A cationic host displaying positive cooperativity in water

Abstract

The affinity of guanidinium and Cu(II) containing hosts for polycarboxylate guests is studied in water by using UV-visible spectroscopy and isothermal titration calorimetry. By combining a Cu(II) coordination site and a diguanidinium moiety around a single scaffold it is found that the Gibbs free-energy release upon binding is greater than could be expected based on the sum of the free energy released by the binding functional groups when operating in isolation. This effect is known as positive cooperativity and has rarely been observed with synthetic hosts in water. The isothermal titration calorimetry data suggest that the source of this positive cooperativity is enthalpic in origin. We propose that covalently positioning the cationic binding moieties in close proximity destabilizes the unbound host, and thereby the stabilizing effect of binding the anionic carboxylates is exothermic and also, the source of positive cooperativity observed herein.

Because of the modest nature of noncovalent interactions, most instances of molecular recognition, both natural and synthetic, are the product of multiple binding events. As the number of these binding events in a host–guest interaction increases, the Gibbs free energy of binding invariably becomes more exergonic and the association becomes more favorable. This effect is general and has been explored in a number of closely related phenomena, including metal chelation (1, 2), multivalency (3), and cooperativity (4–8). The self-assembly of the DNA double-helix is a natural example of cooperative binding; however, the cooperativity seen when hemoglobin binds multiple diatomic oxygen molecules is allosteric in nature and is a fundamentally different phenomenon than we are discussing herein.

Isothermal titration calorimetry (ITC) has allowed significant insight into the nature of molecular-recognition events because of its unique capacity to deliver a full suite of binding data (K_a, ΔG, ΔH, and TΔS) in a single titration. Our group has been interested in the application of ITC for the elucidation of the nature of cooperative binding events in water, specifically by probing the thermodynamic source of negative cooperativity (4), which is the most common form of cooperativity. We also want to determine whether a strategy for developing systems displaying positive cooperativity should focus on the enthalpic or entropic contribution to binding.

Positive cooperativity represents an optimal mode of binding in which the various discreet binding events that collectively drive a host–guest interaction are being used to their full capacity, and indeed, exceed the binding strength that could be expected via the summation of the individual Gibbs free energies of binding. Although far off, a general strategy for achieving positive cooperativity in host–guest systems would signify a comprehensive understanding of binding phenomena, a major goal of the supramolecular chemistry community. Maximizing positive cooperativity in water is an especially important goal because water has long been one of the most difficult media for the molecular recognition chemist, despite being the exclusive solvent in vivo.

What chemists have come to call cooperativity, Jencks, in 1981 (8), first articulated as additivity in the form of Eq. 1. The Gibbs free energy of connection (ΔG_S°) is defined to be positive in the case of positive cooperativity and negative in the case of negative cooperativity. The Gibbs free energy of binding A–B (ΔG_AB°) represents the binding of the polyvalent host and guest as observed in the laboratory, whereas the Gibbs free energy of binding A (ΔG_A°) and B (ΔG_B°) are the intrinsic strengths of the constituent binding events that make up the full host–guest interaction observed as ΔG_AB° (Fig. 1). For a full introduction to the concept of cooperativity and multivalent binding some reviews and illuminating articles are recommended (3, 4, 7–9).

Fig. 1.

A and B are binding functional units that are complementary to different areas of the host. As guest AB they bind in tandem.

As an extension of Jencks' analysis, our group has previously defined ΔH_S° and TΔS_S° as the enthalpy and entropy of connection (Eqs. 2 and 3) (4). ΔH_S° is positive when enthalpy contributes to positive cooperativity and negative when enthalpy contributes to negative cooperativity, whereas TΔS_S° is negative when entropy contributes to positive cooperativity and positive when entropy contributes to negative cooperativity. These thermodynamic variables of connectivity maintain a Gibbs–Helmholtz type dependency (Eq. 4). For clarity we will use the term −TΔS_S°, which is positive when the entropy of connection contributes to positive cooperativity just like ΔG_S° and ΔH_S°.

