Thermodynamics and Kinetics of Guest-Induced Switching between “Basket Handle” Porphyrin Isomers

The synthesis and switching properties of two “basket handle” porphyrin isomers is described. The cis-oriented meso-phenyl groups of these porphyrins are linked at their ortho-positons via benzocrown-ether-based spacers, which as a result of slow atropisomerization are located either on the same side of the porphyrin plane (cis), or on opposite sides (trans). In solution, the cis-linked isomer slowly isomerizes in the direction of the thermodynamically more stable trans-isomer. In the presence of viologen (N,N'-dialkyl-4,4'-bipyridinium) derivatives, which have different affinities for the two isomers, the isomerization equilibrium could be significantly influenced. In addition, the presence of these guests was found to enhance the rate of the switching process, which was suggested to be caused by favorable interactions between the positively charged guest and the crown ethers of the receptor, stabilizing the transition state energies of the isomerization reaction between the two isomers.


Introduction
Host-guest chemistry provides a valuable platform for studying binding processes observed in nature with the help of relatively simple mimics. Many artificial receptors have been designed, displaying similar features as observed in natural host-guest systems, such as induced-fit binding [1][2][3][4], lock and OPEN ACCESS key mechanisms [5], and cooperative binding effects [6][7][8][9][10][11][12]. Dynamic recognition processes, in which the guest influences the conformation of the receptor, play a crucial role in biological systems and are of particular importance for allosteric binding, regulation or feedback [13][14][15][16][17]. To date, there are a number of examples of artificial dynamic recognition systems that exhibit complexation-induced atropisomerism or conformational changes [18][19][20][21][22][23][24][25][26][27][28][29][30]. The vast majority of these studies, however, is focused on thermodynamic aspects of complex formation, whereas kinetic aspects, while being of significant importance for determining the actual binding mechanisms involved, are not explored. Houk et al. have convincingly demonstrated that the origin of binding affinities between guests and receptors (ranging from small synthetic cavitands to large proteins) are well-understood, and that enzymes do not show any special binding behaviour for their substrates when compared to artificial receptors [31]. This is a powerful reminder that the ability to catalyze reactions arises from transition state interactions and not from substrate binding. Therefore, in order to get a better understanding of the combination of interactions responsible for the nature of transition states in enzymatic systems, it is of key importance to also study the transition states of relatively simple artificial host-guest systems. However, for many of these systems the kinetics of the binding processes are simply too fast to be studied accurately with the help of general methods.
In order to gain detailed insight in the kinetic aspects of complexation-induced conformational changes of dynamic artificial receptors, we have designed a porphyrin-based receptor molecule that interconverts extremely slowly between two distinct conformational isomers. Thanks to this slow exchange, not only the guest-induced kinetics of interconversion between the two isomers could be studied accurately, but in addition also the binding affinities of each of the two isomers towards viologen (N,N'-dialkyl-4,4'-bipyridinium) guests could be determined. A complete kinetic and thermodynamic picture of a guest-induced "switching" was obtained, which revealed that the presence of guests not only influences the thermodynamic outcome, as expected on the basis of the obtained individual equilibrium constants, but also significantly influences the kinetics of the switching process.

Design
We decided to make use of the atropisomerization properties of ortho-meso-phenyl-substituted porphyrins in the design of the receptor. It is known that the restricted rotation of the aryl rings in many of such porphyrins can be extremely slow [32,33] (rates between 10 −4 and 10 −9 s −1 depending on the substitution pattern and metal ion present in the porphyrin), which often allows the isolation of the individual atropisomers. By appending two adjacent-linked binding pockets ("handles") to the porphyrin ortho-phenyl positions, two so-called "basket handle" porphyrin [34][35][36][37][38][39][40] isomers (trans-linked S and cis-linked C; Scheme 1), which can interconvert slowly via atropizomerization, requiring the rotation around two aryl rings, were obtained By appending crown ether handles that are specifically designed for the complexation of viologen derivatives, the adjacent-linked "basket handle" porphyrins are expected to become excellent receptor molecules for these guests. The cis-linked isomer C was expected to have higher affinity for the viologen derivatives than trans-linked isomer S as a result of the interplay of two crown ether handles on the same side of the porphyrin plane in the former isomer.
