Sigmoid enzyme kinetics

Cooperative enzymes show sigmoid or sigmoidal kinetics because the dependence of the initial velocity on the concentration of the substrate is not Michaelis-Menten-like but gives a sigmoid curve (Fig. 8-7). 

PFK displays sigmoidal kinetics for the conversion of fructose-6-P, although not for ATP. The enzyme is allosterically activated by ADP and allosterically inhibited by phos-phoenolpyruvate (fig. 2.6). 

Tt is debatable whether or not this is a control enzyme PEP is certainly well below the KM in any case. The data quoted are for the presence of 500-uM FDP, in which case Michaelis-Menten kinetics hold. In the absence of FDP, sigmoid kinetics holds with a K0 5 of 650 p,M.m... 

Phosphofructokinase has four identical subunits. To explore how sigmoidal kinetics can arise in such an enzyme, consider an enzyme that has just two such subunits, each with its own catalytically active site. We can schematize the binding of substrate to the enzyme as follows ... 

These conclusions are supported by a series of related experiments on the same recombinant pea cytosolic enzyme in which the steady state oxidation of / -cresol has also been found to exhibit sigmoidal kinetics (Celik et al., 1999). In this case, the data were satisfactorily fitted to the Hill equation, Eq. (2),... 

The [S]o.9/[S]o.i ratio for an enzyme that obeys sigmoidal kinetics is 6.5. What is the Tiapp value ... 

The following data were obtained for an enzyme-catalyzed reaction. Determine whether the enzyme obeys hyperbolic or sigmoidal kinetics and calculate or estimate the appropriate kinetic constants (A and or... 

The red ceU enzyme is allosterically regulated by fructose-1,6-diphosphate (FDP). Sigmoid kinetics occur by increasing concentrations of the substrate phosphoenolpyruvate. 

Figure 10.3 ATCase displays sigmoidal kinetics. A plot of product formation as a function of substrate concentration produces a sigmoidal curve because the binding of substrate to one active site increases the activity at the other active sites. Thus, the enzyme shows cooperativity.

The larger subunit is called the catalytic subunit. This subunit displays catalytic activity but is unresponsive to GTP and does not display sigmoidal kinetics. The isolated smaller subunit can bind C TP, but has no catalytic activity. Hence, that subunit is called the regulatory subunit. The catalytic subunit (cj) consists of three chains (34 kd each), and the regulatory subunit (r>) consists of two chains (17 kd each). The catalytic and regulatory subunits combine rapidly when they are mixed. The resulting complex has the same structure, c /, as the native enzyme two catalytic trimers and three regulatory dimers. 

How can we explain the enzyme s sigmoidal kinetics in light of the structural observations Like hemoglobin (p. 188), the enzyme exists man equilibrium between the T stale and the R stale. In the absence of sub-.strate, almost all the enzyme molecules are in the T state. The T state has a low affinity for substrate and hence shows a low catalytic activity, The oc casional binding of a substrate molecule to one active site in an enzyme increases the likelihood that the entire enzyme shifts to the R state with its higher binding affinity. The addition of more substrate has two effects. First, it increases the probability that each enzyme molecule will bind at least one substrate molecule. Second, it increases the average number ot substrate molecules bound to each enzyme. The presence of additional substrate will increase the fraction of enzyme molecules in the more active R state because the position of the equilibrium depends on the number of dc -live sites that are occupied by subslrate. We considered this property, called... 

C. The activity of regulatory enzymes such as fructose-1,6-bisphos-phatase, hexokinase, phosphofructokinase 1, and pyruvate kinase are frequently controlled by binding allosteric effectors. These allosteric enzymes usually exhibit sigmoidal kinetics. Lactate dehydrogenase is not controlled by allosteric effectors and therefore would be expected to exhibit Michaelis-Menten kinetics. 

There is some confusion in the literature about the use of the term "allosteric" for an enzyme. Many authors restrict this term to multi-subunit enzymes that show substrate cooperativity and sigmoidal kinetics. Other authors, however, are less specific and their definitions include enzymes that follow Michaelis- Menten kinetics and have non- or uncompetitive inhibitors. Fortunately, in metabolism, regulated enzymes are generally multi-subunit, cooperative, enzymes and fall into the more specific use of the term. 

Sigmoidal kinetics produce a finer control of change in enzyme activity with change in substrate than Michaelis-Menten kinetics. Many, but not all, control enzymes exhibit sigmoidal kinetics. 

For example, sigmoid kinetics can be found if the enzyme contains an impurity which can combine with the substrate and render it incapable. of being acted upon by the enzyme, and also may be found if the enzyme can exist in two forms of differing activities. 

Several theories of sigmoid kinetics are based on the idea that certain enzyme molecules are composed of a number of subunits which interact with each other. 

In contrast with Michaelian enzymes, which have hyperbolic kinetics, allosteric enzymes, thanks to their sigmoidal kinetics, possess an enhanced sensitivity towards variations in the concentration of an effector or of the substrate. This is the reason why many enzymes that play an important role in the control of metabolism are of the allosteric type. 

Why do chymotrypsin and ATCase have different velocity curves Chymotrypsin and aspartate transcar-bamoylase exhibit different types of kinetics. Chymotrypsin is a nonallosteric enzyme and exhibits hyperbolic kinetics. ATCase is an allosteric enzyme. It has multiple subunits, and the binding of one molecule of substrate affects the binding of the next molecule of substrate. It exhibits sigmoidal kinetics. 

Allosteric enzymes display sigmoidal kinetics when rates are plotted versus substrate concentration. Michaelis-Menten enzymes exhibit hyperbolic kinetics. Allosteric enzymes usually have multiple subunits, and the binding of substrates or effector molecules to one subunit changes the binding behavior of the other subunits. 

In the case of the oligomeric enzymes the kinetic cooperativity is more complex. The interactions between the subunits can influence the rate (speed) of the transition or even alter the three-dimensional structure of the subunits themselves. Weakly coupled subunits generate no sigmoidal substrate saturation curve and in this instance the kinetic cooperativity can be greater or smaller than the corresponding substrate binding cooperativity. This is the case for V2, as it can be seen from the values of h exf(13)-... 

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