The flexibility–complementarity dichotomy in receptor–ligand interactions

Synthetic supramolecular complexes provide an opportunity for quantitative systematic exploration of the relationship between chemical structure and molecular recognition phenomena. A family of closely related zinc porphyrin–pyridine complexes was used to examine the interplay of conformational flexibility and geometric complementarity in determining the selectivity of molecular recognition events. The association constants of 48 zinc porphyrin–pyridine complexes were measured in two different solvents, toluene and 1,1,2,2-tetrachloroethane (TCE). These association constants were used to construct 32 chemical double mutant cycles to dissect the free energy contributions of intramolecular H-bonds between the phenol side arms of the porphyrins and the ester or amide side arms of the pyridine ligands. Effective molarities (EM) for the intramolecular interactions were determined by comparison with the corresponding intermolecular H-bonding interactions. The values of EM do not depend on the solvent and are practically identical for amide and ester H-bond acceptors located at the same site on the ligand framework. However, there are variations of an order of magnitude in EM depending on the flexibility of the linker used to connect the H-bond acceptors to the pyridine ligands. Rigid aromatic linkers give values of EM that are an order of magnitude higher than the values of EM for the corresponding ester linkers, which have one additional torsional degree of freedom. However, the most flexible ether linkers give values of EM that are also higher than the values of EM for the corresponding ester linkers, which have one less torsional degree of freedom. Although the penalty for conformational restriction on binding is higher for the more flexible ether linkers, this flexibility allows optimization of the geometric complementarity of the ligand for the receptor, so there is a trade off between preorganization and fit.


Introduction
The principle of preorganization proposed by Cram suggests that any complexation-induced reduction in conformational mobility reduces binding affinity. 1It is entropically unfavorable to shi numerous conformations available to exible hosts and guests to the limited conformational ensemble required for optimal binding, 2 so perfect conformational complementarity between a rigid host and a rigid guest can lead to extremely high binding affinities. 3 For example, Anderson showed that complexes of a cyclic zinc porphyrin oligomer with multivalent ligands were much more stable than the corresponding complexes of linear porphyrin oligomers. 4In these systems, preorganization leads to a remarkable increase of four orders of magnitude in binding affinity.However, the design of perfect complementarity in a rigid host-guest complex is challenging, because such systems are less tolerant of subtle geometric mismatches compared with more exible systems. 5Nature uses exible molecules that fold up to achieve high affinity binding, and this strategy has been adopted in the area of foldamers to make synthetic hosts. 6These results suggest that an alternative way to obtain high binding affinity is to use exible hosts or guests that undergo cooperative conformational changes upon binding. 7e have been developing families of closely related zinc porphyrin-pyridine complexes to quantify the detailed relationship between chemical structure and cooperativity, which governs the behaviour of supramolecular systems. 8Fundamental structure-activity studies of this type will provide quantitative design rules to guide the construction of supramolecular receptors and assemblies.In a previous study, we investigated the thermodynamic advantages of freezing out a rotor to preorganize one of the components of a zinc porphyrinpyridine complex. 9In a series of sixteen different supramolecular architectures, we found that the stabilities of the complexes consistently increased by about 5 kJ mol À1 when a rotor was removed from the ligands.This result indicates that preorganization offers a signicant thermodynamic advantage in terms of receptor-ligand binding affinity and is consistent with results obtained from a range of different experiments in the literature.3i,10 To test the generality of this principle, we have now designed a new set of ligands with increased conformational exibility.Extrapolation of the results above would suggest that addition of a new rotor to the ligand framework should decrease binding affinity by a further 5 kJ mol À1 .However, we show here that this is not the case.For a series of sixteen different supramolecular architectures, addition of a rotor consistently increases binding affinity by about 3 kJ mol À1 , which indicates that the relationship between conformational exibility, preorganization and binding affinity is far from simple.

