Stopped-Flow Kinetic Analysis of the Interaction of Cyclo[8]pyrrole with Anions

Abstract

The on and off rates corresponding to the binding of two test anions (acetate, AcO⁻ and dihydrogen phosphate, H₂PO₄⁻ studied as their tetrabutylammonium salts) to diprotonated cyclo[8]pyrrole have been determined in CH₃CN using stopped-flow analyses carried out at various temperatures. For dihydrogen phosphate, this afforded the activation enthalpies and entropies associated with both off and on processes. The different dynamic behavior seen for these test anions underscores the utility of kinetic analyses as a possible new tool for the advanced characterization of anion receptors.

Anion binding has emerged as an important sub-discipline within the broader field of supramolecular chemistry.^1–4 Considerable work has been devoted to the synthesis of new anion receptors and to the characterization of their complexes at equilibrium.^1–7 Yet, few studies have addressed the problem of anion binding dynamics. To date, some insights into the dynamics of receptor-anion interactions (i.e., on and off rates) have been obtained via the use of NMR exchange techniques.^8,9 However, the accessible time scales are limited and the nature of the process in question must be inferred.

While not well studied, dynamic considerations touch on a number of issues that are critical to both biological and synthetic anion recognition, including apparent receptor-substrate specificities, especially those observed under conditions of slow receptor-anion exchange, as well as the rates of through-membrane ion transport and the viability of liquid-liquid extraction processes.¹⁰ Both extraction and through-membrane transport are dynamic phenomena, meaning the actual utility of an otherwise promising receptor system is likely to be limited if either ion uptake or release is too slow.^9–11 The same is true for ion-selective electrodes.¹² These potential limitations provide a specific incentive to understand the kinetics of anion recognition.

One approach that might allow the kinetics of anion recognition to be probed in quantitative fashion involves the use of stopped-flow. This technique is frequently used to study the dynamics of enzyme-substrate interactions. It has also recently begun to attract the attention of supramolecular chemists for the analysis of, for example, receptor-cation binding kinetics.¹¹ However, in spite of its potential utility, this technique has yet to be extended to the study of anion binding. Here, we report the use of the stopped-flow technique to monitor the on and off rates of two test anions, namely acetate (AcO⁻) and dihydrogen phosphate (H₂PO₄⁻), binding to diprotonated cyclo[8]pyrrole ([C8 • 2H]²⁺; cf. Scheme 1). To the best of our knowledge, this is the first time the kinetic parameters associated with an anion binding event have been measured in quantitative terms.

Scheme 1.

Model used to fit the kinetic data obtained upon mixing C8 • 2HCl with TBAOAc.

Cyclo[8]pyrrole (C8), an expanded porphyrin reported by our group in 2002, is able to interact with oxyanions, specifically the sulfate dianion, as was inferred from a single crystal X-ray diffraction analysis.¹³ Follow-up work focused on the application of an organic-solubilized version of C8 as a possible sulfate extractant. The diprotonated form of this cyclo[8]pyrrole was found to display selectivity for sulfate over nitrate under conditions of aqueous-organic extraction, even in the presence of high concentrations of the latter species.¹⁴ However, this same work also led to the inference that the utility of C8 as an extractant was limited by the kinetics of anion exchange. More recently carboxylate and dihydrogen phosphate monoanions were found to bind to C8 in its diprotonated form ([C8 • 2H]²⁺), as revealed through the significant UV-Vis changes upon titration with the corresponding tetrabutylammonium salts. The interactions with carboxylate anions has recently been exploited to create a supramolecular dyad capable of undergoing photoinduced electron transfer.¹⁵ This latter work, based on the use of a pyrene butyric acid salt, prompted the present study. Specifically, we felt it important to characterize the ‘lifetime’ of the supramolecular donor acceptor, [C8•2H]²⁺—carboxylate complex formed in solution prior to photoexcitation. Understanding the kinetics of association/dissociation is also viewed as being critical to the analysis of other anion-recognition based ET systems.¹⁶

