Hexokinase enzyme kinetics

In addition to acting on enzyme kinetics, Glc-6-P solubilizes hexokinase, thus reducing the efficiency of the enzyme when the reaction product accumulates. The total... 

For example, Bachelard used [Mgtotai]/[ATPtotai ] = 1 in his rate studies, and he obtained a slightly sigmoidal plot of initial velocity versus substrate ATP concentration. This culminated in the erroneous proposal that brain hexokinase was allosterically activated by magnesium ions and by magnesium ion-adenosine triphosphate complex. Purich and Fromm demonstrated that failure to achieve adequate experimental control over the free magnesium ion concentration can wreak havoc on the examination of enzyme kinetic behavior. Indeed, these investigators were able to account fully for the effects obtained in the previous hexokinase study. ... 

Hexokinase is present in all cells of all organisms. Hepatocytes also contain a form of hexokinase called hexokinase IV or glucokinase, which differs from other forms of hexokinase in kinetic and regulatory properties (see Box 15-2). Two enzymes that catalyze the... 

Hexokinase does not yield parallel reciprocal plots, so the Ping Pong mechanism can be discarded. However, initial velocity studies alone will noi discriminate between the rapid equilibrium random and steady-state ordered mechanisms. Both yield ihe same velocity equation and families of intersecting reciprocal plots. Other diagnostic procedures must be used (e.g., product inhibition, dead-end inhibition, equilibrium substrate binding, and isotope exchange studies). These procedures are described in detail in the author s Enzyme Kinetics behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems, Wiley-Interscience (1975),... 

Fig. 11-9 Enzyme kinetics of glucokinase and hexokinase. This is a schematic only and shows glucokinase having a maximal velocity that is 10 times greater than that of hexokinase, while the K of hexokinase for glucose (0.1 mM) is 1/lOOth of that for glucokinase (10 mM).

A kinetic procedure employing the reverse reaction is coupled to the enzymes hexokinase and glucose-6-phosphate dehydrogenase, as used by Nielson and Ludvigson after the method of Oliver (J ). This procedure was later modified and optimized by Rosalki (38). 

Brain hexokinase is inhibited by its product glucose-6-phosphate and to a lesser extent by adenosine diphosphate. The isoenzyme of hexokinase found in brain may be soluble in the cytosol or be attached firmly to mitochondria [2 and references therein]. An equilibrium exists between the soluble and the bound enzyme. The binding changes the kinetic properties of hexokinase and its inhibition by Glc-6-P resulting in a more active enzyme. The extent of binding is inversely related to the ATP ADP ratio, i.e. conditions in which energy utilization... 

Because ATP and GTP are required in many biosynthetic and mechanochemical reactions, the ability to manipulate their concentrations is particularly important in many kinetic studies. The three enzymes most commonly employed for this purpose are hexokinase, phosphofruc-tokinase, and alkaline phosphatase. Each of these enzymes offers advantages and disadvantages, and one must consider the design requirements for any particular experiment before using one of these to deplete ATP or GTP. 

Haldane relationships can also be useful in characterizing isozymes or the same enzyme isolated from a different source. Reactions catalyzed by isozymes must have identical equilibrium constants, but the magnitudes of their kinetic parameters are usually different (e.g., the case of yeast and mammalian brain hexokinase ). Note that the Haldane relationship for the ordered Bi Bi mechanism is = Hmax,f p i iq/(f max.r ia b)- This same... 

For this reason, these alternative routes for isotope combination with enzyme-substrate and/or enzyme-product complexes ensures that raising the [A]/[Q] or [B]/[P] pair will not depress either the A< Q or the B< P exchanges. Fromm, Silverstein, and Boyer conducted a thorough analysis of the equilibrium exchange kinetic behavior of yeast hexokinase, and the data shown in Fig. 2 indicate that there is a random mechanism of substrate addition and product release. 

Rose and co-workers first demonstrated that a proteo-lyzed form of hexokinase forms a sticky (or sluggishly dissociable) complex with glucose. The generalized application of this approach to the kinetic characterization of multisubstrate enzymes has been treated in detail. See also Partition Coefficient Radiospecific Activity Stickiness... 

Figure 1. Plot of v/V ax versus the millimolar concentration of total substrate for a model enzyme displaying Michaelis-Menten kinetics with respect to its substrate MA (i.e., metal ion M complexed to otherwise inactive ligand A). The concentrations of free A and MA were calculated assuming a stability constant of 10,000 M k The Michaelis constant for MA and the inhibition constant for free A acting as a competitive inhibitor were both assumed to be 0.5 mM. The ratio v/Vmax was calculated from the Michaelis-Menten equation, taking into account the action of a competitive inhibitor (when present). The upper curve represents the case where the substrate is both A and MA. The middle curve deals with the case where MA is the substrate and where A is not inhibitory. The bottom curve describes the case where MA is the substrate and where A is inhibitory. In this example, [Mfotai = [Afotai at each concentration of A plotted on the abscissa. Note that the bottom two curves are reminiscent of allosteric enzymes, but this false cooperativity arises from changes in the fraction of total "substrate A" that has metal ion bound. For a real example of how brain hexokinase cooperatively was debunked, consult D. L. Purich H. J. Fromm (1972) Biochem. J. 130, 63.

