On the mechanism of action of gated molecular baskets: The synchronicity of the revolving motion of gates and in/out trafficking of guests

We used dynamic 1H NMR spectroscopic methods to examine the kinetics and thermodynamics of CH3CCl3 (2) entering and leaving the gated molecular basket 1. We found that the encapsulation is first-order in basket 1 and guest 2, while the decomplexation is zeroth-order in the guest. Importantly, the interchange mechanism in which a molecule of CH3CCl3 directly displaces the entrapped CH3CCl3 was not observed. Furthermore, the examination of the additivity of free energies characterizing the encapsulation process led to us to deduce that the revolving motion of the gates and in/out trafficking of guests is synchronized, yet still a function of the affinity of the guest for occupying the basket: Specifically, the greater the affinity of the guest for occupying the basket, the less effective the gates are in “sweeping” the guest as the gates undergo their revolving motion.


Introduction
Covalent and self-assembled molecules with a natural cavity, i.e., molecular capsules [1,2], employ several mechanisms to trap and release guests capable of residing in their inner space [3][4][5]. The so-called "slippage" scenario [6], in which a guest makes its way to and from the host by forcing the expansion of its aperture [7], appears frequently. The "gating" scenario [8], on the other hand, includes a conformational change in the host to create an opening that is large enough for a guest to "squeeze" its way in or out of the host. In the case of selfassembled hosts, however, the slippage, gating and possible partial or full disassembly of the capsule constitute mechanistic alternatives for the exchange of guests [4]. In the last decade, we [9][10][11][12][13][14] and others [7,8,[15][16][17][18] have studied gated molecular encapsulation in artificial and natural systems [19].  (2). Electrostatic potential surfaces of basket 1 and guest 2 were computed with Spartan (AM1) [20].
In particular, we designed gated molecular baskets ( Figure 1) and employed both experimental and theoretical methods to gain an understanding of their mechanism of action [4]. These dynamic hosts comprise a semirigid platform with three aromatic gates appended to its rim through CH 2 "hinges" (Figure 1). The gates were set to interact by hydrogen bonding to control the opening and closing of the basket and thereby the rate by which a guest enters or departs the cavity of the basket [12][13][14]. Indeed, the action mechanism of the basket has been addressed [14], yet the exact role of the gates in the process of the in/out guest exchange necessitates additional scrutiny. In particular, a careful inspection of the additivity of free energies [21] pertaining to the constrictive ΔG ‡ in/out and intrinsic ΔG°b inding energies of the guests [11] as well as the racemization of the basket ΔG ‡ rac (i.e., opening and closing, see below in Figure 6) reveals a systematic disparity (ΔG° + ΔG ‡ rac + ΔG ‡ sterics ≠ ΔG ‡ out , see below in Figure 7). In order to address this conundrum, we have employed methods of experimental (dynamic NMR) and computational chemistry (steered molecular dynamics, SMD) to inspect the relationship between the gates revolving at the rim of the host and the in/out exchange of guests. The results of our study suggest that for guests with a greater propensity to occupy the interior of the basket (i.e., more negative ΔG°) the process of gating is poorly synchronized with the guest exchange. The gates undergo a revolving motion to sweep the space but are concurrently less effective in enforcing the ejection of the guest from the cavity. Moreover, the results of dynamic 1 H NMR measurements of CH 3 CCl 3 (2) entering and departing basket 1 (Figure 1) suggest the absence of an interchange mechanism [22] in which a molecule of CH 3 CCl 3 directly displaces another CH 3 CCl 3 residing in the interior of the gated basket.

Results and Discussion
The encapsulation stoichiometry and the intrinsic binding (ΔG°) In an earlier study [13], we reported on the tendency of basket 1 to trap CH 3 CCl 3 (2) as a guest, and we hereby elaborate on the equilibrium thermodynamics of the recognition event ( Figure 2). The incremental addition of 2 to a CD 2 Cl 2 solution of 1 (0.67 mM, 298.0 K) caused considerable 1 H NMR chemical shifts of the resonances corresponding to the presence of the basket (Figure 2). At 298.0 K, the formation and degradation of [basket-CH 3 CCl 3 ] complex was sufficiently fast on the "NMR time scale": The nonlinear least-squares fitting of the binding isotherm to a 1:1 binding model provided K a = 54 ± 1 M −1 (R 2 = 0.998, Figure 2) [23].