Approach
The key parameter that is used to quantify chelate cooperativity is effective molarity (EM), which measures the thermodynamic advantage of an intramolecular interaction compared with the corresponding intermolecular interaction. 11Measurement of EM using synthetic porphyrin-pyridine complexes is illustrated in Fig. 1.If we consider stepwise formation of the zinc-nitrogen coordination bond and the H-bond in the complex in Fig. 1b, then K ref EM represents the association constant for formation of an intramolecular interaction, where K ref is the association constant for formation of the corresponding intermolecular interaction (Fig. 1a).Strictly, the H-bond in Fig. 1b is a second intermolecular interaction, but in this paper, we will refer to this interaction as intramolecular, because it governs the second step of the process shown in Fig. 1b.By comparing the intramolecular (K ref EM) and intermolecular (K ref ) association constants for H-bond formation, the effective molarity (EM) can be experimentally determined.
However, the intramolecular association constant K ref EM cannot be measured directly.We therefore use a chemical double mutant cycle (DMC) to dissect out the free energy contribution of an intramolecular H-bond from the overall stability of a complex (Fig. 2).11d,12 Complex A in Fig. 2 is held together by a coordination bond and a H-bond.Complex B has no H-bond, so the difference between the free energy changes for formation of complexes A and B provides a measurement of the free energy contribution of the H-bond in complex A. However, when the H-bond acceptor is removed from the ligand, there are secondary effects.For example, there might be a change in the zinc-nitrogen interaction, so a control experiment is needed to measure this effect.The difference between the free energy changes for formation of complexes C and D measures change in the zinc-nitrogen interaction in a system that does not make a H-bond.Thus the difference between the A to B mutation and the C to D mutation allows us to dissect out the free energy contribution of the intramolecular H-bond to the overall stability of complex A using eqn (1).This approach accounts for all changes in secondary interactions, which cancel in a pairwise manner in the DMC (assuming that free energy contributions are additive).8a,11d,12 The free energy change measured by the DMC, DDG 0 , can then be used to determine the EM for the intramolecular interaction using eqn (2).8a Fig. 1 (a) Formation of an intermolecular H-bond.(b) Stepwise equilibria in the formation of a porphyrin-pyridine complex containing an intramolecular H-bond.K ref is the association constant for formation of the corresponding intermolecular H-bond.K 0 is the intermolecular association constant for formation of the zinc-nitrogen interaction.K ref EM is the association constant for formation of the intramolecular Hbond, and EM is the effective molarity for the intramolecular interaction.Some bonds and substituents on the porphyrin are not shown for clarity.
We have used this approach to study the effect of conformational restriction on supramolecular effective molarities using families of complexes exemplied in Fig. 3a and b.Compared with the ligand in Fig. 3b, the ligand in Fig. 3a has one less degree of conformational freedom in the linker which connects the H-bond acceptor to the ligand.To explore the role of conformational exibility further, we have developed new family of more exible ligands exemplied by the complex illustrated in Fig. 3c.All three ligand families have a H-bond acceptor located at identical positions on the framework but a different number of rotors in the linker.Comparison of EM values for the three ligand families in 48 different supramolecular architectures provides new insight into the relationship between conformational exibility, geometric complementarity and chelate cooperativity.

Results and discussion
Fig. 4 shows the structures of porphyrin receptors used in this work.Porphyrins P1a-P4a have peripheral phenol H-bond donor groups at different locations, and P1b-P4b are the corresponding non-H-bonding controls with methoxy groups.The three ligand families (aromatic linker, ester linker and ether linker) are shown in Fig. 5.The ligands are equipped with two different H-bond acceptor groups, amide (Le) and ester (Lf).The corresponding control ligands (Lb), which cannot make Hbonds, are also shown.

