Enzyme association-dissociation equilibria

An inhibitory complex formed by preincubating Mg, phosphate and NaF binds to the enzyme and affects the association/dissociation equilibrium. 

A relatively common feature of many problems involving molecular weight determination of biopolymers is that of association-dissociation equilibrium. Subunit structure of enzyme proteins is well recognized (1), and methods of dissociation of subunits to obtain monomer molecular weight are widely utilized (2). A previous paper described the application of an equilibrium gel partition method to the analysis of macromolecular association in a monomer-dimer case (3). The experimental parameters in a system utilizing the Sephadex series of gel filtra-... 

This association/dissociation is assumed to be a rapid equilibrium, and is the enzyme substrate dissociation constant. At equilibrium,... 

E] enzyme concentration [S] substrate concentration [ES] concentration of the enzyme-substrate complex [P] product concentration ki association equibbrium rate constant k i dissociation equilibrium rate constant (rate constant of the back reaction). 

In all the above-mentioned studies, only the tetramer has catalytic activity. The only claims for an active dimer 106,107) are not supported by satisfactory experimental evidence. Deal and co-workers 104, 108) have, on the other hand, presented extensive studies of the ATP-induced dissociation of GPD to inactive dimers and monomers at low temperatures. Furthermore, these subunits display very little unfolding, which has been taken to imply that dissociation is the major factor in the activity loss. These results were confirmed 24) with the rat skeletal muscle enzyme, which dissociates at 0° to inactive dimers in the absence of ATP. In addition, the activity transport studies of Hoagland and Teller 109) have given strong evidence that only the tetrameric form is active and that the presence of all three substrates promotes tetramer formation. It was also shown that rabbit muscle enzyme exists in a dimer-tetramer equilibrium in dilute aqueous solution at 5°, with an association constant... 

Cooperative substrate binding results in sigmoidal v versus [S] curves (Fig. 8.1). The Michaelis-Menten model is therefore not appMcable to cooperative enzymes. Two major equihbrium models have evolved to describe the catalytic behavior of cooperative enzymes the sequential interaction and concerted transition models. The reader should be aware that other models have also been developed, such as equilibrium association-dissociation models, as well as several kinetic models. These are not discussed in this chapter. 

All enzymatic reactions are initiated by formation of a binary encounter complex between the enzyme and its substrate molecule (or one of its substrate molecules in the case of multiple substrate reactions see Section 2.6 below). Formation of this encounter complex is almost always driven by noncovalent interactions between the enzyme active site and the substrate. Hence the reaction represents a reversible equilibrium that can be described by a pseudo-first-order association rate constant (kon) and a first-order dissociation rate constant (kM) (see Appendix 1 for a refresher on biochemical reaction kinetics) ... 

Thus, as described by Equation (2.1), the equilibrium dissociation constant depends on the rate of encounter between the enzyme and substrate and on the rate of dissociation of the binary ES complex. Table 2.1 illustrates how the combination of these two rate constants can influence the overall value of Kd (in general) for any equilibrium binding process. One may think that association between the enzyme and substrate (or other ligands) is exclusively rate-limited by diffusion. However, as described further in Chapter 6, this is not always the case. Sometimes conformational adjustments of the enzyme s active site must occur prior to productive ligand binding, and these conformational adjustments may occur on a time scale slower that diffusion. Likewise the rate of dissociation of the ES complex back to the free... 

Consider the enzyme-catalyzed and noncatalyzed transformation of the ground state substrate to its transition state structure. We can view this in terms of a thermodynamic cycle, as depicted in Figure 2.4. In the absence of enzyme, the substrate is transformed to its transition state with rate constant /cM..M and equilibrium dissociation constant Ks. Alternatively, the substrate can combine with enzyme to form the ES complex with dissociation constant Ks. The ES complex is then transformed into ESt with rate constant kt , and dissociation constant The thermodynamic cycle is completed by the branch in which the free transition state molecule, 5 binds to the enzyme to form ESX, with dissociation constant KTX. Because the overall free energy associated with transition from S to ES" is independent of the path used to reach the final state, it can be shown that KTX/KS is equal to k, Jkail (Wolfenden,... 

For a binding reaction we can pick whether we show the reaction as favorable or unfavorable by picking the substrate concentration we use. Association constants have concentration units (M-1)- The equilibrium position of the reaction (how much ES is present) depends on what concentration we pick for the substrate. At a concentration of the substrate that is much less than the dissociation constant for the interaction, most of the enzyme will not have substrate bound, the ratio[ES]/[E] will be small, and the apparent equilibrium constant will also be small. This all means that at a substrate concentration much less than the dissociation constant, the binding of substrate is unfavorable. At substrate concentrations higher than the dissociation constant, most of the enzyme will have substrate bound and the reaction will be shown as favorable (downhill). (See also the discussion of saturation behavior in Chap. 8.)... 

In the derivation according to Michaelis and Menten, association and dissociation between free enzyme E, free substrate S, and the enzyme-substrate complex ES are assumed to be at equilibrium, fCs = [ES]/([E] [S]). [The Briggs-Haldane derivation (1925), based on the assumption of a steady state, is more general see Chapter 5, Section 5.2.1.] With this assumption and a mass balance over all enzyme components ([E]total = [E]free + [ES]), the rate law in Eq. (2.3) can be derived. 

A number of recent studies have shown that under certain conditions, FABMS indeed can very accurately measure the balance of ionic species in ongoing chemical reactions in solutions. These studies include the determination of acid dissociation constants (2), equilibrium constants for enzyme catalyzed reactions (1), metal-ligand association constants 03), and measurements of... 

An antenna remains in a plume 1 s and an antenna is not an isolated system, as is required to reach equilibrium. The kinetic properties of the PBP-ligand complexes may be more important to the function of PBPs as potential filters than the equilibrium dissociation constants. Thus, ligands with very fast association rate constants and very slow dissociation rate constants are more likely to be bound at the pore surfaces and to traverse the sensillar lymph unharmed by the powerful pheromone-degrading enzymes in the lymph (see below). Thus, in order to understand the function of PBPs, it is essential to obtain more data on binding kinetics. 

By using a resonant mirror biosensor, the binding between YTX and PDEs from bovine brain was studied. The enzymes were immobilized over an aminosilae surface and the association curves after the addition of several YTX concentrations were checked. These curves follow a typical association profile that fit a pseudo-first-order kinetic equation. From these results the kinetic equilibrium dissociation constant (K ) for the PDE-YTX association was calculated. This value is 3.74 p,M YTX (Pazos et al. 2004). is dependent on YTX structure since it increases when 44 or 45 carbons (at C9 chain) group. A higher value, 7 p,M OH-YTX or 23 p,M carboxy-YTX, indicates a lower affinity of YTXs analogues by PDEs. 

Not all reversible inhibitors have an instantaneous effect on the rate of an enzymatic reaction. Some inhibitors, known as slow-binding enzyme inhibitors, can take a considerable time to establish the equilibrium between the free enzyme and inhibitor, and the enzyme-inhibitor complex. This time period may be on the scale of seconds, minutes, or even longer. The enzyme-inhibitor complexes have slow off (dissociation) rates, but the on (association) rates may be either slow or fast. Hence, the term slow binding does not necessarily indicate a slow binding of inhibitor to enzyme but rather the fact that reaching equilibrium is a... 

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