Cooperativity in the self-assembly of porphyrin ladders

Abstract

Cooperativity is a general feature of intermolecular interactions in biomolecular systems, but there are many different facets of the phenomenon that are not well understood. Positive cooperativity stabilizes a system as progressively more interactions are added, and the origin of the beneficial free energy may be entropic or enthalpic in origin. An “enthalpic chelate effect” has been proposed to operate through structural tightening that improves all of the functional group interactions in a complex, when it is more strongly bound. Here, we present direct calorimetric evidence that no such enthalpic effects exist in the cooperative assembly of supramolecular ladder complexes composed of metalloporphyrin oligomers coordinated to bipyridine ligands. The enthalpic contributions of the individual coordination interactions are 35 kJ·mol⁻¹ and constant over a range of free energies of self-assembly of −35 to −111 kJ·mol⁻¹. In rigid well defined systems of this type, the enthalpies of individual interactions are additive, and no enthalpic cooperative effects are apparent. The implication is that in more flexible, less well defined systems such as biomolecular assemblies, the enthalpy contributions available from specific functional group interactions are well defined and constant parameters.

Cooperativity is of fundamental importance for understanding molecular recognition processes in chemistry and biology. If two molecules bearing one complementary binding site interact to give a complex of stability ΔG, then two molecules bearing n complementary binding sites generally interact to give a complex with stability larger than nΔG. This phenomenon is known as positive cooperativity. The factors that are responsible for cooperative intermolecular interactions can be divided in two groups: entropic factors relating to the loss of motion of the molecules and enthalpic factors due to the reinforcement of the bonds. The simplest formulation of the entropic factors is the chelate effect: an interaction working in isolation must pay the entropic cost of bringing two molecules together, but when multiple interactions are made, this price is paid only once, so additional interactions make a bigger contribution to stability than the first one (1–3). The entropic term also includes any change in the internal rotations and vibrations of the molecules. Enthalpic contributions to cooperative binding can come from secondary functional group interactions, conformational changes, or polarization of the interacting groups. However, enthalpy and entropy are intimately related, so an increase in the enthalpic driving force for complexation has a direct impact on the mobility of the molecules involved in the complex. For weak intermolecular interactions, the entropy lost on formation of the first interaction is only a fraction of the total possible loss, because the molecules retain a good deal of independent mobility. As the number of interactions increases, the molecular interface tightens and more entropy is lost. The reduction in intermolecular motion has consequences for the enthalpy of interaction. As the complex tightens, the enthalpy contribution from each individual interaction becomes more favorable, leading to the widespread observation of entropy–enthalpy compensation (4, 5).

The precise nature of the compensation phenomenon has some important consequences. If the two parameters change in such a way that the net contributions to the free energy of the system cancel exactly, then entropy–enthalpy compensation is a structural phenomenon that reports on the degree of organization/crystallinity that persists in a molecular complex. For example, large differences in enthalpy and entropy of binding to membrane-bound biological receptors have been used to classify the difference between agonists and antagonists that differ little in binding affinity but induce quite different structural responses from the receptor (6, 7). If the compensation of enthalpy and entropy is imprecise, then an increase the enthalpy of interaction could lead to an additional favorable contribution to the free energy of binding through the mechanism of structural tightening. This phenomenon has been dubbed the enthalpic chelate effect and is likely to be of greatest significance in processes that involve the cooperation of large numbers of weak interactions, biomolecular folding, binding, and catalysis. Thus, the stability of a folded protein will be larger than one might expect by simply adding up the free-energy contributions of all of the interactions involved, and this finding has important implications, for example, in any attempts to predict protein three-dimensional structure from sequence or model processes such as protein folding that rely on simple force fields that are essentially additive (8–12). There is considerable experimental evidence that the binding of substrates to proteins leads to structural tightening (13–17), and if this process were associated with a significant additional free energy contribution, then it may be the enthalpic chelate that is the key missing factor in our understanding of the remarkably high binding affinities and the rate accelerations that are achieved by biological molecules (13, 18–20).