Binding studies
The association constants for formation of the 48 complexes between the 8 porphyrins and the 6 ether ligands (L9 and L10) were measured using UV/Vis absorption titrations and uorescence titrations both in toluene and in TCE (see Experimental section for details).All titration data t well to a 1 : 1 binding isotherm, and the results are listed in Tables 1 and 2 for toluene and TCE respectively.Association constants for the complexes formed by the L2, L3, L7 and L8 ligand families in toluene and in TCE have been reported previously. 9

DMC analysis
The association constant data in Tables 1 and 2 are illustrated graphically in Fig. 6.The results are colour coded according to the role of the complex in the DMC.Complexes that can make  an intramolecular H-bond (blue), are generally more stable than the complexes that cannot (yellow, green and red).The complexes containing ligands that can make a phenol-amide Hbond (Le, dark blue) are more stable than complexes containing ligands that can make a phenol-ester H-bond (Lf, pale blue), because amides are stronger H-bond acceptors.The free energy contributions of intramolecular H-bonds were determined using the data in Tables 1 and 2 and eqn (1).The results are listed in Tables 3 and 4 for toluene and TCE respectively.In toluene, 12 of 16 complexes make detectable intramolecular Hbonds.In TCE, 11 of 16 complexes make detectable H-bonds.
An inherent assumption of the DMC methodology is that the free energy contributions from individual interactions are additive.Fig. 7 compares the total free energy contribution due to H-bonding interactions in complexes of one-armed ligands, which can only make one H-bond, and complexes of the corresponding two armed ones, which can make two identical Hbonds.The free energy contribution due to two H-bonds, DDG 0 (2), is double the contribution of one H-bond, DDG 0 (1), in all of the systems studied here, conrming the validity of the additivity assumption.
Fig. 8 shows that the free energy contributions due intramolecular H-bonds in complexes where the ligands have an ether linker are generally more favourable than for the corresponding interactions in complexes where the ligands have an ester linker.In contrast, the free energy contributions due to Hbonds in complexes where the ligands have an aromatic linker are practically identical to the corresponding complexes where the ligands with an ether linker.However, these free energy measurements are perturbed by differences in the intrinsic Hbond strength, which is perturbed by the linker, and in the degeneracies of the complexes.For the two armed ligands with the rigid aromatic linker (L8), formation of two H-bonds in the cis binding mode is geometrically impossible, so the degeneracy of the fully bound state is two.In contrast, the corresponding two-armed ester and ether linker ligands (L3 and L10) can form doubly H-bonded complexes in both the cis and trans binding modes, so the degeneracy of the fully bound state is six (see ESI for details †).Thus if we want to isolate the inuence of linker exibility on intramolecular H-bonding, we have to use the values of EM to remove the inuence of these complicating factors.

