Arresting “Loose Bolt” Internal Conversion from −B(OH)2 Groups is the

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Arresting “Loose Bolt” Internal Conversion from –B(OH)2 Groups is the Mechanism for Emission Turn-On in orthoAminomethylphenylboronic Acid-Based Saccharide Sensors Xiaolong Sun, Tony D. James, and Eric Van Anslyn J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b12877 • Publication Date (Web): 23 Jan 2018 Downloaded from http://pubs.acs.org on January 23, 2018

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Journal of the American Chemical Society

Arresting “Loose Bolt” Internal Conversion from –B(OH)2 Groups is the Mechanism for Emission Turn-On in orthoAminomethylphenylboronic Acid-Based Saccharide Sensors Xiaolong Sun,† Tony D. James,*,‡ and Eric V. Anslyn*,† †

Department of Chemistry, University of Texas at Austin, Austin, Texas, 78712, United States



Department of Chemistry, University of Bath, Bath, BA2 7AY, United Kingdom

ABSTRACT: Different mechanisms for the emission turn-on of ortho-aminomethylphenylboronic acids with appended fluorophores in response to saccharide binding in aqueous media have been postulated, such as photo-induced electron transfer (PET), “pKa switch”, and disaggregation. However, none of the hypotheses is consistent with all the data for boronic acid-based sensors. To create a unifying theory that can explain the data, we performed a series of experiments to explore the origin of the emission turn-on with several boronic-acid based sensors upon binding fructose. First, we showed that the receptors and their complexes with fructose are solvent-inserted, with no B-N interactions. Second, we verified that the sensors are not aggregated. Third, in pure methanol, that exchanges -B(OH)2 to –B(OMe)2 groups, we found no fluorescence response upon binding fructose. We propose this occurs via lessening of internal conversion mechanisms. To investigate this proposal further, we performed a solvent isotope effect study. The fluorescence of the probes in D2O (-B(OH)2 → -B(OD)2) does not change upon fructose binding. It is well accepted that -OD oscillators are less efficient energy acceptors due to their lower frequency vibrational modes. Thus, our studies reveal that modulating the B(OH)2-induced internal conversion (an example of a “loose bolt effect’) explains how potentially all orthoaminomethylphenylboronic acid-based fluorescence sensors signal the presence of sugars.

INTRODUCTION Boronic acids groups are the most common functionalities introduced into unnatural receptors to ensure some degree of vicinal diol, catechol, or α-hydroxy carboxylate binding in water.1,2 Thus, they are the most-commonly used functional groups in fluorescent saccharide sensing.3 In these sensors, it is critical to have an aminomethyl group ortho to the boronic acid,4,5 or electron withdrawing groups,6,7 in order for the boronic acid to bind the aforementioned functional groups near neutral pH in protic media. The paradigmatic sugar sensors arose from Shinkai’s group,4 and one prominent example is compound 1 (Figure 1). Since the inception of these sensors, many other groups have incorporated oaminomethylphenylboronic acids into a variety of chemical designs to improve affinity, tune selectivity, increase quantum yield, and/or modulate the wavelength of emission.8-10 The mechanism by which the fluorescence turns on in this class of sensors has been debated. Originally, a PET mechanism was proposed based on a modulation of the strength of a Lewis-acid/base interaction between the boronic acid/boronate ester with the nitrogen lone pair on the o-aminomethyl group (Scheme 1A).4,5,11 An alternative mechanism was proposed involving a switch between a B-N Lewis interaction in the boronic acid to a solvent insertion upon diol binding, referred to as a “pKa-switch” mechanism (Scheme 1B).12,13 Our group subsequently showed that both boronic acids and boronate esters are

predominately solvent inserted.10,14 Thus, neither of these mechanisms can be correct. Therefore, we undertook a detailed study of the photophysics of compound 1.15 OH HO

B

OH

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Figure 1. Structures of ortho-aminomethylphenylboronic acid-based saccharide sensors 1 and 2.

