Kinetics and Mechanism of Cation‐Induced Guest Release from Cucurbit[7]uril

Abstract The release of two organic guests from cucurbit[7]uril (CB7) was selectively monitored by the stopped‐flow method in aqueous solutions of inorganic salts to reveal the mechanistic picture in detail. Two contrasting mechanisms were identified: The symmetric dicationic 2,7‐dimethyldiazapyrenium shows a cation‐independent complex dissociation mechanism coupled to deceleration of the ingression in the presence of alkali and alkaline earth cations (Mn+) due to competitive formation of CB7–Mn+ complexes. A much richer, unprecedented kinetic behaviour was observed for the ingression and egression of the monocationic and non‐symmetric berberine (B+). The formation of ternary complex B+–CB7–Mn+ was unambiguously revealed. A difference of more than two orders of magnitude was found in the equilibrium constants of Mn+ binding to B+–CB7 inclusion complex. Large cations, such as K+ and Ba2+, also promoted B+ expulsion from the ternary complex in a bimolecular process. This study reveals a previously hidden mechanistic picture and motivates systematic kinetic investigations of other host–guest systems.


Introduction
The rigid, biocompatible cucurbituril (CBn, n = 5-8) macrocycles are widely used building blocks in supramolecular chemistry and nanotechnology. [1] They have acontinuously expanding range of applications in the biomedicine, [2] drug delivery, [3] catalysis [4] and sensing. [5] The nonpolar,l ow-polarisability CBn cavity readily includes hydrophobic moieties, whereas the high electron density of the carbonyl-laced portals facilitates the interaction with cations. Thee lectrostatic and hydrophobic effects combined with the complementary dimensions of CBn interior and guests leads to particularly strong binding of cationic organic compounds. [6] Metal cations (M n + )a re readily coordinated by the oxygen atoms of the host entrance with higher binding affinity to CBn than to the well-known classicalc ation receptor 18-crown-6. [7] The cooperative binding of several Ca 2 + or Na + ions to thioflavin-(CB7) 2 complex was found to produce highly fluorescent supramolecular nanocapsules, [8] whereas the coordination of transition-metali ons to the rim of CB7 altered the photodeazetation of encapsulated bicyclic azoalkane guests. [9] Na + addition can be used to induce the transfer of neutral red dye from the CB7 cavity to the pocket of bovine serum albumin. [10] Kinetic data on guest capture and release are essential for many applicationso fC B n complexes, [11] including the rational design of molecular switches, [12] self-sorting systems [13] and light-driven control of supramolecular assemblies. [14] Time-resolved NMR studies demonstrated that the experimentally measured rate constant for ingression of the cyclohexylmethylammonium ion into CB6s ubstantially diminished with increasing Na + concentration,w hereas the egression rate constant barely changed. [15] The increasei nc ation size caused an approximately twofold increase in the ingressionr ate constant, but the egression rate constantr emained essentially constant for such CB6 complexes. [15] Competitiveb inding of Na + decelerated the inclusiono fo rganic guests in CB7 into the time range of the stopped-flow technique. [16] The formation of Na + -CB7 and Na + -CB7-Na + complexes lessened the concentration of free CB7 and thereby slowed down the bimolecular ingression. Systematic time-resolveds tudies on 2-naphthyl-1ethylammonium encapsulation demonstrated that this guest neither expelled Na + nor produced at ernary complex in the reactions with Na + -CB7. [17] Ad itopic guest, namely the Nphenyl-2-naphthylammonium cation, produced two typeso f 1:1c omplex with CB7. When the phenylg roup was embedded in the macrocycle, the binding of Na + to the complex slowed down the guest release. In contrast, Na + sped up the exit of the guest through competitive expulsion when the naphthyl moiety was confined. [18] Such investigations are possible if the association of M n + with guest-CBn complexes leads to changes in the luminescence characteristics,a sw as observed in severalinstances. [19] It is knownf or CBn host-guest complexes that the apparent binding constant of guest encapsulation is reduced in the presence of inorganic salts, [5c, 15, 20] but it is unknownt ow hat extent this effect arises from competitive binding of M n + to form CBn-M n + complexes or from the formation of less-stable guest-CBn-M n + ternary complexes. Although it is difficult to obtain such mechanistic insights by affinity measurements, we show here that these two scenarios can be easily distinguished by kinetic studies. However,i ti s not yet fully understood how the variousm etal cations influence the kinetics and mechanism of guest exit from the CBn cavity. Specifically,t he monitoring of the decomplexation kinetics will give