Enzyme equilibria kinetic properties

The basic kinetic properties of this allosteric enzyme are clearly explained by combining Monod s theory and these structural results. The tetrameric enzyme exists in equilibrium between a catalytically active R state and an inactive T state. There is a difference in the tertiary structure of the subunits in these two states, which is closely linked to a difference in the quaternary structure of the molecule. The substrate F6P binds preferentially to the R state, thereby shifting the equilibrium to that state. Since the mechanism is concerted, binding of one F6P to the first subunit provides an additional three subunits in the R state, hence the cooperativity of F6P binding and catalysis. ATP binds to both states, so there is no shift in the equilibrium and hence there is no cooperativity of ATP binding. The inhibitor PEP preferentially binds to the effector binding site of molecules in the T state and as a result the equilibrium is shifted to the inactive state. By contrast the activator ADP preferentially binds to the effector site of molecules in the R state and as a result shifts the equilibrium to the R state with its four available, catalytically competent, active sites per molecule. 

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... 

THE COMBINED EQUILIBRIUM AND STEADY-STATE TREATMENT. There are a number of reasons why a rate equation should be derived by the combined equilibrium and steady-state approach. First, the experimentally observed kinetic patterns necessitate such a treatment. For example, several enzymic reactions have been proposed to proceed by the rapid-equilibrium random mechanism in one direction, but by the ordered pathway in the other. Second, steady-state treatment of complex mechanisms often results in equations that contain many higher-order terms. It is at times necessary to simplify the equation to bring it down to a manageable size and to reveal the basic kinetic properties of the mechanism. 

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... 

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. 

In order to understand the regulation of the TCA cycle, it is necessary to look at the AG values for the various reactions and the kinetic properties of the enzymes. Values for the non-equilibrium reactions are tabulated below as Table 9.4 ... 

A reaction between an enzyme, E, and substrate, S, to give a product, P, starts with binding of substrate to enzyme to form a complex, E S. This is similar to the interaction of ligand and receptor, L + R = L R, that we encountered before. The strength of this complex, expressed by an equilibrium constant, and the rate of conversion of E S into product, expressed by a kinetic constant, are two major parameters used to describe kinetic properties of an enzyme. The mathematical formalism used for enzyme kinetics today has been developed by North American chemists Leonor Michaelis and Maud Menten and subsequent authors and it is habitually called MM kinetics. 

Although the activity of the enzyme is a kinetic property, we can grasp the essence of the regulatory mechanism by the study of a simple equilibrium system. In the following we redefine the concept of activity of the enzyme in such a way that its variation upon the addition of B can be studied by an equilibrium system. 

H (the original nomenclature was T, and R). Suppose that the conformation L is the more active one for instance, the active site in H is partially or totally blocked for binding the substrate A. Clearly, any factor that shifts the equilibrium concentration toward L will increase the activity of the enzyme. A shift toward //will lead to inhibitory effect. At this point we can leave the kinetic properties of the enzyme and focus on the mechanism of shifting the equilibrium concentrations of L and H by an effector B. 

Interestingly, although many transition state analogs bind noncovalently to the target enzyme s active site via a one-step kinetic mechanism (Scheme la) and would therefore be expected to exhibit no time-dependent properties of inhibition, inhibitors with Kj values of < 10 10 M (like coformy-cin) usually have a slow onset of inhibition kobserved < 10 2 s 1 (i.e., an approach to equilibrium inhibition of > 1 min).161 This is merely an assay artifact due to... 

The scaled elasticities of a reversible Michaelis Menten equation with respect to its substrate and product thus consist of two additive contributions The first addend depends only on the kinetic propertiesand is confined to an absolute value smaller than unity. The second addend depends on the displacement from equilibrium only and may take an arbitrary value larger than zero. Consequently, for reactions close to thermodynamic equilibrium F Keq, the scaled elasticities become almost independent of the kinetic propertiesof the enzyme [96], In this case, predictions about network behavior can be entirely based on thermodynamic properties, which are not organism specific and often available, in conjunction with measurements of metabolite concentrations (see Section IV) to determine the displacement from equilibrium. Detailed knowledge of Michaelis Menten constants is not necessary. Along these lines, a more stringent framework to utilize constraints on the scaled elasticities (and variants thereof) as a determinant of network behavior is discussed in Section VIII.E. 

Enzymatic Catalysis. Enzymes are biological catalysts. They increase the rate of a chemical reaction without undeigoing permanent change and without affecting the reaction equilibrium. The thermodynamic approach to the study of a chemical reaction calculates the equilibrium concentrations using the thermodynamic properties of the substrates and products. This approach gives no information about the rate at which the equilibrium is reached. The kinetic approach is concerned with the reaction rates and the factors that determine these, eg, pH, temperature, and presence of a catalyst. Therefore, the kinetic approach is essentially an experimental investigation. 

Earlier studies on the properties of phosphorylases isolated from various sources have indicated that their subunits are similar in size with about 100,000 daltons.15-17 The reaction proceeds in a rapid equilibrium random Bi-Bi mechanism as has been shown by kinetic studies with rabbit skeletal muscle phosphorylases a18-20 and b,21,22 rabbit liver enzyme,23 potato tuber enzyme,24 and the enzyme from E. coli.25) In contrast, the substrate specificities for various glucans differ considerably depending on the enzyme sources. The rabbit muscle enzyme has high affinity for branched glucans such as glycogen and amylopectin but low affinity for amylose and maltodextrin.26,27 The potato tuber enzyme can act on amylose, amylopectin, and maltodextrin but only poorly on glycogen,28,29 while the E. coli enzyme shows high affinity for maltodextrin.10 ... 

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... 

Modem methods for study of metal-activated enzymes include NMR and ESR spectroscopy, water relaxation rates by pulsed NMR (PRR), atomic absorption, Mbssbauer, X-ray and neutron diffraction, high-resolution electron microscopy, UV/visible/IR spectroscopy, laser lanthanide pertubation methods, fluorescence, and equilibrium and kinetic binding techniques. Studies with Mg(II)-activated enzymes have been hampered by the lack of paramagnetic or optical properties that can be used to probe its environment, and the relative lack of sensitivity of other available methods initial velocity kinetics, changes in ORD/CD, fluorescence, or UV properties of the protein, atomic absorption assays for equilibrium binding, or competition with bound Mn(II) °. Recent developments in Mg and 0-NMR methodology have shown some promise to provide new insights . ... 

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