In his their original studies, using a pH titration of receptor 1 with and without fructose, Shinkai and James reported an approximate 30 to 40-fold turn-on response in 2:1 water/methanol with 50 mM NaCl solution.4 This result was among many that demonstrated these types of sensors were a revolutionary discovery. Of the 30- to 40fold turn-on of 1, we recently reported that 10- to 15-fold of this turn-on results from a disaggregation phenomenon, simply due to the presence of fructose in solution (Scheme 1C).15 Importantly, however, this same study revealed that an additional 2- to 3-fold turn-on resulted directly from fructose binding. The literature reveals that the turn-on from o-aminomethylphenylboronic acidbased fluorescence sensors is usually in this range, i.e. 2 to 5-fold.9,16-20

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Journal of the American Chemical Society However, the chemical phenomenon resulting in this 2-5 fold turn-on was not delineated in our earlier study, and hence further exploration was needed. Thus, we intentionally sought a sensor that is highly water soluble, thereby removing any complication from aggregation. For these purposes we chose receptor 2, which James has recently used for the detection of peroxynitrite.21-23 Albeit possessing a large planar aromatic core, it is decorated with imide solubilizing functionality and a short PEG chain. Described herein are a series of experiments leading to the conclusion that non-radiative decay pathways from the –B(OH)2 group lead to internal conversion (a “loose bolt effect’) which is arrested when boronate esters are formed, thereby turning the fluorescence on upon sugar binding (Scheme 2). (A)

cessfully employed as DNA targeting, anticancer and cellular imaging agents.24,25 Due to their excellent photophysical and photochemical properties, N-substituted-1,8naphthalimides are widely used as D–π–A chromophores in the design of fluorescent probes.26 80000 2 only 2 plus Fructose

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Figure 2. Fluorescence pH titration for boronic acid probe 2 (4 µM) (circles) and 2 with fructose complex (2: 4 µM; Fructose: 100 mM) (squares) in water. pH of the solution was adjusted by sodium hydroxide (1 N) and hydrogen chloride (1 o N). Ex = 450 nm, slit/slit: 2 nm/2 nm, at 25 C.

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Scheme 1. (A) Change in the strength of an N−B bonding interaction upon sugar binding; (B) Breaking of an N−B bond and insertion of solvent upon sugar binding; (C) Aggregation and disaggregation with solvent insertion.

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Scheme 2. Fluorescence change of probe 2 in the absence and presence of fructose.

RESULTS AND DISCUSSION pH Studies As alluded to above, compound 2 is composed of an oaminomethylphenylboronic acid as the receptor and a 4amino-1,8-naphthalimide, functionalized with 2-(2aminoethoxy)ethanol, as a reporter.21 Functional Nsubstituted-1,8-naphthalimide derivatives have been suc-

The first step was to confirm the binding of fructose with a pH titration in the same manner as was used to reveal the emission turn-on of 1.16 Importantly, in the pH range between 7 and 10 (Figure 2), the fluorescence is considerably greater in the presence of fructose, and the maximum turn-on response is approximately 3.0-fold; in the range found for similar compounds.4,11,15 This confirms both fructose binding and emission turn-on. The other pH ranges reveal additional aspects of the emission modulation. In the pH range between 2 and 5.5, a strong fluorescence is observed for 2 with and without fructose. In this pH range, the R-B(OH)2 group is trigonal planar, and it is known there is little to no sugar binding at pHs below the pKa’s of boronic acids.10,27 As the first pKa of the boronic acid (i.e. hydroxylation of the boron, Scheme 3) is approached by raising the pH, an anionic boronate (R-B(OH3)-) is created without the presence of fructose, and the fluorescence turns off for reasons we discuss below. In the presence of fructose, a 2-fructose complex is formed within the conditions of pHs 6-11. Interestingly, in the presence of fructose, there is a reproducible bump in the titration in the range of pH 5.5, which was also found in the titration of 1.4,11,15 At pHs around the first pKa, fructose binds to varying extents (no binding below this pKa and full binding above this pKa). Thus, the pH titration reveals slight fluorescence differences of intermediate boronic acid/boronate ester species involving unbound, partially bound, and fully bound fructose. At pHs above 10.0, both the fluorescence of 2 and the 2-fructose complex drop owing to an expected Photoinduced Electron Transfer (PET) from an amine lonepair through deprotonation of the ammonium (pKa2, Scheme 3). It should be noted that while the amine lone

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Journal of the American Chemical Society pair is typically considered the source of the PET quenching, Czarnik has reported that boronate anions created upon sugar binding, when missing the o-aminomethyl group, can also PET quench.28 In this study, we focus on the pH range between 7-9, where boronic acid-saccharide sensors possessing o-aminomethyl groups have been proven most effective.