There have been many studies of cooperative effects in intermolecular binding (21–28), but it is very difficult to pin down the existence or otherwise of an enthalpic chelate effect, because of the complexity of the systems that make it difficult to separate individual contributions to the overall behavior. Structural changes in complexes of vancomycin with peptide derivatives in water have provided clear-cut experimental evidence for tightening in strongly bound complexes (29), and similar signatures of structural tightening (and loosening) have been found in protein–ligand interactions (6, 7, 13–17). Whitesides and coworkers (30) presented a study of the thermodynamics of binding of a vancomycin trimer with its corresponding trimeric ligand and showed that the enthalpy of binding was additive. However, the flexibility of the linkers between the subunits almost certainly would wash out any potential structural tightening in this system. Our experiments on more rigid synthetic H-bonded complexes in chloroform show that the free-energy contributions of individual functional group interactions are independent of the overall stability of a complex (31, 32). Although these observations suggest that there are no additional forces that impact the association constant in these systems (other than the classical chelate effect), the experiments do not directly address the issue of enthalpy and entropy changes. For example, structural tightening in a strongly bound complex could lead to a more favorable enthalpy for the individual binding interactions that is exactly compensated by entropy changes to render the net change in the free energy contribution negligible. In this work, we present experiments on a different system where enthalpy changes can be measured directly as a function of the overall stability of the complex.

The design requirements are as follows.

1. The components of the complexes should be relatively rigid molecules that fit together perfectly, to minimize complications introduced by strain, changes in conformation, or restriction of intramolecular degrees of freedom.

2. The individual interaction sites should be sufficiently remote to minimize through bond or through space cross-talk.

3. The complexes should be stable enough for accurate isothermal titration calorimetry (ITC) (K_a > 10³ M⁻¹ for reliable ITC), and the individual interactions should be associated with appreciable enthalpy changes so that differences can be detected.

Porphyrin ladders provide the ideal solution (Fig. 1). Rigid linear porphyrin oligomers form double-stranded complexes with rigid linear bifunctional ligands that act as the rungs. The overall stability of the ladder complex increases with the length of the porphyrin oligomer (22), so these systems are ideally suited to measurement of the enthalpic chelate effect. In Anderson’s ladders, the porphyrins become more conjugated on formation of the ladder, which could have an effect on the enthalpy of interaction. To avoid this problem, we designed and synthesized a previously undescribed kind of tetraphenylporphyrin oligomer and studied the ladder complexes formed with 4,4′-bipyridine (Fig. 2).

Fig. 1.

Cartoon representation of the porphyrin ladder–bipyridine assembly.

Fig. 2.

Synthesis of the porphyrin oligomers.

Results and Discussion

Characterization of the Ladder Complexes and Measurement of the Overall Ladder Stability.

The UV/visible (UV/Vis) absorption spectra of the porphyrins are all very similar, indicating that there is no electronic communication between the oligomer chromophores as expected. The porphyrins were first titrated with pyridine to quantify any intramolecular effects on the Zn–N interactions in the oligomers. Titrations were monitored by using UV/Vis absorption spectroscopy to give the microscopic association constants (K_m) shown in Table 1. The presence of amide substituents on the meso positions leads to a small but measurable difference compared with the solubilizing group. To test that complexation of the first ligand does not affect complexation at the next site in an oligomer, the data for the dimer 2 were fit to both 1:1 and 2:1 binding isotherms. In this compound, the binding sites are identical, and any differences between K_m from the 1:1 fit and the microscopic values of K₁ and K₂ from the 2:1 fit would indicate deviation from ideal behavior. However, no measurable differences were observed, and we conclude that the different binding sites present in the oligomers can be considered independent.

Table 1.

Stability constants of the porphyrin ladder and enthalpy per interaction

Porphyrin	Km,* M−1	logKOpen†	logKladder†	ΔGladder,† kJ·mol−1	ΔH/interaction,‡ kJ·mol−1
1a	1,660	3.6 ± 0.1	6.3 ± 0.1	−35.2 ± 0.6	−33.4 ± 3.3
1b	3,750	4.1 ± 0.1	7.1 ± 0.3	−39.8 ± 1.7	−36.2 ± 1.2
2	2,120	7.5 ± 0.1	12.3 ± 0.1	−68.8 ± 0.8	−34.0 ± 3.1
3	2,620	12.1 ± 0.4	19.9 ± 0.6	−111.2 ± 3.4	−35.9 ± 3.1

Errors are quoted at 95% of confidence.

*Determined by UV/V is titration.

^†Determined by NMR titration. K_open and K_ladder are the overall stability constants for formation of the ladder and the open complex from free porphyrin and bipyridine.

