand the equilibria involving ion pair and ion aggregates. The reactive ion in a different state of aggregation will exhibit different values of k . ... 

The mathematical model for substrate transport with reaction can be used to devise a general approach to predict reaction rates in catalyst particles. The observed rate is defined in terms of the intrinsic rate and an effectiveness factor... 

The rate ratio analysis must also account for entropy effects associated with the limited mobility of the substrate relative to the active site within the polymer. Roucls and Ekerdt (16) measured the relative rates for hydrogenation of cyclooctene and cyclohexene over an immobilized rhodium complex and found that the rate for cyclooctene was less than that for cyclohexene for the homogeneous rhodium complex, RhCl(PPh3)3, and in 1, 2, and 3 X dlvlnylbenzene polystyrene resins. Furthermore, they found that the relative rate differed with dlvlnylbenzene content. The relative rates were shown to be intrinsic rate ratios (16). Roucls and Ekerdt proposed that sterlc constraints due to the presence of the polysier support in the vicinity of active rhodium affected activity. All the rhodium sites were exposed to the same substrate concentration the sites displayed a different Inherent activity toward the two substrates. 

POLYMERIC REAGENTS AND CATALYSTS ) Intrinsic rate of substrate reaction... 

By carrying out a homogeneous reaction in the organic phase with the organic substrate and a known quantity of QY (instead of using MY), the intrinsic rate constant of the organic reaction can be found. 

Recently, kinetic and specdoscopic studies gave a mechanistic explanation of the role of water in the aldol reaction with aromatic aldehydes. While the addition of water increases the catalyst concentration by suppression the formation of parasitic species such as the oxazolidinone, decreases the relative concentration of key minimum intermediates by Le Chatelier s principle, shifting the equilibrium towards proline (1). The net effect on the reaction rate of these opposing roles would differ when different substrates are used in the reaction, with the intrinsic rate per active catalysts species within the cycle being suppressed by the added water in the aldol reaction of acetone with aromatic aldehydes [37]. 

The AG s and the symmetry factors are independent of AG (i.e., of the potential and the nature of fhe substrate) in a range of moderate variation of AG [92]. Hence k, k c, k c, and fcgg (intrinsic rate constants) are almost constant for a given reaction, provided that r and Zj, that is, the surface structure, stay unchanged. 

We can use eq. to calculate the intrinsic rate of substrate removal, but first we need a value for the cell density. In the limiting case, this is just the density of a single cell, which we can calculate as ... 

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