In light of this potential benefit, we set out to perform stopped flow analysis of the interactions between a simple test carboxylate salt, tetrabutylammonium acetate (TBAOAc), and the bis-HCl salt of C8 (C8 • 2HCl). Since it was found to provide a good spectral signature, an effort was also made to extend this analysis to include the dihydrogen phosphate anion. As detailed below, the present kinetic study also facilitated a determination of the system energetics, including key thermodynamic values, such as enthalpy (ΔH), entropy (ΔS), and free energy change (ΔG). This was accomplished for both anions through van’t Hoff analyses made using association constants (K_a) determined at various temperatures through either steady-state measurements, kinetic measurements, or a combination of both. In the case of dihydrogen phosphate, on and off-rates could be determined at multiple temperatures. This allowed for an Eyring analysis and yielded the activation parameters (ΔH^‡, ΔS^‡) for both the on and off-processes. Access to these latter values is limited without quantitative kinetic data.¹

Results and Discussion

Steady state titrations were carried out between TBAOAc and C8 • 2HCl in CH₃CN, resulting in large spectral changes in the UV-Vis region amenable to study by stopped-flow (Figure 1a). On the basis of a Job plot analysis and curve fits, a 1:1 binding stoichiometry was inferred (Figure 1b). Proton NMR spectroscopic studies provided support for anion binding, as opposed to deprotonation; i.e., no loss in the NH proton signal was seen upon treatment with excess anion (see Figure S2).

Figure 1.

(a) Steady-state spectral titration performed between C8 • 2HCl (1.1 × 10⁻⁵ M) and TBAOAc in CH₃CN at 298 K (TBA = tetrabutylammonium). (b) A Job plot was also constructed; it displayed a maxima at a mole fraction of 0.5, as would be expected for a 1:1 binding stoichiometry.

The apparent association (formally displacement) constant, K_a, for the binding of TBAOAc to C8 • 2HCl in CH₃CN was determined at various temperatures through UV-Vis spectra titrations wherein the host concentration is held constant upon addition of guest. At 298 K (rt) the K_a was found to be on the order of 2 × 10⁵ M⁻¹ and at 243 K, the K_a was found to be on the order of 9 × 10⁴ M⁻¹ (see Figure S1). This steady-state data led us postulate that the binding dynamics would be governed by a one-step binding process, as shown in Scheme 1. To test this hypothesis, stopped flow analyses were carried out in CH₃CN monitoring the change in absorbance from 300–700 nm under conditions of rapid mixing. More specifically, two separate syringes were loaded with stock solutions of the host, C8•2HCl at 8 μM, and the guest, TBAOAc at various concentrations in CH₃CN. As is typical in a stopped-flow set-up, both syringes are automatically, and simultaneously engaged to release the same amount (100 μL) of each of the two different solutions into a mixing chamber with a quartz window. This results in a twofold dilution of the stock solutions and a rapid mixing. After an initial period in which mixing is presumed to occur (typically 1–3 ms and often referred to as the “dead time”), the flow is stopped and the optical spectra are recorded as a function of time.¹⁸

As might be expected given the relatively high K_a value recorded for this anion, the kinetics of interaction with acetate proved to be extremely fast. Indeed, in order to observe any change in the spectral features of C8•2HCl on the ca. millisecond stopped flow time scale, low temperature (243 K) analyses had to be carried out and relatively low host concentrations (4 μM) had to be employed. Under these conditions, time-dependent optical changes were observed for a variety of TBAOAc concentrations, as shown in Figure 2 (for the actual time-dependent spectral changes, see Figure S4).

Figure 2.

(a) Kinetic traces produced by mixing C8•2HCl (4 μM final post-mixing concentration) with TBAOAc at the following final concentrations: 5, 10, 20, 30, 50 μM in CH₃CN at 243 K. The mixing time (ca. 3 ms) is shown as dotted lines in these traces. The solid lines represent the fit of a single exponential decay of the signal, giving the observed rate constant, k_obs; see text for details (b) Plot of k_obs as a function of the concentration of guest, AcO⁻ with a solid line showing the fit to k_obs = k₁[AcO⁻] + k₋₁, where k₁ is the slope, and k₋₁ is the y-intercept.

