Michaelis-type equilibrium constant

Considering only the first two steps in the reaction sequence, which is appropriate for most acylating inhibitors, the affinity of the inhibitor for the enzyme is given by the Michaelis-type equilibrium constant,... 

The reservoirs affect the concentration of the cycle species in two ways. The first is through the direct influx represented by the first term in each of eqs. (10.2). The second and more interesting way is through control of the enzyme activities, where the reservoir species F and T are allowed to become effectors of the enzymes. The type of control modeled is noncompetitive allosteric binding of the effectors, where each effector binds to the enzyme independently, as shown in fig. 10.2. In this scheme, the enzyme with effector bound is assumed to have altered catalytic activity toward its substrate compared to that of the enzyme without effector bound. The scheme as shown also relies on the simplifying assumptions that (1) the association and dissociation between enzyme and substrate are unaffected by the binding of the effector, and (2) the binding of substrate to enzyme is much faster than the conversion of bound substrate to product. Under these assumptions, the Michaelis constant Km represents the equilibrium constant for... 

Reversible inhibition occurs rapidly in a system which is near its equilibrium point and its extent is dependent on the concentration of enzyme, inhibitor and substrate. It remains constant over the period when the initial reaction velocity studies are performed. In contrast, irreversible inhibition may increase with time. In simple single-substrate enzyme-catalysed reactions there are three main types of inhibition patterns involving reactions following the Michaelis-Menten equation competitive, uncompetitive and non-competitive inhibition. Competitive inhibition occurs when the inhibitor directly competes with the substrate in forming the enzyme complex. Uncompetitive inhibition involves the interaction of the inhibitor with only the enzyme-substrate complex, while non-competitive inhibition occurs when the inhibitor binds to either the enzyme or the enzyme-substrate complex without affecting the binding of the substrate. The kinetic modifications of the Michaelis-Menten equation associated with the various types of inhibition are shown below. The derivation of these equations is shown in Appendix S.S. 

The parameters of the Michaelis-Menten type kinetics were calculated for the reactions and are summarized in Table II. The apparent Michaelis constant values (Km) are rather large, indicating that the concentration of the complex at the equilibrium state is not high, unlike ordinary enzymatic reactions. The ratio of kJKm against the second-order rate constant with sulfuric acid (k2) can be considered to be an indication of the rate enhancement. The ratio increased with increasing mole fraction of the vinyl alcohol repeating unit in the copolymer and with... 

Enzymatic reactions are usually characterized by a parameter, the Michaelis-Menten constant or KM, which is determined by the efficiency of the first equilibrium reaction for the formation of ES. That is, KM is the concentration in mM of S at which the initial rate of the overall process, V0, is one-half of the maximum rate, Vma possible. The maximum rate occurs when all of E is converted to ES. Each particular type and concentration of E and S, and each set of reactions conditions, has its own KM, and the Michaelis-Menten equation describes the relationship between Vo, [S] (the concentration of S), Vmax and Km for a given amount of E under a fixed set of conditions, as follows ... 

All single concentration terms present, but one Michaelis constant is zero. The addition of the substrate whose is zero must be in rapid equilibrium, and it must add first or second. No mechanisms of this type are known. See Viola and Cleland (13) for the possible mechanisms, which are very unrealistic. 

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