Enzymatic initial rates

It is during this steady state period that the rates of enzymatic reactions are traditionally measured and the parameter measured is the initial rate v of product formation - that is the formation of the first few percent of the products so that the substrate is not depleted and the products(s) have not yet accumulated. 

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. 

We examined the effect of restricted conformation on the activation entropy by kinetic studies at various temperatures [34]. Three kinds of substrates were subjected to the reaction phenylmalonic acid as the standard compound, ortho-chlorophenylmalonic acid as a substrate with an electron-withdrawing group, and indane-l,l-dicarboxylic acid as a conformationally restricted compound. The initial rates of the enzymatic decarboxylation reaction of three compounds were measured at several substrate concentrations at 15 °C, 25 °C, and 35 °C. The kcat and values at each temperature were obtained by a Lineweaver-Burk plot,... 

The components of the coupling system should neither inhibit nor activate the primary enzyme. Moreover, care must be exercized to ascertain that the auxiliary enzyme (s) is not contaminated with other minor enzyme activities capable of influencing the primary enzymatic activity. The results from any coupled enzyme assay must exactly match the results obtained with other valid initial rate assays to ensure that the presence of the auxiliary system in no way affects the activity of the primary enzyme. This is typically accomplished by comparing data obtained from the coupled assay with stopped-time assay results to ensure that similar results are obtained. 

Regulation of enzymic activity occurs via two modes (cf. Ref. 50) alteration of the substrate binding process and/or alteration of the catalytic efficiency (turnover number) of the enzyme. The initial rate of a simple enzymatic reaction v is governed by the Michaelis-Menten equation... 

The enzyme invertase catalyzes the hydrolysis of sucrose to glucose and fructose. The rate of this enzymatic reaction decreases at higher substrate concentrations. Using the same amount of invertase, the initial rates at different sucrose concentrations are given in Table P3.9. 

At any given instant in an enzyme-catalyzed reaction, the enzyme exists in two forms, the free or uncombined form E and the combined form ES. At low [S], most of the enzyme is in the uncombined form E. Here, the rate is proportional to [S] because the equilibrium of Equation 6-7 is pushed toward formation of more ES as [S] increases. The maximum initial rate of the catalyzed reaction (Prnax) is observed when virtually all the enzyme is present as the ES complex and [E] is vanishingly small. Under these conditions, the enzyme is saturated with its substrate, so that further increases in [S] have no effect on rate. This condition exists when [S] is sufficiently high that essentially all the free enzyme has been converted to the ES form. After the ES complex breaks down to yield the product P, the enzyme is free to catalyze reaction of another molecule of substrate. The saturation effect is a distinguishing characteristic of enzymatic catalysts and is responsible for the plateau observed in Figure 6-11. The pattern seen in Figure 6-11 is sometimes referred to as saturation kinetics. 

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. 

The initial rate of reaction for the enzymatic cleavage of deoxyguanosine triphosphate was measured as a function of initial substrate concentration as follows (Kornberg et al., J.Biol.Chem., 233, 159, 1958) ... 

Determine the total protein in triplicate by the Bradford method using bovine serum albumin as standard solution [2], Determine the enzymatic activity of jack fruit crude extract in triplicate by measuring the absorbance at 410 nm of o-quinone produced by the reaction between 2.8 mL of 0.05 mol L 1 catechol solution and 0.2 mL of supernatant solution in 0.1 mol L 1 phosphate buffer solution (pH 7.0) at 25°C. The initial rate of enzyme-catalyzed reaction is a linear function of time for 1.5-2.0min. One activity unit is defined as a quantity of enzyme that causes the increase of 0.001 absorbance per minute under conditions described above [1]. 

In the thermolysin-catalyzed solid-to-solid dipeptide synthesis of equimolar amounts of Z-Gln-OH and H-Leu-NH2 as model substrates, the water content was varied from 0 to 600 mL water (mol substrate)-1 and enzyme concentration in the range 0.5-10 g (mol substrate)-1 to achieve 80% yield and initial rates of 5-20 mmol (s kg)-1 (Erbeldinger, 1998). When the water content is decreased from the 1.6-molal lowest substrate concentration, the initial rate increases tenfold to a pronounced optimum at 40 mL water (mol substrate)-1 and falls to much lower values in a system with no added water, and to zero in a rigorously dried system. The behavior at a higher water content was demonstrated through variation of the enzyme content to be caused by mass transfer limitations at low water levels, the effects reflect the stimulation of the enzymatic activity by water. Preheating of the substrates or ultrasonic treatment had no significant effect on the system. 

The initial, rather rapid increase in CER found in the second stage of two-phase batch cultivation was somewhat unexpected. We decided to compare this value to the initial rates of glucose and cellobiose formation in in vitro enzymatic hydrolysis experiments (Figs. 4 and 5). The enzyme loadings were chosen to represent the actual enzyme-to-substrate ratio relevant to the point of cellulose addition and the point of maximum CER. 

The initial rate enzyme kinetics uses very low enzyme concentrations (e.g., 0.1 juM to 0.1 pM) to investigate the steady-state region of enzyme-catalyzed reactions. To investigate an enzymatic reaction before the steady state (i.e., transient state), special techniques known as transient kinetics (Eigen and Hammes, 1963) are employed. The student should consult chapters of kinetic texts (Hammes, 1982 Robert, 1977) on the topics. KinTekSim (http //www.kintek-corp.com/kintek-sim.htm) is the Windows version of KINSIM/FITSIM (Frieden, 1993) which analyzes and simulate enzyme-catalyzed reactions. 

