Enzyme kinetic constants

Enzyme kinetic constants are calculated by nonlinear regression analysis with computer software, such as GraFit (Erithacus Software Limited,... 

Yokoyama, K. Kayanuma, Y. Cyclic voltammetric simulation for electrochemically mediated enzyme reaction and determination of enzyme kinetic constants. Anal Chem. 1998, 10, 3368—3376. 

Hence, both a high affinity of the oxime to the "inhibited" or phosphylated AChE and a high regeneration rate (ky) are critical for oxime efficacy. Using in vitro enzyme kinetic constants and in vivo inhibitor and oxime... 

Estimations of enzyme kinetic constants have been used previously to explain the substrate selectivity exhibited by pea and spinach stromal ATI (Frentzen, eta/., 1983). We have determined the acyl substrate affinity constants and maximal velocities for the enzymes isolated from chloroplasts of three chilling sensitive species and will rely upon previously published values for spinach and pea for our discussion. We have not determined Km values for G3P in tne presence of acyl-ACPs for any of these enzymes. 

Enzyme kinetic constant A in chloroplasts from spinach maize peas (mesophyll) B in Escherichia coli... 

FIGURE 14.7 Substrate saturation curve for au euzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v= Fnax- That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H9O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme. 

Uncompetitive antagonism, form of inhibition (originally defined for enzyme kinetics) in which both the maximal asymptotic value of the response and the equilibrium dissociation constant of the activator (i.e., agonist) are reduced by the antagonist. This differs from noncompetitive antagonism where the affinity of the receptor for the activating drug is not altered. Uncompetitive effects can occur due to allosteric modulation of receptor activity by an allosteric modulator (see Chapter 6.4). 

Microsomes are widely used to study the metabolism of xenobiotics. Enzymes can be chararacterized on the basis of their requirement for cofactors (e.g., NADPH, UDPGA), and their response to inhibitors. Kinetic studies can be carried out, and kinetic constants determined. They are very useful in studies of comparative metabolism, where many species not available for in vivo experiment can be compared with widely investigated laboratory species such as rats, mice, feral pigeon, Japanese quail, and rainbow trout. 

Complex inactivation kinetics caused by enzyme-catalyzed decomposition of epoxide kinetic constants calculated from initial rates of inactivation. Approximate value calculated from half-life in the presence of 50 mAf inhibitor. 

Optimization of Substrate Concentrations. Computer analyses of enzyme kinetics may be very useful for the calculation of enzyme constants, eliminating the tediim associated with manual calculations. Recently, computer models for optimizing reagent concentrations have been described but these models require so many experimental points that the model rests on the experimental data rather than having predictive usefulness (31). 

Catalysis by flavoenzymes has been reviewed and various analogues of FAD have been prepared e.g. P -adenosine-P -riboflavin triphosphate and flavin-nicotinamide dinucleotide ) which show little enzymic activity. The kinetic constants of the interaction between nicotinamide-4-methyl-5-acetylimidazole dinucleotide (39) and lactic dehydrogenase suggest the presence of an anionic group near the adenine residue at the coenzyme binding site of the enzyme. ... 

The kinetics of the lipoxygenase was studied in aqueous media [25]. The affinity of the enzyme for its substrate LA is very high. When LA is in excess in the medium it becomes the inhibitor of the reaction [Fig. 5(a)]. HP is also competitive inhibitor. The experimentally determined kinetic constants are ... 

TLi used was between 0 and 7.33 mM (equivalent to 22 mM LA). TL initially dissolved in the organic phase, was hydrolyzed in the presence of the lipase at the liquid-liquid interface. Liberated LA transferred to the aqueous phase in which it reacted with lipoxygenase. Enzyme preparations and concentration were the same as those already chosen for determination of kinetic constants. 

When examining the first moments of the reaction, the kinetic constant k3 is usually small enough to be neglected. If the enzyme is inactivated, the acyl-enzyme cannot be kinetically distinguished from the Michaelis complex. Thus, the minimum kinetic scheme for inactivation is described by Eq. 11.2 ... 

Equations (2.10) and (2.12) are identical except for the substitution of the equilibrium dissociation constant Ks in Equation (2.10) by the kinetic constant Ku in Equation (2.12). This substitution is necessary because in the steady state treatment, rapid equilibrium assumptions no longer holds. A detailed description of the meaning of Ku, in terms of specific rate constants can be found in the texts by Copeland (2000) and Fersht (1999) and elsewhere. For our purposes it suffices to say that while Ku is not a true equilibrium constant, it can nevertheless be viewed as a measure of the relative affinity of the ES encounter complex under steady state conditions. Thus in all of the equations presented in this chapter we must substitute Ku for Ks when dealing with steady state measurements of enzyme reactions. 