The addition of viologen derivatives should therefore result in the slow switching of the equilibrium in the direction of isomer C, a process that allows the accurate determination of both the thermodynamics and the kinetics involved. Scheme 1. Synthesis of basket handle isomers X, S and C.

Synthesis
A mixture of "basket handle" porphyrin isomers X, C and S (Scheme 1) was prepared in an overall yield of 52% by reacting ditosylate 1 [41] with 5,10,15,20-tetrakis(meso-o-hydroxyphenyl)porphyrin 2 [42] under basic conditions in DMF at 110 °C. The three different isomers could be separated by preparative TLC and were obtained in a ratio X:S:C = 4:8:1. The individual isomers were identified with the help of 1 H-NMR spectroscopy in CDCl 3 (Figure 1a), and in addition the X-Ray structure of the S-isomer was determined (Figure 1b). Isomer X has an S 2 symmetry, and as a result the 1 H-NMR spectrum revealed only four resonances for all the 32 crown ether protons H-3, H-4, H-5 and H-6, and one single resonance for the β-pyrrolic porphyrin protons. Isomers S and C have C 2h and C 2v symmetry, respectively, and as a result the crown ether proton resonances show AB-patterns in the 1 H-NMR spectra and two distinct resonances for the β-pyrrolic protons. The resonances of the protons of the handles of S (H-1-H-6) are significantly shifted upfield in comparison to those of C, which indicates that they experience more shielding from the porphyrin ring-current. This can be understood since in S there is space to position both handles in the proximity of the porphyrin, whereas in C this is sterically impossible. Also the pyrrole NH resonances of S are shifted upfield compared to those of C, which suggests that the ring currents of the phenyl groups of the handles shield the center of the porphyrin more in S than in C. These combined observations indicate that, unlike in the X-ray structure of S in which the handles bend away from the porphyrin plane (Figure 1b), in solution they are on average folded over the porphyrin plane. This folding was confirmed by a 2D-ROESY NMR measurement which showed nOe contacts between the handle phenyl protons H-1 and H-2 and the β-pyrrole protons and H-10, respectively. Figure 1. (a) 1 H-NMR spectra (400 MHz) of "basket handle" porphyrin isomers X, S and C in CDCl 3 with proton assignments based on COSY and 2D-ROESY NMR experiments. See Scheme 1 for proton numbering. (b) X-ray structure of isomer S (protons have been omitted for clarity).

Isomerization
As observed in other adjacent-linked "basket handle" porphyrins [36] the adjacent-cis-linked isomer C and the adjacent-trans-linked isomer S slowly interconvert in time. Figure 2 reveals that upon standing, the resonances of S in the 1 H-NMR spectra increase in intensity at the expense of those of C. Isomer S is thermodynamically significantly more stable than isomer C, since equilibrium is reached at a ratio of S/C = 7.6. This observation is in contrast with results in a previous report, in which the switching of a hexyl-bridged basket-handle porphyrin resulted in equimolar amounts of the adjacent-cis-linked and adjacent-trans-linked isomers at equilibrium [43], as would statistically be expected. The rate constants for the isomerization process (k C→S ) could be simply determined by first order analysis of the decrease in the relative intensities [44] of the resonances of C in time.
The equilibrium constants (K S/C = [S] eq /[C] eq ) were obtained at different temperatures from the ratio between S and C at equilibrium, after which the rate constant k S→C could be calculated indirectly from K S/C = k C→S /k S→C . Isomerization experiments in which the switching from S to C was monitored provided identical values for k S→C as were obtained by the indirect method via K S/C and k C→S . The calculated constants are presented in Table 1.  Table 1. Calculated rate constants for the switching of C to S (k C→S ) and for the switching of S to C (k S→C ) at different temperatures, and the equilibrium constant K that represents the ratio of S/C at equilibrium. 25 2.8 × 10 −6 3.7 × 10 −7 7.6 32. 5 6.0 × 10 −6 1.0 × 10 −6 5.8 40 1.5 × 10 −5 2.8 × 10 −6 5.3 47. 5 3.2 × 10 −5 6.8 × 10 −6 4.7 a Estimated error 5%; b Estimated error 15%; c Calculated from k S→C = k C→S /K.