Each kinetic trace obtained could be fit to a single exponential decay as shown in Figure 2. This gave an observed rate constant, k_obs, which was then plotted vs the concentration of guest.^18,19 A straight line was obtained, as would be expected for a one-step equilibrium process. By fitting to the equation, k_obs = k₁[AcO⁻] + k₋₁, the on rate constant (k₁) and off rate constant (k₋₁) could be obtained. This gave values of k₁ = (1.9 ± 0.2) × 10⁷ M⁻¹ s⁻¹ and k₋₁ of 200 ± 20 s⁻¹, respectively. A value for the K_a, (9.5 ± 0.9) × 10⁴ M⁻¹, was determined from the ratio of k₁/k₋₁. This kinetically-derived association constant proved to be the same within experimental error as that determined by the direct titration discussed above. This concordance, although not a ‘proof’, serves as important check for the kinetic parameters obtained via stopped flow. The off-rate of 200 s⁻¹ corresponds to a lifetime, τ, of 5 ms; this is long enough to allow intra-ensemble charge separation and recombination as assumed in the previous electron transfer study.¹⁵

We next analyzed the binding of dihydrogen phosphate (TBAH₂PO₄) to C8 • 2HCl. This tetrahedral anion, in contrast to simple carboxylates, is known to form 2:1 complexes with protonated expanded porphyrins, although 1:1 complexes dominate under most solution phase conditions.^20–22 This complexity made H₂PO₄⁻ useful as a test anion. The raw spectra obtained upon stopped-flow mixing at 253 K are shown in Figure 3.²³ These data provide support for the conclusion that there are at least two steps; a fast phase (Figure 3a) and a slow phase (Figure 3b). It was thus inferred that a reasonable analysis would involve a two-step binding model. Our proposed mechanism involves the binding of first one, and then a second H₂PO₄⁻ (P), as shown in eqs 1 and 2 (Figure 3d).

Figure 3.

Optical spectra obtained when C8•2HCl (10 μM) is mixed under stopped flow conditions with the 500 μM of TBAH₂PO₄ in CH₃CN at 253 K from (a) 2–20 ms and (b) 20–500 ms. (c) Change in the spectral intensity at 425 nm observed when C8 • 2HCl (10 μM) is mixed with 50, 100, 200, 400, 500 μM of TBAH₂PO₄ in CH₃CN at 253 K (all concentrations are final, post-mixing). The dotted lines are experimental data points corresponding to the decay in the C8 absorbance at 425 nm, while the solid lines are the best fits obtained using a global fitting procedure.²⁴ (d) Equations used for the global fitting analysis shown in part (c), wherein ‘P’ represents H₂PO₄⁻.

Using a global fitting analysis for a two-step process, a k₁ of (2.65 ± 0.1) × 10⁵ M⁻¹ s⁻¹ and a k−1 of 16.6 ± 0.3 s⁻¹ were calculated for the first binding step.²⁴ These values were then used to estimate an association constant, K_a of (1.6 ± 0.1) × 10⁴ M⁻¹. The same global kinetic analysis gave k₂ = (4.1 ± 0.5) × 10³ M⁻¹ s⁻¹ and k₋₂ = (3.9 ± 0.6) s⁻¹ for the second step. These latter values, while not well-determined, allowed an equilibrium constant of ca. 1 × 10³ M⁻¹ to be estimated for the second step. This value is an order of magnitude smaller than the K_a for the first event.

The data were also analyzed by conventional methods, wherein k_obs was plotted as a function of the guest concentration. This gave concordant values for the on and off rates for the first step as shown in Figure 4 and in Table 1 (the raw data are given in Figures S4–S7). Unlike acetate, the slower kinetics of interaction between C8 • 2HCl and TBAH₂PO₄ allowed for analysis of the dynamics over a range of temperatures. Figure 4 shows the results of such an analysis carried out at 243, 253, and 273 K.