O

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water that facilitates B-N bonds,13,31 this interaction is not found (Figure 4). Because the structure derived from acidic water has the amine protonated, there is a trifluoroacetate counterion in the unit cell.

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Scheme 3. Different pKa for probe 2 with the changing of the pH, referring to Figure 2.

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Structural Analysis Next, we moved to confirm the boron hybridization and solvent insertion as a function of pH (Scheme 2). In a series of earlier papers,29,30 we reported the chemical shifts for trigonal planar boronic acids (28-30 ppm) and tetrahedral solvent-inserted boronic acids or boronate esters (8-12 ppm), while any B-N dative bonds resonate between 14-16 ppm. With these shifts in mind, 11B-NMR spectra of 50 mM probe 2 were carried out in D2O and CD3OD at 27 °C. At a pH below 3, a peak at 30 ppm (Figure S1) was found, which is indicative of trigonal-planar boron. The chemical shift of probe 2 (50 mM) was approximately 10.6 ppm in neutral D2O (Figure 3A), which is indicative of a tetrahedral solvent-inserted boronate anion. Increasing addition of fructose (300 – 500 mM) hardly led to a signal change, but showed that the boron retains a tetrahedral geometry. Similarly, probe 2 gave a broad boron peak at 9.0 ppm in CD3OD in the absence of fructose, but continuous addition of fructose led to a sharper signal at 11 ppm (Figure 3B), revealing a tricoordinate boronate anion fructose complex. Therefore, in the neutral pH region (pH 710) of the titration (Fig 2.), the structure of the boronic acid in 2 is tetrahedral with a tricoordinate fructose (analogous to solvent insertion with a bidentate sugar), consistent with previously reported oaminomethylphenylboronic acids.15,29 As with our other studies, no B-N bonding interactions are found in either the boronic acid or boronate esters, and thus PET quenching or “pKa switch” mechanisms are not operative. While not successful in growing crystals of 2 in the neutral pH range of the titration, we were successful at pHs below 3. Single-crystal X-ray crystallographic studies for 2 grown from either acetonitrile or water (Figure 4) show that 2 has a trigonal planar boronic acid in the solid state, as revealed from the 11B-NMR spectra. Even when the crystal was grown from acetonitrile, rather than acidic

b.

a.

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Figure 3. B NMR for titration of probe 2 with fructose in D2O (A) and CD3OD (B). (a) Probe 2 (50 mM); (b) probe 2 (50 mM) + Fructose (300 mM); (c) probe 2 (50 mM) + Fructose (500 mM). The peak at 18.5 ppm in B-a. is a borax impurity commonly arising from the synthesis or contamination in the starting materials. (i) (ii)

Figure 4. Crystal structure of 2 grown from acetonitrile (i) and water (ii) in acidic conditions. Pink balls represent boron atoms and red balls represent oxygens (see Supporting Information).

Spectroscopy Fluorescence spectroscopic studies were then employed to investigate the mechanism for turn-on emission of 2 (λabs = 440 nm, ε = 9500 M−1 cm−1) upon binding fructose. As anticipated, in water, there is a slightly larger than two-fold fluorescence increase for probe 2 (4 µM) with addition of fructose (0 – 0.1 M) in a dose-dependent manner (Figure 5). The resulting isotherm saturates with in-

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Journal of the American Chemical Society creasing fructose, and a one-to-one binding isotherm resulted in an association constant K = (1.3 ± 0.16) × 102 M−1 (Figure 6), slightly lower than other similar boronic acids.15,19 Gratifyingly, the emission values at this pH with and without fructose are nearly identical to the values at pH 7.4 found during the pH titration (Figure 2 and Figure S2). (A)

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Figure 5. Fluorescence titration for boronic acid probe 2 (4 µM) with fructose (0 – 0.1 M) in pure water (A) (pH 7.4) and pure methanol (B). Inserted figure in (A) is a magnification of the 700-1000 nm region. Ex = 450 nm, slit/slit: 2 nm/2 nm, o at 25 C.

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Figure 6. Binding affinity between boronic acid 2 and fructose based on change in fluorescence at 530 nm plotted against the concentration of fructose and fitted to a one-toone binding curve.

