Turnover number, definition

Palladium(II) complexes provide convenient access into this class of catalysts. Some examples of complexes which have been found to be successful catalysts are shown in Scheme 11. They were able to get reasonable turnover numbers in the Heck reaction of aryl bromides and even aryl chlorides [22,190-195]. Mechanistic studies concentrated on the Heck reaction [195] or separated steps like the oxidative addition and reductive elimination [196-199]. Computational studies by DFT calculations indicated that the mechanism for NHC complexes is most likely the same as that for phosphine ligands [169], but also in this case there is a need for more data before a definitive answer can be given on the mechanism. 

The turnover number of an enzyme is defined as the maximum number of moles of substrate reacted per mole of enzyme (or molecules per molecule) per minute under optimum conditions (i.e., saturating substrate concentration, optimum pH, etc). If 2 mg/cm3 of a pure enzyme (50,000 molecular weight, Michaelis constant Km = 0.03 mole/m3) catalyzes a reaction at a rate of 2.5 jumoles/nUksec when the substrate concentration is 5 x 10 3 moles/m3, determine the turnover number corresponding to this definition and the actual number of moles of substrate reacting per minute per mole of enzyme. 

However, the pathways for these reactions, particularly in the gas phase, have been only -.rtially characterized. In a wide variety of these reactions, coordinatively unsaturated, highly reactive metal carbonyls are produced [1-18]. The products of many of these photochemical reactions act as efficient catalysts. For example, Fe(C0)5 can be used to generate an efficient photocatalyst for alkene isomerization, hydrogenation, and hydrosilation reactions [19-23]. Turnover numbers as high as 3000 have been observed for Fe(C0)5 induced photocatalysis [22]. However, in many catalytically active systems, the active intermediate has not been definitively determined. Indeed, it is only recently that significant progress has been made in this area [20-23]. 

Catalyst stability can be defined in terms of turnover number (TON). A textbook definition of this is ... 

Enzyme activity refers to the rate at which a particular enzyme catalyzes the conversion of a particular substrate (or substrates) to one or more products under a given set of conditions. Usually, activity refers to the contribution of many enzyme molecules (often expressed simply as activity per mg of protein or similar) but, in its simplest form, activity refers to the contribution of a single enzyme molecule. The turnover number of an enzyme-substrate combination refers to the number of substrate molecules metabolized in unit time (usually a period of 1 s) under a given set of conditions (see later). These definitions appear, at first glance, to be largely self-explanatory. However, many factors contribute to the final activity of an enzyme, and these must be considered during any assessment of such activity. 

The principal limitation of these data is the lack of definition of the individual forms for the CYP2C subfamily. Analysis of this subfamily has remained problematic due to high cross-reactivities of all of the distinct forms with most antibody preparations. In addition, Western blot analysis does not distinguish between active and inactive forms of the protein. Furthermore, distinct enzymes may have different affinities for coenzymes necessary for catalytic activity, which will serve to unlink abundance of the protein and its catalytic activity. Therefore the assumptions must be made that the ratios of active to inactive protein are similar for all forms and that all forms have similar affinities for coenzymes. These assumptions may not be justified. However, even with these limitations, the study of Shimada et al. (1994) contributes greatly to our understanding of relative enzyme abundance in human liver. In addition, the relative abundance data, coupled with the absolute P450 content (per unit protein) and the turnover numbers for enzyme-specific substrates (per unit protein), can provide an estimate of the turnover number for individual enzymes in the human liver membrane environment. This provides an important benchmark for evaluation of turnover number data from cDNA-expressed enzymes. 

As is the case with all biologically active chemicals (i.e., enzymes and substrates), activity (i.e., turnover number and Km) is the relationship between a defined response and the concentration that causes it. Table G.0.1 shows some flavor activities and their definitions. 

The catalyst turnover number (TON) and the turnover frequency (TOF) are two important quantities used for comparing catalyst efficiency. Their definitions, however, vary slightly among the three catalysis fields. In homogeneous catalysis, the TON is the number of cycles that a catalyst can run through before it deactivates, i.e., the number of A molecules that one molecule of catalyst can convert (or turn over ) into B molecules. The TOF is simply TON/time, i.e., the number of A molecules that one molecule of catalyst can convert into B molecules in one second, minute, or hour. In heterogeneous catalysis, TON and TOF are often defined per active site, or per gram catalyst. This is because one does not know exactly how many... 

The Michaelis constant was determined to be = 0.60 mM. Turnover numbers are relatively low (kcai 0.4 x lO /min) but are definitely present. Furthermore, we found that the template molecule itself is a powerful competitive inhibitor with = 0.025 mM, i.e. it is bound more strongly than the substrate by a factor of 20. It is remarkable that such a strong binding of substrate or template occurs in water-acetonitrile 1 1. Binding in aqueous solution by the usual electrostatic interactions or hydrogen bonding is much weaker. 

The term turnover number can be used in two ways. One way, which has been redefined as molecular activity or molar activity, is the number of moles of substrate transformed per minute per mole of enzyme (units per micromole of enzyme) under optimum conditions. Since many enzymes are oligomers containing n subunits, another possible turnover number is the number of moles of substrate transformed per minute per mole of active subunit or catalytic center (under optimum conditions). This latter definition of catalytic power is called... 