the deepest insight into the subtle details of the mechanism of guest release in salt solutions:I nacompetitive binding mechanism, the rate of hostguest complex dissociation should be independent of the cation concentration, whereas the guest egression rate from a guest-CBn-M n + ternary complex will be cation-dependent.I n reality,itc an be expected that the competitive binding mechanism is alwaysp resent.T he practical challengingt ask is therefore to evaluate whether or not this is complemented by as imultaneously present mechanism in which guest release occurs from aguest-CBn-M n + ternary complex. The commonly appliedk inetic analysis procedure-fitting of the kinetic traces for host-guest association recorded after mixing of host and guest solutions [11,21] -provides consistent butn ot sufficiently accurate results, because three unknown parameters (i.e.,a "signal parameter" for converting the concentration to fluorescence intensity,r ate constantso fi ngression and egression) must be optimised. In addition, the rate of bimolecular complexation reactions is influenced by the initial concentrations of the variouss pecies produced in the solution,w hich can be calculated only if the association constantsa nd the binding mechanism are known. The interpretation of the salt effect on the unimolecular complexd issociation is much simpler and permits selective measurement of the rate constant of guest release k out with high accuracy,a sw eh ave shown recently. [22] In essence, as trongly bindingo rganic competitor is added in excess to as olution of the host and guest to trigger complex dissociation of the host-guest complex according to ap seudofirst order kineticp ath. Notably,u nknown concentrations of the individual species/complexes initially present, that is, CB7, CB7-M n + ,M n + -CB7-M n + and guest-CB7 do not influence k out and thus permit the determination of k out with the required high accuracy.I nt his study,w eu tilised the k out method to investigate systematically the effects of inorganic salts on the competitive versus ternary complex formation/dissociation kinetics and mechanism of host-guest complexation with CB7. The investigationsr evealed the effect of the size and charge of M n + on the rate and the importance of each dissociation step. In addition, we unravelled whether increasing the positive charge of the encapsulated molecule alters the dynamics of decomplexation. Berberine (B + ), as inglyc harged pharmaceutically important isoquinoline alkaloid, and 2,7-dimethyldiazapyrenium (MDAP 2 + )d icationic dye were chosen as guest compounds because of their high binding affinity and the considerable alteration of their fluorescent behaviour upon confinement in CB7. [19c, 23] Scheme 1p resentst he structural formula of the utilised compounds.

Results
MDAP 2 + + exit from its CB7 complex is independentoft he type and concentration of cations As af irst example, the dicationic and symmetric MDAP 2 + was used as ag uest for CB7. It is unlikely that formation of ternary complex MDAP 2 + -CB7-M n + can occur,b ecause the positively charged ends (i.e., N-CH 3 groups) of this guest are symmetrically placed at the portals of CB7 in the MDAP 2 + -CB7 complex, [23] which should prevents imultaneous associationo fa metal cation M n + with the CB7 portal.T herefore, the system of MDAP 2 + and CB7 can be expected to only show the hallmarks of the competitive, salt-induced complex-dissociation mechanism, which makes it as uitable,s impler starting point. The markeda lteration of its absorption and fluorescences pectra upon addition of CB7 ( Figure S1 in the Supporting Information) implied formation of an inclusion complex. The significantly weakere mission of MDAP 2 + at 454 nm when excited at 339 nm in water than in the cavity of CB7w as exploited to selectively detect complex dissociation by mixinge quimolar solutionso fM DAP 2 + and CB7 (5 mm at t = 0s)w ith as olution of 1-adamantylammoniumc ation (AH + ,300 mm at t = 0s). The exponentialf luorescence-intensity decay ( Figure S2 ai nt he Supporting Information) was rather slow; an onlinearl east-squares fit provided k out = 0.015 AE 0.001 s À1 for the rate constanto f MDAP 2 + egression from the cavity of CB7 in water.
The experiments were repeated at variousC a(NO 3 ) 2 or Ba(NO 3 ) 2 concentrations. As seen in Ta ble1,t he obtained k out valuesb arely varied with the concentration and type of salt. In explorative experiments at high concentrations (140 mm), Li + and Na + salts showed similar results, that is, salt-independent k out values for releaseo fM DAP 2 + from the MDAP 2 + -CB7 complex. Thus, it can be concluded that inorganic cations have negligible interaction with the MDAP 2 + -CB7 inclusion complex, that is, as expected, ternary-complex formation does not occur.H ence, MDAP 2 + dissociation can be modelled by the simpler eaction stepsp resented in Scheme 2.