The switching from C to S was monitored at four different temperatures ( Figure 3a) from which, with the help of van't Hoff and Eyring plots, the entropic (ΔS) and enthalpic (ΔH) contributions to the activation energy (ΔG ≠ ) and the free energy of binding (ΔG°) could be determined. The resulting energy diagram with all these parameters is presented in Figure 3b. The switching process is unfavorable both in entropy and in enthalpy, but the majority of the free energy of activation (ΔG ≠ ) is enthalpic in origin (the proposed mechanism will be presented later).
The obtained parameters ΔS° and ΔH° (Figure 3b) revealed that the formation of the trans-linked isomer S is enthalpically more favorable than the cis-linked isomer C, whereas the latter is entropically more likely to form. The value of ΔH° suggests that S experiences more stabilizing intramolecular interactions than C. These are presumably π-π interactions between the phenyl groups of the handles and the porphyrin plane, and additional van der Waals interactions. The entropic parameters suggest that C is more disordered than S, which could be the result of a restricted motion of the handles in S as a result of the intramolecular binding interactions (entropy-enthalpy compensation [45]). Another possibility is that S needs to organize more solvent molecules in a defined shell than C, which would result in the release of solvent to the bulk upon switching from S to C, thereby accounting for the entropic gain. The observation that C dissolves significantly better in the used solvent mixture than S could validate this hypothesis, although solubility depends on more factors.

Binding of Viologen Derivatives
The binding of viologen derivatives V1, V2, and V3 ( Figure 4) to isomers C and S was investigated. As a result of the high kinetic stabilities of C and S, no detectable isomerization was observed in the first few hours after their separation, which allowed the study of the binding properties of the individual isomers. A 1 H-NMR titration between C and V1 revealed that V1 binds strongly to this receptor in a face-to-face geometry with respect to the porphyrin [46]. The addition of increasing amounts of V1 to C resulted in large downfield complexation induced shift (CIS) values of the crown ether proton resonances (H-3 to H-6), which indicates that their position in the proximity of the porphyrin is replaced by V1 ( Table 2). The pyrrole NH resonances of C shifted dramatically upfield upon complex formation, indicating their shielding by the aromatic rings of V1. Also the signals of V1 displayed large upfield shifts compared to their original positions, confirming their position in the proximity of the shielding porphyrin ring current. The addition of one equivalent of V1 resulted in the full binding to C, stressing the strong affinity between the components. To derive an accurate value for the association constant (K CV1 ), the binding of V1 to C was investigated at lower concentrations ([C] ≈ 10 −6 M) with the help of a fluorescence titration. The addition of increasing amounts of V1 to a solution of C resulted in the quenching of the porphyrin fluorescence of the receptor. The obtained binding curve could be fitted with a 1:1 binding isotherm and the association constant was calculated to be K CV1 = 3 × 10 5 M −1 (Table 3).   Table 3. Association constants (K a ) and binding free energies (ΔG°) at 298 K and the enthalpic (ΔH°) and entropic (ΔS°) contribution to the binding free energy between isomers C and S and viologen guests.
