Michaelis parameters enzyme reactions

Before NMR spectroscopy and mass spectrometry revolutionized the structural elucidation of organic molecules, UV spectroscopy was an important technique and was used to identify the key chromophore of an unknown molecule. The importance of UV is much diminished nowadays, but it still retains its place in certain applications, such as the determination of kinetic parameters, (the Michaelis constant) and A cat (the turnover rate of an enzyme, in molecules per second), for a number of enzymic reactions and in the analysis of pharmaceuticals. 

A substrate is converted to a product by the catalytic action of an enzyme. Assume that the Michaelis-Menten kinetic parameters for this enzyme reaction are ... 

The Monod kinetic parameters, and Ks, cannot be estimated with a series of batch runs as easily as the Michaelis-Menten parameters for an enzyme reaction. In the case of an enzyme reaction, the initial rate of reaction can be measured as a function of substrate concentration in batch runs. However, in the case of cell cultivation, the initial rate of reaction in a batch run is always zero due to the presence of a lag phase, during which Monod kinetics does not apply. It should be noted that even though the Monod equation has the same form as the Michaelis-Menten equation, the rate equation is different. In the Michaelis-Menten equation,... 

In contrast to [E]free, [E]total is observable. Eq. (2.3) is written with fCM, the Michaelis constant, instead of the equilibrium binding constant Ks unless the enzyme reaction is very fast (Section 2.3.3.) i.e., in almost all cases, fCM = Ks. In Eq. (2.3), the reaction rate is traditionally denoted by v [concentration/time] and fccat is the reaction rate constant [time4]. The equation describes a two-parameter kinetics, with a monotonically rising reaction rate with respect to substrate concentration and saturation at high substrate concentration. The maximum reaction rate at saturation is denoted by vmax, with vmax = fccat[E], The fCM value corresponds to the substrate... 

Mass transfer can alter the observed kinetic parameter of enzyme reactions. Hints of this are provided by non-linear Lineweaver-Burk plots (or other linearization methods), non-linear Arrhenius plots, or differing Ku values for native and immobilized enzymes. Different expressions have been developed for the description of apparent Michaelis constants under the influence of external mass transfer limitations by Homby (1968) [Eq. (5.69)], Kobayashi (1971), [Eq. (5.70)], and Schuler (1972) [Eq. (5.71)]. 

Interestingly, a fully appropriate model was developed at the same time as the Langmuir model using a similar basic approach. This is the Michaelis-Menten equation which has proved to be so useful in the interpretation of enzyme kinetics and, thereby, understanding the mechanisms of enzyme reactions. Another advantage in using this model is the fact that a graphical presentation of the data is commonly used to obtain the reaction kinetic parameters. Some basic concepts and applications will be presented here but a more complete discussion can be found in a number of texts. ... 

When the QCM technique was employed for the starch hydrolysis, all kinetic parameters both of the enzyme binding process (kon. koff and JCj) and the hydrolysis process (kcat) could be obtained simultaneously on the same device, as shown in Table 3. In the conventional enzyme reactions in the bulk solution, Michaelis-Menten kinetics have been applied to obtain both the Michaelis constant (Km) and the hydrolysis rate constant (kcat) according to Eq. 16. If koff > kcat, the Km value is thought to be the apparent dissociation constant (K = koff/kon) ... 

The time required to reach steady-state potential reading is dependent on the enzyme layer thickness because of the diffusion parameter for the substrate to reach the active sites of the enzyme and of the electroactive species to diffuse through the membrane to the sensor. A mathematical model relating the thickness of the membrane, d, the diffusion coefficient, D, the Michaelis constant, K, and the maximum velocity of the enzyme reaction, Vmax, has been developed ... 