The slow MDAP 2 + egression probably arises from the substantiala ctivation enthalpy of the process. The guests bearing double positive charges are usually more strongly boundi n CB7 than the singly chargedo nes because of their enhanced electrostatic interactions with the electron-rich oxygen atoms at the portalso ft he host. [1c, d, 24] In addition, the passage of large MDAP 2 + through the CB7 portali se xpectedt ob es terically hindered. [23] In general, we believe that salt-insensitivedissociationk inetics are expected for doubly charged guests with symmetric chargel ocalisation near the CBn portals, while for singly or uncharged guests,d ifferent mechanisms (e.g.,t ernary-complex formation;s ee below for berberine) may occur depending on the type and concentrationo fi norganic cations present.
B + + exit from its CB7 complex is stronglydependent on the type and concentration of cations In contrastt oM DAP 2 + ,t he alkaloid berberine (B + )i ss ingly positivelyc harged with ac harged elocalisation near one end of the molecule. Besides, the calculated complex structure with CB7 indicates ah ighly non-symmetric complex geometry, which suggests that one CB7 portal area may be available for simultaneous M n + binding. [19c] B + is ap articularly advantageous guest compound for mechanistic studies because it has negligible emission in water but is highly fluorescenti nt he cavity of CB7. [19c] Hence, the variation of its fluorescencei ntensity directly reflects changes in the concentration of CB7-bound B + .T og ain insightinto the reactionsteps leading to inclusion-complex dissociation in the presence of salts, we selectively monitored B + egression from CB7b yt he k out method. [22] As ar epresentative example, Figure1 shows the fluorescence intensity decrease at 505 nm in the equimolar solutiono fB + and CB7 after mixing with AH + solutionint he presence of various CaCl 2 concentrations. Because of the dilution,afraction of B + -CB7 complex dissociated and AH + quickly occupied the cavity of free CB7. Thereby,t he back-formation of B + -CB7 was essentially irreversibly blockeda nd the exponentialf luorescence intensity decays showed re-establishment of the equilibrium by diminution of the B + -CB7 concentration.T he fit of the stopped-flow traces ( Figure 1) with an exponential function provided the apparent rate constants of B + exit from CB7 (k out ). When the amount of Ca 2 + was increased, the incipient fluorescenceintensity decreased because the competitive association of Ca 2 + with CB7 interfered with B + inclusion.As imilar effect was found in the presence of Li + and Mg 2 + cations. Figure 2s hows that k out increases and reaches ap lateaua t high M n + concentrations.T his phenomenon is due to the associationo fc ations with the B + -CB7 complex. Subsequently,B + dissociates faster from the produced ternary complex (B + -CB7-M n + ). As the fraction of B + -CB7-M n + grows, the apparentr ate constants gradually increasea nd the changes level off at high cation concentrations at which the ternary complex dominates.
To uncover whether also the type of anion affects the kinetics and mechanism of B + dissociation from CB7, measurements were carriedo ut in variousp otassium salt solutions. Changing the anion modified the kinetic traces only to an egligible extent, and the calculated parameters agreedw ithin the limit of experimental errors (Table 2). This observation also indicates that ionic strengthd oes not influence B + release, because otherwised ifferent resultsw ould be expected in the solutionc ontainingd oubly charged SO 4 2À than in the presence of singly chargedC l À and NO 3 À anions.  Scheme2.Mechanism of MDAP 2 + release from CB7.
Chem.E ur.J.2020, 26,7433 -7441 www.chemeurj.org In view of the cation-dependentb ut anion-independentd issociationk inetics, we therefore proposeacomposite mechanism of B + releasef rom its CB7 complex, that is, ac ombination of both of the usual competitive binding mechanisms (as also found for MDAP 2 + ,s ee above) and the new ternary-complex-based dissociation pathway from the simultaneously present B + -CB7-M n + complexes (Scheme 3).
For testingo ur mechanistic hypothesis, the equilibrium constant of B + -CB7-M n + formation K BCM and the rate constant of B + exit from the ternary complex k out (BCM)w ere determined by fitting the experimental data to Equation (1), which models the cation-dependent ternary-complex-basedd issociation pathway (see the Supporting Information for the derivationo f the mathematical expression).
where, k out (BC) is the rate constant of B + -CB7 dissociation measured in the absence of salts (0.81 AE 0.08 s À1 )a nd b/a the relative fluorescencey ield of B + -CB7-M n + and B + -CB7 at the detection wavelength (505 nm).
