Michaelis-Menten form

In summary, the simple Michaelis-Menten form of Equation (12.1) is usually sufficient for first-order reactions. It has two adjustable constants. Equation (12.4) is available for special cases where the reaction rate has an interior maximum or an inflection point. It has three adjustable constants after setting either 2 = 0 (inhibition) or k = 0 (activation). These forms are consistent with two adsorptions of the reactant species. They each require three constants. The general form of Equation (12.4) has four constants, which is a little excessive for a... 

The absence of retardation by V(IV) rules out a mechanism analogous to that of Mn(III) oxidation. Mn(II) ions strongly catalyse reaction , altering the kinetics to those observed for the Mn(II)-catalysed oxidation of oxalic acid by V(V) (preceding sub-section) except that the [V(V)] dependence has a Michaelis-Menten, form rather than being first-order. E is reduced from 19.7 to 6.9 kcal.mole , and a similar mechanism is believed to operate. 

The kinetic equation used here is an enzymatic Michaelis-Menten form with product inhibition... 

Again, Vmax may be substituted for JtrcEa, producing the Michaelis-Menten form of the rate law, that is,... 

This can be put in the Michaelis-Menten form but with the concentration of the inhibitor. 

The steady state solution has the Michaelis-Menten form for competitive inhibition... 

As we have seen, the catalytic cycle flux provides a useful metric for analyzing enzyme kinetics. In this section, we analyze the turnover time for catalytic cycles and show that the quasi-steady rate law arises from the mean cycle time [151]. In addition, we show that for arbitrary mechanisms for a single-substrate reaction, the steady state rate law can always be expressed using the Michaelis-Menten form... 

In an enzyme-catalyzed reaction with stoichiometry A B. A is consumed at a rate given by an expression of the Michaelis-Menten form ... 

Pharmacokinetic models involving nonlinear kinetics of the Michaelis-Menten form have the important extrapolation characteristic of being linear at low dose levels. This low dose linearity contrasts with the low dose nonlinearity of the multihit and Weibull models. Each model, pharmacokinetic, multihit, and Ifeibull, has the desirable ability to describe either convex (upward curvature) or concave (downward curvature) dose-response relationships. Other models, stich as the log normal or multistage, are not consistent with concave relationships. However, the pharmacokinetic model differs from the multihit and Heibull in that it does not assume the nonlinear behavior observed at high dose levels will necessarily correspond to the sane nonlinear behavior at low dose levels. 

The oxygen consumption rate as a function of tissue tension is considered to have a Michaelis-Menten form. [It has been shown (8) that neuron activity increases to a much higher rate as tissue oxygen tension decreases (injury potential) and then it drops off to essentially zero. This would indicate that a true Michaelis-Menten form would not be followed.] A zero-order reaction is assumed for high tissue tension a first-order reaction is then imposed when the tension drops to a prescribed value, and then the consumption rate is set equal to zero at a second prescribed tissue tension (i.e., PT > 30 mm Hg, zero-order reaction, 20 < PT < 30 mm Hg, first-order reaction, and PT < 20, zero consumption). When the consumption rate goes to zero, the model restricts oxygen transport in the reverse direction (tissue to blood) even if the blood tension drops below the tissue tension. This assumption was included to achieve a flat plateau like the experimental results however, it is still open to speculation. Back diffusion can be considered in the model by simply removing a diode from the computer circuit. (This assumes a barrier to tissue washout.)... 

If the concentration of B is held constant, the variation of v with [A] is of the Michaelis-Menten form. This may be shown for the case in which we have an excess of B. Thus, if [B] is sufficiently large, we may neglect the first two terms in the denominator of (10,26), and the result is... 

Precisely as we proceeded in the discussion of the simple pore, we can derive the predictions of the simple carrier for the procedures of zero trans and equilibrium exchange. Simple Michaelis-Menten forms are obtained with the maximum velocity and half-saturation concentrations listed in Table 4. 

This is clearly a simple Michaelis-Menten form with a maximum velocity of u, 2 — 1 half-saturation concentration Kfl = /T/ 2i/ ee- The infinite trans... 

This equation is easily transformed into the Michaelis-Menten form [18] applied for homogeneous enzyme catalysis. The rate of the reaction rises with increasing substrate concentration tending to the constant value w ,ax (Eq. (12-6)), where Km is the Michaelis factor corresponding to the substrate... 

If it is assumed that the substrate binding and proton equilibria are rapidly maintained, then the initial rate can be put in the standard Michaelis-Menten form ... 

Illustration 9.1 - Michaelis-Menten Form of a Rate Equation for a More Complieated Enzyme-catalyzed Reaction... 

Finally, dividing both numerator and denominator by the factor multiplying [S] in the denominator produces the final Michaelis-Menten form of the rate equation, i.e.,... 

The kinetic model for this reaction follows a Michaelis-Menten form for a reversible reaction, which... 

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