The results indicate that brain hexokinase does indeed operate by way of a sequential kinetic mechanism, and subsequent kinetic studies with reversible inhibitors support this conclusion. These comments reinforce the wisdom of remaining wary of mechanistic inferences drawn solely on the basis of initial rate studies alone. See also Initial Rate Enzyme Assays... 

The four forms of hexokinase found in mammalian tissues are but one example of a common biological situation the same reaction catalyzed by two or more different molecular forms of an enzyme. These multiple forms, called isozymes or isoenzymes, may occur in the same species, in the same tissue, or even in the same cell. The different forms of the enzyme generally differ in kinetic or regulatory properties, in the cofactor they use (NADH or NADPH for dehydrogenase isozymes, for example), or in their subcellular distribution (soluble or membrane-bound). Isozymes may have similar, but not identical, amino acid sequences, and in many cases they clearly share a common evolutionary origin. 

This enzyme plays a key role in the metabolism of glucose and other related sugars. The physical and kinetic properties of yeast hexokinase have been extensively studied. Numerous recent studies have been made of its role in the phosphoryl transfer reaction. 

Unlike many enzymes, hexokinase has a broad substrate specificity. A partial list of substrates for the sugar site is presented in Table II. Structures for some of these compounds are given in Fig. 10. It should be pointed out that kinetic constants for the various substrates were obtained under a variety of conditions with different forms and modifications of the enzyme. 

In a two-substrate reaction similar to that catalyzed by hexokinase, two basic mechanisms may be at work. First, a ping-pong reaction may be occurring in which the enzyme shuttles between a stable enzyme intermediate, such as a phosphorylated enzyme, and a free enzyme. Second, the reaction may be sequential, in which case no reaction occurs until both substrates are on the enzyme. There are two types of sequential mechanisms. If one substrate cannot bind until after the addition of the other substrate the mechanism is said to be ordered. However, if they can combine in any order the mechanism is said to be random. The various kinetic methods for distinguishing between these mechanistic forms have been summarized by Cleland (52). The evidence for and against these possible kinetic schemes will now be summarized for yeast hexokinase. 

In the absence of added glucose, hexokinase was found to catalyze the very slow hydrolysis of MgATP (59). This has been explained by assuming that water has replaced glucose at the active site of the enzyme. This ATPase activity can be inhibited by compounds that inhibit the hexokinase activity (60) and can be stimulated by compounds such as D-xylose or D-lyxose which lack the terminal -CH2OH of glucose (61). The ATPase reaction has been used to support evidence that hexokinase has a random kinetic mechanism, since it shows that ATP can bind to hexokinase in the absence of glucose (62). 

From pH kinetic studies, Viola and Cleland have proposed that hexokinase requires a group on the enzyme that must be unprotonated for the forward... 

The standard free energy change is about —5 kcal/mol, and the equilibrium constant is about 5,700. Thus, equilibrium considerations indicate a potential for this reaction to occur. The potential can be converted to reality only by an enzyme with appropriate kinetic properties. Hexokinases purified from various tissues typically have a Michaelis constant for glucose between 10 and 20 /am. Thus, by the expenditure of ATP, hexokinase can convert glucose in the micromolar... 

Structural studies of the oxy-Cope catalytic antibody system reinforce the idea that conformational dynamics of both protein and substrate are intimately intertwined with enzyme catalysis, and consideration of these dynamics is essential for complete understanding of biologically catalyzed reactions. Indeed, recent single molecule kinetic studies of enzyme-catalyzed reactions also suggest that different conformations of proteins are associated with different catalytic rates (Xie and Lu, 1999). In addition, a number of enzymes are known to undergo conformational changes on binding of substrate (Koshland, 1987) that lead to enhanced catalysis two examples are hexokinase (Anderson and Steitz, 1975 Dela-Fuente and Sols, 1970) and triosephosphate isomerase (Knowles, 1991). 

Hexokinase catalyzes the phosphorylation of glucose and fructose by ATP. However the Km for glucose is 0.13 mmol L-1, whereas that for fructose is 1.3 mmol L-1. Assume is the same for both glucose and fructose and the enzyme displays hyperbolic kinetics [Eq. (9.5)]. (a) Calculate the normalized initial velocity of the reaction (i.e., V(/Umax) for each substrate when [S]0 = 0.13, 1.3, and 13.0 mmol L-1. (b) For which substrate does hexokinase have the greater affinity ... 

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