To determine the latter quantity,t he fluorescence-intensity variation was measured upon gradual addition of M n + to B + -CB7 solution in steady-state titrations. In these experiments, we used 0.020 mm B + and 1mm CB7 concentrationst o ensure total complexation of B + and to facilitate B + -CB7-M n + formation.T he samples were excited at 420 nm, at whicht he molar absorption coefficient of B + -CB7 is relatively low (e = 5300 m À1 cm À1 ), to prevent inner-filter effects. As at ypical example,F igure 3s hows the fluorescence intensities at various  [a] In water. [25] [b] From fluorescenced isplacement titration. [7] [c]Average of the resultso ff luorescence displacementt itration and isothermal titration calorimetry experiments. [7] [d] By isothermal titrationc alorimetry. [7] [e] This reactions tep does not take place.
Ca 2 + concentrations. Initially,t he intensity remains constant because Ca 2 + has moderate binding affinity to B + -CB7. The intensity decreasea bove 3mm Ca 2 + concentration is attributed to transformation of B + -CB7 into the more weakly emitting B + -CB7-Ca 2 + .A bove approximately 6mm Ca 2 + ,t hat is, when B + -CB7 is fully converted to the more weakly emitting B + -CB7-Ca 2 + ,t he fluorescencei ntensity levels off and the emission is assigned to B + -CB7-Ca 2 + .T he 50-foldl arger total amount of CB7 compared with that of B + guarantees that free CB7 remains in large excess and, as ac onsequence, the concomitantf ormationo fC B7-Ca 2 + complex does not induce B + releasei nt he appliedC a 2 + concentration range. Indeed,c omputer modelling calculations showed (TableS1i nt he Supporting Information) that competitive binding of Ca 2 + to CB7 causes negligible change in B + concentrations and less than 0.14 %o ft he total B + amount is free under the conditions of our study.T he ratio of the intensities at the plateau and the initial ranges of Figure 3g ives the b/a parameter of Equation (1). Other cations bring abouts imilar behaviour to that shown in Figure 3, and the derived b/a values are practically constant within the limit of experimental errors ( Table 2). The results shown in Figure 2w ere analysed by using Equation (1) with b/a values. Ta ble 2s ummarises the calculated K BCM and k out (BCM) parameters. The metal-cation radii in water [25] and the equilibrium constants of 1:1b inding of M n + to CB7 K CM are also included. The mechanism observed with Li + ,M g 2 + andC a 2 + cations also prevails at low K + or Ba 2 + concentrationsw hen B + -CB7 dominates. The red lines in Figure 4r epresent the results of the nonlinear least-squares fit of Equation (1) to the experimental data measured at the low cation amounts. The calculated equilibrium constants for B + -CB7-M n + formation K BCM and the rate constants of the unimolecular dissociation of B + from the ternary complexes k out (BCM) match the trend found with smaller cations ( Table 2). The former quantity significantly varies, whereas less then twofoldc hange is found in k out (BCM). Despitet he similarr adii of K + and Ba 2 + ,t he latter ion produces am ore stable ternary complex because of its higher positive charge.
Similarly,t he affinity of CBn-M n + complexes increases with increasing net chargeo ft he cation due to increased iondipole interaction with the carbonyl-fringed portalso ft he CBn macrocycles (see Table 2a nd ref. [7]) Likewise, despite the barely different sizes of Li + and Mg 2 + ,amuch highera ssociation strength K BCM was found for the doubly-charged Mg 2 + . The binding affinity to B + -CB7 complex considerably increases with increasing size of the cation in the series Mg 2 + < Ca 2 + < Ba 2 + .S uch an effect also appears for K + comparedw ith Li + , for which more than one order of magnitude differencei s found in K BCM .