3.5 × 10 3 a −20. Molecular modeling revealed that V1 preferably accommodates its positive charges in between the two "handle" crown ether rings of C. The complex adopts a so called suit [2]ane [47] geometry in which the positive charges are wrapped inside the crown ether sleeves of the suit-shaped receptor C (see Figure 5a). Since it is impossible to directly derive the exact geometry of the complex with the help of NMR techniques, and attempts to obtain an X-ray structure of the complex were unsuccessful, it was decided to compare the binding between C and V1 with that between C and V2. V2 cannot adopt the proposed suit [2]ane geometry as a result of the presence of 3,5-di-tert-butylphenyl blocking groups, which can impossibly slip through the crown ether rings of C. A 1 H-NMR titration between C and V2 indicated that V2 adopts a different binding geometry with C than V1. Although V2 also binds in a face-to-face orientation with respect to porphyrin plane of C, as can be concluded from the observed upfield shift of the pyrrole NH proton resonances of the receptor (Table 2), the CIS values for all the other proton resonances are significantly different for the complex between C and V2 when compared to the complex between C and V1. Moreover, the association constant for the binding of V2 to C is almost two orders of magnitude lower than that for the binding of V1 to C (Table 3). These combined results strongly suggest that V1 indeed binds to C in the proposed suit [2]ane geometry, whereas V2 adopts a geometry as indicated in Figure 5b. In addition to the binding to C, the binding of V1 to trans-linked S was investigated. A 1 H-NMR titration revealed complex formation between V1 and S, which was expressed in large CIS values for the proton resonances of V1 and S. As observed for the binding of V1 with C, the pyrrole NH proton resonances and aromatic viologen signals shifted upfield, whereas the crown ether proton resonances shifted downfield (Table 2), which suggests a binding geometry in which the porphyrin ring of S and the aromatic rings V1 adopt a face-to-face orientation (Figure 5c). The experimentally obtained binding curve could however not be fitted with a 1:1 binding isotherm, which strongly points in the direction of 1:2 complex formation between S and V1. This was moreover indicated by the CIS value of the pyrrole NH proton signals of S (Table 2). These signals shifted significantly further upfield upon complexation of V1 than in the complex between V1 and C (and other known face-to-face viologen-porphyrin complexes known in literature [41,48,49]), which indicates that this is the result of the presence of two viologen molecules that are sandwiching the porphyrin (Figure 5d). Data analysis of the binding curves with a 1:2 host-guest binding isotherm gave a satisfying fit with association constants of 1.3 × 10 4 M −1 and 6 × 10 2 M −1 for the binding of the first (K SV ) and second (K VSV ) molecule of V1 to S, respectively. Considering the statistical factor of 4 for the difference in binding of the first and the second identical guest molecule to a bivalent receptor, there is a negative cooperative effect for the binding of the second molecule of V1 to S with an α-value of 0.18. This is most probably caused by the repulsive interactions between the positive charges of the two viologen derivatives [50].
Because the guest-induced switching between the conformers, which will be presented in the following sections, is performed at elevated temperatures, the effect of temperature on the binding constants of V1 to S and C, respectively, was studied with the help of fluorescence titrations. Although V1 was shown to form 1:2 host-guest complexes with S at 1 H-NMR concentrations (10 −3 M), at the used experimental concentrations of the fluorescence titrations (10 −6 M) 1:2 complex formation was so marginal that it could be ignored, and the obtained fluorescence titration curves could therefore be fitted with the use of simple 1:1 binding isotherms. This was emphasized by both the good fits and the calculated value of the association constant that were obtained from the fluorescence titration for the 1:1 complex between V1 and S, which was in very good agreement with the value of K SV obtained from the 1 H-NMR titration experiment at the same temperature [51]. With the use of Van het Hoff plots, the enthalpic (ΔH°) and entropic (ΔS°) contributions to the total free binding energy (ΔG°) of V1 with S and C, respectively, could be determined. Quite surprisingly, the calculated parameters revealed that the differences in binding strength between V1 and C and V1 and S, respectively, are mainly entropic in origin (Table 3). Similar values were obtained for the binding enthalpy (ΔH°). Complex formation between C and V1 is slightly favorable in entropy, whereas complex formation between S and V1 is unfavorable in entropy. Intuitively, two good reasons can be envisaged why the binding of V1 to C should be enthalpically more favorable than the binding of V1 to S. The first reason is that isomer C can provide more stabilizing interactions to V1 than isomer S as a result of the presence of two crown ether handles, which can both interact with the viologen guest, on the same side of the porphyrin plane. The second reason is that within isomer S more intramolecular interactions are present than within C, which have to be overcome in order to accommodate V1 (as suggested by the value of ΔH° for the switching process as presented above). The fact that no enthalpic difference is observed between the two binding processes, and that the difference in binding is mainly entropic in origin, therefore suggests that the binding of viologen derivatives to both isomers depends to a crucial extent on the desolvation of the viologen derivatives upon complex formation. Isomer C can fully accommodate the positive charges of the viologen, thereby perfectly shielding it from the solvent (Figure 5a). In contrast, isomer S is only capable of shielding one of the positive charges of the viologen from the solvent (Figure 5c). As a result, the binding of V1 to C is accompanied by the release of more solvent molecules to the bulk than the binding of V1 to S, which accounts for the observed difference in binding entropy.