As thermodynamic studies of cooperativity continue to be published, it is becoming increasingly clear that multiple factors contribute to Jencks' original analysis of positive cooperativity. Jencks' analysis relied on similar logic as metal-chelation chemistry. It can be deduced that an entropic benefit must be gained in the tethering of multiple binding events because the entropic penalty of losing translational motion must be paid once in total, instead of once for each of the binding events. However, this thermodynamic truism has not commonly manifested itself in the form of positive cooperativity, in part because of the complexities of the solution phase, especially with competitive solvents such as water. Competitive solvents are able to engage charged and polar binding moieties in hydrogen bonding, dipole–dipole interactions, and charge–dipole interactions. Some examples of ion pairing and metal coordination binding events in water are known to be entropically driven (10, 11), by solvent rearrangement, and it has been shown that the reduced solvation surface of the “whole” guest (A–B) versus the “parts” (A and B) can contribute to an entropic disfavorability of tethering (4). Another reason that the entropic benefit of connection is not commonly observed to give a positive Gibbs free energy of connection is loss of conformational freedom inherent in tight binding (see below).

In the Jencks model, the ability of complementary binding functionalities (e.g., a hydrogen-bond donor and acceptor) to interact is easily compromised when such functionalities are each part of a larger molecule incorporating multiple discreet binding moieties. As all of the binding interactions between a host and guest seek their complementary parts, it is logical to consider that they will not all be able to access the ideal distance and conformation that represents the most stable interaction mode for that binding event. As such, one would expect enthalpy to scale imperfectly as the binding events between a host and guest multiply, unless the host and guest are able to associate in a configuration ideal for all of the constituent binding events (Fig. 2). Such a task seems difficult theoretically; however, it has been achieved on a few occasions (6, 9). Just as positive cooperativity has not emerged from entropic benefits, so has negative cooperativity not been regularly linked to enthalpy (4, 6). It should be noted that one system displaying positive cooperativity in water was shown to be entropically derived; however, it was attributed to a solvent displacement gain and not to the translational entropy factors of the Jencks model (5).

Fig. 2.

A model of incomplete binding interaction caused by tethering.

A corollary to Jencks' original considerations has been proposed by Williams and Westwell (7) and has proven useful in providing a more complete picture of the nature of cooperative binding. It has been found in a variety of systems that when binding interactions occur as an ensemble the effect is more than additive with respect to enthalpy (6). The magnified exothermicity of a polyvalent system, however, has never been reported to result in a positive ΔG_S°. It is believed that as a host–guest interaction becomes tighter residual motion and binding mode diversity are proportionally lost: an entropically unfavorable situation (12). Although ΔG° is normally observed to become more favorable as binding events are tethered, the entropic loss that accompanies enthalpic strengthening has regularly been implicated in a final analysis of why negative cooperativity results (6). Of the two known examples of positive cooperativity using a synthetic host, one was found to be entropically driven (5), and the other was observed without the benefit of ITC to determine the thermodynamic source of its positive cooperativity (13).

In light of the seemingly inescapable entropic penalty of strong binding, we reason that a system that displays positive cooperativity must have a fundamental binding quality that is not present in the constituent binding moieties in isolation: an “X factor.” From the literature, one example of such an X factor seems to be active in the prodigious chelating ability of EDTA (1). In EDTA, the polyanionic character is believed to have a destabilizing effect on the unbound form so that its ability to bind cations is strongly assisted by the exothermic release associated with the relief of several electrostatic repulsions. Similarly, spherand-type cation receptors have been shown to bind more strongly when the unbound host suffers from configurational deformation because of the repulsion of electron pairs between oxygens in the binding pocket (14). Systems such as spherands and EDTA, which have a conspicuous destabilizing force in the unbound state, seem to be archetypes around which a formal demonstration of positive cooperativity in water could be designed. We wondered whether an organic receptor using a mixture of metal coordination and ion-pair binding events could be a possible candidate for a system displaying positive cooperativity in a manner similar to the EDTA chelating effect.

To achieve positive cooperativity our strategy was to exploit the destabilizing effect of electrostatic repulsion to instill in the full host a secondary binding force unavailable to the constituent binding moieties. In this way, we hoped to promote positive cooperativity in water, or at least to observe a system whose negative cooperativity was minimal compared with previous systems. We hypothesized that any progress toward a positively cooperative system would come from enthalpic gains derived from the alleviation of electrostatic repulsions in the unbound host.

Results and Discussion

Design Criteria.

