Hyperbolic inhibition

More complex kinetics that does not fit hyperbolic inhibition or activation are also possible. These cases usually involve combinations of activation or inhibition with a second component resulting from two-substrate kinetics, e.g., sigmoidal, biphasic, or substrate inhibition kinetics. An example is activation followed by inhibition. The inhibition component occurs when two substrates in the active site displaces the inhibitor. 

Other inhibition models of NH4 and NO3 uptake have been based on enzyme kinetics (e.g., noncompetitive inhibition Frost and Franzen (1992)). Whether or not the analogy is strictly applicable, this would appear to have a more sound biological basis than the Wroblewski (1977) exponential function. Yajnik and Sharada (2003) defined general equations for a two-nutrient interaction that can be reduced to hyperbolic inhibition such as that employed by Frost and Franzen (1992) and Parker (1993). 

The literature on NO3/NH4 interactions generally assigns the effect of NO3 on NH4 to Case 3 (no effect) and the effect ofNH4 on NO3 to Case 1. Yajnik and Sharada argue for Case 2, to which point we will return. Obviously, i a = h, Eq. (33.3) reduces to the familiar hyperbolic uptake without inhibition (Case 3). Case 1 is equivalent to the hyperbolic inhibition employed by Frost and Franzen (1992), Parker (1993), Loukos et al. (1997), and Christian et al. (2002a). Yajnik and Sharada (2003) further defined coefficients k = /b and c = -a/b such that Eq. (33. 3a) becomes... 

Figure 3. Determination of inhibition constants in hyperbolic inhibition by a differential method. Graphical presentation of Eqs. (6.8) and (6.9), assuming that a-2 and fi = 0.5...

Figure 4 shows the survey of different t)q)es of nonlinear hyperbolic inhibition mechanisms and their characteristics. A basic property of aU nonlinear mechanisms, shown in Fig. 4, is that the double reciprocal plot of i/uq versus /A, in the presence of different constant concentrations of an inhibitor is a family of straight lines with a common intersection point. This common intersection point is found either in the I, in, or in the IV quadrant, depending on the mechanism only in Case 5 (hyperbolic uncompetitive type), the double reciprocal plot is a family of parallel straight lines without a common intersection point. 

From the survey of different hyperbolic inhibition patterns outlined above, we may single out the following general conclusions ... 

Let us, now, depart from monosubstrate reactions and turn our attention to a much more realistic case of a hyperbolic inhibition in bisubstrate reactions (Segel, 1975 Dixon Webb, 1979 f rich Allison, 2000). In the rapid equilibrium reaction (6.14), A and B are the substrates while I is a nonexclusive inhibitor ... 

For a monosubstrate reaction, the kinetic model is analogous to a general model for a nonlinear hyperbolic inhibition, described in Chapter 6 (Section 6.1) ... 

The nonessential activation, in the general case, is a hyperbolic nonlinear activation. Analogous to hyperbolic inhibition, we can derive a number of different activation mechanisms, by inserting different values for a and into Eq. (7.2), as was described in Chapter 6 (Section 6.3), for different types of hyperbolic inhibitions. However, in activation processes, it is always iS>i. 

Since the multifunctional forms of plant ACCase function as dimers, we examined the binding to and subsequent inhibition of the enzyme by graminicides. Curve fits for the binding of quizalofop or fluazifop were generated for an equation of simple hyperbolic inhibition or the Hill equation. Maize ACCase 1 exhibited little cooperativity in binding graminicides but ACCase 2 (of reduced sensitivity) showed... 

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