The HPLC assay method is particularly useful when it is necessary to obtain initial rate data for a study of an enzymatic activity. Optimal assay conditions for the HPLC must be established first. Usually, the optimization process involves the determination of several variables, such as the optimal substrate concentration, pH, temperature, and enzyme concentration. It is assumed that the reader is familiar with the problems associated with assay conditions such as pH, buffer, and temperature. This chapter discusses only factors that might present problems for the HPLC assay method. For additional information, see the works cited in the General References. 

If it is not possible to obtain an end point or complete conversion to product, substrate concentrations can be determined from the rate dependence of the enzyme reaction under conditions where [S] KM (Sect. 8.2.2). The sensitivity of the method is not as great as can be achieved by using equilibrium end point measurements, since accuracy depends on analysis of the initial rate of enzymatic turnover. 

In this case, the question is whether H+ should be considered a third substrate. It has, in fact, been treated in this manner by researchers, who have shown that if both pymvate and NADH concentrations are maintained at saturating levels, the initial rate of the enzymatic reaction is pH dependent, showing a Gaussian-like curve over the pH range 6-8. Data taken on the alkaline side of this curve may be used to obtain a KmU value, or, alternately, the alkaline pH value at Vm ix/2 value may be read... 

Enzymatic assay methods are classified as fixed-time assays, fixed-change assays, or kinetic (initial rate) assays. Kinetic assays continuously monitor concentration as a function of time pseudo-first-order conditions generally apply up to 10% completion of the reaction to allow the initial reaction rate to be determined. If the initial substrate concentration is > 10Km, then the initial rate is directly proportional to enzyme concentration. At low initial substrate concentrations (< 0.1 Km), the initial rate will be directly proportional to initial substrate concentration (cf. Chapter 2). For enzyme quantitation, a plot of initial rate against [E] provides a linear... 

The rate of an enzymatic reaction is proportional to its reaction temperature. For most enzymatic reactions, values of Qio (the relative reaction rates at two temperatures differing by 10 °C) vary from 1.7 to 2.5. However, an increase in the rate of the catalyzed reaction is not the only effect of increasing temperature on an enzymatic reaction. In theory, the initial rate of reaction measured instantaneously wiU increase with a rising temperature, hi practice, however, a... 

Enzymatic action can be defined on three levels operational kinetics, molecular architecture, and chemical mechanism. Operational kinetic data have given indirect information about cellulolytic enzyme mode of action along with important information useful for modeling cellulose hydrolysis by specific cellulolytic enzyme systems. These data are based on measurement of initial rates of enzyme hydrolysis with respect to purified celluloses and their water soluble derivatives over a range of concentrations of both substrate and products. The resulting kinetic patterns facilitate definition of the enzyme s mode of action, kinetic equations, and concentration based binding constants. Since these enable the enzymes action to be defined with little direct knowledge of its mechanistic basis, the rate equations obtained are referred to as operational kinetics. The rate patterns have enabled mechanisms to be inferred, and these have often coincided with more direct observations of the enzyme s action on a molecular level [2-4]. 

Further studies on this system with carbobenzoxyglycyl-L-phenylalanine (CGP) and carbobenzoxyglycyl-L-leucine (CGL) as the substrates led to the conclusion that orthophosphate, pyrophosphate, oxalate, citrate, and cyanide did not affect the initial rate of hydrolysis significantly (Neurath and de Maria, 1950). In the presence of these anions, competitive inhibition by the liberated amino acid was found to occur. These authors concluded that the anions had no effect on the enzymatic activation process and that the hypothesis that carboxypeptidase is a magnesium enzyme was devoid of experimental evidence. 

A minimal enzymatic reaction, in which the substrate, S, is converted into the product, P, is shown in Eq. (10.1). Under initial-rate conditions ([P]q = 0), product release is a kinetically irreversible step (k 3[P]Q = 0) as shown. 

Like enzyme concentration, choice of mediator and its concentration can have a major impact on the polymer properties. Kaplan and coworkers demonstrated the influence that the choice of -diketone can exceed on yield and polymer characteristics (Table 6.2) [12]. So far, detailed studies clarifying the influence of -diketone structure on enzyme activity are missing. Steric and electronic effects influence both, the rate of the enzymatic initiation reaction as well as the rate of the chain growth reaction [12, 25]. 

Enzymatic reactions are usually characterized by a parameter, the Michaelis-Menten constant or KM, which is determined by the efficiency of the first equilibrium reaction for the formation of ES. That is, KM is the concentration in mM of S at which the initial rate of the overall process, V0, is one-half of the maximum rate, Vma possible. The maximum rate occurs when all of E is converted to ES. Each particular type and concentration of E and S, and each set of reactions conditions, has its own KM, and the Michaelis-Menten equation describes the relationship between Vo, [S] (the concentration of S), Vmax and Km for a given amount of E under a fixed set of conditions, as follows ... 

The activity of the native and modified SC was also studied for the reaction methanolysis of APEE, using the substrate, methanol, itself as a solvent. This was done for three different salt-enzyme preparations, consisting of 99% salt, 50% salt, and no added salt (except that present in buffer). It was found that the PEG modification resulted in a six- to sevenfold increase in the initial rates of conversion for the cases with no surfactant and with T 20 (Table 2). AOT was found to reduce the activity of the enzyme preparations in all experiments conducted in the solvent methanol. Previous reports on enzymatic conversion in organic solvents have shown the effect of the solvent dielectric constant on enzyme activity for salt-free enzymes [22], Relationship between activity of AOT and PEG-modified SC to the hydrophobicity coefficient of various solvents has also been studied [20], however, only for the enzymes without salt-lyophilization. The decrease in activity of enzymes in organic solvents is attributed to the decreased water availability in organic media. Additionally, as the dielectric constant increases, the potential for removal of the... 

---