Single-substrate reaction, kinetics

Interpretation of the kinetic phenomena for single-substrate reactions The Michaelis-Menten mechanism... 

It expresses the velocity (v) of a single-substrate reaction (Equation C1. 1.1) in terms of substrate concentration at time zero ([S]) and the kinetic constants KM and V. is defined as the limiting maximal velocity for the reaction, which is observed when all of the enzyme is present as ES. KM, known as the Michaelis constant, is a pseudoequilibrium constant, which equals the concentration of substrate at which the reaction velocity equals one-half Vtrax (Figure Cl. 1.1). 

Determination of the kinetic constant for a bi-substrate reaction is carried out in a similar manner to that for single substrate reactions. This is achieved by investigating only one substrate at a time, while the other is kept at a set concentration which is usually its saturation concentration. Thus, to determine the Km and Kmax of substrate A, B is kept constant at a saturating level while the reaction of A is investigated at different concentrations. The experimental conditions are then reversed to determine the kinetic constants of B. Thus, the kinetic constants for a bi-substrate reaction are determined using two separate kinetic plots, as discussed previously for the conditions where concentrations of A or B limit the rate of the reaction. Clearly, the conditions under which the rates are determined must be quoted for any determination. 

As we have seen, the catalytic cycle flux provides a useful metric for analyzing enzyme kinetics. In this section, we analyze the turnover time for catalytic cycles and show that the quasi-steady rate law arises from the mean cycle time [151]. In addition, we show that for arbitrary mechanisms for a single-substrate reaction, the steady state rate law can always be expressed using the Michaelis-Menten form... 

Figure 7-3 shows that glucose uptake by erythrocytes and liver cells exhibits kinetics characteristic of a simple enzyme-catalyzed reaction involving a single substrate. The kinetics of transport reactions mediated by other types of proteins are more complicated than for uniporters. Nonetheless, all protein-assisted transport reactions occur faster than allowed by passive diffusion, are substrate-specific as reflected in lower Kjn values for some substrates than others, and exhibit a maximal rate (Vjjjax)-... 

The kinetic parameters and Umax are estimated from the Michaelis-Menten equation and provide quantitative information regarding enzyme function. or the Michaelis constant is operationally defined as the concentration of substrate at which half-maximal velocity of the reaction is achieved (Fig. 4.1). With respect to the single substrate reaction scheme (Scheme 4.1), it should be realized that is equal to k + k2)lkx and thus is the amalgamation of several rate constants. With respect to affinity, unfortunately, is frequently (and incorrectly) used interchangeably with which is the substrate dissociation constant. Though may sometimes approximate the two do not have to be equal and numerous examples exist where these parameter values vary dramatically. 

In analyzing the role of diffusion in IME reactions, we assume that the reaction follows single-substrate MM kinetics and that there is no appreciable change in temperature or pH. Then the following nondimensional mass balance can be written for a single spherical pellet ... 

Monomolecular reactions, that is single substrate reactions, take place according to first-order kinetics in that their velocity is directly proportional to the first power of the concentration of the substrate. 

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

Most enzymes catalyse reactions and follow Michaelis-Menten kinetics. The rate can be described on the basis of the concentration of the substrate and the enzymes. For a single enzyme and single substrate, the rate equation is ... 

Typical single-substrate enzymatic reactions can be described by the kinetic scheme (see Refs. 1 and 2 for more extensive discussions). 

While many enzymes have a single substrate, many others have two—and sometimes more than two—substrates and products. The fundamental principles discussed above, while illustrated for single-substrate enzymes, apply also to multisubstrate enzymes. The mathematical expressions used to evaluate multisubstrate reactions are, however, complex. While detailed kinetic analysis of multisubstrate reactions exceeds the scope of this chapter, two-substrate, two-product reactions (termed Bi-Bi reactions) are considered below. 

In the presence of sucrose alone as the single substrate, initial reaction rates follow Michaelis-Menten kinetics up to 200 mM sucrose concentration, but the enzyme is inhibited by higher concentrations of substrate.30 The inhibitor constant for sucrose is 730 mM. This inhibition can be overcome by the addition of acceptors.31,32 The enzyme activity is significantly enhanced, and stabilized, by the presence of dextran, and by calcium ions. 

A kinetic description of large reaction networks entirely in terms of elementary reactionsteps is often not suitable in practice. Rather, enzyme-catalyzed reactions are described by simplified overall reactions, invoking several reasonable approximations. Consider an enzyme-catalyzed reaction with a single substrate The substrate S binds reversibly to the enzyme E, thereby forming an enzyme substrate complex [/iS ]. Subsequently, the product P is irreversibly dissociated from the enzyme. The resulting scheme, named after L. Michaelis and M. L. Menten [152], can be depicted as... 

Figure E5.7 displays the kinetic progress curve of a typical enzyme-catalyzed reaction and illustrates the advantage of a kinetic assay. The rate of product formation decreases with time. This may be due to any combination of factors such as decrease in substrate concentration, denaturation of the enzyme, and product inhibition of the reaction. The solid line in Figure E5.7 represents the continuously measured time course of a reaction (kinetic assay). The true rate of the reaction is determined from the slope of the dashed line drawn tangent to the experimental result. From the data given, the rate is 5 jumoles of product formed per minute. Data from a fixed-time assay are also shown on Figure E5.7. If it is assumed that no product is present at the start of the reaction, then only a single measurement after a fixed period is necessary. This is shown by a circle on the experimental rate curve. The measured rate is now 16 jumoles of product formed every 5 minutes or about 3 /rmoles/minute, considerably lower than the rate derived from the continuous, kinetic assay. Which rate measurement is correct Obviously, the kinetic assay gives the true rate because it corrects for the decline in rate with time. The fixed-time assay can be improved by changing the time of the measurement, in this example, to 2 minutes of reaction time, when the experimental rate is still linear. It is possible to obtain...

Reversible inhibition occurs rapidly in a system which is near its equilibrium point and its extent is dependent on the concentration of enzyme, inhibitor and substrate. It remains constant over the period when the initial reaction velocity studies are performed. In contrast, irreversible inhibition may increase with time. In simple single-substrate enzyme-catalysed reactions there are three main types of inhibition patterns involving reactions following the Michaelis-Menten equation competitive, uncompetitive and non-competitive inhibition. Competitive inhibition occurs when the inhibitor directly competes with the substrate in forming the enzyme complex. Uncompetitive inhibition involves the interaction of the inhibitor with only the enzyme-substrate complex, while non-competitive inhibition occurs when the inhibitor binds to either the enzyme or the enzyme-substrate complex without affecting the binding of the substrate. The kinetic modifications of the Michaelis-Menten equation associated with the various types of inhibition are shown below. The derivation of these equations is shown in Appendix S.S. 

The steady-state kinetics of a simple single-substrate, single-binding site, single-intermediate-enzyme catalysed reaction in the presence of competitive inhibitor are shown in Scheme A5.5.1. 

The simplest enzymatic system is the conversion of a single substrate to a single product. Even this straightforward case involves a minimum of three steps binding of the substrate by the enzyme, conversion of the substrate to the product, and release of the product by the enzyme (Scheme 4.6). Each step has its own forward and reverse rate constant. Based on the induced fit hypothesis, the binding step alone can involve multiple distinct steps. The substrate-to-product reaction is also typically a multistep reaction. Kinetically, the most important step is the rate-determining step, which limits the rate of conversion. 

The kinetics of enzyme reactions was first established by Michaelis and Menten, following the earlier work of Henri [23]. The famous Michaelis-Menten equation for the kinetics of an enzyme reaction with a single substrate is often written [23]... 

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