Sb Bovine Isocitrate Dehydrogenase Citrate

The velocity of the isocitrate dehydrogenase catalysis vs. concentration of the inhibitor Mn2+-citrate shows a complex variation with C/. Initial curvature upward is followed by gradual decline with a shoulder for CI between 2 to 4 mM.

Preliminary analysis showed that the model was more complex than that in Table 6.13. Testing with a variety of models suggested that the data contained three distinct regions of response to Mn2+-citrate. The set of chemical equations in Box 6.4 was found to lead to a model giving the best fit to the data [1].

Here Vmax is the apparent Vmzx in the absence of concentration dependent binding of I, and through V3 represent the velocity contributed by each state of the enzyme. The model implies three different binding sites for

Box 6.3 Basis of model for simple competitive inhibition.

Table 6.13 Model for Simple Inhibition of Enzyme Kinetics Assumptions: Michaelis-Menten kinetics with inhibition as in Box 6.3.

Regression equation:

0 1 + KïCj 1 + KÏC", Regression parameters: Data:

Special instructions: Run a series of nonlinear regressions with successively increasing fixed integer n values beginning with n = 1 until the best standard deviation of regression is achieved the inhibitor. Other models were tested but the fits were poor and not justified statistically. The binding of inhibitor to the enzyme M can be linked to the change in velocity using the linkage methods described earlier in this chapter. For data following the behavior in Figure 6.10, the model is summarized in Table 6.14.

The parameters obtained from analysis of the data in Figure 6.10 using the model in Table 6.14 shows that Mn2+-citrate first stimulates activity characterized by Ki = 0.25 m M (n = 2). Strongly inhibitory sites become bound at higher citrate concentrations with K2 = 3.83 m M(m = 2), dramatically decreasing activity. As citrate concentration increases further, an apparent modulation of inhibition occurs, with K3 = 1.54 mM (q = 4). The curve in Figure 6.10 is the composite of all these interactions. A complete discussion of the biological implications of these results has been given [1],

B.7. Interactions of Drugs with DNA

Binding sites and equilibrium constants for the binding of drug molecules to deoxyribonucleic acid (DNA) can be estimated by a technique called footprinting analysis [9, 10]. The experimental data that needs to be col-

^max, -Kl

Vu K2

V2

M + nl^

Mln + ml ^

MlmIn

MK3

MInIq + ml ^

MImInIq(V3)

Box 6.4 Chemical equation model for inhibition of isocitrate dehydrogenase by Mn2+-citrate.

Box 6.4 Chemical equation model for inhibition of isocitrate dehydrogenase by Mn2+-citrate.

Figure 6.10 Main plot: V0 at Vmax conditions (+ moles/min/mg) vs. mM concentration of Mn2+-citrate complex (M); the concentration of free-Mn2+ was fixed at 80 +M and that of Mn2+-isocitrate at 250 +M, variations of Mn2+-citrate were then calculated. Data were fitted with model in Table 6.14 (adapted with permission from [1].)

Figure 6.10 Main plot: V0 at Vmax conditions (+ moles/min/mg) vs. mM concentration of Mn2+-citrate complex (M); the concentration of free-Mn2+ was fixed at 80 +M and that of Mn2+-isocitrate at 250 +M, variations of Mn2+-citrate were then calculated. Data were fitted with model in Table 6.14 (adapted with permission from [1].)

lected is the rate of cleavage of the DNA at specific sites vs. the concentration of drug in the system.

The model for analysis of the data involves the combination of linked functions for all of the binding equilibria involving the drug and the DNA. The analysis is based on the fact that equilibrium binding of drugs to DNA may inhibit the DNA cleavage reactions at the specific site at which the drug is bound.

The footprinting experiment involves exposing the DNA to a drug bound by equilibrium processes, then cleaving the DNA backbone with the enzyme DNase I or some other cleavage agent [9]. If the equilibrium-binding drug

Table 6.14 Model for the Complex Enzyme Inhibition in Box 6.4 Assumptions: Inhibition mechanism as in Box 6.4.

Regression equation:

k"c"___kfc?___mc"jk\ci, i + kici (i + k?C7)(i + /qcp (i + tf?C7)(i + /qcp_ K1C"IV2 K^CJKidV,

(1 + K^C})( 1 + iqcp (1 + K^C"}){ 1 + Regression parameters: Data:

Special instructions: Run a series of nonlinear regressions with successively increasing fixed integer n, m, and q values until the best standard deviation of regression is achieved i/ _ r max , v

inhibits cleavage, the fragments of oligonucleotide products that terminate at the binding site will be present in smaller amounts in the product mixture obtained after the cleavage is quenched. Radiolabeled DNA is used, and analysis of the products is done by electrophoretic sequencing methods. Detection is by autoradiography. These experiments generate plots of autoradiographic intensity of the oligonucleotide fragments vs. concentration of the drug [9, 10].