Guest-Induced Switching: Thermodynamics
As a result of the higher affinity of V1 for C than for S (∆∆G° = 7.6 kJ/mol), it would be expected that in the presence of the guest the equilibrium should be switched further in the direction of the thermodynamically less favorable isomer C. Because S is 5 kJ/mol more stable than C (Figure 4b), it could theoretically result in an equilibrium situation which has its free energy shifted maximally 2.6 kJ/mol in the direction of C, and which would be translated into a ratio of approximately 74% C and 26% S at equilibrium, or [S] tot-eq /[C] tot-eq = 0.36. A first isomerization experiment, in which a mixture of S and V1 was annealed at 80 °C in toluene/acetonitrile 1:1 (v/v) for 12 h, indeed revealed that the conformational equilibrium had shifted in the direction of C. After workup and purification of the reaction mixture, the different isomers were isolated in a ratio of approximately C:S = 2:1. This ratio is strikingly different from the ratio obtained after annealing isomer S under the same experimental conditions but in the absence of V1, which amounted to C:S ≈ 1:5.
In order to gain more detailed information about the guest-induced switching, it was decided to follow the switching from S to C in the presence of V1 with the help of 1 H-NMR spectroscopy. The 1 H-NMR spectra of a mixture of S (1 mM) and V1 (1.3 mM) in CDCl 3 /CD 3 CN 1:1 (v/v) at 37.5 °C revealed that in time isomer C was formed at the expense of isomer S (Figure 6), resulting in a final equilibrium ratio of [S] tot-eq /[C] tot-eq = 0.56 (64% C and 36% S). This ratio is different from the ratio (0.36) mentioned above because of the different solvent mixture and the different temperature. To further explore the switching effect of V1, the isomerization from S to C in solutions containing varying concentrations of this guest was monitored by 1 H-NMR spectroscopy. The measurements revealed that there is an optimal concentration of V1 in which the equilibrium ratio (Figure 7a and Table 4), after which increasing concentrations of V1 resulted slowly in the shifting back of the conformational ratio in the direction of [S] tot . This observation is attributed to the possibility of also forming the 1:2 complex between S and V1, as presented in Figure 8. At relatively low concentrations of V1, the equilibrium will shift towards the 1:1 complex between V1 and C (since K CV > K SV ) and thus in the direction of [C] tot . At further increasing concentrations of V1, however, the formation of the 1:2 complex between S and V1 will become more favorable, which results in a shifting back of the equilibrium situation towards [S] tot . This behavior follows directly from Equation (1), which presents the equilibrium constant (K switch ) as a function of free V1 in solution ([V]) and all the individual equilibrium constants: In Equation (1), K S/C is the equilibrium constant between S and C in the absence of viologen guests, K SV and K CV are the association constants of V to S and C, respectively, for the formation of the 1:1 complexes, and K VSV is the association constant for the formation of the 1:2 complex between S and V. The concentration of free V is obviously directly related to the concentration of isomers C and S in solution, but it is clear from Equation (1) that there will exist a concentration of V in which K switch has a minimum value and thus that [C] tot will be maximal. The value for K switch as a function of different equilibrium constants and concentrations of V1 could be determined numerically with the use of Mathematica ® . Although the experimental data did not exactly match the theoretical calculations on the basis of all the experimentally derived individual equilibrium constants, as can be seen in Figure 7a (which is not surprising, since four equilibrium constants are involved, some of which have errors of up to 30% and K VSV had to be estimated), the trend in switching is clearly as would be expected on the basis of the binding model in Figure 8. Moreover, the data could be fitted with the assumed binding model and the calculated equilibrium constants as obtained by the fit did not deviate significantly from the experimentally derived values for the individual equilibrium constant (see Figure 7a).   