Cooperativity and Anticooperativity

When L can complex more than one M, cooperative binding can occur. There are many definitions of cooperativity but they are all consistent with the following criterion [7] a system is 

In particular, for a ditopic receptor that can bind successively two M (see above), the criterion for cooperativity is K21/K11 1/4, i.e. complexation of a second M is made easier by the presence of a bound M. 

For instance, a cooperative effect was observed with the bisanthraceno-crown ether 7.1 [11]. Complexation with a sodium ion brings closer together the two anthracene units which favors excimer formation, as revealed by the increase of the excimer band appearing in the fluorescence spectrum. This makes easier the binding of a second ion to form a 2 1 (metahligand) complex. The ratio of the stability constants K21/K11 determined in acetonitrile from absorption spectra is equal to 

In contrast, an anticooperative effect was observed in the bis-crown calixarene 7.2, a fluorescent molecular sensor for cesium [12]. The complexation of a second cesium ion is made more difficult by the presence of a bound cesium ion, as shown by the value of K21 that is is in fact much smaller than Kn (log Kn = 6.68 log K21 = 3.81 in ethanol). The ratio K21/K11 is 1.3 x 10 , i.e. much smaller than the statistical value of 1/4. Such an anticooperative effect is most likely due to electrostatic repulsion between the two cations an unfavorable conformational change induced in the free crown by the bound cation in the other crown can also be invoked. 

---

Figure 1. Illustration of lone electron pair preferences in alcohol dimers, cooperative and anticooperative binding sites for a third monomer, ring strain and steric repulsion in alcohol trimers, alternation of residues in alcohol tetramers, and chain, branch, and cyclic hydrogen bond topologies in larger clusters.

In some earlier publications the term cooperativity is used for positive cooperativity and anticoop-erativity is used for negative cooperativity. In this book cooperativity is used whenever g 1. Sometimes, when there is positive cooperativity one says that a ligand at a supports or favors the binding of a ligand at b, and vice versa. 

Cooperative and Anticooperative Energy Effects in Systems with Classical Hydrogen Bonds... 

The antiperiplanar arrangement of the carbanionic orbital and the o-acceptors in aromatic systems can be achieved by introducing endocyclic heteroatoms. The known hydride affinities for N-containing aromatics generally reflect the stabilizing effect of endocyclic o C-N orbitals (Figure ll ijfP- However, the situation is far from simple and cannot be readily explained by the combination of electrostatic and hyperconjugative interactions alone. A computational dissection of the complex interplay of multiple orbital interactions in these systems has not been undertaken so far but it is likely that the observed non-additivity of such effects reflects cooperativity and anticooperativity of stereoelectronic interactions. 

An important consequence of quantal charge transfer between ions and ion pairs (dipoles) is the appearance of non-pairwise-additive cooperative or anticooperative contributions that have no counterpart in the classical theory. These nonlinear effects strongly stabilize closed-CT systems in which each site is balanced with respect to charge transfers in and out of the site, and disfavor open-CT systems in which one or more sites serves as an uncompensated donor or acceptor. This CT cooperativity accounts for the surprising stability of cyclic (LiF) clusters, which are strongly favored compared with linear structures. 

Realistic three-dimensional computer models for water were proposed already more than 30 years ago (16). However, even relatively simple effective water model potentials based on point charges and Leimard-Jones interactions are still very expensive computationally. Significant progress with respect to the models ability to describe water s thermodynamic, structural, and dynamic features accurately has been achieved recently (101-103). However, early studies have shown that water models essentially capture the effects of hydrophobic hydration and interaction on a near quantitative level (81, 82, 104). Recent simulations suggest that the exact size of the solvation entropy of hydrophobic particles is related to the ability of the water models to account for water s thermodynamic anomalous behavior (105-108). Because the hydrophobic interaction is inherently a multibody interaction (105), it has been suggested to compute pair- and higher-order contributions from realistic computer simulations. However, currently it is inconclusive whether three-body effects are cooperative or anticooperative (109). 

It should be noted that interactions of A, B, and C with the receptor may mutually influence one another in both cooperative or anticooperative fashion. Furthermore, the coordinating role that conjugate C is playing in self-assembly (Scheme 1-23) may be pushed into the background or may even be absent entirely while interacting with the receptor. 

In this case, is the apparent overall association constant (overall stability constant). Bowser and Chen have discussed in detail the consistency of theory and experimental data. In their study, a 1 2 stoichiometry has been investigated and cooperative or anticooperative reaction types have been distinguished. 

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. 

A smaller secondary microscopic association constant compared to the first binding constant (k, = k2 > k2, = kl2) results in anticooperative binding behavior in cases A and B. If k, = k2 < k2i = kl2, as in cases D and E, the cooperative binding yields a higher amount of higher-order complexes. 

When Kab is small (no "mixed" dimer) Eq. 7-16 also simplifies to Eq. 7-45 for completely cooperative binding with the value K given by Eq. 7-17. On the other hand, if KAB is large compared to KAA and KBB, anticooperativity (negative cooperativity) will be observed. The saturation curve will contain two separate steps just as in the binding of protons by succinate dianion (Fig. 7-5). 

These template polymerizations suffer from three fundamental problems (i) In most cases the binding of the polymer to the template is stronger than the binding of the monomer due to the cooperativity of the interaction between the polymers. As a consequence the newly formed macromolecules are not released from the template and multiple replication is not possible without multiple separation steps, (ii) We lack the possibility to start the polymerisation reaction at the terminal group of the monomer-template complex, (iii) While a weak interaction between the template and the monomer is favourable to allow easy separation of the template and the newly formed macromolecule, it leads to incomplete complexation of the template and interraption of the polymerisation along the chain. A solution of these problems would require a relatively strong complexation of the monomers in combination with sufficient anticooperativity in the complexation of the polymer. The latter however would inevitably impede the polymerisation reaction and require therefore a living polymerisation mechanism which does not suffer from a slowed down rate of polymerisation. 

---