Detection limits for enzyme-based potentiometric biosensors are governed by the iimate detection limits of the membrane electrode toward the product of the enzyme reaction, as well as the kinetics of the enzymatic reaction (Michaelis-Menten constant and turnover number of the enzyme), and mass transfer rate of substrate into the enzymatic layer. Carr and Bowers developed in detail the theory of how such parameters affect the response curves of such sensors [48]. Generally, enzyme-based potentiometric biosensors respond to target substrates over the concentration range of 0.01 mM to 10 mM. In the case of the urea example mentioned earlier, limited selectivity of the nonactin-based ammonium membrane electrode over potassium ions k ... 

The efficiency of solution-phase (two aqueous phase) enzymatic reaction in microreactor was demonstrated by laccase-catalyzed l-DOPA oxidation in an oxygen-saturated water solution, and analyzed in a Y-shaped microreactor at different residence times (Figure 10.24) [142]. Up to 87% conversions of l-DOPA were achieved at residence times below 2 min. A two-dimensional mathematical model composed of convection, diffusion, and enzyme reaction terms was developed. Enzyme kinetics was described with the double substrate Michaelis-Menten equation, where kinetic parameters from previously performed batch experiments were used. Model simulations, obtained by a nonequidistant finite differences numerical solution of a complex equation system, were proved and verified in a set of experiments performed in a microreactor. Based on the developed model, further microreactor design and process optimization are feasible. 

Briggs Haldane (1925) removed the restrictive assumption that the enzyme-substrate complex is in equilibrium with free enzyme and substrate and introduced the steady state model, which gives the Michaelis parameters, ATm and a more complex meaning. The principles of steady state kinetics of enzyme reactions can be demonstrated with the more realistic, though still oversimplified, model of Haldane (1930). This contains the minimum number of intermediates, namely enzyme-substrate and enzyme-product complexes ... 

This is exactly what the Haldane relations demonstrate for the sequence of intermediates in enzyme reactions. They are useful criteria when changing Michaelis parameters are compared to the equilibrium constant for an enzyme catalysed reaction. We shall return to this problem in section 5.1, when we discuss how transient kinetic analysis can be used to determine the equilibrium constants of individual steps. In this connection the equations which express the concentrations of the intermediates in terms of the fraction of total amount of enzyme in the reaction mixture will turn out to be useful. Many enzyme reactions can be studied in both directions and the two sets of parameters for the reactions starting on either side (with S or P as the substrate) - Kh, and - give further insight. 

Note that p. has units of reciprocal time—for example, h. Model parameter p max is referred to as the maximum growth rate, because p. has a maximum value of p max when 5 Ks. The second model parameter, Ks, is called the Monod constant. The Monod equation has the same form as the Michaelis-Menten equation, a standard rate expression for enzyme reactions (Bailey and Ollis, 1986 Fogler, 2006). 

Michaelis-Menten kinetics A general two-parameter enzyme reaction model in which the reaction velocity, V, is given by ... 

A basic theory of enzyme action was proposed in 1913 when Michaelis and Menten developed a mathematical expression to rationalize the hyperbolic plot of Vj as a function of [S]. The Michaelis-Menten equation aims to describe the interrelationship between the parameters pertaining to an enzymic reaction. This accomplishment was based on two assumptions ... 

FIGURE 1.14 The first two rows show the normal absorptions for substrate (continuous curves) and product (dashed curves) concentrations of the enzyme-catalyzed reaction without inhibition, based on the logistical temporal approximation, and on the IF-Lambert temporal solution, respectively the third row depicts the difieience between IF-Lambert and logistical counterpart for substrate or product normal absorption progress curves on the columns, the plots are presented for the enzyme/substrate ratio e taking the in vitro and almost the in vivo values, from 10" to 10 and equal or greater than 10, respectively the employed kinetic parameters are the maximum velocity of enzyme reaction 1 O Mxsr and the Michaelis... 

Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

Let us consider the determination of two parameters, the maximum reaction rate (rITOIX) and the saturation constant (Km) in an enzyme-catalyzed reaction following Michaelis-Menten kinetics. The Michaelis-Menten kinetic rate equation relates the reaction rate (r) to the substrate concentrations (S) by... 

---