Host 1 is tetracationic and therefore able to accommodate up to four carboxylate groups in a small guest molecule such as 1,2,3,4-butanetetracarboxylate. Two carboxylates can chelate at the Cu(II) center (although the axial coordination site is longer and weaker than the equatorial site) (15, 16), leaving one carboxylate for each of the guanidiniums.^‡ In this way, host 1 is conceptually cleavable into its Cu(II) center 2 and its bis-guanidinium portion 3 (Fig. 3), with each part able to accommodate up to two carboxylates per guest. The purpose of segregating the individual binding events is to accurately quantify the intrinsic strength of binding, ΔG_A° or ΔG_B°, as defined by Jencks (8).

Fig. 3.

Cationic hosts (Left) and carboxylate guests (Right). The carboxylate guests are 1,2,3,4-butanetetracarboxylate, tricarballate, glutarate, succinate, and acetate.

The copper site has been isolated in the form of the bis-aminomethylpyridine Cu (II) ligand–metal complex 2. The bis-guanidinium site is isolated in model host 3 in which the portion of host 1 that is equipped with a tridentate copper ligand has been capped with an acyl amide group, rendering it nonfunctional as an anion binding site in the competitive aqueous media. It is important to note that any hydrophobic binding in host 1 from the face of the aromatic ring will be similarly available in 3, so all of the overt binding functionalities in host 1 have been accounted for in the two model hosts. Therefore, any positive cooperativity will be an intrinsic property of the specific arrangement of these binding entities in host 1.

Each host and guest has one or more associated counter ions. The cationic hosts have exclusively chloride counter anions, whereas the anion guests have exclusively sodium cations. The salt metathesis that is inherent in our studies always involves the creation of the same salt (NaCl) and therefore is not what differentiates the host–guest thermodynamics. For similar reasons, the buffer concentration and solution pH are kept constant throughout.

Binding Studies.

The results of binding studies between hosts 1-3 and the pertinent carboxylate guests are shown in Table 1. The ITC titrations were undertaken in pH 7.4 Hepes-buffered (60 mM) solution with the host molecule in the cell and the guest carboxylate as the titrant. When possible, affinity constants from ITC were confirmed with UV-visible (Vis) spectroscopy. For the UV-Vis titrations, the Cu(II) absorbance shift as a function of guest added was plotted and fit to a 1:1 binding curve (17) to obtain the association constant.

Table 1.

Host–guest binding affinities and thermodynamic values

Host	Guest	Ka, M−1, UV-Vis	Ka, M−1, ITC	ΔG, kcal/mol, UV-Vis	ΔG, kcal/mol, ITC	ΔH, kcal/mol	TΔS, kcal/mol
1	Acetate	5.3 ± 1.4 × 102	Enthalpically neutral	−3.70 ± 0.16
	Succinate	5.5 ± 1.7 × 103	2.57 ± 0.28 × 103	−5.08 ± 0.19	−4.66 ± 0.07	−0.14 ± 0.04	4.52 ± 0.08
	Glutarate		1.36 ± 0.15 × 103		−4.28 ± 0.07	0.73 ± 0.21	5.01 ± 0.22
	Tricarballate		2.34 ± 0.26 × 103		−4.60 ± 0.07	−1.16 ± 0.33	3.44 ± 0.34
	Tetracarboxylate		1.94 ± 0.21 × 104		−5.86 ± 0.07	−1.95 ± 0.56	3.91 ± 0.56
2	Acetate	3.5 ± 0.3 × 101	1.61 ± 0.18 × 101	−2.11 ± 0.05	−1.65 ± 0.07	1.45 ± 0.16	3.10 ± 0.17
	Succinate	1.7 ± 0.1 × 102	1.15 ± 0.13 × 102	−3.05 ± 0.04	−2.81 ± 0.07	1.01 ± 0.29	3.82 ± 0.30
	Glutarate		1.08 ± 0.12 × 102		−2.78 ± 0.07	1.61 ± 0.46	4.39 ± 0.47
3	Acetate		1.29 ± 0.14 × 101		−1.52 ± 0.05	0.31 ± 0.09	1.83 ± 0.10
	Succinate		3.39 ± 0.37 × 101		−2.09 ± 0.07	−0.16 ± 0.05	1.93 ± 0.09
	Glutarate		5.29 ± 0.58 × 101		−2.36 ± 0.06	0.31 ± 0.09	2.67 ± 0.11