Moreover, unlike compound 1 where an excimer was found via an emission at long wavelengths, indicating aggregation,15 no emission could be observed for 2 before or after addition of fructose in the 700-1000 nm region (insert, Figure 5A). This confirms that 2 is not aggregated under the experimental conditions. In our evaluation of compound 1,15 to further investigate its aggregation, we contrasted its behavior with an analogue missing the boronic acid. In a titration with fructose, the behavior of the sans boronic-acid analogue of 1 and 1 itself was nearly identical. This was used as evidence that the mere presence of fructose in solution causes disaggregation of com-

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pounds similar to 1. However, an analogue of 2 missing the boronic acid (3) does not show any change in fluorescence upon titration with fructose. Figure S4 shows the lack of response of 3 to the addition of fructose in methanol or water, as may be anticipated because this compound is not aggregated, and because it lacks a boronic acid to bind the sugar.

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However, most telling, the performance of probe 2 (4 µM) is entirely different upon fructose (0 – 0.1 M) addition in pure methanol (Figure 5B) as compared to water. The fluorescence starts at a much higher value and hardly changes upon the binding of fructose. However, the 11B NMR studies on 2 revealed a 2 ppm change, indicating binding indeed occurs between probe 2 and fructose in methanol (Figure 3B). This is the same phenomenon we previously reported for compound 1, which indicated that 1 is not aggregated in methanol. Given that compound 2 is neither aggregated in water or methanol, but it shows a turn-on of emission towards fructose in water, which is entirely missing in methanol, a fundamental question arises that we believe is the key to how o-aminomethylphenylboronic acids appended to fluorophores routinely show a 2 to 5-fold fluorescence turn-on when binding sugars in water – “What is fundamentally different about the structure of 1 or 2 in water and in methanol?” Scheme 2 and Scheme 4 show the structures of 2 in water and methanol, respectively. Of course, there are many differences to consider. One would be the extent to which the compound is folded on itself due to hydrophobic collapse. Further, the strength of interactions with the inserted solvent in the boronate anion (water inserted) or boronate ester (methanol inserted) is expected to be subtly different, i.e. the Lewis coordination of O-H vs O-Me to boron, as well as the extent of amine protonation from the solvent, must differ to some degree. But, there is one obvious difference - the B-OH groups are replaced with BOMe groups. The fact that the replacement of B-OMe groups in both 1 and 2 with B-OR groups (where R denotes a sugar) does not change the fluorescence, yet the replacement of B-OH groups with B-OR groups in water does turn-on the emission, is key to the puzzle. It is well recognized that water, as a solvent, acts to quench fluorescence by accepting electronic excitation energy into vibrational states, leading to non-radiative decay pathways.32 As anticipated, both compounds 1 and 2 show lower fluorescence in water than in methanol. The finding that the overall quantum yield of emission of 1 and 2 is significantly higher in methanol is consistent with the common solvatochromic behavior of fluorophores.32-34 Similarly, one might anticipate that high frequency vibrations in the –B(OH)3- group, i.e. an internal conversion

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Journal of the American Chemical Society mechanism commonly referred to as the “Loose Bolt Effect” (Scheme 2), could play a similar role as water. Just as a loose bolt can absorb energy from a running motor via vibrating and further loosening (or tightening), a highfrequency rotor in resonance with an electronic excited state can absorb energy. The loose bolt theory35,36 thus states that flexible groups or substituents absorb energy, inducing nonradiative decay pathways to the ground state and quenching fluorescence.37 In our case, the proposal would be that the ‘‘loose bolt’’ enhances internal conversion because electronic energy ‘‘leaks out’’ through – B(OH)3- vibrations.38 When in methanol, the water induced quenching is significantly arrested, but so is any quenching from B-OH groups because they all exist as BOMe groups (Scheme 4). Such quenching by intramolecularly attached hydroxyls (R-OHs) has been reported in other cases.39,40 OH

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Figure 7. (A) Fluorescence spectra for boronic acid probe 2 (4 µM) in H2O and D2O. (B) Fluorescence titration for boronic acid probe 2 (4 µM) with fructose (0 – 0.26 M) in D2O. o Ex = 450 nm, slit/slit: 2 nm/2 nm, at 25 C.

