Binding isotherm cooperativity

Usually non-cooperative and non-Unear binding isotherms were observed in alkaloid-B-DNA complexation and the data were fitted to a theoretical curve drawn according to the excluded site model [126] developed by McGhee and von Hippel [127] for a non-Unear non-cooperative ligand binding system using the following equation ... 

In order to compute the binding isotherm (Section 2.1) of any system, one must know all the microstates of the system. This cannot be done for even the smallest binding system. However, in order to understand the origin of cooperativity and the mechanism by which ligands cooperate, it is sufficient to consider simple models having only a few macrostates. This understanding will be helpful for the selection of methods to extract information from experimental data, and for the meaningful interpretation of this information. 

Figure 4.14. Binding isotherms and their derivatives for a system of double-site molecules with no genuine cooperativity. The full lines correspond to pure H (on the Ihs) and pure L (on the rhs). The equilibrated Bis, 0, are the dotted curves corresponding to the system described in Eq. (4.6.4). The frozen-in BI are the dashed curves (withx2 = 1/2) (a)q = 1, qu = 100 (b) q = I, qfj= 1000 ...

Figure 5.12 shows the BI and the quantities g(C) - 1 for this model. This illustration shows that although the binding isotherms seem to belong to a negative cooperative system, it is, in fact, meaningless in general to refer to the cooperativity of the system where there exists more than one type of cooperativity. In Fig. 5.12a, the curve starts with positive cooperativity, mainly due to the indirect part, i.e.,... 

We note that in spite of the large differences in the two sets of results reported in Table 5.3, the binding isotherms computed with these three sets of results were almost indistinguishable on the scale of Fig. 5.19. The most important differences between the calculated correlations and those reported by Senear et al. are, first, there is a large negative cooperativity between sites a and c, while Senear et al. assumed from the outset that no long-range cooperativity exists, and second, the triplet correlation is not additive, i.e., neither Sj nor 62 is zero, while Senear et al. assumed from the outset that 82 = 0. 

Figure 6.2. Binding isotherms and the average correlation, g(C) - 1 for the tetrahedral (T), square (S), and linear (L) models. The sites are identical and all correlations are due to direct ligand-ligand pairwise additive interactions, (a) Curves for positive cooperativity, S(2) = 10 (b) curves for negative coopera-tivity, S(2) = 0.1. Note that in these systems the cooperativity increases in absolute magnitude from L to S to T.

While there are several books that deal with the subject matter of this volume, the only one that develops the statistical mechanical approach is T. L. Hill s monograph (1985), which includes equilibrium as well as nonequilibrium aspects of cooperativity. Its style is quite condensed, formal, and not always easy to read. The emphasis is on the effect of cooperativity on the form of the PF and on the derived binding isotherm (BI). Less attention is paid to the sources of cooperativity and to the mechanism of communication between ligands, which is the main subject of the present volume. 

Bowser and Chen (10) have calculated some theoretical binding isotherms (/z - /zs = /([L]) for anticooperative, noncooperative, and cooperative complex formation at two equivalent binding sites with arbitrarily chosen microscopic constants see Table 1. 

The sigmoidal shape of the O2 binding isotherm, i.e., the cooperativity of O2 binding, is dependent on the concentration of the Hb solution (Fig. 2). As the solution is diluted, the relative concentration of free afi dimers increases, and unlike the tetramer, the free dimer binds O2 noncooperatively with high affinity. Thus, the true tetramer-binding curve is observed only at the highest Hb concentrations At lower concentrations, the experimental isotherm reports a mixture of tetramer and free dimer (1). 

The binding Isotherms for the Interaction of the anthracycllne antibiotics, adriamycin and daunorubicin, with calf thymus DNA, measured by phase partition techniques, are shown In Figure 3. Both drugs show Initially Increasing binding Isotherms, Indicative of a cooperative binding process, and reach a maximum... 

As can be seen from the binding isotherms shown in Figure 2, the interactions of silver ion with HEMA and HVMEMA are also cooperative. However, the rise in 0Ag at the inflection point is less steep for these copolymers than for the polyacrylic acid the steepness decreases in the order PAA > HEMA > HVMEMA. 

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