Indeed, the results of a variable temperature 1 H NMR study (400 MHz, CD 2 Cl 2 ) of 1 (0.67 mM) containing CH 3 CCl 3 (2) (1.07 mM) was in line with the formation of the 1:1 complex; note that extrapolation of the fitted line gives K a of 86 ± 16 M −1 at 298.0 K, which is akin to the value obtained in the titration experiment. Furthermore, the van't Hoff analysis of the 1 H NMR data revealed that the encapsulation is also driven by enthalpy (ΔH° = −3.56 ± 0.06 kcal/mol, Figure 2). Indeed, the computed electrostatic potential surface (AM1, Spartan) [20] of guest 2 is complementary to the one corresponding to the concave interior of 1 ( Figure 1). Furthermore, compound 2 (93 Å 3 , Spartan) occupies 42% of the inner space of 1 (221 ± 9 Å 3 )  [11], which is close to the packing coefficient of liquids and thereby a good indicator of a stable assembly [24].
The rate law characterizing guest exchange and the constrictive binding (ΔG ‡ in/out ) We performed 1 H, 1 H-EXSY [25] and selective inversiontransfer [26,27] NMR measurements (400 MHz, CD 2 Cl 2 ) to examine the rate laws characterizing the trafficking of CH 3 CCl 3 (2) to and from basket 1. At concentrations of CH 3 CCl 3 as a guest comparable to those of host 1, the EXSY measurements (250.0 ± 0.1 K) allowed us to extract (MNova software) the magnetization rate coefficients k* in and k* out (Figure 3).
At higher concentrations of CH 3 CCl 3 with respect to host 1, however, we noticed an intense T 1 noise coinciding with the [CH 3 CCl 3 ] out signal, thus preventing the accurate determination of the volume of the corresponding cross peak. Accordingly, we had to turn to selective inversion-transfer NMR measurements to obtain the values of k* in and k* out . The exchange rate constants k* in and k* out (characterizing the longi-tudinal magnetization of the hydrogen nuclei in CH 3 CCl 3 altering the chemical/magnetic environment) are by the nature of the experiment pseudo-first-order in character (see below) [25,26].
On the basis of the reaction stoichiometry ( Figure 2), we initially made the assumption that the entrapment is first-order in both [basket] and [CH 3 CCl 3 ]. Accordingly, the rate of the forward reaction is given as: As per the earlier discussion, the pseudo-first-order constant k* in describes the longitudinal magnetization of the hydrogen nuclei in CH 3 CCl 3 transferring from the bulk solvent (δ = 2.70 ppm, Figure 3) to the interior of 1 (δ = −2.45 ppm, Figure 3).
Correspondingly, the rate of the forward reaction (entrapment) can be formulated as: From Equation 1 and Equation 2, we furthermore derive: If the proposed model is valid, then the experimentally determined k* in will be linearly proportional to the concentration of free basket 1. Indeed, when the value of k* in is plotted against the concentration of free basket 1, there is an apparent linear dependence, with the slope of the fitted curve k in = 2.1 ± 0.3 × In accordance with this theoretical model, we completed a series of selective inversion-transfer [27] NMR measurements of 1 (1.65 mM) and CH 3 CCl 3 (16-200 mM) in CD 2 Cl 2 at 250.0 ± 0.1 K ( Figure 5). In the experiment, the proton resonance corresponding to [CH 3 CCl 3 ] out was selectively inverted, resulting in the perturbation of the longitudinal relaxation of both [CH 3 CCl 3 ] out and [CH 3 CCl 3 ] in due to chemical exchange over the course of variable delay time τ (180° x (selective) -τ -90° x (nonselective) -τ d ). Upon the integration of both signals (I in and I out ), we subjected the data to nonlinear least-squares fitting of I in/out versus τ using the proposed solutions of the McConnell equations [27] describing the relaxation of the hydrogen nucleus residing in two environments ( Figure 5A). For the fitting, the longitudinal relaxation rate (1/T 1 ) of hydrogen nuclei in CH 3 CCl 3 was determined separately by using a classical selective inversion-recovery NMR pulse sequence. When the experimental k* in was plotted against the equilibrium concentration of CH 3 CCl 3 , there indeed appeared