Other Boronic Acid-Based Sensors

O N O

H 3C B O

internal conversion. Only when there is significant internal conversion from –B(OH)3- vibrations can there be emission turn-on upon converting to –B(OR)3- groups.

Fluorescence Intensity

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N H N

H

Scheme 4. Structure of probe 2 in methanol with -B(OH)2 methylated. “Loose bolt” fluorescence internal conversion was stopped due to formation of -B(OR)2 oscillators.

Armed with the theory that arresting the internal conversion of the fluorophores in 1 and 2 from -B(OH)3- vibrations by their conversion to -B(OR)3- (R being a methyl of methanol, or a sugar, or even a deuterium) is the mechanism by which emission turns on, we checked to see if this was a general phenomenon.

Solvent Isotope-Effect The most common method of analyzing quenching via –OH vibrations is to perform a solvent isotope effect, converting the –OH groups to –OD.32,34,41,42 It is well recognized that the lower energy of –OD’s vibrations are less efficient in energy transfer from excited states of fluorophores.43 Thus, to explore internal conversion in the modulation of fluorescence by -B(OH)3- vibrations, we simply repeated several of the experiments discussed above in D2O. There was an overall 2.5-fold fluorescence increase of probe 2 (4 µM) in D2O over H2O, and a 1.5-fold increase for analogue 3 (4 µM) in D2O over H2O (Figure 7A and Figure S5). Thus, quenching from the solvent is lower in D2O for both 2 and 3, but there is also an additional quenching arising from -B(OH)3- compared to B(OD)3- as revealed by the fact that 2 has a larger turn-on than 3. However, most telling, the addition of fructose (0 – 0.26 M) hardly affects the emission of 2 in D2O (Figure 7B). Clearly under conditions where we have shown binding in H2O with fructose is occurring, the same must occur in D2O, but there is no emission turn-on response. This is because in D2O, the -B(OD)3- vibrations are not as effective in internal conversion quenching as -B(OH)3vibrations, and the fluorescence change upon replacing – B(OD)3- with –B(OR)3- vibrations has a minimal effect on

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Fluorescent probe 4 was designed to be an analogue of the classic Shinkai boronic acid probe 1, but with an appended hexylamine to increase water solubility (see Supporting Information). Unlike compound 1, there is no excimer observed in an aqueous environment confirming no aggregation, and thus a disaggregation phenomenon for 4 is not operable (Figure 8 and S6). Fructose titration (0 – 0.16 M) to probe 4 (8 µM) in water revealed a 2.2-fold emission enhancement (Figure 8A). The isotope effect discussed above revealed an overall 1.9-fold fluorescence increase of probe 4 (8 µM) in D2O over H2O (Figure 8B). Yet, fructose (0 – 0.13 M) addition hardly affects the emission in D2O (Figure S7). While in methanol, probe 4 (8 µM) displayed a stronger emission than in water after conversion of -B(OH)3- vibrations to -B(OMe)3- vibrations, and addition of fructose again induced only a very slight fluorescence enhancement, likely due to residual water in the methanol (Figure S8).

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Figure 8. (A) Fluorescence titration of 4 (8 µM) with fructose (0 – 0.16 M) in water; (B) Fluorescence spectra for boronic acid probe 4 (8 µM) with -B(OH)3 vibrations by conversion to -B(OMe)3 , -B(OD)3 and -B(OR)3 , where R is fructose. Ex o = 368 nm, slit/slit: 2 nm/2 nm, at 25 C.

As a final test, we analyzed compound 5 bearing a pyrene fluorophore. In water, there is a five-fold fluorescence turn-on for probe 5 (8 µM) with the addition of fructose (0 – 0.2 M) in a dose-dependent manner (Figure 9A) resulting in an association constant K = 33 M−1 (Figure S9). The isotope effect test revealed an overall 5-fold fluorescence increase of probe 5 (8 µM) in D2O over H2O (Figure 9B), which indicated arresting of internal conversion after changing -B(OH)3- vibrations to -B(OD)3- vibrations. As expected, fructose (0 – 0.35 M) addition hardly affects the emission in D2O (Figure S10). Significantly, the probe 5-fructose complex displays an identical fluorescence intensity with -B(OD)3-, which supports our “Loose Bolt” internal conversion theory from the –B(OH)2 groups. Noticeably, 5 (8 µM) demonstrated a very weak fluorescence in methanol and fructose addition did not change the intensity (Figure S11). (A)

