Velocity maximal

It is essential to maintain high, maximal velocities of enzymatic activity for the attainment of optimal therapeutic efficacy. As a general rule, only enzymes whose MichaeHs-Menten constants He between 1—100 ]lM are effective as dmgs (16) because most substrates for therapeutically useful enzymes are present ia body fluids and cells at suhmillimolar concentrations. 

Figure 11.1 A plot of the reaction rate as a function of the substrate concentration for an enzyme catalyzed reaction. Vmax is the maximal velocity. The Michaelis constant. Km, is the substrate concentration at half Vmax- The rate v is related to the substrate concentration, [S], by the Michaelis-Menten equation ...

Figure 11-9 shows tliat tlie inhibitor does not alter but increases the observed (i.e., concentration of the substrate that produces half the maximal velocity in the presence of a competitive inhibitor). The observed is defined by... 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

The allosteric model just presented is called a K system because the concentration of substrate giving half-maximal velocity, defined as -K0 5, changes in response to effectors (Figure 15.11). Note that Vjnax is constant in this system. 

The Michaelis constant is the substrate concentration at which is half the maximal velocity (V 3 /2) attainable at a particular concentration of enzyme. thus has the dimensions of substrate concentration. The dependence of initial reaction velocity on [S] and may be illustrated by evaluating the Michaelis-Menten equation under three conditions. 

Figure 41-11. A comparison of the kinetics of carrier-mediated (facilitated) diffusion with passive diffusion. The rate of movement in the latter is directly proportionate to solute concentration, whereas the process is saturable when carriers are involved. The concentration at half-maximal velocity is equal to the binding constant (KJ of the carrier for the solute. maximal rate.)...

Vmaxiinjlux or efflux) = Maximal velocity of the saturable transporter Km(injiux or efflux) = Michaelis constant for the saturable transporter Q = Concentration of drug inside the lumen of the intestine CSnt(i) = Concentration of drug inside the enterocyte in compartment i... 

A plot of the initial reaction rate, v, as a function of the substrate concentration [S], shows a hyperbolic relationship (Figure 4). As the [S] becomes very large and the enzyme is saturated with the substrate, the reaction rate will not increase indefinitely but, for a fixed amount of [E], it reaches a plateau at a limiting value named the maximal velocity (vmax). This behavior can be explained using the equilibrium model of Michaelis-Menten (1913) or the steady-state model of Briggs and Haldane (1926). The first one is based on the assumption that the rate of breakdown of the ES complex to yield the product is much slower that the dissociation of ES. This means that k2 tj. 

Km is the Michaelis constant. In some cases such as hydrolases or lactic dehydrogenases (T2), the velocity may fall again with higher substrate concentrations, so that there is an optimum substrate concentration which approximates the theoretical value V, the maximal velocity, following the theory of Michaelis and Menten... 

It has been found experimentally that in most cases v is directly proportional to the concentration of enzyme [.E0] and that v generally follows saturation kinetics with respect to the concentration of substrate [limiting value called Vmax. This is expressed quantitatively in the Michaelis-Menten equation originally proposed by Michaelis and Menten. Km can be seen as an apparent dissociation constant for the enzyme-substrate complex ES. The maximal velocity Vmax = kcat E0. ... 

In the case of carboxylesterase-catalyzed hydrolysis (Table 8.1), the Michaelis constant consistently indicated relatively low affinity for the enzyme, with a variation between substrates of one order of magnitude. Even less variation was seen in the maximal velocity of the reaction. It is interesting to note that, for the four compounds where comparisons are possible, a direct relationship exists between the rate of hydrolysis in plasma and the Vmax of carboxylesterase hydrolysis, suggesting comparable catalytic mechanisms. 

The Km can be calculated from the graph as the concentration of the reaction when the velocity is half the maximal velocity or V ax/2. 

PRPP 5-PhosphoribosyI 1-diphos- Vmax.V Maximal velocity (of an... 

A straight line whose perpendicular distance from a curve becomes progressively smaller as the distance from the origin at [0,0] becomes greater. For example, in a plot of velocity versus [Substrate Concentration] for an enzyme-catalyzed reaction, the asymptote reaches the maximal velocity when the enzyme molecules become saturated with substrate. 

In enzyme-catalyzed kinetics, one must necessarily deal with the behavior of a multistep reaction scheme. For initial rate enzyme processes, one typically deals with collections of rate constants which appear in the form of the maximal velocity Um (shortened to U) or the specificity constant VJK (shortened to VIK). Accordingly, enzyme kineticists will use °V and °V/K as an easy way to indicate the respective isotope effects [(Um)H/(Um)D ] and [(VJK )u/(VJK )b], respectively. 

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