Although the model can be quite complex and may involve a large number of interacting equilibria, the binding can be explained by equations similar to the following:

In the footprinting experiment, M; represents the jth binding site on the DNA, X is the drug, and MjX represents the drug bound to the /'th site on DNA. The equilibria are expressed in concentrations of bound and unbound sites on DNA, so that

[MjX] = concentration of sites at which drug is bound,

[X] - concentration of free drug,

[Mj] = concentration of free sites without bound drug.

Using the same symbols and definitions as in Table 6.1, with n = 1, fM,o = fraction of free sites, fM,i = fraction of bound sites, fx ft = fraction of free drug, fx, i = fraction of bound drug.

Experimentally, the cleavage reaction must be terminated early so that each product results from only a single specific cleavage reaction of a DNA molecule. This yields product intensities in the analysis that are directly proportional to the probability of cleavage at the sites along the chain. If these conditions are fulfilled, the radiographic spot intensity is directly proportional to the rate of cleavage (/?,) at a given site, expressed as

where k, is the rate constant for cleavage at the /th site, and [A] is the concentration of cleavage agent.

A given drug may bind at a site on the DNA encompassing several base pairs. For example, binding sites for actinomycin D (actD) span four base pairs [9]. For a position on the DNA or the nucleotide in a region where the drug binds, the drug blocks cleavage to an extent governed by its binding equilibrium constant at that site. In such cases, the cleavage rate (i.e., spot intensity) decreases as the concentration of drug increases [9]. On the other hand, for long DNA molecules with multiple sites, spot intensities for cleavage at sites between those that bind the drug increase with increasing concentration of the drug.

Structural changes in the DNA may be induced by drug binding. They may cause increases or decreases in cleavage rates that are not predicted by the simple picture of binding just discussed. Finally, sites having relatively small binding constants may exhibit intensity vs. [X] plots showing cleavage rates enhanced at low drug concentrations and decreased at higher concentrations [9, 10].

Models for the DNA footprinting data are constructed based on eq. (6.56) combined with the definition of fM,i based on eq. (6.55). The preceding paragraph delineates the different types of qualitative behavior to expect in the data. In the discussion that follows, we give only an outline of how such models can be built. Full details of the model building and other complications of footprinting analysis are beyond the scope of this chapter, and the reader is referred to two excellent reviews articles on the subject [9, 10].

The essential feature of model building is to link eq. (6.56) to the correct expression for (1 - fMjX) = fMt0. This is then inserted into an expression for spot intensity (/,), such as

where fc, is the product of /c; and the proportionally constants between /, and Ri. Some examples of these expressions are given in Table 6.15.

Each system studied by quantitative footprinting is somewhat unique, and an appropriate model must be built starting from the factors summarized in Table 6.15. Additional factors may also have to be considered, such as the influence of unlabeled carrier DNA on the free drug concentration, as

Table G.15 Components of Models for the Cleavage Rate Measured by Spot Intensity in DNA Footprinting

Independent binding sites:

Adjacent binding sites k and j with mutual inhibition:

Adjacent binding sites k and j in which binding to one site excludes binding to the other site:

''■' = k'^{l + Ki{X} + Kk[X]) Concentration of free drug, where Ke is a regression parameter:

Regression parameters: Data:

12.0

12.0

10 20 30

[Actinomycin], |jM

10 20 30

[Actinomycin], |jM

Figure 6.11 Footprinting plots for the 139 base pair DNA fragment for selected sites in the region 85-138 of the fragment. Solid symbols are experimental gel spot intensities. Fits computed according to the best model considering strong and weak binding sites are shown

10 20 30

[Actinomycin], |jM

10 20 30

[Actinomycin], |jM

Figure 6.11 Footprinting plots for the 139 base pair DNA fragment for selected sites in the region 85-138 of the fragment. Solid symbols are experimental gel spot intensities. Fits computed according to the best model considering strong and weak binding sites are shown well as weak binding sites [9, 10], Nonlinear regression analysis is then done, with the error sum defined on the basis of the intensities of all the sites for all Cx■ Thus,

Iii is the dependent variable, and Cx and the site number j are the two independent variables. The data consists of sets of normalized intensities vs. Cx for each site, and all data are analyzed simultaneously. Simplex algorithms have been used to minimize S in this analysis.

The case of ActD with a 139 base pair DNA fragment, as well as other examples, have been discussed in detail [9, 10], A later paper reported binding constants for both high and low affinity sites on the same 139 base pair DNA fragment [11], The authors showed that both types of sites must be considered in the model, even if only the high-affinity binding constants are desired. Binding constants for 14 sites on the DNA were obtained. Examples of some of the graphical results presented in the work reveal

tn m

ffl 4.0

10 20 30 40

[Actinomycin], |jM

10 20 30

[Actinomycin], |jM

10 20 30

[Actinomycin], pM

[Actinomycin], pM

as open symbols and dashed lines Sites 89, 90, 95, 96, and 108 are enhancement sites. Sites 133, 136, and 138 show strong binding. (Adapted with permission from [11], copyright by the American Chemical Society.)

sites that exhibit strong binding and also those whose binding is enhanced as drug concentration is increased (Figure 6.11).

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