Zero order rate constants maximum velocity

On the basis of kinetic studies [75-77], Smith suggested that the major factors governing the choice of two alternative metabohc routes are the first-and zero-order rate constants of the two reactions. The first-order rate constant in conjugation reactions may not be subject to serious species variations, but the zero-order rate constant depends not only on the mobihzation rate of glycine, glucuronic acid, etc., which is different in different species, but also on the compound metabohzed. The compound may affect the zero-order rate constant either by virtue of its tissue level, which depends on dose, or by its effect on the maximum velocity of the enzymatic reaction [23]. 

Most biological reactions fall into the categories of first-order or second-order reactions, and we will discuss these in more detail below. In certain situations the rate of reaction is independent of reaction concentration hence the rate equation is simply v = k. Such reactions are said to be zero order. Systems for which the reaction rate can reach a maximum value under saturating reactant conditions become zero ordered at high reactant concentrations. Examples of such systems include enzyme-catalyzed reactions, receptor-ligand induced signal transduction, and cellular activated transport systems. Recall from Chapter 2, for example, that when [S] Ku for an enzyme-catalyzed reaction, the velocity is essentially constant and close to the value of Vmax. Under these substrate concentration conditions the enzyme reaction will appear to be zero order in the substrate. 

Plot of substrate concentration versus initial velocity of an enzyme-catalyzed reaction. Segment A At low substrate concentration, the reaction follows first-order kinetics with respect to substrate concentration i.e., V — < [S], where k is a reaction rate constant. Segment B At high substrate concentration, maximum velocity (Umax) is attained (saturation kinetics), and any further increase in substrate concentration does not affect the reaction rate the reaction is then zero-order with respect to substrate but first-order with respect to enzyme. is the value of [S] corresponding to a velocity of j Vmax-... 

Notes 1. Vi, Ka, Kb and Kia are maximum velocity, Michaelis-Menten constants for A and B, and inhibition constant for A respectively. 2. The Order bi bi reactions may display zero (known as Theorell-Chance mechanism), one and two ternary complexes. All of them give the rate equation in the same Cleland form. 

As a reminder both limiting cases are just assumptions leading to approximations/ ). In the same way that the maximum rate in the zero-order case can never be reached as outlined above, even at very low substrate concentrations the calculated velocity from eqn (4.1) will never exactly match the specificity constant (see also the inset of Figure 4.1) ... 

The concentration of substrate also influences the initial velocity but not in a simple manner (Figure 6.3b). At a constant [E], the hyperbolic plot obtained with different initial sutetrate concentrations shows that the rate is initially proportional to [S], i.e. first order with respect to substrate. (In the orders of chemical reactions, the reaction is first order when its rate is proportional to the first power of the concentration of just one reactant.) At extremely high substrate concentrations, the reaction rate approaches a constant rate (Section 6.2). This is the maximum velocity (For attainable for this particular [E]. The available active sites of all the enzyme molecules are occupied by the substrate the enzyme is saturated. To increase the rate, additional active sites must be made available by the addition of more enzyme. The reaction rate at V is independent of [S] and is zero order with respect to substrate. Between the extremities, the reaction is a mixture... 

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