Inhibition and Activation in Enzyme Reactions

2 Linearized Form of the Integrated Michaelis-Menten Equation 

For a constant-volume BR, integration of the Michaelis-Menten equation leads to a form that can also be linearized. Thus, from equation 10.2-9, 

A major limitation of the linearized forms of the Michaelis-Menten equation is that none provides accurate estimates of both Km and Vmax. Furthermore, it is impossible to obtain meaningful error estimates for the parameters, since linear regression is not strictly appropriate. With the advent of more sophisticated computer tools, there is an increasing trend toward using the integrated rate equation and nonlinear regression analysis to estimate Km and While this type of analysis is more complex than the linear approaches, it has several benefits. First, accurate nonbiased estimates of Km and Vmax can be obtained. Second, nonlinear regression may allow the errors (or confidence intervals) of the parameter estimates to be determined. 

To determine Km and Vmax, experimental data for cs versus t are compared with values of cs predicted by numerical integration of equation 10.3-3 estimates of Km and Vmax are subsequently adjusted until the sum of the squared residuals is minimized. The E-Z Solve software may be used for this purpose. This method also applies to other complex rate expressions, such as Langmuir-Hinshelwood rate laws (Chapter 8). 

The simple Michaelis-Menten model does not deal with all aspects of enzyme-catalyzed reactions. The model must be modified to treat the phenomena of inhibition and 

---

Figure 9-13 (A) An enzyme with binding sites for allosteric inhibitor I and activator J. Conformer A binds inhibitor I strongly but has little affinity for activator J or for substrate S. Conformer B binds S and catalyzes its reaction. It also binds activator J whose presence tends to lock the enzyme in the "on" conformation B. Conformers A and B are designated T and R in the MWC model of Monod, Wyman, and Changeux.80 (B) Inhibited and activated dimeric enzymes.

Enzyme inhibitors and activators may be detemoined by employing enzyme reactions. The easiest technique is to measure the decrease or increase in the rate of the enzymatic reaction. Or the enzyme may be titrated with an inhibitor (or vice versa), and the amount of inhibitor required to completely inhibit the reaction measured. Trace elements, for example, have been determined by their inhibition or activation of enzyme reactions. 

While iso-enzymes show regular variations in their molecular structure, it is the difference in their catalytic activity that is most significant. They often show different inhibition and activation effects, permitting one iso-enzyme to function under conditions that would reduce the activity of another and it is likely that such variations aid the control of the same reaction under different cellular or tissue conditions. 

Figure 1.1. Opposite) Sulpha drugs and their mode of action. The first sulpha drug to be used medically was the red dye prontosil rubrum (a). In the early 1930s, experiments illustrated that the administration of this dye to mice infected with haemolytic streptococci prevented the death of the mice. This drug, while effective in vivo, was devoid of in vitro antibacterial activity. It was first used clinically in 1935 under the name Streptozon. It was subsequently shown that prontosil rubrum was enzymatically reduced by the liver, forming sulphanilamide, the actual active antimicrobial agent (b). Sulphanilamide induces its effect by acting as an anti-metabolite with respect to /iflra-aminobenzoic acid (PABA) (c). PABA is an essential component of tetrahydrofolic acid (THF) (d). THF serves as an essential co-factor for several cellular enzymes. Sulphanilamide (at sufficiently high concentrations) inhibits manufacture of THF by competing with PABA. This effectively inhibits essential THF-dependent enzyme reactions within the cell. Unlike humans, who can derive folates from their diets, most bacteria must synthesize it de novo, as they cannot absorb it intact from their surroundings...