Figure 4.

Plots of the pseudo-first order rate constant vs. the concentration of guest for the stopped flow data involving C8 • 2HCl and TBAH₂PO₄ at 243 (■), 253(●), and 273 (▲) K, wherein the concentration of the guest is in excess relative to the host. In this case k₁ or k_on is given by the slope of the line and k₋₁ or k_off is given by the y-intercept. These values are summarized in Table 1.

Table 1.

Summary of the calculated k₁ (k_on) and k₋₁ (k_off) and the Kinetically Derived Association Constants (K_a) for C8 • 2HCl and H₂PO₄⁻

T, K	k1, M −1s−1a	k−1, s−1a	Ka, M−1	k1, M−1s−1	k−1, s −1b	Ka, M−1
298	3.9 × 106	84	4.6 × 104
273	6.8 × 105	37	1.8 × 104	6.5 × 105	27.3	2.4 × 104
253	2.6 × 105	23	1.1 × 104	2.6 × 105	13.3	1.9 × 104
243	1.2 × 105	10	0.9 × 104

^aRate constants and K_a calculated by the conventional method shown in the graph above.

^bRate constants and K_a calculated by global fitting analysis using the KinTek software.¹⁸

In order to check the mechanistic assumptions on which the kinetic analysis was based, a steady state titration was performed at 253 K in CH₃CN (cf. Figure 5a). This study was carried out under conditions identical to those used for the kinetic analysis, i.e. the same temperature, concentration of C8 • 2HCl, and solvent. This congruity allowed us to compare with confidence the two sets of association constants obtained from these disparate procedures. With the exception of several initial points ascribed to the formation of a 1:2 (phosphate-to-C8) complex, a binding isotherm in agreement with the kinetic results was obtained when the concentration of the guest was plotted vs. the change in absorbance for C8.²⁵ Shown in Figure 5b is the overlay of the expected binding isotherm based on a simulation using the full set of kinetic data seen in Figure 3 and that obtained from an independent steady state analysis. Gratifyingly, the resulting binding curves match well.

Figure 5.

(a) Steady-state titration of C8•2HCl (11 μM) with increasing quantities of TBAH₂PO₄ in CH₃CN at 253 K. (b) Binding isotherm for the steady state titration of C8•2HCl and TBAH₂PO₄ shown in part (a) (■) and the simulated binding isotherm based on a global fit to the kinetic data recorded at 253 K (●).

A comparison between the association constants for C8 and H₂PO₄⁻ obtained at various temperatures was carried out. On this basis, it was inferred that the kinetically derived K_a value decreases with decreasing temperature. This is indicative of an endothermic reaction, wherein there is a largely positive entropy contribution. This is common for ion-pairing events, wherein desolvation occurs to afford a largely positive entropy change.^{26, 27} On the other hand, the complex itself is highly unrestrained (e.g., not held in a particular configuration). Given the planar structure of C8 and the 2+ charge, such an inference seems reasonable.

These data also allowed for van’t Hoff analyses, from which ΔH and ΔS values of 4.4 kcal • mol⁻¹ and 36 cal • K⁻¹ • mol⁻¹, respectively, were determined.²⁸ A similar decrease in K_a as a function of temperature was also seen for TBAOAc, where the van’t Hoff plot yielded a ΔH value of 2.8 kcal • mol⁻¹ and a ΔS value of 33.7 cal • K⁻¹ • mol⁻¹ (Figure 6b, Table 2).

Figure 6.

Van’t Hoff analysis for C8 with (a) H₂PO₄⁻and (b) AcO⁻; here, lnK_a is plotted as a function of 1/T. This is based on the equation lnK_a = (ΔS/R) − (ΔH/RT), which yields ΔH/R as the slope and ΔS/R as the y-intercept.

Table 2.