^‡Determined by ITC.

The stability constants of the ladder complexes were determined by ¹H NMR titrations. On titration of bipyridine into a solution of porphyrin in deuterochloroform, the signal due to the β protons of the porphyrin experiences a downfield shift that reaches a maximum when the ladder stoichiometry is reached. After this point, the signals begin to shift back upfield. The signals due to bipyridine also experience a maximal upfield shift when the ladder stoichiometry is reached. This result is indicative of the formation of a ladder complex that dissociates into open complexes in excess bipyridine (Fig. 3a) (22). Similar behavior was observed for all three porphyrins. The chemical shift data were fit to a model that allowed for the presence of the three detectable species, free porphyrin, the ladder complex, and the open complex, using specfit (33). The results are shown in Table 1.

Fig. 3.

Titration experiments used to characterize the speciations and thermodynamics of assembly. (a) ¹H NMR titration of bipyridine (B) into 2 (Left) and 3 (Right). The downfield shift of the porphyrin β protons reaches a maximum at the ladder stochiometry and then shifts back as excess B induces opening. (b) ITC addition of B to 2 (Left) and 3 (Right). Addition of B results in heat release when the ladder is formed. Further addition of B opens the ladder but does not have a detectable enthalpic effect. (c) Speciation for the ITC experiments in b, calculated from the values of K_ladder and K_open determined by ¹H NMR titration.

Measurement of the Enthalpy of Interaction by ITC.

ITC experiments were performed under conditions designed to maximize formation of the ladder complex, i.e., maximum concentration of porphyrin in the cell and bipyridine in the titration syringe. With this configuration, initial addition of ligand leads exclusively to formation of the ladder complex, and when the stoichiometric amount of bipyridine is reached, the ladder will start to break up to give the open complex. Thus, the first phase of the titration provides a measure of the enthalpy of formation of the ladder, and the second provides a measurement of the difference between the enthalpy of the Zn–N interactions in the cooperatively assembled ladder and the noncooperative open complex (Fig. 3). The data were fit to a 1:1 binding isotherm to give the enthalpy change per mole of Zn–N bond, i.e., the average enthalpy change for all of the Zn–N bonds formed in the process. The results show that in all of the complexes, the average enthalpy of Zn–N interaction is the same within error (Table 1 and Fig. 4). Even the small difference between the dimer and trimer is consistent with the increase in the number of amide substituents in the latter system. Moreover, no detectable enthalpy changes were observed in the second phase of the ITC experiments. In other words, the enthalpy changes associated with the formation of Zn–N interactions in the cooperative ladder complexes are practically identical to those in the noncooperative open complexes.

Fig. 4.

ΔH per interaction as function of the overall stability of the ladder complex.

Our results for these relatively rigid macromolecular assemblies show that the enthalpy contributions associated with individual binding sites are independent of the overall stability of the complex. Thus, the properties of the complex can be understood as the sum of the properties of the constituent interactions. We conclude that structural tightening leading to a more favorable enthalpy of interaction and a more favorable free energy of binding is not a general mechanism in molecular recognition. Although structural tightening is clearly a feature of more flexible systems like biopolymers, our results suggest that the free energy contribution associated with this phenomenon is likely to be small compared with other factors, such as changes in conformational mobility (32, 34). In proteins, additive interactions between side chains have been successfully used to account for cooperative effects on folding (21, 23, 24). Further evidence is required to establish any link between the observation of structural tightening and consequent free energy benefits in binding and catalysis.

Materials and Methods

Synthesis of Porphyrin Oligomers.

The synthesis of monomer 1a and oligomer precursors 4 and 5 are described in ref. 35. Dimeric porphyrin 2 was synthesized by reaction of an excess of monoaminoporphyrin 4 with terephthaloyl chloride, followed by treatment with zinc acetate. The synthesis of trimer 3 required the synthesis of the intermediate diacid porphyrin 6, by reaction of porphyrin 5 with an excess of terephthalic acid chloride. Trimer 3 was obtained as the condensation product of 6 with an excess of monoaminoporphyrin 4 in the presence of 2-ethoxy-1-ethoxycarbonyl-1,2-dihydroquinoline (EEDQ), followed by metallation with zinc acetate. Monomer 1b was synthesized to quantify the effect of the amide groups on the strength of the Zn–N bond. Diaminoporphyrin 5 was coupled with an excess of 4-t-butyl benzoyl chloride, and the product was metallated with zinc acetate to give 1b (for details, see Supporting Text and Figs. 5–7, which are published as supporting information on the PNAS web site).

