Substrate disappearance rate

Figure 17.15 Relationships of (a) microbial population specific growth rate, (i, versus substrate concentration after Monod (1949), and (b) consequent substrate disappearance rate, d[i]/dt, versus substrate concentration.

Kinetic data exist for all these oxidants and some are given in Table 12. The important features are (i) Ce(IV) perchlorate forms 1 1 complexes with ketones with spectroscopically determined formation constants in good agreement with kinetic values (ii) only Co(III) fails to give an appreciable primary kinetic isotope effect (Ir(IV) has yet to be examined in this respect) (/ ) the acidity dependence for Co(III) oxidation is characteristic of the oxidant and iv) in some cases [Co(III) Ce(IV) perchlorate , Mn(III) sulphate ] the rate of disappearance of ketone considerably exceeds the corresponding rate of enolisation however, with Mn(ril) pyrophosphate and Ir(IV) the rates of the two processes are identical and with Ce(IV) sulphate and V(V) the rate of enolisation of ketone exceeds its rate of oxidation. (The opposite has been stated for Ce(IV) sulphate , but this was based on an erroneous value for k(enolisation) for cyclohexanone The oxidation of acetophenone by Mn(III) acetate in acetic acid is a crucial step in the Mn(II)-catalysed autoxidation of this substrate. The rate of autoxidation equals that of enolisation, determined by isotopic exchange , under these conditions, and evidently Mn(III) attacks the enolic form. 

This proportionality is called the yield of the particular biological process, and it is commonly denoted as Y. For carbon-limiting substrates oxidized by aerobes, biomass yields are usually near 0.5 g biomass-g"1 carbon (Neidhardt et al., 1990). Using yield information relevant to a particular compound/microbial species combination, we can now relate the production rate of new cells to the disappearance rate of the chemical of concern ... 

An ideal test for measuring milk-clotting activity has never been devised, but numerous methods have been tried. In practice, activity is determined by the speed with which the enzyme clots milk under a set of specified conditions. This differs from the usual procedure in enzyme chemistry where one measures the rate at which the products of an enzyme-catalyzed reaction appear, or conversely, the rate at which the substrate disappears. 

The velocity v of an enzymatic reaction is defined as the rate at which a substrate disappears or at which a product is formed, the two being identical ... 

Before kinetic constants can be evaluated, it is critical to find the correct concentration of enzyme to use for the assays. If too little enzyme is used, the overall absorbance change for a reaction time period will be so small that it is difficult to detect differences due to substrate concentration changes or inhibitor action. On the other hand, too much enzyme will allow the reaction to proceed too rapidly, and the leveling off of the time course curve as shown in Figure E5.7 will occur very early because of the rapid disappearance of substrate. A rate that is intermediate between these two extremes is best. For the dopachrome assay, it is desirable to use the level of tyrosinase that gives a linear absorbance change at 475 nm for 2 minutes. 

By considering that both substrate and oxygen must be present in the system for the occurrence of photoreaction, it is assumed that the total disappearance rate of substrate per unit surface area, rx, follows a second-order kinetics of first order with respect to the substrate coverage and of first order with respect to the oxygen coverage ... 

In the cases of Langmuir and Freundlich isotherms, it has been assumed that the total disappearance rate of substrate per imit surface area, Vj, follows a pseudo-first-order kinetics with respect to the substrate concentration which is expressed by its fractional coverage. The same assumption is made for R-P isotherm however, as the R-P isotherm relates an adsorbed amount (and not a fractional coverage) with the equilibrium concentration... 

The total disappearance rate of substrate per unit surface area, rx, gets of zero order so that Equation (15) can be written as ... 

In a number of cases extra attention must be paid to the substrate balance. If product is produced during the growth phase, it may not be possible to separate out the amount of substrate consumed for growth from that consumed to produce the product Uiider these circumstances all the substrate consumed is lumped into the stoichiametric coefficient, and the rate of substrate disappearance is... 

The formation of the dicyclopropylmercury alone or in combination with the adsorbed radical type intermediates accounts for the observation that the substrate disappears at a faster rate than the reduction product appears The dicyclopropylmercury can then accept an electron to produce the anion and a cyclopropylmercury radical which in combination with the mercury surface becomes an adsorbed radical (equation 7) which can be recycled through the pathway of equation 5 or equation 6. The anions formed in equation 3, equation 5, and equation 7 react at the surface with acetonitrile solvent (equation 8) to yield the hydrocarbon. When deuterated acetonitrile was used the hydrocarbon isolated contained 76% deuterium The anion can also react with the electrolyte, tetraethylammonium bromide, in an elimination reaction (equation 9) to produce hydrocarbon, ethylene and triethylamine, all of which have been identified in the reaction mixture ... 

