Enzyme Michaelis-Menton kinetics

Enzymes and micelles resemble each other with respect to both structure (e.g., globular proteins and spherical aggregates) and catalytic activity. Probably the most common form of enzyme catalysis follows the mechanism known in biochemistry as Michaelis-Menton kinetics. In this the rate of the reaction increases with increasing substrate concentration, eventually leveling off. According to this mechanism, enzyme E and substrate A first react reversibly to form a complex EA, which then dissociates to form product P and regenerate the enzyme ... 

Allosteric enzymes constitute an important class of enzymes whose catalytic activity can be regulated. These enzymes, which do not conform to Michaelis-Menton kinetics, have multiple active sites. These active sites display cooperativity, as evidenced by a sigmoidal depen-dence of reaction velocity on substrate concentration. 

Activation at high substrate concentrations not only explains the failure of butyrylcholinesterase to follow simple Michaelis-Menton kinetics, but also explains the enigma of substrate inhibition of the enzyme using either benzoylcholine (A21, T7) or acetyl- or butyryl-salicylcholine as substrates. The proposal made by Hastings is analogous to that of Myers (M24, M25) for the inhibition of acetylcholinesterase by excess substrate, in this case acetylcholine. 

Finally, we end the chapter with a discussion of nature s catalysts enzymes. In fact, we allude to enzymes throughout the chapter. The general manner in which enzymes catalyze reactions is still a matter of debate, and so we present several theories. Our examination of enzymes is in preparation for a few specific enzymatic examples given in Chapters 10 and 11 as highlights for organic reaction mechanisms. Enzymes also provide an excellent setting in which to discuss Michaelis-Menton kinetics, the most common kinetic scenario used for catalysis. We also return to our analysis of the power of changing the thermodynamic reference state to examine reactivity, and show the manner in which an enzyme becomes "perfect". 

As mentioned above, phospholipases are distinguished from general esterases by the fact that they interact with interfaces in order to function. The difference in reaction velocity with substrate concentration for these two types of enzymes is illustrated in Figure 7.6. Whereas esterases show classical Michaelis-Menton kinetics, the phospholipases show a sudden increase in activity as the substrate (phospholipid) concentration reaches the critical micellar concentration (CMC) and the molecules tend to form aggregates or micelles with the polar ends in the aqueous environment... 

A model of such structures has been proposed that captures transport phenomena of both substrates and redox cosubstrate species within a composite biocatalytic electrode.The model is based on macrohomo-geneous and thin-film theories for porous electrodes and accounts for Michaelis—Menton enzyme kinetics and one-dimensional diffusion of multiple species through a porous structure defined as a mesh of tubular fibers. In addition to the solid and aqueous phases, the model also allows for the presence of a gas phase (of uniformly contiguous morphology), as shown in Figure 11, allowing the treatment of high-rate gas-phase reactant transport into the electrode. 

Non-linear pharmacokinetics are much less common than linear kinetics. They occur when drug concentrations are sufficiently high to saturate the ability of the liver enzymes to metabolise the drug. This occurs with ethanol, therapeutic concentrations of phenytoin and salicylates, or when high doses of barbiturates are used for cerebral protection. The kinetics of conventional doses of thiopentone are linear. With non-linear pharmacokinetics, the amount of drug eliminated per unit time is constant rather than a constant fraction of the amount in the body, as is the case for the linear situation. Non-linear kinetics are also referred to as zero order or saturation kinetics. The rate of drug decline is governed by the Michaelis-Menton equation ... 

This mechanism is important for compounds that lack sufficient lipid solubility to move rapidly across the membrane by simple diffusion. A membrane-associated protein is usually involved, specificity, competitive inhibition, and the saturation phenomenon and their kinetics are best described by Michaelis-Menton enzyme kinetic models. Membrane penetration by this mechanism is more rapid than simple diffusion and, in the case of active transport, may proceed beyond the point where concentrations are equal on both... 

Here k is the rate constant for the irreversible reaction, Ceo is the total enzyme concentration, Cs is the substrate concentration, and is the Michaelis-Menton constant. Both k and KM may be functions of pH, temperature, and other properties of the fermentation medium. From this kinetic expression, we see that at high substrate concentrations the rate of product formation is independent of Cs and is approximately equal to kCm-This is due to the presence of a limited amount of enzyme, which is required for the reaction to proceed, and adding more substrate under these conditions will not cause the reaction rate to increase further. At low substrate concentrations, the rate of product formation becomes first-order with respect to Cs- Under these conditions the substrate concentration becomes the determinant for product formation, and increasing Cs produces a proportional increase in rate. The rate is also proportional to the total enzyme concentration under all conditions of substrate concentration. 

This form of the rate expression is called the Michaelis-Menton form and is used widely in describing enzyme catalyzed reactions. The following example illustrates the use of linear regression in order to obtain r ,ax and from experimental kinetic data. 

Describe the Michaelis-Menton eqnation as it relates to enzyme kinetics. 

In addition, the concept of linear responses to graded levels of nutrient input is not consistent with the kinetics of enzymes or enzyme systems. A curved response for individual animals would be expected just as a Michaelis-Menton relationship is expected with increasing substrate concentration for an enzyme. Curved responses have been observed when lysine a-ketoglutarate reductase activity (a simple enzyme system) and lysine oxidation to CO2 (a more complicated pathway) were measured (Blemings et al, 1994). Lysine metabolism in liver homogenates may not be directly related to whole animal responses (an animal is not a big enzyme). An animal is a system of pools and fluxes, however, and there does not appear to be a set of discrete on/off switches. 

A characteristic feature of active transport mechanisms is the existence of a maximal rate, which is ascribed to saturation kinetics analogous to the kinetics for enzymic reactions (Michaelis-Menton). A maximal rate for the transport of taurocholate can be demonstrated in vitro and in vivo (11,14,17, 19). Unfortunately, the interpretation that the observed maximal transport... 

Equation 9 is a hyperbolic relationship, similar to the Michaelis-Menton equation derived for enzyme kinetics (104) the Langmuir equation as applied to adsorption on soils (105), and an adaptation of these models for dechlorination by Fe that we published previously (13). As such, all four models are capable of describing site saturation phenomena commonly found in heterogenous systems however, only the new model (equations 8 and 9) explicitly distinguishes thermodynamically-related parameters from the kinetic constants. 

Estimation of Kinetic parameters of Enzyme Catalysed Reaction S % Michaelis - Menton rate equation % Reaction rate - (-ra) = (kl Cs)/(Km+Cs)... 

The parameter for enzymes that characterizes the sensitivity level for sensors based on the uses of enzymes is the kinetic parameter known as the Michaelis-Menton constant (A m)- Again enzymes can be found... 

The rates of enzyme-catalyzed reactions do not lit simple models for first- or second-order kinetics. Typically, the rate is a nonlinear function of concentration, as shown in Figure 1.9. At low substrate concentrations, the reaction appears first order, but the rate changes more slowly at more moderate concentrations, and the reaction is nearly zero order at high concentrations. A model to explain this behavior was developed in 1913 by L. Michaelis and M. L. Menton [6], and their names are still associated with this type of kinetics. The model presented here is for the simple case of a... 

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