In addition to experiments in which switching was induced by V1, also experiments were carried out in which switching was triggered by the doubly blocked guest V2 and the guest V3 (1-methyl-4-phenylpyridinium hexafluorophosphate). As can be seen in Figure 9, also V2 is capable of switching the equilibrium in the direction of C, which indicates that this guest has a higher affinity for C than for S. This binding process was further confirmed by the gradually upfield shifting aromatic resonances of the guest in time upon switching from S to C in the 1 H-NMR spectra. Although the binding of V2 to S was not studied in detail, it is obvious that C can provide more stabilizing interactions (or cause more solvent shielding upon complex formation) to V2 than S. The switching experiment in the presence of V3 (20 equiv.) revealed that this guest is not capable of switching the equilibrium in the direction of [C] tot . Instead, it causes the opposite effect and the equilibrium is shifted more in the direction of [S] tot (Figure 9). This observation suggests that S has a higher affinity for V3 than C, which is more or less in line with expectation since only one handle is needed for the accommodation of the single positive charge of V3 [52].

Guest-Induced Switching: Kinetics
In addition to the thermodynamics we also investigated the kinetics of the guest-induced switching. The observed initial rates (k S→C-obs ) in solutions with different concentrations of V1 at 37 °C were calculated from the initial 25% of the switching curves, as obtained by 1 H-NMR spectroscopy. The data, which are presented in Figure 7b and Table 4, reveal that the observed initial rates increase upon increasing concentrations of V1, and reach a maximum value after which they decrease again. This decrease is fully in line with expectation, since increased concentrations of V1 shift the initial equilibrium further in the direction of the 1:2 host-guest complex VSV (Figure 8) in which both handles are restricted from rotation. The initial increase in rate in solutions with lower concentrations of V1, on the other hand, is surprising and suggests that the switching is enhanced by the presence of V1. Statistically, it can be expected that the switching rate from S to C in the presence of V1 (k SV→CV , see Figure 9) is a factor 2 lower than in the absence of V1 (k S→C ) as a result of the restricted rotation of one of the handles of S upon complex formation with V1. If a viologen-induced rate enhancement is not taken into account, the observed switching rates (k S→C-obs ) should therefore decrease upon complex formation between V1 and S, and drop even further upon a further increase in concentration of V1, as a result of 1:2 host-guest complex formation. In order to be able to fit the experimental data, a rate enhancement factor (cf) has to be included into the model. The initial rate (k S→C-obs ) should evolve as a function of [S], [SV] and [VSV] according to Equation (2), in which k SV→CV is defined according to Equation (3) in which both the statistical factor of 0.5 and the rate enhancement factor is taken into account: Since the individual constants k S→C , K SV and K VSV were determined separately (see above), the magnitude of the factor cf could be calculated. To this end, the expected overall initial rate constants were calculated with the help of Mathematica ® as a function of the magnitude of cf and the concentration of V1 (which determines the ratios of [S], [SV] and [VSV]). The calculated rates as a function of V1 are presented as the framework in Figure 7b, and from this framework it can be concluded that the magnitude of cf is approximately 4, hence the switching rate is enhanced in the presence of V1 by a factor of 4. In order to stress the acceleration of the switching process in the presence of V1, the expected kinetic curve of switching from S to C under the same conditions, assuming cf = 1, is presented in Figure 9. In addition to V1, also V2 clearly accelerates the switching process, as can be observed in Figure 9 and Table 4. The observed rate (k S→C-obs ) in the presence of V3, on the other hand, is lower than k S→C (Table 4), which indicates that the switching rate is not enhanced by V3.