a hyperbolic dependence ( Figure 5B) in agreement with Equation 6 (k* in 1/[CH 3 CCl 3 ]). The fitting of the data to Equation 6 was inaccurate as only a few experimental points characterize the dependence ( Figure 5B), although computing k in from each data point would give a value of this coefficient (~2 × 10 3 M −1 ·s −1 ) similar to that determined in the EXSY experiment ( Figure 4). In accordance with the 2-D EXSY and selective inversion-transfer results, we conclude that the entrapment is first-order in both basket 1 and guest 2. On the basis of the reaction stoichiometry (Figure 2), the rate law for 2 leaving the encapsulation complex can be described as: (7) Alternatively, the rate of the same process expressed through the NMR magnetization transfer rate coefficient k* out is: (8) As in the case above, the manipulation of Equation 7 and Equation 8 gives Equation 9: In accordance with this theoretical model, we increased the concentration of guest 2 (16-200 mM) with respect to 1 (1.65 mM) and measured k* out using the selective inversion-transfer NMR pulse sequence. Markedly, there was essentially no interdependence between k* out (21 ± 3 s −1 ) and the concentration of guest 2 ( Figure 5C); the curve indeed shows a small slope, but the intercept of 18.1 suggests that this is likely an artifact. 2-D EXSY measurements would give a rate coefficient k* out = 10 ± 0.1 s −1 , which was also found to be independent of the external concentration of the basket/guest (Figure 4). The departure of CH 3 CCl 3 from its complexed form [basket-CH 3 CCl 3 ], therefore, follows a dissociative mechanism [4]. Notably, a molecule of solvent CD 2 Cl 2 and not another CH 3 CCl 3 (interchange mechanism) displaces the encapsulated guest. In fact, the inspection of CPK models as well as molecular dynamics studies (see below) revealed that the departure of CH 3 CCl 3 (93 Å 3 ) demands (a) "opening" of at least two gates, (b) disruption of internal N-H … N hydrogen bonds, and (c) distortion of the framework of the basket. We further reason that in the case of a direct exchange of two CH 3 CCl 3 molecules, the departure of CH 3 CCl 3 would create an empty host, and therefore vacuum, before another guest of the same kind can take its place. Note that two large compounds (overall ~186 Å 3 ) cannot simultaneously occupy the interior of 1 (~220 Å 3 ).

Computational examination of the in/out trafficking
To gain mechanistic insight into the departure of CH 3 CCl 3 (2) from the interior of basket 1, we completed a series of steered molecular dynamics (SMD) simulations using the AMBER 10.0 suite of programs [29][30][31][32]. Without applying any external force on the entrapped CH 3 CCl 3 , we first found that this guest would, within 10 ns, adopt many positions inside host 1, although the one depicted in Figure 6A is obtained after 1 ns (Supporting Information File 1). The N-H … N hydrogen bond contacts along the top of the basket were also monitored throughout the 10 ns simulation. Importantly, the distance between each pair of amide-hydrogen and pyridine-nitrogen atoms was found to be invariant (~2 Å, see Supporting Information File 1).
In addition, the width of each side aperture (the span between adjacent carbonyl oxygen atoms) also remained constant at 6.3 Å throughout the simulation ( Figure S3, see Supporting Information File 1). We then selected multiple trajectories for "pulling" the guest from the host ( Figure 6A). Markedly, the departure of CH 3 CCl 3 necessitated the cleavage of at least two intramolecular N-H … N hydrogen bonds in 1 ( Figure 6B) with a simultaneous expansion of the host ( Figure 6B). That is to say, the "slippage" of CH 3 CCl 3 (with gates in the "closed" position) does not appear to be a viable mechanistic scenario. Note that our simulation did not include solvent molecules (CD 2 Cl 2 ) displacing the entrapped CH 3 CCl 3 , as suggested by the kinetic study. The substitution of the guest by the solvent should perhaps cause an even greater distortion of the framework of the basket.