¹H NMR Binding Studies.

¹H NMR titrations were carried out by preparing a 3-ml sample of the porphyrin oligomer at known concentration (0.1–10 mM) in CDCl₃. Then, 0.6 ml of this solution was removed, and a ¹H NMR spectrum was recorded. An accurately weighed sample of bipyridine was then dissolved in 2 ml of the porphyrin solution (so that the concentration of host remained constant during the titration). The concentration of bipyridine was 10 times larger than that of porphyrin. Aliquots of bipyridine solution were added successively to the NMR tube containing the porphyrin solution, and the ¹H NMR spectrum was recorded after each addition. Changes in chemical shift for the porphyrin aromatic signals were analyzed by using specfit (Version 3.0; ref. 33). This program allows calculation of the association constant for ladder formation (K_ladder) and formation of the open complex (K_open) in the same experiment. Aggregation was insignificant at the concentrations used (see below).

UV/Vis Binding Studies.

UV/Vis titrations were carried out by preparing a 5-ml sample of the porphyrin oligomer at known concentration (0.1–10 μM) in CDCl₃. Two milliliters of this solution was removed, and a UV/Vis spectrum was recorded. An accurately weighed sample of pyridine was then dissolved in 2 ml of the porphyrin solution (so that the concentration of porphyrin remained constant during the titration). The concentration of pyridine was 50 times larger than that of porphyrin. Aliquots of pyridine solution were added successively to the cell containing the porphyrin solution, and the UV/Vis spectrum was recorded after each addition. Changes in absorbance for a Q band of the porphyrin were fitted to a 1:1 binding isotherm, using uvtit_hg (36). The concentration of binding sites rather than of molecules was used. This method allowed us to determine the average microscopic constant (K_m). Oligomer 2 has two identical binding sites that should have the same microscopic binding constant, if the binding sites are independent. The experimental data for this oligomer also were fit to a 1:2 binding isotherm, using the program uvtit_hgg (36). This program allowed independent determination of the microscopic constant of both processes and would detect differences between them. The values of K_m obtained by using uvtit_hgg and uvtit_hg were virtually identical. uvtit_hg and uvtit_hgg are modified versions of the programs nmrtit_hg (36) and nmrtit_hgg (36), respectively, adapted to the fitting of UV data rather than ¹H-NMR data (36).

ITC Measurements.

ITC experiments were performed on a VP-ITC calorimeter (Microcal, Amherst, MA). In a typical ITC titration experiment, porphyrin oligomer was dissolved in HPLC grade CHCl₃ at a concentration of 0.1–1 mM, and the solution was loaded into the sample cell of the microcalorimeter. A solution of bipyridine 8–10 times more concentrated than the cell solution was loaded into the injection syringe. The number of injections was between 55–270, and the volumes of the injections were between 1–5 μl. The thermogram peaks were integrated by using origin (Version 5.0, Microcal), and the resulting data were fit to a 1:1 binding isotherm by using itctit_hg_hh_gg (32). This program requires the previous determination of the dimerization parameters (K_d and ΔH_d) for the two components and fits the data to a 1:1 binding isotherm, taking into account the dimerization equilibria for both the host and guest. To study dimerization of the individual components, the compound was dissolved in HPLC grade CHCl₃ with a concentration 10–100 times the expected dissociation constant and loaded into the injection syringe. Pure solvent was loaded into the sample cell of the microcalorimeter. The number of injections was between 50 and 80, and the volume of the injection was between 3 and 8 μl. The thermogram peaks were integrated by using origin v (Version 5.0, Microcal), and the resulting data were fit to a dimerization isotherm by using itcdil_dimer (32). For all of the components except trimer 3, the dimerization constant and the dimerization enthalpy are too low to be measured with any accuracy, (K_d < 10 M⁻¹; ΔH_d < 5 kJ·mol⁻¹). This result also implies that the dimerization processes have no effect in the titration experiments in these cases. For trimer 3, K_d was 170 M⁻¹ and ΔH_d −11.5 kJ·mol⁻¹ and these values were used to fit the data for 3.

Abbreviations

ITC

isothermal titration calorimetry

UV/Vis

UV/visible.