Double positive cooperativity

A ratio used to assess the degree of cooperativity exhibited by an enzyme. It is equal to the true Ymax value (typically extrapolated from the high-substrate-concen-tration end of a double-reciprocal plot) divided by the apparent Emax value obtained from extrapolating the asymptote in the low-substrate-concentration portion of the double-reciprocal plot. For a noncooperative system, Ry will equal one positively cooperative systems will have values greater than one and negatively cooperative systems will have values less than one . This method requires good estimates of the asymptotes. 

Polyether containing 2,2 -bipyridil units 8 spontaneously forms a double helicate 9 by multiple coordination with Cu+ ions [13]. This process of self-organization is enforced by the proper orientation of coordinated bipyridyl units analogous to that shown in Figure 1.2. It is characterized by a positive cooperativity yielding no partly assembled species. 

Fig. 3a-d. A diagrammatic representation of double-stranded helicates (23, 34] containing (a) two, (b) three, (c) four, and (d) five 2,2 -bipyridine subunits [23], The Cu(I) ions function as a template around which the helicates can assemble. Furthermore, this assembly process exhibits (i) self-self recognition in the preferential pairing to the same ligand in the presence of others in the reaction mixture, and (ii) positive cooperativity in which the complexation of one metal ion facilitates the binding of the next... 

In addition to the closed cyclic trimer, the open trimers displayed in Fig. 5.22 in which the central molecule acts as (a) simultaneous donor-acceptor, d-a, (b) double donor, d-d, and (c) double acceptor, a-a were considered as well . In the first case, one would expect positive cooperativity, which is confirmed by an attractive total three-body interaction energy equal to about 10% of the two-body contribution. Most of this three-body term is due to the SCF-deformalion, as in the cyclic structure. The double-donor is bound by only about 1/10... 

Helicate self-organization-positive cooperativity in the self assembly of double-helical metal-complexes, A. Pfeil and J.-M. Lehn, J. Chem. Soc., Chem. Commun., 1992, 838. 

The nonlinear 2 2 function kinetics should be differentiated from other nonlinear kinetics such as allosteric/cooperative kinetics (Bardsley and Waight, 1978) and the formation of the abortive substrate complex (Dalziel and Dickinson, 1966). The cooperative kinetics (of the double reciprocal plots) can either concave up (positive cooperativity) or... 

Pfeil A, LehnJ-M. Hehcate self-organisation positive cooperativity in the self-assembly of double-hehcal metal complexes. Chem Soc Chem Commun. 1992 838—840. 

Kofranek et al. [219] also performed a complete vibrational analysis so as to obtain the frequencies of all modes within the harmonic approximation. The stretching frequency of the HCN monomer was calculated to be 3654 cm" with the double-C basis set. Formation of the dimer lowers the frequency of the proton-donor molecule by 80 cm S as indicated in the first row of Table 26. This frequency drops further by 30 cm when a third molecule is added (to the other end of the chain) subsequent red shifts are 28 and 16 cm" as the chain continues to grow. The intermolecular H N stretching frequency is fairly low, only 122 cm for (HCN)2. Commensurate with the positive cooperativity exhibited and the increasing complexation energy, the frequency of this stretch increases as the chain elongates. The shift is 43 cm in the transition from dimer to trimer, with smaller but significant increases observed for subsequent additions of HCN. 

Cooperativity is crucial in designing molecular constituents for the functional supra-molecular self-assemblies. Especially when increasing numbers of components are involved, high degrees of positive cooperativity are usually d anded for the self-assembly of a desired architecture with high fidelity and specific performance. The double helix is one such functional assembly. 

Figure 1. Idealized (A) velocity vs. substrate concentration and (B) double reciprocal plots (Lineweaver-Burk) for enzymes demonstrating (a) hyperbolic (classical Michaelis-Menten) behavior (b) positive cooperativity (c) negative cooperativity.

Copper(I) tends towards a tetrahedral coordination geometry in complexes. With 2,2 -bipyr-idine as a chelate ligand a distorted tetrahedral coordination with almost orthogonal ligands results. 2,2 -Bipyridine oligomers with flexible 6,6 -links therefore form double helices with two 2,2 -bipyridine units per copper(I) ion (J. M. Lehn, 1987,1988). J. M. Lehn (1990 U. Koert, 1990) has also prepared such helicates with nucleosides, e.g., thymidine, covalently attached to suitable spacers to obtain water-soluble double helix complexes, so-called inverted DNA , with internal positive charges and external nucleic bases. Cooperative effects lead preferentially to two identical strands in these helicates when copper(I) ions are added to a mixture of two different homooligomers. 

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