Effective molarities
In order to determine the values of EM, the association constants for formation of the corresponding intermolecular interactions (K ref ) were measured by 1 H NMR titrations using the compounds shown in Fig. 9.In all cases, the data t well to a  2015, 6, 1444-1453 | 1447 1 : 1 binding isotherm.The results are listed in Table 5 and compared with values estimated using literature H-bond parameters and eqn (3) (K calc ). 14T ln (3) There is a good agreement between the experimental and calculated values, and this conrms that the measurements of K ref for the very weak phenol-ester H-bonds are reliable.
Complexes held together by multiple non-covalent interactions are actually a mixture of partially and fully bound states.For example, the complex shown in Fig. 1b is a mixture of a partially bound state, which only has the zinc-nitrogen coordination bond, and a fully bound state, which has both the coordination bond and the H-bond.The observed association constant, K obs , for this system would be the sum of the association constants of all of the bound states (eqn (4)).
For complexes studied here, there are multiple H-bonding sites, so statistical factors that account for the degeneracy of each partially bound state must also be included.For the onearmed ligand complexes formed with the Pa porphyrins, there are four possible H-bonding interactions, so the value of K obs is given by eqn (5).
For the two-armed ligand complexes, we assume that EM for the formation of the second H-bond is the same as the value of EM for formation of the rst H-bond.Thus the value of K obs is given by eqn ( 6) for ligands with the aromatic linker and eqn (7) for ligands with the ester or ether linkers.The statistical factors are different for the aromatic linker, because these ligands can only form two H-bonds simultaneously in the trans binding mode, whereas the other ligands can form two H-bonds in both cis and trans binding modes.
The value of K 0 varies with the structure of the ligand, but these differences cancel out in the DMC, so the values of EM can be calculated using eqn (8) for one-armed ligands, eqn (9) for two-armed ligands with the aromatic linker and eqn (10) for two-armed ligands with ester or ether linkers.The values of EM are shown in Tables 6 and 7 for measurements in toluene and in TCE respectively.
Table 4 Free energy contributions from amide-phenol and esterphenol H-bonds (DDG 0 /kJ mol À1 ) determined using the chemical double mutant cycle in Fig. 2 at 298 K in TCE a a Average error over the data set is AE1 kJ mol À1 .Complexes that do not make detectable H-bonds are shaded.Fig. 7 Total free energy contribution due to intra-molecular Hbonding for ligands with two identical side arms, DDG 0 (2), compared with data for the corresponding one-armed ligands, DDG 0 (1).Data for ligands with an ether linker are shown in blue (L9 and L10), ester linker in black (L2 and L3) and aromatic linker in grey (L7 and L8).The line corresponds to DDG 0 (2) ¼ 2DDG 0 (1).
Fig. 12 compares the values of EM measured for the three different types of linker.Although there is considerable scatter in the data, the values of EM for complexes with the aromatic linker are generally higher than the corresponding values measured for the more exible ether linker by a factor of about 3.However, the values of EM for complexes with the ester linker are generally lower than the corresponding values for the more exible ether linker, again by a factor of about 3.These results Fig. 8 Total free energy contribution due to intra-molecular Hbonding for ligands with an ether linker, DDG 0 (ether linker), compared with data for the corresponding ligands with an ester linker (black) and aromatic linker (grey), DDG 0 (other linker).The line corresponds to DDG 0 (other linker) ¼ DDG 0 (ether linker).and L8). 9 The line corresponds to EM(TCE) ¼ EM(toluene).indicate that the relationship between conformational exibility and EM is not straightforward: there is a trade off between the ability of exible ligands to optimize geometric complementarity, which improves binding affinity, and restriction of conformational degrees of freedom, which reduces binding affinity.Thus the most rigid ligands, L7f and L8f, which have aromatic linkers, do not make detectable H-bonds with P3a, whereas the corresponding exible ligands, L9f and L10f, which have ether linkers, make H-bonds worth 2 to 5 kJ mol À1 .When geometric complementarity is more optimal, the most rigid ligands, which have aromatic linkers, make the strongest Hbonds with the highest values of EM: for example, the EM values for the complexes formed between P3a and the most rigid ligands, L7e and L8e, which have aromatic linkers, are 380-500 mM compared with 120-160 mM for the most exible ligands, L9e and L10e, which have ether linkers.

Conclusions
The thermodynamic properties of a family of 48 new zinc porphyrin-pyridine complexes have been compared with closely related complexes described previously.Chemical double mutant cycles were used to dissect the contributions of intramolecular H-bonds in 96 different complexes.Comparison of the free energy contributions from the DMCs with association constants for the corresponding intermolecular interactions was used to determine the values of EM, which quantify chelate cooperativity in these systems.The values of EM vary with the degree of conformational exibility of the ligands.8c The values of EM for the most exible ligands, which have ether linkers, lie in between the values of EM for two sets of more rigid ligands with aromatic and ester linkers.The most rigid ligands make high affinity complexes with the porphyrin receptors only when there is good geometric complementarity. 9More exible ligands can adapt their conformation to optimize interactions where geometric complementarity is poor, and this results in more stable complexes than found for the rigid ligands.The advantage of induced t geometric complementarity and the disadvantage of restriction of conformational degrees of freedom in exible ligands compete to determine the overall effect of conformational exibility on binding affinity.7a Flexible systems are usually easier to synthesize than highly preorganized rigid molecules, and the results presented here suggest that the additional synthetic effort required to prepare highly preorganized systems may not be a rewarding strategy in supramolecular design.Flexible molecules, which adapt to the optimum conformation upon complexation, provide a good alternative for building supramolecular systems with high binding affinity.