Mechanism
The magnitudes of the rate constants and the enthalpic and entropic contributions to the transition state energy for the switching process between the isomers C and S are all very similar to the values observed for atropisomerization of ortho-meso-phenyl-substituted porphyrins, involving rotations around one single bond [53][54][55][56][57][58][59]. This suggests that the mechanism of isomerization between C and S is not significantly different from other porphyrin atropisomerization processes. For this reason, the switching between S and C most probably does not occur not via simultaneous but via consecutive rotations around the two porphyrin meso-phenyl rings. As a result, the switching consists of two steps that have similar activation barriers, with in between them a local energy minimum in which the handle is halfway the switching process (T in Figure 10). The energy level of T is unfavorable compared to both the energy levels of S and C making that it cannot be observed experimentally. The presence of V1 in the switching process is expected to have a significant influence on the relative energy levels. The same interactions that cause that the complex CV is energetically more favorable than the complex SV ( Figure 10 Also the rotation around the second porphyrin meso-phenyl ring in the switching process from T to C is energetically more favorable as a result of these interactions. The viologen guest thus lowers the barriers associated with the switching process and effectively pulls the handle through to the other side of the porphyrin. Note that these same interactions should also cause a similar rate enhancement while switching back from C to S, in line with the principle of microscopic reversibility. The observation that both V1 and V2 (which binds in 90 degrees rotated geometries with respect to the porphyrin) accelerate the switching process is in line with this mechanism, since independent of the geometry of the eventual complexes, both V1 and V2 can exert these stabilizing interactions in the transition state. V3 most probably accommodates its positive charge inside one crown ether handle and is consequently not capable of stabilizing the transition state involving the switching of the other handle, which accounts for the apparent absence of rate enhancement in the presence of V3. Figure 10. Proposed energy landscape of the switching between C and S in absence and in the presence of V1.

Materials and Methods
All solvents and chemicals were used as received. K 2 CO 3 was dried in an oven (150 °C). Chloroform and acetonitrile used in fluorescence titration experiments were distilled from CaCl 2 . Preparative TLC was performed on Merck (Darmstadt, Germany) silica glass plates (TLC Silica gel 60 F 254 ). Fluorescence experiments were performed on a Perkin-Elmer LS50B luminescent spectrometer (Waltham, MA, USA) equipped with a thermostatted cuvette holder. UV-Vis spectra were recorded on a Cary 100 Conc UV-Vis spectrometer (Varian, Middelburg, The Netherlands). Maldi-TOF mass spectrometry was performed on a Bruker Biflex III spectrometer (Billerica, MA, USA). NMR spectra were taken on a Varian (Palo Alto, CA, USA) Inova 400 (400 MHz, 1 H and 2D spectra) or on a Bruker (Billerica, MA, USA) DMX300 (75 MHz, 13 C spectra) and calibrated to an internal standard of tetramethylsilane.The synthesis of ditosylate 1 was reported elsewhere [41]. The syntheses of 5,10,15,20-tetrakis(meso-o-hydroxyphenyl)porphyrin 2 [42], V1 [41] and V2 [60] are also described in the literature.

"Basket Handle" Isomers X, S and C
A suspension of 1 (0.90 g, 1.51 mmol), 5,10,15,20-tetrakis(meso-p-hydroxyphenyl)-porphyrin 2 (0.50 g, 0.74 mmol) and K 2 CO 3 (1 g, 7.2 mmol) in DMF (250 mL) was reacted for 16 h under an argon atmosphere at 110 °C. After filtration of the salts and evaporation of the solvents the product was purified by column chromatography (3% MeOH in CHCl 3 (v/v)) yielding 450 mg (52%) of a mixture of isomers X, S and C. The three isomers could be separated by preparative TLC (5:5:1 toluene/ethyl acetate/acetonitrile (v/v/v)) to give the products in a ratio of X:S:C = 4:8:1. (adjacent-trans-linked S could also be selectively crystallized out of a mixture of 5:1 acetonitrile/chloroform (v/v) containing isomers C and S) The separate products were dissolved in a minimal amount of CHCl 3 and to this solution n-pentane was added. This resulted in precipitates, which were collected by centrifugation and dried under vacuum at low temperatures yielding the different isomers X, S and C as purple solids. In order to prevent isomerization between C and S, both speed and low temperatures are of essential importance in the separation process.