A catalyst, in its simpler definition, is a substance that enables a chemical reaction to proceed at an usually faster rate or under different conditions (such as at a lower temperature) than otherwise possible. The catalyst interacts with the reagents and intermediates of reaction but is regenerated to the initial state during the reaction cycle. The turnover number (TON) indicates how many cycles a single catalytic center could perform the reaction cycle without being deactivated. In complex reactions with multiple possible products (the usual case in chemistry), the catalyst enables us to maximize a specific reaction pathway and thus to provide a selective synthesis. 

The definition of turnover number is the moles of substrate converted to product per mole of enzyme per second. The unites are sec . ... 

The definition of turnover number TON (moles product/mole metal)... 

Molecular Activity. Many enzymes have thus far been isolated in pure and crystallized form. In these cases, the molecular activity can be determined it is defined as the number of molecules of substrate transformed per minute per molecule of enzyme (or the number of mmoles of substrate per mole of enzyme, i.e. the number of enzyme units p er Mmole of enzyme). The term turnover number" has also been applied to this definition ( nd similar ones). For the calculation of molecular activity, the activity of the enzyme and its molecular weight must be known. A large molecular activity indicates a rapid reaction. Very large molecular activities have been found in the cases of acetylcholinesterase (18 X 10 ). The usual values range from several thousand to ten thousand molecules of substrate per enzyme molecule per minute, still a rather rapid turnover. 

The definition of turnover time is total burden within a reservoir divided by the flux out of that reservoir - in symbols, t = M/S (see Chapter 4). A typical value for the flux of non-seasalt sulfate (nss-SOl"") to the ocean surface via rain is 0.11 g S/m per year (Galloway, 1985). Using this value, we may consider the residence time of nss-S04 itself and of total non-seasalt sulfur over the world oceans. Appropriate vertical column burdens (derived from the data review of Toon et ai, 1987) are 460 fxg S/m for nss-801 and 1700 jig S/m for the sum of DMS, SO2, and nss-S04. These numbers yield residence times of about 1.5 days for nss-S04 and 5.6 days for total non-seasalt sulfur. We might infer that the oxidation process is frequently... 

Attempts to determine how the activity of the catalyst (or the selectivity which is, in a rough approximation, the ratio of reaction rates) depends upon the metal particle size have been undertaken for many decades. In 1962, one of the most important figures in catalysis research, M. Boudart, proposed a definition for structure sensitivity [4,5]. A heterogeneously catalyzed reaction is considered to be structure sensitive if its rate, referred to the number of active sites and, thus, expressed as turnover-frequency (TOF), depends on the particle size of the active component or a specific crystallographic orientation of the exposed catalyst surface. Boudart later expanded this model proposing that structure sensitivity is related to the number of (metal surface) atoms to which a crucial reaction intermediate is bound [6]. 

The results of adsorption and desorption of CO mentioned above suggest that for the reaction at low temperature, the sites for relatively weakly chemisorbed CO are covered by the deposited carbon and the reaction occurs between molecularly adsorbed CO and oxygen on the carbon-free sites which are the sites for relatively strongly chemisorbed CO. Therefore, the definition of the turnover rate at 445 K remains as given in Equation 1. For the reaction at 518 K, however, this definition becomes inappropriate for the smaller particles. Indeed, to obtain the total number of Pd sites available for reaction, we now need to take into consideration the number Trp of CO molecules under the desorption peak. Furthermore, let us assume that disproportionation of CO takes place through reaction between two CO molecules adsorbed on two adjacent sites, and let us also assume that the coverage is unity for the CO molecules responsible for the LT desorption peak, since this was found to be approximately correct on 1.5 nm Pd on 1012 a-A O (1). Then, the number Np of palladium sites available for reaction at 518 K is given by HT/0 + NC0 LT s nce t ie co molecules under the LT desorption peak count only half of the available sites. Consequently, the turnover rate at 518 K should be defined as ... 

By definition, the turnover frequency is expressed per number of active sites. So, catalytic samples that differ only in the amount active sites must exhibit the same values of turnover frequency. If not, heat and mass transfer phenomena are present. Specifically, the correct measurement of intrinsic kinetic data in heterogeneous catalysis is difficult due to the effect of heat and mass transfer, especially inside the pores of high specific-area materials. The turnover frequency reveals these phenomena. In other words, in the case of supported... 

The turnover frequency allows performance comparison between different catalyst systems, biological and/or non-biological. Its threshold is at 1 event per second per active site. According to the definition, a turnover frequency can be determined only if the number of active sites is known (Chapter 9, Section 9.2.3). For an enzyme reaction obeying Michaelis-Menten kinetics, Eq. (2.15) holds. 

Table 10.2 presents the kinetic information for the main reactions, in which the frequency factors have been calculated from turnover-frequency (TOF) data [8, 9]. This term, borrowed from enzymatic catalysis, quantifies the specific activity of a catalytic center. By definition, TOF gives the number of molecular reactions or catalytic cycles occurring at a center per unit of time. For a heterogeneous catalyst the number of active centers can be found by means of sorption methods. Let us consider that the active sites are due to a metal atom. By definition [15] we have ... 

For heterogeneous reactions involving fluid and solid phases, the areal rate is a good choice. However, the catalysts (solid phase) can have the same surface area but different concentrations of active sites (atomic configuration on the catalyst capable of catalyzing the reaction). Thus, a definition of the rate based on the number of active sites appears to be the best choice. The turnover frequency or rate of turnover is the number of times the catalytic cycle is completed (or tumed-over) per catalytic site (active site) per time for a reaction at a given temperature, pressure, reactant ratio, and extent of reaction. Thus, the turnover frequency is ... 

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