We can now relate the kinetic constants kCM, Ku, and kcJKM to specific portions of the enzyme reaction mechanism. From our discussions above we have seen that the term kCM relates to the reaction step of ES conversion to ES. Hence experimental perturbations (e.g., changes in solution conditions, changes in substrate identity, mutations of the enzyme, and the presence of a specific inhibitor) that exclusively affect kCM are exerting their effect on catalysis at the ES to ES transition step. The term KM relates mainly to the dissociation reaction of the encounter complex ES returning to E + S. Conversely, the reciprocal of Ku (1IKU) relates to the association step of E and S to form ES. Inhibitors and other perturbations that affect the... 

Figure 2.8 Relationship between steady state kinetic constants and specific portions of the enzyme reaction pathway.

For our purposes the most important factor that can impact the individual steady state kinetic constants is the presence of an inhibitor. We will see in Chapter 3 how specific modes of inhibitor interactions with target enzymes can be diagnosed by the effects that the inhibitors have on the three steady state kinetic constants. 

In this chapter we have seen that enzymatic catalysis is initiated by the reversible interactions of a substrate molecule with the active site of the enzyme to form a non-covalent binary complex. The chemical transformation of the substrate to the product molecule occurs within the context of the enzyme active site subsequent to initial complex formation. We saw that the enormous rate enhancements for enzyme-catalyzed reactions are the result of specific mechanisms that enzymes use to achieve large reductions in the energy of activation associated with attainment of the reaction transition state structure. Stabilization of the reaction transition state in the context of the enzymatic reaction is the key contributor to both enzymatic rate enhancement and substrate specificity. We described several chemical strategies by which enzymes achieve this transition state stabilization. We also saw in this chapter that enzyme reactions are most commonly studied by following the kinetics of these reactions under steady state conditions. We defined three kinetic constants—kai KM, and kcJKM—that can be used to define the efficiency of enzymatic catalysis, and each reports on different portions of the enzymatic reaction pathway. Perturbations... 

An inhibitor that binds exclusively to the free enzyme (i.e., for which a = °°) is said to be competitive because the binding of the inhibitor and the substrate to the enzyme are mutually exclusive hence these inhibitors compete with the substrate for the pool of free enzyme molecules. Referring back to the relationships between the steady state kinetic constants and the steps in catalysis (Figure 2.8), one would expect inhibitors that conform to this mechanism to affect the apparent value of KM (which relates to formation of the enzyme-substrate complex) and VmJKM, but not the value of Vmax (which relates to the chemical steps subsequent to ES complex formation). The presence of a competitive inhibitor thus influences the steady state velocity equation as described by Equation (3.1) ... 

The very slow dissociation rates for tight binding inhibitors offer some potential clinical advantages for such compounds, as described in detail in Chapter 6. Experimental determination of the value of k, can be quite challenging for these inhibitors. We have detailed in Chapters 5 and 6 several kinetic methods for estimating the value of the dissociation rate constant. When the value of kofS is extremely low, however, alternative methods may be required to estimate this kinetic constant. For example, equilibrium dialysis over the course of hours, or even days, may be required to achieve sufficient inhibitor release from the El complex for measurement. A significant issue with approaches like this is that the enzyme may not remain stable over the extended time course of such experiments. In some cases of extremely slow inhibitor dissociation, the limits of enzyme stability will preclude accurate determination of koff the best that one can do in these cases is to provide an upper limit on the value of this rate constant. 

Carrier-mediated transport is linear with mucosal solute concentration until this concentration exceeds the number of available carriers. At this point the maximal solute flux (7max) is independent of further increases in mucosal solute concentration. In the linear range of solute flux versus mucosal concentration (C), the proportionality constant is the ratio of / to the solute-carrier affinity constant (Km). This description of Michaelis-Menten kinetics is directly analogous to time changes in mass per unit volume (velocity of concentration change) found in enzyme kinetics, while here the appropriate description is the time change in solute mass per unit surface area of membrane supporting the carrier. 

As an example, consider an early calculation of isotope effects on enzyme kinetics by Hwang and Warshel [31]. This study examines isotope effects on the catalytic reaction of carbonic anhydrase. The expected rate-limiting step is a proton transfer reaction from a zinc-bound water molecule to a neighboring water. The TST expression for the rate constant k is... 

Methods similar to those discussed in this chapter have been applied to determine free energies of activation in enzyme kinetics and quantum effects on proton transport. They hold promise to be coupled with QM/MM and ab initio simulations to compute accurate estimates of nulcear quantum effects on rate constants in TST and proton transport rates through membranes. 

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