The revolving of the gates and the racemization of basket 1 The aromatic gates in basket 1 interact through hydrogen bonding, as exemplified by a large downfield shift of the signal corresponding to (O=C)N−H protons (δ = 11.6 ppm at 298.0 K, Figure 2) [13]. In addition, the aromatic gates are dynamic, each one revolving about its axis to give rise to two enantiomeric conformers 1 A and 1 B (Figure 7A). The interconversion kinetics of the 1 A/B racemization can be followed by dynamic NMR spectroscopy in which a singlet corresponding to H a /H b nuclei at high temperatures is seen to split into two doublets at low temperatures. In particular, the revolving rate of the gates is temperature dependent, thereby governing the lifetime of H a or H b nuclei, each residing in a particular chemical environment (τ = 1/k rac ); the hydrogen nuclei are observed as separate resonances when τ >> 1/Δν(H a/b ) [33]. Accordingly, we performed the classical line-shape analysis of H a /H b resonances (WinDNMR-Pro software) to obtain the rate constants (k rac ) and corresponding activation energies ΔG ‡ rac characterizing the racemization of basket 1 ( Figure 7B). Evidently, the rate at which the aromatic gates in 1 revolve is a function of the com- pound occupying the inner space: With CH 3 CCl 3 the gates are less dynamic than with CD 2 Cl 2 occupying the cavity ( Figure 7B).

On the action mechanism of the basket
Is there a relationship between the aromatic gates sweeping the space and guests trafficking to and from the basket [11]? That is to say, will the gates expel the entrapped guest each time that they alter their propeller-like orientation ( Figure 8)? First, our kinetic measurements suggest that guest CH 3 CCl 3 (2) enters basket 1 by substituting solvent (CD 2 Cl 2 ) molecule(s), while exactly the opposite occurs during the dissociation (Figure 8). Given this exchange scenario, we deduce that 1 A -CH 3 CCl 3 shall transform into 1 B -CH 3 CCl 3 via intermediate 1-CD 2 Cl 2 ( Figure 8). That is, the formation of 1-CD 2 Cl 2 from 1 A -CH 3 CCl 3 is accompanied by either reorientation or reinstatement of the gates, and therefore, there is an equal likelihood that 1-CD 2 Cl 2 will yield 1 A -CH 3 CCl 3 or 1 B -CH 3 CCl 3 ( Figure 8); this reasoning is also supported by the fact that the gates of the solvated basket revolve at a higher rate ( Figure 7B). In accordance with such a racemization mechanism, we apply the statistical correction to the measured k rac to obtain k rac′ (k rac′ = 2k rac = 616 s −1 , Figure 7B) [34]. This particular rate coefficient should more precisely describe the process of racemization.
In addition, the decomplexation of CH 3 CCl 3 follows a late transition state [14] whereby its affinity for populating the interior of the basket should decrease to a somewhat smaller value than described by ΔG°. Given the delicacy of the proposed partitioning, will the additivity of free energies and the relationship ΔG ‡ rac′ + ΔG° + ΔG ‡ sterics ~ ΔG ‡ out still hold? Figure 8: The departure of CH 3 CCl 3 from 1 A -CH 3 CCl 3 gives rise to the less stable 1-CD 2 Cl 2 , which upon entrapment of another CH 3 CCl 3 gives either 1 A -CH 3 CCl 3 or 1 B -CH 3 CCl 3 . The 1 A/B -CH 3 CCl 3 interconversion occurs with CH 3 CCl 3 departing (BR 1 mechanism) or remaining (BR 2 mechanism) in the cavity.
In reality, when the internal hydrogen bonds are broken and the gates open up the guest does not have to depart the basket cavity. That is to say, the gates should be able to revolve to allow the interconversion of 1 A -CH 3 CCl 3 into 1 B -CH 3 CCl 3 without even ejecting the guest. Accordingly, we hereby propose that the conversion of 1 A -CH 3 CCl 3 into 1 B -CH 3 CCl 3 (i.e., racemization) occurs by two routes, BR 1 and BR 2 , one with (BR 1 ) and another without (BR 2 ) the concomitant guest exchange (Figure 8).
It follows that, during the departure of CH 3 CCl 3 , the measured racemization of 1 (ΔG rac′ ) includes energetic contributions from two pathways (ΔG ‡ rac′ = ΔG ‡ BR1 + ΔG ‡ BR2 ) of which only BR 1 should be incorporated in the additivity assessment. It is therefore convenient to partition the energetic contribution of the two "competing" BR 1 and BR 2 routes to ΔG ‡ rac′ (ΔG ‡ rac′ = ΔG ‡ BR1 + ΔG ‡ BR2 ) to corroborate fully the role of the gates. However, this is a difficult task, but for guest molecules holding strongly onto the basket (more negative ΔG°) there should be a greater contribution from the RG 2 pathway during the racemization.