Remarkably different, new kineticf eatures appeared at high K + and Ba 2 + concentrationsw hen B + -CB7-M n + outweighed B + -CB7 (Figure 4). Under these conditions, the apparent rate constant of B + egression did not level off but linearly increased,w hich implies that large cations reacted with B + -CB7-M n + in ab imolecular process. This is the first case in which such ab imolecular substitution mechanism wasc learly demonstrated in the guest exchange of cucurbiturils. The motion of M n + toward ternary complex B + -CB7-M n + is probably coupled with the displacement of B + from the host cavity and the production of M n + -CB7-M n + complex.T his reaction is akin to the S E 2t ype of electrophilic substitution in organic chemistry,i nw hich the formationo ft he new bond and the breaking of the old bond take place simultaneously via a single transition state. The optimal size of M n + is important, because cationsw ith radius of approximately 100 pm or smaller appear unable to participate in such ap rocess, whereas organic cations aret oo big and usually have delocalised charge, which makes this type of reaction unfavourable. From the linear contribution of the dependence of k out on M n + concentration,anapproximately 20-fold larger rate constant is derived  for bimolecular B + removal by Ba 2 + than by K + (k out (BCMM) in Ta ble 2). Because of its double positive charge, the former ion more efficiently promotes the expulsion of B + .
To gain information on the relative importance of the dissociation pathways via ternary complex formation compared with the decomplexation due to the competitive binding of M n + to CB7, we calculated how the concentrationo ft he speciesp articipating in equilibria and the [B + -CB7-M n + ]/ [CB7-M n + ]m olar ratio changes with the total amounto ft he constituents and the type of M n + .W ef ocusedo nt he salt concentration range in which M n + -CB7-M n + formation does not play an important role. Derivation of the formulas is shown in the Supporting Information. The K BCM values were taken from Ta ble 2a nd the previously published equilibrium constants were used for the association of metal cations [7] and berberine [26] with CB7. As ar epresentative example, Figure 5s hows the calculated relationship between the concentration of the components andt he total Ca 2 + concentrationi ne quimolar B + and CB7 solution. The same total host and guest concentrations were employed as in the measurement of the data plotted in Figure 2C ([B + ] total = [CB7] total = 0.25 mm). In the absence of salt, 66 %o ft he guest is complexed. When Ca 2 + concentration is raised,t he amounto fC B7-M n + steeply grows at the expense of B + and B + -CB7. Less than 12 %o f[ B + ] total is converted to B + -CB7-Ca 2 + in such dilute solution.A sam easure of the relative importance of ternary-complex formation compared with competitive associationw ith CB7, we chose the ratio of B + -CB7-M n + and CB7-M n + concentrations( [BCM]/ [CM]). Figure 6s hows this quantity as af unctiono fM n + concentration in equimolar B + and CB7 solutions. As expected, [BCM]/[CM] considerably grows with increasing total concentration of the constituents, but the smallest increasea ppears in Ba 2 + solutions because the affinities of this cation to CB7 and B + -CB7 differ the most (Table 2). In 4 mm B + and CB7 solution, 1.6 mm Ca 2 + or 5.6 mm K + concentration is enough to outweigh the competitive bindingo fM n + to CB7 by ternarycomplexf ormation. Above these concentrationsB + release from ternary complex B + -CB7-M n + dominates over indirect decomplexation of B + -CB7 through competitive CB7-M n + formation.
Association to form guest-CB7-M n + ternary complexes has been suggested, [15, 18-, 19c, 27] but neither their binding constants nor the effect of M n + variation on the rate constants of the dissociation pathways has been revealed. Previous fluorescencelifetimem easurements showedt ernary-complex formation of B + -CB7 with Na + or 1-butyl-3-methylimidazolium cation. [19c] Kinetic studies on the CB6 complex of 4-methylbenzylammonium implied that not only competitive binding of K + occurred, but also the ternary complex was produced. [27] Association of cyclohexylmethylammonium-CB6 inclusionc omplex with Na + was taken into account in the analysis of the salt-concentration dependence of the apparent binding constants. [15] The CB7 complex of the ditopic N-phenyl-2-naphthylammonium was able to coordinate Na + cation only if the phenyl moiety of the guest was embedded in the hostc avity,a nd 51 AE 2s À1 was reported for the rate constant of guest release. [18] This is about an order of magnitude larger than the corresponding k out (BCM) values found for B + -CB7-M n + dissociation. In the latter case, the exit probably has ah ighera ctivation enthalpy.P revious studies demonstrated that the passage of B + through the tight CB7 portal requires structural deformation of hosta nd guest. [26,28] The releaseo ft he much smaller phenylg roup is sterically less hindered and can occur withoutb uild-up of steric/conformational strain.  MDAP 2 + + inclusion into the CB7 cavity is competitively slowed down by CB7-portal-bound M n + + cations To revealt he salt effect on k in ,e quimolar solutions of MDAP 2 + and CB7 (5 mm at t = 0s)w ere mixed and the rise of the fluorescencei ntensityw as recorded at 454 nm at various Ca(NO 3 ) 2 or Ba(NO 3 ) 2 concentrations. Ar epresentative kinetic profile is shown in Figure S2 bi nt he Supporting Information. Figure 7 shows the considerable decrease of k in with increasing salt concentration. The findings are attributedt ol essening of the amount of unboundC B7 stemming from its competitive association with one or two M n + .
