Turnover rate, with enzyme catalysis

Because zeolites can also be manufactured with various proportions of aluminate, a catalyst can be tailored to meet the exact requirement of the process. It is calculated that the medium-pore zeolite ZSM-5 (a), operating at 454 °C and lOOtorr (1.3 X 10" Pa) pressure of hexane, can crack more than 37 molecules per active site per minute. At 538 °C the turnover rises to over 300 molecules per minute per active site. Other catalytic processes - toluene disproportionation, xylene isomerization, and methanol conversion (see later) - operate even faster, with hexane isomerization showing a turnover of as much as 4 x 10 per minute per active site. This indicates that rates of catalytic reactions with zeolites equal or exceed rates for enzyme catalysis. 

Important inherent characteristics of an enzyme that should be considered are the substrate affinity, characterized by the Michaelis constant the rate of turnover fecat> providing the catalytic efficiency fecat/ M. and the catalytic potential. Several attempts to compare enzyme catalysis with that of platinum have been published. Direct comparisons are difficult, because enzyme electrodes must be operated in aqueous electrolyte containing dissolved substrate, whereas precious metal electrodes aie often supplied with a humidified gaseous stream of fuel or oxidant, and produce water as steam. It is not straightforward to compare tme optimal turnover rates per active site, as it is often unclear how many active sites are being engaged in a film of enzyme on an electrode. 

Importantly, carbonic anhydrase II is one of the most efficient biological catalysts known and it catalyzes the hydration of CO2 with a turnover rate of 10 sec at 25 C (Khalifah, 1971 Steiner et al, 1975). With kcaJKm = 1.5 X 10 sec carbonic anhydrase II is one of a handful of enzymes for which catalysis apparently approaches the limit of diffusion control. Since transfer of the product proton away from the enzyme to bulk solvent comprises a kinetic obstacle [an enzyme-bound group with ap/C, of about 7 cannot transfer a proton to bulk solvent at a rate faster than 10 sec (for a review see Eigen and Hammes, 1963)], the observed turnover rate of 10 sec" requires the participation of buffer in the proton transfer. 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

The turnover frequency, N, (commonly called the turnover number) defined, as in enzyme catalysis, as molecules reacting per active site in unit time, can be a useful concept if employed with care. In view of the problems in measuring the number of active sites discussed in 1.2.4, it is important to specify exactly the means used to express Q in terms of active sites. A realistic measure of such sites may be the number of surface metal atoms on a supported catalyst but in other cases estimation on the basis of a BET surface area may be the only readily available method. Of course, turnover numbers (like rates) must be reported at specified conditions of temperature, initial concentration or initial partial pressures, and extent of reaction. 

Another facet of these asymmetric hydrogenations, which has been quantified by the detailed studies referred to above, are the extraordinary rates of reaction. Thus the turnover rates of several of these systems approach or exceed 102 sec-1 and therefore are comparable to many classes of enzymic catalysis. This high reactivity was important for the utilization of such catalysts for commercial operation. It should be appreciated that use of the expensive rhodium together with a very expensive ligand system presents a potential bar to commercial utility. However, the extremely high turnover rates that can be realized with these systems at low temperatures allows their use in such minute amounts that intact recycle is not required and they are merely recovered for their precious metal content. 

For the real-time single-turnover detection of fluorogenic reactions, catalytic reactions with fast turnover rates (or fast product dissociation) pose a time resolution challenge, as single-molecule fluorescence detection often requires detection of hundreds of photons to obtain statistically significant information. For these fast enzymes, one can vary the substrates, use enzyme variants from different organisms, or use mutants to slow the catalysis down. 

Despite enormous progress in understanding Bi2-mediated reactions, several seminal questions remain. Two issues of great interest are the molecular mechanism of cobalt-carbon bond activation in coenzyme B12 and the function of the trans axial ligand in catalysis. While the cobalt-carbon bond of coenzyme B12 is relatively weak, it must be further activated by a factor of two (in terms of BDE) upon enzyme complexation to yield bond homolysis rates consistent with enzyme turnover rates. The role of the trans axial base has received a great deal of attention. The novel... 

The partition ratio is an important parameter in assessing the efficacy of a suicide inhibitor. The partition ratio, r, is defined as the ratio of turnover to inactivation events ideally, r would equal zero. That is, every catalytic event between enzyme and the suicide inhibitor would result in inactivated enzyme, with no release of reactive inhibitor product. The value for the partition ratio can be determined in several ways. If the kinetic constants can be determined individually, r is the ratio of the rate constants for catalysis and inactivation. 

There is also some confusion between different branches of catalysis in a way TOF (or similar concepts) are defined. In enzymatic catalysis, the turnover rate is referred to as a turnover number (T ON), defined as the maximum number of molecules of substrate that an enzyme can convert to product per catalytic site per unit of time. The concept of TON is also applied in homogeneous (organometaUic) catalysis with a different meaning, defining the number of moles of substrate that a mole of catalyst can convert before becoming inactivated. It is apparendy clear that TON (dimensionless) can be infinite if there is no deactivation. The concept of TOF in organometaUic catalysis is used to refer to the turnover per unit time. 

The solvent d5mamics, i.e., the in vitro and in vivo conditions, and natural breathing , i.e., the quantum fluctuations in the active site, of the enzyme molecule need to be counted in a more complete picture of enzymic catalysis. However, the quantum (fluctuating) nature of the enzymic reactions can be visualized by combining the relationship between the catalytic rate and temperature (7) (DeVault Chance, 1966) with that between the reaction rate and the turnover number or the effective time of reaction (Ar) via Heisenberg relation... 

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