Manual uorescence titrations
Fluorescence titrations were carried out using a Hitachi F-4500 Fluorescence Spectrophotometer at 298 K.A 10 mL solution of porphyrin at known concentration (0.04-0.05 mM) was prepared in spectroscopic grade solvent.Then, 2 mL of this host solution was loaded into a 1 cm path length uorescence cuvette, and the uorescence emission spectra was recorded from 500 to 750 nm exciting at 427 nm.A 2 mL solution of ligand (0.1-1 mM) was prepared using the host stock solution, so that the concentration of host remained constant throughout the titration.Aliquots of ligand solution were added successively to the cuvette, and the emission spectrum was recorded aer each addition.Changes in uorescence emission were t to a 1 : 1 binding isotherm in Microso Excel to obtain the association constant.Each titration was repeated at least three times, and the experimental error is quoted as twice the standard deviation at a precision of one signicant gure.

Fig. 2
Fig. 2 Chemical double mutant cycle (DMC) for measurement of the free energy contribution of an intramolecular H-bond to the stability of complex A.

Fig. 3
Fig. 3 Zinc porphyrin complexes with pyridine ligands that have a H-bond acceptor located at the same position on the ligand framework but varying degrees of conformational flexibility (a) rigid linker, (b) one additional rotor, and (c) two additional rotors.The key rotatable bonds are highlighted in blue, and the restricted rotors are highlighted in red.

Fig. 5
Fig. 5 Pyridine ligands equipped with amide (Lf) or ester (Le) H-bonds acceptors and the corresponding control ligands with no H-bonding groups (Lb).

Fig. 6
Fig. 6 Association constants (log K/M À1 ) measured in (a) toluene and (b) TCE.The data are colour coded according to the role in the DMC.(c) Schematic representation of the chemical double mutant cycle used to extract information on the magnitude of the intramolecular Hbonding interaction between H-bond acceptor A and H-bond donor D in complexes formed between a zinc porphyrin (P) and a pyridine ligand (L).

a
Average error over the data set is AE50%.b No interaction detected.

a
Average error over the data set is AE50%.b No interaction detected.

Fig. 10
Fig. 10 Comparison of effective molarities (EM) for formation of intramolecular H-bonds in toluene with the corresponding values measured in TCE.Data for ligands with an ether linker are shown in blue (L9 and L10), ester linker in black (L2and L3) and aromatic linker in grey (L7 and L8).9The line corresponds to EM(TCE) ¼ EM(toluene).

Fig. 11
Fig.11Comparison of effective molarities (EM) for formation of intramolecular phenol-amide H-bonds, log EM(Le), with the corresponding values measured for phenol-ester H-bonds, log EM(Lf).Data for ligands with an ether linker are shown in blue (L9 and L10), ester linker in black (L2 and L3) and aromatic linker in grey (L7 and L8).9The line corresponds to log EM(Le) ¼ log EM(Lf).

Fig. 12
Fig. 12 Comparison of effective molarities (EM) measured for formation of intramolecular H-bonds for ligands L9 and L10, log EM(ether linker), with the values measured for the corresponding ligands with an ester linker (L2 and L3 in black) and aromatic linker (L7 and L8 in grey), log EM(other linker).The solid line corresponds to log EM(other linker) ¼ log EM(ether linker), and the dashed lines correspond to log EM(other linker) ¼ log EM(ether linker) AE 0.5.

Table 1
Association constants (K/M À1 ) for the formation of 1 : 1 complexes in toluene at 298 K (with percentage errors in brackets)

Table 5
Association constants (M À1 ) for the formation of intermolecular H-bonded complexes measured by 1 H NMR titrations in d 2 -TCE and d 8 -toluene at 298 K (K ref ) and estimated using eqn (3) (K calc )

Table 6
Effective molarities (EM/mM) for intramolecular amidephenol and ester-phenol H-bonds measured at 298 K in toluene a

Table 7
Effective molarities (EM/mM) for intramolecular amidephenol and ester-phenol H-bonds measured at 298 K in TCE a