In general, M n + cations associate with CB7 to form CB7-M n + and (potentially also) M n + -CB7-M n + complexes. [7, 17, 20c] These processes reduce the amount of free CB7 andc onsequently, decelerate the bimolecular guest ingressioni nto CB7. (In a simple pictorial model, the bound cations can be considered to be lids closingt he CBn portals. [9,29] )I ft he guest-CB7-M n + ternary complex is not produced and [CB7] ! [M n + ], then the variation of k in is expected to follow Equation (2): where the rate constant of guest encapsulationi nt he absence of salt k 0 in is multiplied by the fraction of free CB7 at total metal cation concentration [M n + ]a nd K CM and K MCM are the equilibrium constants of CB7-M n + and M n + -CB7-M n + formation, respectively.T he coordination of the second M n + to CB7-M n + has asmall binding constant due to electrostatic repulsion (e.g., K MCM = 11 m À1 was reported for Na + cation). [19c] Hence, M n + -CB7-M n + is not expected to playa ni mportant role at the concentrations used in the determination of k in .I ndeed, Equation (2) provides ag ood rationale for "mechanistically simple" MDAP 2 + guest inclusion. The best fits of the experimental results with Equation (2) provided K CM = 17 000 m À1 and K MCM = 0 m À1 for Ca 2 + ,w hereas 65 000 and 150 m À1 were found for the binding constants of CB7-Ba 2 + and Ba 2 + -CB7-Ba 2 + production. The obtained K MCM data can be considered estimates, because the quality of the fit is not sensitive to these values. The K CM values are in accordance with the previously published results. [7] The good agreement of the experimental data with the calculated curves in Figure7 and the reasonable values of the derived parameters confirm that ternary complex MDAP 2 + -CB7-M n + is not produced. The salt effect on the rate of MDAP 2 + ingression into CB7 stems from the competitive binding of M n + to the host.
B + + inclusion occursboth into free CB7 and into the CB7-M n + + complex To unravel how formation of the ternary complex B + -CB7-M n + and the competitive bindingo fM n + cationst oC B7 modify the apparent rate constant of B + encapsulation k in ,fluorescenceintensity versus time traces werer ecorded after rapid mixing of equimolar (0.25 or 0.5 mm at t = 0s)B + and CB7 solutionsi n the presence of different amount of salts. Figure S3 in the Supporting Information shows representative results obtained in CaCl 2 solutions. The initial slope of the signals decreasesw ith increasing Ca 2 + concentration, and this indicates deceleration of B + capture.T he concomitant lessening of the fluorescence intensity in the equilibrium arises from the combined effects of the diminution of the amount of B + -CB7a nd the formation of the more weakly emitting B + -CB7-M n + complex.T he analysis of the kinetic results provided the k in values presented in Figure 8a nd Ta ble S2 in the Supporting Information. For the system of CB7 and B + ,s ubstantial deviation of the experimental data from the trend predicted by Equation (2) is clearly found (see Figure 8), which points again to a" rich" complex formation/dissociation mechanism for this host-guest complex. From this, we can concludet hat the salt effect on k in cannotb er ationalised by the simple competitive binding of M n + to CB7. In line with the mechanisticp ictures derived for B + egression from CB7 and according to the principle of microscopicreversibility,the deviation between the experimentally determined ingression rates and the theoretical trends predicted by Equation (2) suggest that B + enters not only free CB7 but also the cavity of CB7-M n + .T he latter reaction has probablyasmaller rate constant because the CB7-bound M n + sterically and electrostatically hinders the ingression of the cationic guest, but it cannotb ei gnored, because the rate and contribution of the process grows upon gradual addition of M n + due to the rising CB7-M n + concentration.

