Disappearance of substrate

Runge-Kutta. Consider the disappearance of substrate in an enzyme-catalyzed reaction that follows Michaelis-Menten kinetics ... 

As the enzyme itself is usually the focus of interest, information on the behavior of that enzyme can be obtained by incubating the enzyme with a suitable substrate under appropriate conditions. A suitable substrate in this context is one which can be quantified by an available detection system (often absorbance or fluorescence spectroscopy, radiometry or electrochemistry), or one which yields a product that is similarly detectable. In addition, if separation of substrate from product is necessary before quantification (for example, in radioisotopic assays), this should be readily achievable. It is preferable, although not always possible, to measure the appearance of product, rather than the disappearance of substrate, because a zero baseline is theoretically possible in the former case, improving sensitivity and resolution. Even if a product (or substrate) is not directly amenable to an available detection method, it maybe possible to derivatize the product with a chemical species to form a detectable adduct, or to subject a product to a second enzymatic step (known as a coupled assay, discussed further later) to yield a detectable product. But, regardless of whether substrate, product, or an adduct of either is measured, the parameter we are interested in determining is the initial rate of change of concentration, which is determined from the initial slope of a concentration versus time plot. 

For the enzyme-substrate reaction of Example 2, the rate of disappearance of substrate is given by... 

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. 

The usual procedure for measuring the rate of an enzymatic reaction is to mix enzyme with substrate and observe the formation of product or disappearance of substrate as soon as possible after mixing, when the substrate concentration is still close to its initial value and the product concentration is small. The measurements usually are repeated over a range of substrate concentrations to map out how the initial rate depends on concentration. Spectro-photometric techniques are used commonly in such experiments because in many cases they allow the concentration of a substrate or product in the mixture to be measured continuously as a function of time. 

When the decomposition in question involves more than one bond in a concerted homolysis, as in an azoalkane (Equation 9.39), the disappearance of substrate is unaffected by recombination, but the number of R radicals available in the bulk solution to initiate other processes is less than two for each molecule of initiator consumed. Most experimental efforts to determine amount of cage recombination in these instances are of either the crossover or the scavenger type. In a crossover experiment, one decomposes a mixture of R—N=N—R and R —N=N—R geminate recombination must yield only R—R and R —R, whereas the separated radicals will recombine randomly to a statistical mixture of R—R, R —R, and R—R. 101... 

An enzyme assay measures the conversion of substrate to product, under conditions of cofactors, pH and temperature at which the enzyme is optimally active. High substrate concentrations are used so that the initial reaction rate is proportional to the enzyme concentration. Either the rate of appearance of product or the rate of disappearance of substrate is measured, often by following the change in absorbance using a spectrophotometer. Reduced nicotinamide adenine dinucleotide (NADH) and reduced nicotinamide adenine dinucleotide phosphate (NADPH), which absorb light at 340 nm, are often used to monitor the progress of an enzyme reaction. 

Enzyme assays The amount of enzyme protein present can be determined (assayed) in terms of the catalytic effect it produces, that is the conversion of substrate to product. In order to assay (monitor the activity of) an enzyme, the overall equation of the reaction being catalyzed must be known, and an analytical procedure must be available for determining either the disappearance of substrate or the appearance of product. In addition, one must take into account whether the enzyme requires any cofactors, and the pH and temperature at which the enzyme is optimally active (see Topic C3). For mammalian enzymes, this is usually in the range 25-37°C. Finally, it is essential that the rate of the reaction being assayed is a measure of the enzyme activity present and is not limited by an insufficient supply of substrate. Therefore, very high substrate concentrations are generally required so that the initial reaction rate, which is determined experimentally, is proportional to the enzyme concentration (see Topic C3). 

In the assay by Klein and Haas (1990), the substrate, 5-bromouracil, is separated from the reaction mixture by chromatography on Hypersil ODS 2. The mobile phase was 0.02 M potassium phosphate buffer (pH 5.6)-methanol (94 6, v/v). The column effluent was monitored at 275 nm. The rate of disappearance of substrate was obtained from the slope of the line obtained by plotting the concentrations of 5-bromouracil against the incubation times. 

The rate of disappearance of substrate, -r, results from substrate used for cell growth and substrate used for cell maintenance. 

The rate of the overall reaction can be expressed in terms of the disappearance of substrate S,... 

Because the enzyme substrate and the products are unstable, it is difficult to measure the disappearance of substrate or the formation of products as is usual in enzymatic assays. Routine assays for SOD usually employ an indirect assay in which one unit of enzyme activity is defined as the amount of enzyme that inhibits the reaction of 02 with the indicator by 50%. The most frequently used method for measuring SOD activity employs the xanthine/xanthine oxidase reaction for... 

The advanced stages of oxidation must be marked by appreciable disappearance of substrate and this factor may be introduced into the above equation if one assumes at a first approximation that the unoxidized substrate present at any given time is equal to that present initially less the concentration of hydroperoxides formed, i.e. [RH] = [RH]0 - [ROOH] (14). This assumption leads to the following equation ... 

One of the keys to defining an enzyme catalytic reaction pathway is the identification of enzyme reaction intermediates. The criteria (Scheme 1) to establish an enzymatic reaction pathway with a postulated intermediate may be defined by addressing the following questions (1) Can the intermediate be isolated and its structure determined directly or if it is unstable can analysis of breakdown products support the postulated structure. (2) Is the chemical rationale of the reaction intermediate based upon chemical precedent and reasonable thermodynamics. and (3) Is the intermediate kinetically competent , in other words, is it formed and broken down at the enzyme active site on a timescale that is consistent with the disappearance of substrate and the formation of product. ... 

A characteristic of the phenol hydroxylation reaction was that there was a lag between the disappearance of substrate and the appearance of products (Figure 6). No intermediates were observed. This led us to believe that the substrate was being absorbed into the interlayers and oxidation taking place there. 

The first two equality signs in Eq. (2.2) show that the rate (u) is defined in terms of appearance of product or disappearance of substrate (Plowman, 1972 Cornish-Bowden, 1995). The next equality specifies that this is a first-order reaction, because it states that the rate is proportional to the concentration of reactant A. Finally, it is clear that Ao = A -i- P. 

Figure 5.15. Concentration versus time S plot for the disappearance of substrate under different kinetic systems reaction orders n = 0, 1/2, 1, and 2 and Monod kinetics (M).

This is a closed system and the falling off in the speed of the reaction can be accounted for by the disappearance of substrate S and the accumulation of products P so that eventually equilibrium conditions are established when... 

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