In ITC, the unitless value c refers to the product of the association constant K_a (M⁻¹) and the concentration of the receptor (mol/liter) in the sample cell. Wiseman et al. (18) originally defined acceptable c values as falling between 1 and 1,000 to ensure a thermogram of sufficient curvature to be fit by the binding isotherm for the determination of K_a and ΔH. Unfortunately, implicit in the study of noncovalent binding events in isolation is the observation of exceptionally low K_a values (10–100 M⁻¹), which would require unreasonable experimental concentrations to achieve c ≥ 1. Some of the ITC data in this article were determined at c values as low as ≈0.02, however, Turnbull and Daranas (19) have argued that c values as low as 0.001 are acceptable provided that the titrations are taken well past the two equivalents of ligand used in Wiseman's example, and the thermogram is allowed to develop into a hyperbolic isotherm of sufficient curvature. Indeed, their study supports “the validity of all values of K_a,” while advocating “caution in the interpretation of ΔH°.” We therefore proceed confidently in our analysis of cooperativity, which is a Gibbs free-energy phenomenon, while we cautiously offer thermodynamic explanations of our findings when dealing with the lowest-affinity systems (K_a < 100).

In the case of acetate binding to host 1 only the UV-Vis data could be used to give the binding constant (K_a = 5.3 × 10² M⁻¹, −3.7 kcal/mol; 1 kcal = 4.184 kJ) because of the thermoneutrality of the binding event, which makes it insensitive to ITC. The ΔGs of binding succinate (K_a = 2.6 × 10³ M⁻¹, −4.7 kcal/mol), glutarate (K_a = 1.4 × 10³ M⁻¹, −4.3 kcal/mol), and tricarballate (K_a = 2.3 × 10³ M⁻¹, −4.6 kcal/mol) are all roughly the same, but the thermodynamic basis of these associations is distinct. The enthalpic contribution to the host 1 association with the dicarboxylates is quite small in the case of succinate (ΔH = −0.1 kcal/mol) and unfavorable in the case of glutarate (ΔH = 0.7 kcal/mol). In contrast, the association of tricarballate with host 1 is more exothermic (ΔH = −1.2 kcal/mol), but the tighter binding results in an apparent entropic penalty as the TΔS term is less favorable by >1 kcal/mol when the third carboxylate is present (tricarballate TΔS = 3.4 kcal/mol versus average TΔS = 4.8 kcal/mol for the dicarboxylates). This apparent trend of enthalpy/entropy compensation does not extend to 1,2,3,4-butanetetracarboxylate binding to host 1, as the enthalpy and entropy both become more favorable (ΔH° = −2.0 kcal/mol, TΔS° = 3.9 kcal/mol) upon addition of the fourth carboxylate.

The binding affinities of the model hosts 2 and 3 to the small carboxylates acetate, succinate, and glutarate, were also examined. Host 2 showed a small entropically driven affinity for acetate (K_a = 16 M⁻¹, −1.7 kcal/mol) and an affinity of an order of magnitude more for the dicarboxylates. The trend within host 3 is the same as hosts 1 and 2 with ΔG° generally decreasing (more exergonic) as the number of guest carboxylates increases from one (acetate, K_a = 13 M⁻¹, −1.5 kcal/mol) to two (succinate, K_a = 34 M⁻¹, −2.1 kcal/mol; glutarate, K_a = 53 M⁻¹, −2.4 kcal/mol). The association of host 3 with all three small carboxylate guests was slightly lower than that of host 2, as may be expected given the coordinative nature of the copper–carboxylate interaction of host 2 in comparison to the pure ion-pairing nature of the guanidinium–carboxylate interaction present in host 3.

Cooperativity Analysis.