Enzymes can be assayed spectrophotometrically by following the rate at which a product appears or a substrate disappears. If neither substrate nor product has a distinct absorption peak, then it is often possible to couple the reaction of interest to another that does yield a light-absorbing product. In... 

Table 6 Initial reaction rates of styrene and isoprene hydrogenation measured as rates of substrate disappearance) and compositions of reaction products at half-life of sub-...

Michaelis and Menten found that the rate of substrate disappearance with time could be expressed as... 

The essential property of glycolytic oscillations is illustrated by fig. 2.4a and b as well as table 2.1 sustained periodic behaviour is observed only in a precise range of substrate injection rates. This observation, carried out in yeast extracts (Hess Boiteux, 1968b, 1973 Hess et al, 1969), was confirmed (Von Klitzing Betz, 1970) in suspensions of intact yeast cells (fig. 2.5). Below a critical value of the substrate injection rate, the system reaches a stable steady state. When this rate increases, oscillations occur, but they disappear when the substrate injection rate exceeds a second, higher, critical value. This disappearance is reversible, as shown by fig. 2.4b. The period of glycolytic oscillations is of the order of several minutes and diminishes as the substrate injection rate increases (Hess et al, 1969 Hess Boiteux, 1973 see table 2.1). 

For sufficiently low values of the substrate injection rate, the steady state lies on the left limb of the sigmoid nullcline since the slope (da/dy) is positive, the steady state is stable. As v progressively increases, the steady state moves to the right and remains at first stable until it reaches the region of negative slope on the nullcline. As soon as condition (2.26) is satisfied, the steady state becomes unstable and oscillations occur. A further increase in v results in the displacement of the steady state further to the right on the product nullcline, until a second critical value of the substrate injection rate is reached beyond which condition (2.26) ceases to be satisfied the steady state recovers its stability and oscillations disappear. 

The previously described assays for detecting substrate disappearance or half-life, however, are not suitable for the determination of metabolic rates, which are required for the kinetic delineation of individual... 

A rate law describes the dependence of the rate of product formation (or substrate disappearance) at steady state on the concentrations of catalyst, cocatalysts, substrates, and ligands. A fact that is not generally appreciated is that the functional form of the rate law often depends on the range of experimental variables investigated, as will be shown subsequently. 

Enzyme reactions may be followed continuously, or sampled at fixed time intervals. Either the product of the reaction, or the residual substrate can be measured, although in a two-stage reaction in which an intermediate forms, only substrate disappearance gives a true measure of the reaction rate. Continuous ultraviolet (u.v.) recording methods are easily performed with enzymes that utilise NAD or NADP as co-enzyme. The reduced forms of both these substances exhibit strong absorption peaks at 334 nm and 366 nm. The formation or disappearance of the reduced form of either co-enzyme is thus readily followed in an enzyme reaction mixture which does not contain additional ultraviolet absorbing material, e.g. malate dehydrogenase. 

In stopped-flow studies with spectrophotometric observation, one can observe the disappearance of AdoCbl in the holoenzyme. When a solution of apoenzyme and AdoCbl is mixed with substrate, the rate is typically at the stopped-flow limit, with 3x10 s" for ethanolamine ammonia lyase, ribonucleotide reductase, glutamate mutase and methylmalonyl-CoA mutase. In the latter two systems, it was found that the deuterated form of the substrate reacted about 30 times more slowly. These observations were taken to suggest that Co—C bond homolysis is not the rate-controlling step but is coupled to hydrogen atom abstraction from the substrate. This is consistent with the failure to observe the CHjAdo radical. 

In devising assays for soil enzymes it is necessary to ensure that the reaction catalysed is biochemically mediated, and that the rates of reaction, whether based on substrate disappearance or product formation, are not influenced by their participation in other reactions, biological or physico-chemical. Enzyme activities may also be influenced by the time and conditions of soil storage between sampling from the field and assay. The basic requirements for establishing soil enzyme assays, the advantages and disadvantages of selected assay conditions, and the responses of different enzymes to soil pretreatments have been reviewed in detail elsewhere 19 > 113 j i 2 / > 128 > 149 ... 

The rate parameters for the reactions of e (aq) with substrates are generally determined by monitoring the disappearance of the hydrated electron at 600-700 nm. The first order rate parameters are generally determined over a range of substrate concentrations and the second order rate parameter calculated from the resulting linear relation. The data available for such studies with Pu ions are presented in Table IV. 

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