In one of our prior studies [13,14], we measured kinetic and thermodynamic parameters pertaining to the exchange of five isosteric (same-size) guests 3-7 to and from basket 1 (Figure 9). When ΔG ‡ rac′ + ΔG° is computed for each guest and the values plotted against ΔG ‡ out , a linear relationship appears (R 2 = 0.99, Figure 9A). Note that ΔG ‡ sterics is not included in this analysis as it is unknown; however, we anticipate that the value of the parameter should show minimal fluctuations for the series of isosteric guests 3-7. Importantly, the greater the affinity of a particular guest for occupying the interior of the basket (ΔG°), the greater the deviation of the calculated ΔG ‡ rac′ + ΔG° (black line, Figure 9A) from the experimental ΔG ‡ out (red line, Figure 9A). The variation of ΔΔG = (ΔG ‡ rac′ + ΔG°) − ΔG ‡ out with intrinsic binding energies ΔG° of 3-7 is shown in Figure 9B. The trend is evident, supporting the notion that for guests having greater propensity to occupy the basket (ΔG°) the BR 2 pathway is more greatly involved in the 1 A -CH 3 CCl 3 / 1 B -CH 3 CCl 3 racemization. As already discussed, the BR 2 pathway contributes to the measured ΔG ‡ rac′ , yet it is not involved in the exchange of guests.

Conclusion
Describing mechanisms by which dynamic hosts entrap/release guests is a challenging task necessitating experimental and computational scrutiny. Notably, one can use NMR spectroscopic methods for understanding the equilibrium kinetics characterizing the rate law of molecular encapsulation processes. Our study, accordingly, describes the rate law characterizing the encapsulation of guest CH 3 CCl 3 by the gated basket 1. Importantly, the entrapment reaction is first-order in each compound, while the complex dissociation is zeroth-order in guest CH 3 CCl 3 . Furthermore, examination of the additivity of free energies corresponding to different molecular events can assist in the understanding of the operation of gated hosts and, in particular, can help to reveal the explicit role of the gates. On the basis of these results, we deduced that the synchronicity in the revolving motion of the gates and in/out trafficking of guests is a function of the affinity of the guest for occupying the gated basket. The greater the affinity, the less effective the gates are in "sweeping" the guest as the gates undergo their revolving motion. This result is important for exploring the utility of gating for controlling the outcome of chemical reactions occurring in confined space but also for the understanding of the effective conversion of energy at the molecular level and the preparation of molecular machines [36,37]. [25]: A solution of basket 1 and guest 2 in CD 2 Cl 2 (J. Young NMR tube) was cooled to 250.0 ± 0.1 K inside the NMR probe and allowed to equilibrate for 1.0 h. A series of gradient NOESY experiments was run with a relaxation delay of 5 × T 1 and mixing times (τ m ) of 0 ms and three others ranging from 40 ms to 250 ms, such that the cross-peaks were clearly resolved; the spin-lattice relaxation time (T 1 = 3.30 s) for the free guest was determined by performing a standard inversion-recovery pulse sequence with a relaxation delay (τ d ) of at least 5 × T 1 . Each of the 128 F 1 increments represented the accumulation of at least two scans. The corresponding integrals were determined by using MNova software from Mestrelab Research, after phase and baseline corrections in both dimensions. The magnetization exchange rate constants (k* in and k* out ) were, at each mixing time τ m , calculated by using the EXSYCalc program (Mestrelab Research). The mean values of k* in and k* out are reported with the standard deviation as an experimental error. [27]: A solution of basket 1 and guest 2 in CD 2 Cl 2 (J. Young NMR tube) was cooled to 250.0 ± 0.1 K inside the NMR probe and allowed to equilibrate for 1.0 h. The 1 H spin-lattice relaxation time (T 1 = 3.30 s) for the free guest was determined by a standard inversion-recovery pulse sequence with a relaxation delay (τ d ) of at least 5 × T 1 . By using a selective 1-D inversionrecovery pulse sequence [180° x (selective) -τ -90° x (nonselective) -τ d ], 32 transients were obtained for each variable delay time (τ) with a relaxation delay (τ d ) of at least 5 × T 1 . The absolute integrals corresponding to encapsulated and free guest molecules were, at each mixing time, determined by using TopSpin software from Bruker, and the resulting data was fitted by using the two-site exchange equations described by Led et al. [27] to obtain magnetization exchange rate constants k* in and k* out .

Supporting Information
Supporting Information contains details of the computational studies.

Supporting Information File 1
Details of the computational studies.