Kinetic and Thermodynamic Parameters for the Binding of Indicated Guest in CH₃CN.^a

	AcO−	H2PO4−
ΔH (kcal • mol−1)b	2.8	4.4
ΔS (cal • K−1 • mol−1)b	33.7	36
ΔG (kcal • mol−1)c	−7.2	−6.3
ΔH‡ass (kcal • mol−1)d		8.3
ΔS‡ass (cal • K−1 • mol−1)d,e		−3.0
ΔG‡ass (kcal • mol−1)f		9.2
ΔH‡diss (kcal • mol−1)d		4.6
ΔS‡diss (cal • K−1 • mol−1)d		−34
ΔG‡diss (kcal • mol−1)f		14.7
ΔH(ΔH‡ass − ΔH‡diss)		3.7
ΔS(ΔS‡ass − ΔS‡diss)		31
ΔG(ΔG‡ass − ΔG‡diss)		−5.5

^aError for the listed values is estimated to be ≤ 10% unless otherwise noted.

^bCalculated from van’t Hoff analysis shown in Figure 6.

^cCalculated using the Gibbs-Helmholtz Equation ΔG = ΔH − TΔS at 298 K.

^dCalculated from Eyring analysis shown in Figure 7.

^eEstimated error: 33%.

^fCalculated using the Gibbs-Helmholtz Equation ΔG^‡ = ΔH^‡ − TΔS^‡ at 298 K.

Finally, the activation parameters for both the association and dissociation processes were determined from Eyring plots (Figure 7). Here, the on and off-rates were analyzed separately as a function of temperature and fit to the following equation: $ln(k/T)=[ln(k_{\text{B}}/h)+\mathrm{\Delta }{S}^{‡}/R]-\mathrm{\Delta }{H}^{‡}/(RT)$.²⁹ The resulting values are included in Table 2. In the case of dihydrogen phosphate, the activation enthalpy (ΔH^‡_ass) and entropy (ΔS^‡_ass) for the association of dihydrogen phosphate with C8 were determined to be ΔH^‡_ass = 8.3 kcal • mol⁻¹ and ΔS^‡_ass = −3.0 cal • K⁻¹ • mol⁻¹, respectively (cf. Figure 6a). The ΔH^‡ and ΔS^‡ values for the dissociation were also determined; ΔH^‡_diss = 4.6 kcal • mol⁻¹ and ΔS^‡_diss = −34 cal • K⁻¹ • mol⁻¹, respectively (cf. Figure 6b). These values allowed a ‘check’ for ΔH = ΔH^‡_ass − ΔH^‡_diss= 3.7 kcal • mol⁻¹ and ΔS = ΔS^‡_ass − ΔS^‡_diss = 31 cal • K⁻¹ • mol⁻¹ to be carried out. The standard free energy, ΔG was then calculated to be −5.5 kcal • mol⁻¹ at 298 K. In accord with expectations, these kinetically-derived values were found to agree well within experimental error with those determined by the van’t Hoff analysis described above (i.e., ΔH = 4.4 kcal • mol⁻¹ and ΔS = 36 cal • K⁻¹ • mol⁻¹, and at 298 K, ΔG = −6.3 kcal • mol⁻¹).

Figure 7.

Eyring plots constructed using the (a) on-rates and (b) off-rates from Table 1. This plot is based on the following equation: $ln(k/T)=[ln(k_{\text{B}}/h)+\mathrm{\Delta }{S}^{‡}/R]-\mathrm{\Delta }{H}^{‡}/(RT)$.

Conclusion

The present kinetic studies provide support for the notion that observable differences can underlie the binding of different guests. For instance, even under conditions designed to slow the reaction (low temperature; dilute conditions), the interaction between C8 and acetate achieves equilibrium in about 10 ms in CH₃CN to give a 1:1 complex. Furthermore, no evidence of additional complexation is seen under any of the tested conditions using this particular anion. On the other hand, in the case of dihydrogen phosphate, a 2:1 complex is formed with kinetics that are much slower than those associated with the formation of the initial, dominant 1:1 complex. Based on the notable differences seen for these two test anions we propose that kinetic analyses will have an important role to play in the advanced characterization of new anion binding agents.