X-ray Analysis of S
A single crystal was mounted in air on a glass fibre. Intensity data were collected at −65 °C. A Nonius KappaCCD single-crystal diffractometer (manufacturer, city, country) was used (φ and ω scan mode) using graphite monochromated Mo-Kα radiation. Unit cell dimensions were determined from the angular setting of 227 reflections. Intensity data were corrected for Lorentz and polarization effects. SADABS multiscan correction [61] was applied. The structure was solved by the program CRUNCH [62] and was refined with standard methods using SHELXL97 [63]) with anisotropic parameters for the non-hydrogen atoms. All hydrogens were placed at calculated positions and were refined riding on the parent atoms. A structure determination summary is given in Table 5. CCDC 988037 contains the supplementary crystallographic data for this paper [64].

Determination of Association Constants
The association constants were determined by means of fluorescence-and 1 H-NMR titrations. For the 1:2 binding of S to V1 the experimental error was quite large because of uncertainties involved with determining two association constants from one single binding experiment. The fluorescence titrations giving association constants K SV1 and K CV1 were performed once, and although very good fits were obtained for the individual experiments, the experimental error was chosen on the conservative side (30%). Experimental errors evolving from weighing small quantities of receptor and potential atropisomerization during the experiment could not be fully excluded (all effort was taken to prevent this phenomenon: both S and C were purified directly before the binding studies, analyzed using 1 H-NMR, and kept cold for as long as possible before the binding experiment to prevent the switching). For individual titration data, see below. The association constants for the 1:1 complex formation between the different isomers and viologen derivatives were determined according to standard fitting procedures. The association constants for the 1:2 complex formation between S and V1 in the 1 H-NMR titration experiment were fitted with the use of Mathematica ® , in which the association constant K SV was varied and the fit provided the value of K VSV . In this paper the values for K SV and K VSV of the optimized fit are given. For a detailed description of the procedure we refer to the Supplementary Material.
The assumption that at lower concentrations the binding of V1 to S can be fitted with the use of a 1:1 binding isotherm can also be shown analytically. In a titration of S with a viologen V in which 1:2 complex formation is allowed both the 1:1 complex SV and the 1:2 complex VSV can form. The overall binding process in the titration is therefore: S + 2V ↔ SV + 18VSV. The association constants for the 1:1 (K SV ) and the 1:2 complex formation (K VSV ) are presented in Equations (5) and (6).
From the apparent association constant, which is given in Equation (7), it becomes clear that this constant, which describes the equilibrium of the combined 1:1 and 1:2 complexes, changes upon increasing the concentration of V. There is, however, a certain concentration regime in which the deviations between Equations (5) and (7)

Conclusions
We have shown that the presence of viologen guests has a large influence on the thermodynamics and kinetics of the atropisomerization reaction between an adjacent-cis-linked and an adjacent-trans-linked "basket handle" porphyrin. The thermodynamic product of the guest-induced switching process strongly depends on the relative affinities of the individual isomers for the different viologen guests. In all cases, the switching experiments were in very good agreement with theoretical predictions based on the individual equilibrium constants. The kinetic studies of the switching process revealed that the presence of viologen derivatives actually enhances the rate of the switching process. It is suggested that this enhancement is caused by favorable interactions between the positively charged guest and the crown ethers of the receptor in the process of switching, which stabilize the transition state energies according to a mechanism similar to those proposed by Warshel [65,66] for the stabilization of transition states in enzymatic systems. Although the rate enhancement factor of 4 observed in this switching process is not even close to the rate enhancement observed for natural enzyme systems, which are generally many orders of magnitude larger, the cooperative action of many of these stabilizing interactions could well account for a substantial part of the enzyme proficiencies.