The binding of monocarboxylates and dicarboxylates to the model hosts 2 and 3 is considered representative of the intrinsic strength of binding, ΔG°, for carboxylates interacting with the analogous portions of host 1. Using Jencks' Eq. 1 in our analysis of cooperativity, we have assigned the intrinsic strength of binding at the Cu(II) center of host 1 as ΔG_A°, and the intrinsic strength of binding at the bisguanidinium portion of host 1 as ΔG_B°. ΔG_A° and ΔG_B° are defined by the strength of binding of a particular guest subunit to hosts 2 and 3, respectively. The thermodynamic components of connectivity, ΔH_S° and TΔG_S° (Eqs. 2 and 3) were also calculated to reveal the influences that determine the sign of ΔG_S°. In all cases ΔG_S° is positive and enthalpic in origin (Table 2). The positive ΔG_S° of binding succinate or glutarate to host 1 indicates that the binding interaction is more favorable than is predicted by the summation of the ΔG_A° of acetate coordinating to host 2 and the ΔG_B° of acetate binding to the diguanidinium moiety modeled on host 3. The difference in binding between the whole and the parts depends on whether the whole in question is succinate or glutarate.

Table 2.

Cooperativity values

A–B	A + B	ΔGAB°, kcal/mol	ΔGA° + ΔGB°, kcal/mol	ΔGS°, kcal/mol	ΔHAB°, kcal/mol	ΔHA° + ΔHB°, kcal/mol	ΔHS°, kcal/mol	TΔSAB°, kcal/mol	TΔSA° + TΔSB°, kcal/mol	−TΔSS°, kcal/mol
Succinate	AcetateA + acetateB	−4.66 ± 0.07	−3.17 ± 0.09	+1.49 ± 0.11	−0.14 ± 0.04	+1.76 ± 0.18	+1.90 ± 0.18	+4.52 ± 0.08	+4.93 ± 0.20	−0.41 ± 0.22
Glutarate	AcetateA + acetateB	−4.28 ± 0.07	−3.17 ± 0.09	+1.11 ± 0.11	+0.73 ± 0.21	+1.76 ± 0.18	+1.03 ± 0.28	+5.01 ± 0.22	+4.93 ± 0.20	+0.08 ± 0.30
Tricarballate	SuccinateA + acetateB	−4.60 ± 0.07	−4.33 ± 0.09	+0.27 ± 0.11	−1.16 ± 0.33	+1.32 ± 0.30	+2.48 ± 0.45	+3.44 ± 0.34	+5.65 ± 0.32	−2.21 ± 0.47
Tricarballate	GlutarateA + acetateB	−4.60 ± 0.07	−4.30 ± 0.09	+0.30 ± 0.11	−1.16 ± 0.33	+1.92 ± 0.47	+3.08 ± 0.57	+3.44 ± 0.34	+6.22 ± 0.48	−2.78 ± 0.59
Butanetetra-carboxylate	SuccinateA + succinateB	−5.86 ± 0.07	−4.90 ± 0.10	+0.96 ± 0.12	−1.95 ± 0.56	+0.85 ± 0.29	+2.80 ± 0.63	+3.91 ± 0.56	+5.75 ± 0.31	−1.84 ± 0.64
Butanetetra-carboxylate	GlutarateA + glutarateB	−5.86 ± 0.07	−5.14 ± 0.09	+0.72 ± 0.11	−1.95 ± 0.56	+1.92 ± 0.47	+3.87 ± 0.73	+3.91 ± 0.56	+7.06 ± 0.48	−3.15 ± 0.74

Superscripts denote binding of carboxylate to A (host 2) or B (host 3). Thermodynamic measures of cooperativity are in bold.

Succinate displays greater positive cooperativity than glutarate, and all of succinate's positive cooperativity stems from its positive ΔH_S° (+1.8 kcal/mol), which is able to compensate for the negative cooperativity of its −TΔS_S° (−0.4 kcal/mol). Glutarate, on the other hand, is the only whole guest whose positive ΔG_S° is derived in part from a positive −TΔS_S°. The positive entropy of connection is likely the result of the desolvation of the C3 methylene of glutarate upon binding host 1, an entropically favorable event that is not accounted for in the two acetate interactions that were used to determine the intrinsic strength of glutarate's constituent binding events. This analysis is further supported by the less positive ΔH_S° of the glutarate interaction. The same desolvation process that leads to a positive −TΔS_S° could be enthalpically costly in accordance with the current theory of the endothermic nature of some forms of hydrophobic binding (20).