Conclusion
Selectivem easuremento ft he overall rate constant of inclusion-complex dissociation k out can shed light on subtle mechanistic details of the salt effect that would remaine lusive in the generally conducted kinetic studies on guest ingressioni nto a host. The separate determination of k out is particularly beneficial because 1) it is not influenced by competitive association of the metal cations with CB7, 2) highera ccuracy can be achieved, and 3) ternary guest-host-M n + complexf ormation can be easily proved. The knowledge of k out in aw ide range of salt concentration is essential, not only to distinguish the bimolecular replacement of CB7-bound guest by M n + from the unimolecular guest releasef rom guest-host-M n + ,b ut also to discern the bimolecular expulsion of guest from such at ernary complex. The peculiar exitm echanism of B + revealed in the present study may also be expected for neutral guests or for monocationic guests having highly delocalised chargea nd an extendeda romatic ring system.The CB7 complex of such compounds mayb ep rone to forming at ernary complex with metal cations. Voluminous, multiply charged cations exhibit higher affinity to inclusion complexes and expelg uests more efficiently from the produced ternary complex in ab imolecular reaction. If salt-concentration-independente gression rate is favoured in an application of aC B7 complex, guests with multiple or localised chargem ay be ag ood choice. In fluorescence displacementa ssays, dilute host and guest solutionsa re pref-erable to minimise the effect of ternary complex production. The knowledge of the effect of metal cations on the kineticso f reversible host-guest binding may contribute to the rational design of salt-responsive systems. The properties of the dynamic networks in supramolecular polymerich ydrogels [30] could also be tuned by the addition of salts, and the control of the rate of host-guesta ssociation facilitates the adjustment of gelation kinetics.
Stopped-flow measurements of B + release from CB7 were performed with an Applied Photophysics RX2000 rapid mixing unit connected to aJ obin-Yvon Fluoromax-P photon-counting spectrofluorometer,w hereas the binding kinetics of MDAP 2 + -CB7 complex formation were studied with an SFA-20 rapid kinetic accessory with ap neumatic drive unit from HI-TECH Scientific connected to a Jasco FP-8300 fluorescence spectrometer equipped with a4 50 W xenon arc lamp, double-grating excitation and emission monochromators. Fluorescence spectra were recorded with the same spectrometers without using the kinetic accessory.A ll measurements were carried out at 298 K.
The rate constant of guest release from the CB7 cavity k out was determined by the previously reported method [22] using the competitive strong binding of 1-adamantylammonium cation (AH + )i nC B7. Due to its ideal size complementarity and rigidity,A H + has an extremely large association constant with CB7 (K = 1.7 10 14 m À1 ), which guarantees its very slow exit from the CB7 cavity. [32] Equimolar solutions of guest and CB7 were rapidly mixed in 1:1v olume ratio with AH + solution in the presence of various salt concentrations. To ensure that the bimolecular inclusion was much faster for AH + than for the guest, AH + was employed in at least 20-fold excess. As an indication of the negligible back-formation of guest-CB7 complex after dissociation, we always checked that further increase of the [AH + ]/[guest] molar ratio did not modify the derived k out values. B + release was examined at total concentrations of [B + ] T = [CB7] T = 0.25 mm and [AH + ] T = 5 mm at t = 0s.T he excitation and monitoring occurred at 345 and 505 nm, respectively.M DAP 2 + exit from CB7 was studied at [MDAP 2 + ] T = [CB7] T = 5 mm and [AH + ] T = 300 mm at t = 0s.T he excitation and monitoring took place at 339 and 454 nm, respectively.T he rate constants of ingression were measured by monitoring the fluorescence intensity change after 1:1m ixing of equimolar guest and CB7 solutions in the presence of various amounts of salts. Typical reactant concentrations at t = 0swere 0.5 and 5 mm.F luorescence monitoring was carried out 505 and 454 nm for B + and MDAP 2 + inclusion, respectively.T he experimental data were fitted to the numerical solution of ad ifferential equation describing the time dependence of the Figure 8. Comparison of the measured k in rate constants( squares)w ith the values calculated if only competitiveb inding of M n + to CB7 takes placea nd the B + -CB7-M n + ternary complexi sn ot produced (lines). The lines corre-spondstoK CM = 2400, 14 000 and 1740 m À1 for 1:1a ssociation of K + ,Ca 2 + and Mg 2 + ,respectively, [7] and K MCM = 0 m À1 . fluorescence intensity to calculate the rate constant of inclusion k in while keeping the separately determined k out values constant.