Activation-Inhibition and Function In Vivo. When 0.15M NaCl was added to an orange PE-pectin reaction mixture at pH 7.5, activity was increased 5-fold, and at pH 5 it was increased 100-fold (17). As explained by Lineweaver and Ballou (19), NaCl caused the apparent activation by freeing the enzyme from the inactive ionic complex (pectin-carboxyl). They showed that at pH 5.7 pectic acid inhibited alfalfa PE activity 55% in 0.015M NaCl but only 17% in 0.2M NaCl. At pH 8.5 pectic acid inhibited PE activity only 9% in 0.015 NaCl. They concluded that the stimulation of activity by cations at low pH (17) did not show that cations were essential for activity, but, rather, that cations function by preventing product inhibition, which is greater at low pH. 

Hundreds of metabolic reactions take place simultaneously in cells. There are branched and parallel pathways, and a single biochemical may participate in severm distinct reactions. Through mass action, concentration changes caused by one reaction may effect the kinetics and equilibrium concentrations of another. In order to prevent accumulation of too much of a biochemical, the product or an intermediate in the pathway may slow the production of an enzyme or may inhibit the activation of enzymes regulating the pathway. This is termed feedback control and is shown in Fig. 24-1. More complicated examples are known where two biochemicals act in concert to inhibit an enzyme. As accumulation of excessive amounts of a certain biochemical may be the key to economic success, creating mutant cultures with defective metabolic controls has great value to the production of a given product. 

Price and Radda (338) found that N-acetylimidazole could acetylate up to six tyrosine residues without loss of activity or alteration of Km for substrate however, reaction of about one tyrosine per subunit results in desensitization toward GTP, but the response to ADP is not abolished even by extensive 0-acetylation. Essentially the same results are observed upon nitration with tetranitromethane (TNM). Acetylation does not grossly alter the molecular weight, as measured by sedimentation velocity, or the conformation, as determined by ORD. The GTP site is not protected by NADH alone, but is partially protected (25-50%) by GTP and is at least 75% protected by inclusion of both GTP and NADH in the reaction mixture. Piszkiewicz et al. (339) confirmed these findings by modification with TNM. The reaction is biphasic with initial rapid formation of one residue of 3-nitrotyrosine per subunit. The primary site of reaction is tyrosine-406 in the linear sequence (340). Later (338) the same effect was obtained with chicken GDH with both enzymes there is no influence on activation by ADP. Further, the pH optima of the enzymes are not influenced by the degree of nitration or the inhibition by GTP or activation by ADP (338). 

We recently showed that low-frequency alternating currents (ac) through Na, K-ATPase vesicle suspensions change enzyme activity (21). The ac signals decrease adenosine 5 -triphosphate (ATP) splitting by the normal enzyme, with the maximum effect at about 100 Hz, and increase the enzyme activity when the activity is lowered in different ways, including the introduction of ouabain. Both inhibition and activation by ac signals can be explained by variations in ion activation (22, 23). The frequency dependence is related to the ion mobilities and reaction rate constants in the electrical double layers (20). 

The bound DPN is fully active enzymatically, and participates in coupled reactions with other DPN-dehydrogenases. After DPN has been removed, much larger quantities must be added back to saturate the enzyme, and 3 DPN molecules are bound to each enzyme molecule. Bound DPN is also displaced from the enzyme by PCMB. This reaction may be followed spectrophotometrically, as the DPN-enzyme compound has a broad absorption band with a peak at 360 m/t. When DPN is removed from the enzyme, there is a decrease in optical density in a broad region about 360 m/i. The recombination of DPN with the enzyme restores this band. It has been known for many years that cysteine or another —SH compound is required for activation of the enzyme as usually obtained. Besides PCMB, iodoacetate also inhibits the enzyme, but tiiis inhibition is prevented by phosphoglyceraldehyde. These observations support the concept that the essential —SH groups of the enzyme are involved in the binding of DPN. 

The inhibition of vernolic acid synthesis in the presence of CO demonstrates a cytochrome P-450 involvement in the reaction (4). Since our objective is to clone the gene encoding the enzyme responsible for vernolic acid synthesis, our primary interest was whether we could detect activity in the presence of reductants and inhibition of activity in the presence of CO, each of which was demonstrated. 

---