While the dicarboxylates were considered whole with respect to acetate parts, they served as parts in the study of larger whole guest molecules tricarballate and tetracarboxylate. Succinate and glutarate have been examined to allow for the different possible binding conformations of tricarballate and the tetracarboxylate to host 1. 1,2,3,4-Butanetetracarboxylate, for example, may chelate Cu(II) in a manner resembling succinate (Fig. 4A) or glutarate (Fig. 4B). While the succinate type 7-member ring formed with Cu(II) is known to be more stable (16), the glutarate-type eight-member ring may be induced depending on the preferred geometry of interaction at the bisguanidinium portion of host 1. A succinate type chelation mode by 1,2,3,4-butanetetracarboxylate (Fig. 4A) would present two β-carboxylates toward the bisguanidiniums, whereas a glutarate-type chelation mode (Fig. 4B) would present two γ-carboxylates.

Fig. 4.

Succinate-like (A) and glutarate-like (B) chelation of the host 1 Cu(II) center by 1,2,3,4-butanetetracarboxylate.

The latter mode of bisguanidinium binding is best represented by glutarate, whereas the former is best represented by succinate, thus necessitating the use of both dicarboxylates as model guests for interaction with model hosts 2 and 3. Considering 1,2,3,4-butanetetracarboxylate as a whole guest made of glutarate-like parts is somewhat unfair because of the presence of the glutarate methylene group at carbon 3 that is not represented in the tetracarboxylate. In this way, succinate, which does not have the extra methylene, is an inherently better approximation of half of 1,2,3,4-butanetetracarboxylate, and indeed we observed some important differences between the two dicarboxylates when used as parts in both the tricarballate and 1,2,3,4-butanetetracarboxylate cooperativity analysis (see below).

The least-positive cooperativity in Table 2 is seen in the binding of tricarballate to host 1. Tricarballate can be dissected as either a succinate and an acetate or as a glutarate and an acetate. Also, the tricarballate could bind host 1 in two ways: (i) with succinate or glutarate type chelation (like that shown for 1,2,3,4-butanetetracarboxylate in Fig. 4) of the copper, which allows the remaining carboxylate to engage the diguanidinium portion of host 1, or (ii), with a single carboxylate coordination of the Cu(II) while the guanidiniums are associating with the dicarboxylate. Whether the dicarboxylate in question is succinate or glutarate, the highest absolute sum of ΔG_A° plus ΔG_B° results when ΔG_A° is either dicarboxylate chelating copper and ΔG_B° is the interaction between acetate with host 3. Therefore, as a means of underestimating any positive cooperativity this mode of segregation is used in Table 2.

The low ΔG_S° of binding tricarballate appears to be rooted in the relatively small TΔS_AB° term of tricarballate binding to host 1. When moving from either dicarboxylate to tricarballate binding to host 1 the entropic term is decreased by >1 kcal/mol. The concomitant improvement in ΔH_AB° indicates that tighter binding would reduce residual motion in the binding pocket. Also, any chelation present in tricarballate binding that was not present in the dicarboxylate binding will further freeze out rotational motion.

1,2,3,4-Butanetetracarboxylate may be considered as a whole constructed of two succinate parts (succinate plus succinate^B) or two glutarate parts (glutarate^A plus glutarate^B) as shown in Fig. 4. Both modes of dissection yield positive cooperativity; however, the positive cooperativity is less when glutarates are the parts in question (+0.7 kcal/mol versus +1.0 kcal/mol for succinate parts). The dependence of ΔG_S° on the dicarboxylate used in the cooperativity analysis can be attributed to the extraneous methylene on glutarate. Glutarate binding to host 2 (ΔG_A°) and host 3 (ΔG_B°) is strongly entropically favorable. As such the entropy of connection (−TΔS_S°) is strongly negative (−3.2 kcal/mol) because 1,2,3,4-butanetetracarboxylate binding to host 1 does not involve the desolvation of two methylene carbons present in the two model binding events (one for glutarate in each event). Similarly the ΔH_S° is more positive in the case of glutarate^A plus glutarate^B because of the more endothermic binding of glutarate to the model hosts. The enthalpic cost of glutarate desolvation makes it an imperfect model guest; therefore, the ΔG_S° of 1,2,3,4-butanetetracarboxylate when succinate^A plus succinate^B are the component binding events is probably a more accurate quantification of the system's positive cooperativity.

The Basis of Positive Cooperativity in Water by Using Ion Pairing.