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transfer), and is a dynamic quenching mechanism.44 It is simply another term for vibrational coupling to an electronic excited state that leads to radiationless relaxation, i.e. internal conversion.45-53 On a Jablonski diagram the S1 to S0 transition is horizontal, where the ZPE (zero-point energy) of S1 transitions to an equal energy n-vibrational level of S0, followed by Kasha’s rule vibrational relaxation of S0. Because the probability of the transition depends upon vibrational overlap it is sensitive to any isotopic substitution in the molecules that modifies the vibrational frequencies involved, and this is the basis of the deuterium substitution experiment presented above.54 The solvent, of course, would be most effective in collisional energy transfer if there are vibrational modes that can accept the excited state energy, and water is particularly effective at such, while D2O is not. While such coupling is commonly to the solvent, it also occurs intramolecularly. Internal conversion is the most common mechanism of radiationless relaxation, and thus it is not too surprising that it can occur with synthetic chemosensors. This form of quenching is a short-range phenomenon that falls off exponentially with distance and depends on spatial overlap of donor and quencher molecular orbitals. In Dexter energy transfer, the dominant means of energy transfer is collision. The short distance that makes energy transfer happen is comparable to the collisional diameter. This is the reason why the exchange energy transfer is always referred to with the term “collision.”55 In the cases described herein, the B-OH rotors are 7 to 8 bonds away from the fluorophore. While this may seem too long a distance for the vibrational coupling discussed to occur with the fluorophore, we note that the deuteration experiment described herein seemingly can be explained in no other way. Hence, to understand this dichotomy, we turn to the crystal structure of 2, as well as that of 1 previously reported.15 In both cases the boronic acid resides over the top of the fluorophore, likely driven by solvophobic collapse.32-34 Further, the electronic excited state of the fluorophore will be more polarizable, leading to potential pi-pi attractive forces with the phenyl boronic acid. Thus, while water and alcohols (R-OH) are particularly effective at this form of quenching,32 our studies reveal that B-OH groups can play exactly the same role.

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Figure 9. (A) Fluorescence titration of 5 (8 µM) with fructose in water; (B) Fluorescence spectra for boronic acid probe 5 (8 µM) with -B(OH)3 vibrations by conversion to -B(OD)3 and B(OR)3 , where R is fructose. Ex = 350 nm, slit/slit: 2 nm/2 o nm, at 25 C.

The “loose bolt effect” is an example of Dexter energy transfer (also known as exchange or collisional energy

The PET or pKa switch mechanisms for explaining emission turn-on with 1 or 2 are not supported because both the boronic acid and sugar-boronate esters are entirely solvent inserted in protic media for both receptors. Further, compound 2 and analogous structures 4 and 5 are not aggregated. Thus, to explain the emission turn-on of the sensors in water upon fructose binding, a “loose bolt effect” internal conversion mechanism was postulated. In essence, -OH rotors of -B(OH)2 are functioning as energy acceptors while the fluorophore is the energy donor once excited. Upon replacing the hydroxyls with fructose or methyl groups from methanol, sugars, or even – OD groups, and therefore removing the -OH vibrational states, the internal conversion was suppressed. Apparent-

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Journal of the American Chemical Society ly, this is a general phenomenon for this class of sensors, in that we found consistent behavior for four sensors. We predict that this chemical phenomenon is general, and should be considered for all boronic-acid based sugar sensors.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b01755. Synthetic preparations, experimental procedures, and control experiments with figures (PDF) Crystal structure of compound 2 (CIF)

AUTHOR INFORMATION Corresponding Authors * [email protected] * [email protected]

ORCID Xiaolong Sun: 0000-0003-4003-6924 Tony D. James: 0000-0002-4095-2191 Eric V. Anslyn: 0000-0002-5137-8797

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT Steve Sorey and Angela Spangenberg are thanked for their help with NMR spectroscopy. We thank the National Science Foundation (grants CHE-1212971 and CHE 1665040) and E.V.A. additionally thanks the Welch Regents Chair (F-0046) for funding. T. D. J. wishes to thank the Royal Society for a Wolfson Research Merit Award as well as the EPSRC and University of Bath for support. A. Prasanna de Silva is thanked for helpful discussions.

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