The importance of observing the constituent binding functionalities of host 1 in isolation is apparent upon comparison of the binding strength of the acetate-host 1 complex (UV/Vis data; K_a = 5.3 × 10² M⁻¹, −3.7 kcal/mol) with that of the acetate–host 2 complex (UV/Vis data; K_a = 35 M⁻¹, −2.1 kcal/mol). The mode of binding in both of these systems is similar: a coordinative interaction between the Cu(II) center and the acetate, yet acetate affinity to host 1 is much higher. This binding model is supported in that both affinity constants were determined by observing the change in absorbance of the Cu(II) d-d* transition, a spectral shift necessarily associated with interaction at the Cu(II) center (17). A second point of interest is that acetate binding to host 2 was shown to be endothermic (+1.5 kcal/mol), whereas acetate binding to the full host 1 was found to be enthalpically neutral, that is, the binding can be monitored by UV/Vis spectroscopy but not by ITC. The stronger binding of acetate to host 1 appears to be driven by some exothermic event that counter balances the endothermicity of the carboxylate-Cu(II) coordination event as seen in host 2. This exothermic event seems to be fundamental to host 1 because it emerges in the binding of a single anion, acetate, outside of a cooperativity analysis.

When considering the differences between host 1 and the model hosts 2 and 3 with which the intrinsic strengths of the various binding events have been determined, the most outstanding feature of host 1 is the close proximity of the positive charges. The destabilizing effect of multiple like charges has been implicated in the strongly exothermic binding prowess of EDTA with various metal ions (1). The electrostatic strain when the cationic binding moieties are forced into close proximity in the synthesis of host 1 is relieved in some part by the binding event with anionic carboxylates.

If the destabilization of the unbound host is the sole source of the positive cooperativity, then the strength of this effect must be at least +1.5 kcal/mol. This estimation is based on the assumption that the system would display negative cooperativity in the absence of the electrostatic repulsions that destabilize the unbound host because negative cooperativity has been the conclusion in nearly all of the previous cooperativity studies in water (4, 6, 9).^§ The contribution of charge clustering in host 1 to the positive cooperativity must be in all cases slightly negated by the forces of negative cooperativity, such as improper binding functional group alignment and reduced solvent displacement upon tethering. Therefore the system displaying maximal positive cooperativity (succinate binding host 1; +1.5 kcal/mol) probably represents a fair estimate of the binding enhancement borne from destabilizing the unbound structure of host 1.

Why Does Acetate, and Not Chloride, Contribute to the Relief of Electrostatic Repulsion in Host 1?

Before the addition of one of the carboxylate guests to host 1, the host solution is not devoid of anions. Although probably not proximal to the cationic host in solution, a counter ion exists for each of the charges on host 1. Why then is chloride not able to relieve the electrostatic destabilization of host 1? The answer must be that chloride is indeed providing some anionic relief to host 1 in line with its own binding affinity to Cu(II) and guanidinium-type cations. The stronger binding carboxylate anion is able to associate more strongly with the cationic moieties and, in turn, provide greater relief of electrostatic repulsion. An interesting future study would be to attempt to distinguish between an anion's specific affinity for a positively charged binding moiety and its shape-specific ability to inhabit a binding cleft and stabilize the host as a whole against electrostatic repulsive destabilization.

Conclusion

This cooperativity analysis of host 1 represents an example of positive cooperativity in water where all binding moieties of the host and guest are covalently attached as described by Jencks (8). The source of positive cooperativity was shown to be enthalpic in this case. Although the precise source of this enthalpic positive cooperativity is unclear, we believe it is rooted in the destabilizing effect of the electrostatic repulsion in the unbound form of host 1. The proximity of the chelated Cu(II) ion to the two guanidinium functional groups represents the most fundamental difference between host 1 and hosts 2 and 3 whose carboxylate affinity we used as the intrinsic strength of the binding functional groups of host 1.

The observation of positive cooperativity also implies that the carboxylate guests must be able to access the cationic binding sites of host 1 at or near the ideal distance and orientation involved in the binding of representative fragment carboxylates (acetate, succinate, and glutarate) with hosts 2 and 3. Any disruption of the individual binding events when used in tandem contributes to negative cooperativity (8).

In the system discussed herein we have shown negative cooperativity to be the providence of the entropy of connection (−TΔS_S°), which was negative in almost all cases. The unfavorable entropy of connection likely results from diminished solvent-accessible surface area on larger guest molecules and the reduced residual rotational and vibrational motion in the binding pocket as the host–guest association becomes tighter. Although enthalpic gains were generally countered by a diminishing −TΔS_S°, a fundamental enthalpic favorability associated with tethering the binding events of host 1 resulted in a positive ΔG_S°, which we have estimated to be at least 1.5 kcal/mol for this system. Host 1 uses its metal-coordination and ion-pairing binding sites in such a way that the net ΔG_S° is more favorable than would be predicted by the summation of the intrinsic strength of each binding event (ΔG_A° plus ΔG_B°), resulting in a final analysis of positive cooperativity for all of the guest A–B systems analyzed here. We suspect that many other systems might show a similar effect when submitted to a full thermodynamic analysis.

Materials and Methods

Materials.

Synthetic procedures and compound analysis are reported in supporting information (SI) Text; SI Schemes 1–4 provide a schematic guide to the synthesis of all host compounds. All commercial compounds were obtained from Acros Organics (Geel, Belgium), Aldrich (St. Louis, MO), Fisher (Pittsburgh, PA), and Mallinckrodt (Hazelwood, MO) and used without further purification.

UV-Vis Titrations.

All titrations were performed with a DU-640 UV/Vis instrument (Beckman). A typical UV/Vis titration proceeded as follows, although concentrations were altered as necessary. A cuvette with Hepes-buffered water (60 mM, pH 7.4) served as the blank. A second cuvette was filled with 1 ml of a solution of the Cu(II)-containing host (0.8 mM) in buffered water (Hepes, 60 mM, pH 7.4), and the spectrum of this solution was recorded. A second solution identical to the first except for the presence of guest (20.27 mM) was added in aliquots to the cuvette, and the spectrum was recorded between aliquots. The wavelength of maximum difference between the original solution of host and the final addition of guest was determined, and the absorbance at this wavelength was plotted against guest concentration. Binding constants were calculated by iterative curve fitting in ORIGIN using a 1:1 binding algorithm (17). Errors reported are those returned by ORIGIN after curve fitting.

ITC Experiments.

ITC thermograms were recorded by using an isothermal titration calorimeter from Microcal, Amherst, MA. ORIGIN 5.0 software (Microcal) was used to calculate the equilibrium constant and determine the standard molar enthalpy. The weakness of the observed binding events required that the binding ratio be fixed at 1:1 before curve fitting of the thermogram (10, 19). The ΔHs have been corrected to account for the heat of ionization of the Hepes buffer (1, 21) according to Eq. 5. The protonation state of the carboxylate guests was calculated from published pK_a values (22), and it was assumed that the host–guest interaction would promote the full ionization of the guest molecule. The fraction of the guest still protonated at pH 7.4 was therefore used as an estimate for N. The portion of the ΔG° not attributable to the exothermicity of the binding event was then added to the TΔS portion by using Eq. 6. Because the binding of tricarballate and 1,2,3,4-butanetetracarboxylic acid to host 1 were most affected by this correction, it served chiefly to prevent the overestimation of the enthalpic contributor to positive cooperativity.

A typical ITC experiment is as follows, although concentrations were altered as necessary, usually to generate a sufficiently prominent heat effect from the reaction. A buffered solution of water (Hepes, 60 mM, pH 7.4) was loaded in the reference cell in all cases. A solution of the host (2 mM) in buffer solution (Hepes, 60 mM, pH 7.4) was loaded into the titration cell. The syringe was loaded with ≈250 ul of guest (43.5 mM) also in Hepes buffer (60 mM, pH 7.4). The syringe was positioned in the calorimeter and the following parameters were set: injection size, 10 μl; temperature, 26°C; injection interval, 300 s; cell feedback, 15 μcal. Some titrations experienced aggregation during the early injections. These data were removed, and the curve was fit to the remaining points as described (23). Errors were calculated as the average of two standard deviations for all titrations for which independently repeated data were available (K_a = 11%; ΔH = 28.6%). This method was used because in all cases it returned greater error than did ORIGIN upon curve fitting.

Abbreviations

ITC

isothermal titration calorimetry

VIS

visible.