Tuning the pKa of a pH Responsive Fluorophore and the

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Tuning the pKa of a pH Responsive Fluorophore and the Conse-quences for Calibration of Optical Sensors based on a Single Fluorophore but Multiple Receptors Christian Grundahl Frankær, Martin Rosenberg, Marco Santella, Kishwar J Hussain, Bo W. Laursen, and Thomas Just Sørensen ACS Sens., Just Accepted Manuscript • DOI: 10.1021/acssensors.9b00148 • Publication Date (Web): 14 Feb 2019 Downloaded from http://pubs.acs.org on February 16, 2019

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Tuning the pKa of a pH Responsive Fluorophore and the Consequences for Calibration of Optical Sensors based on a Single Fluorophore but Multiple Receptors Christian G. Frankær†‡*, Martin Rosenberg†, Marco Santella†, Kishwar J. Hussain‡, Bo W. Laursen†* and Thomas J. Sørensen†‡* †

Nano-Science Center & Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark ‡

FRS-systems ApS, Hovedgaden 20, 4621 Gadstrup, Denmark

KEYWORDS: pH responsive fluorescent probes, fluorescence, optical pH sensors, sensor calibration, triangulenium dyes ABSTRACT: Since Sørensen and Bjerrum defined the pH scale, we have relied on two methods for determining pH, the colorimetric or the electrochemical. For pH electrodes, calibration is easy as a linear response is observed in the interesting pH range from 1 to ~12. For colorimetric sensors, the response follows the sigmoidal Bjerrum diagram of an acid-base equilibrium. Thus, calibration of colorimetric sensors is more complex. Here, seven pH responsive fluorescent dyes based on the same diazaoxatriangulenium (DAOTA) fluorophore linked to varying receptor groups were prepared. Photoinduced electron transfer (PeT) quenching from appended aniline or phenol receptors generated the pH response of the DAOTA dyes, and the position of the pKa value of the dye was tuned using the Hammett relationship as guideline. The fluorescence intensity of the dyes in sol-gel matrix environment were measured as a function of pH in universal buffer, and it was found that the dyes behave as perfect pH responsive probes in these conditions. The response of optical pH sensors is non-linear and was found to be limited to 2-3 pH units for a precision of 0.01 pH unit. As sensors with a broader sensitivity range can be achieved by mixing multiple dyes with different pKa values, mixtures of dyes in solution were investigated, and a broad range pH sensor with a precision of 0.006 pH units over a range of 3.6 pH units was demonstrated. Further, approximating the sensor response as linear was considered, and a limiting precision for this approach was determined. As the responses of the pH responsive DAOTA dyes were found to be ideally sigmoidal and as the six dyes were shown to have pKa values scattered over a range from ~2 to ~9, this allows for design of a broad range optical pH sensor in the pH range from 1 to 10. This hypothesis was tested using quaternary mixtures of the different DAOTA dyes, and these were found to behave as a direct sum of the individual components. Thus, while linear calibration is limited to a precision of 0.02 in a range of 2-3 pH units, calibration using ideal sigmoidal functions is possible in the range of 1-10 with a precision better than 0.01, and as good as 0.002 pH units.

Sensing of chemical events using the optical response of dye molecules has been alluring since Sørensen defined colorimetric determination of pH.1, 2 Our ability to manipulate light and detect photons has made fluorescence the main workhorse of optical sensing, where the emission of a single molecule can communicate the concentration of an analyte in the local nanoenvironment.3-22 Some responsive fluorescent probes operate using an inherent ratiometric change in their absorption or emission spectra.2326 These are hard to create and modulate, and is limited to the inherent properties of the dye class. For instance, pH sensitive fluorescein derivatives have been made in excess, but they are all limited by fast photobleaching.27, 28 An alternative approach is to make a modular system, where the fluorescence of a dye is modulated by the state of a receptor.9, 29, 30 This receptor must be a quencher of the fluorophore either when it is bound to the analyte or when it is free.12, 15, 16 In this manner an on/off responsive fluorescent

probe can be made (Figure 1). Most examples use photoinduced electron transfer PeT quenching receptors, although several other design principles have been demonstrated.31 The weakness of this approach is that the readout is not ratiometric. This can be solved by adding a second decoupled fluorophore to the system or using the fluorescence lifetime as readout.32-37 The response of these fluorescent probes occurs as a simple equilibrium, and the readout change, as a function of analyte concentration, can be described as a simple sigmoidal (Figure 1). This has several implications if the responsive fluorophores are integrated in an optical chemosensor. Established i.e. electrochemical chemosensors have a linear response in a broad operational range (Figure 1). Thus, sensor calibration requires two parameters: the slope s, and the intersect b. For a sigmoidal response, four parameters are needed: the background signal y0, the span a, the

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system specific shape parameter, k, (which is the base of the exponential function, see below) and the center point, pK. For a sensor with ideal response, pK and k are known, but it has yet to be documented that these can be fixed in the calibration of an optical chemosensor. Thus, calibration of optical chemosensors has to take the full sigmoidal response into account.

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thesize and was further shown to have a reduced fluorescence quantum yield even when protonated. We use the ideal response of the other six DAOTA dyes to show that broad range colorimetric pH sensors can be made by using a mixture of dyes, and that calibration of the broad range sensor is feasible by either making a linear approximation (precision limited to 0.02), or by using a weighted sum of the sigmoidal functions (precision better than 0.01).

Figure 1. Basic design principle for responsive fluorescent dyes operating by photoinduced electron transfer (PeT) quenching from an electron donating unit that acts as electron donor and receptor for a given analyte. Insert: The response of a membrane based sensor (full) and response of a sensor based on a molecular recognition event (dashed). The background y0, the span a, and the center point pK of the molecular response are indicated.

The sigmoidal response implies that the operational range of the optical chemosensor is limited to 4/k or a range of 100 in analyte concentration.38-40 The operational range can be extended by using multiple responsive molecules, ideally created by affixing receptors with different affinity to the analyte to the same fluorophore.36, 41-47 For the sensor calibration, this implies that two or more sigmoidal functions now must be used, thereby multiplying the number of parameters that have to be determined with the number of dyes used. To determine how many parameters that can be locked when calibrating optical chemosensors, and how to implement the calibration for optical chemosensors, we prepared a series of seven pH responsive triangulenium fluorophores.8, 36, 48 Specifically, we prepared and characterized the series of aniline (4a) or phenol (4b-g) substituted diazaoxatriangulenium DAOTA dyes shown in Scheme 1. The dyes respond to pH as the anilinium and phenol moieties are efficient PeT quenchers only when deprotonated.36, 49 Thus at low pH, the DAOTA fluorescence is intense and at high pH the fluorescence is turned off. We found that the pKa values of the responsive dyes follows the Hammett relationship, and that the pH response of the dyes was close to ideal in aqueous media. While the majority of the compounds could be prepared in good yields, the nitrophenol substituted DAOTA dyes were difficult to syn-

Scheme 1. pH responsive DAOTA fluorophores. Native pKa values of the corresponding phenols and the Hammett parameters of the substituents are shown.50, 51

RESULTS AND DISCUSSION Fluorescent and pH responsive N-alkyl-N’-hydroxyphenyldiazaoxatriangulenium dyes have been prepared previously,36, 52 and the influence of the position of hydroxygroup on the optical properties has been discussed in detail elsewhere.53 Here, the objective was to design dyes with different pKa values. To do so, a series of substituted phenols was selected based on variation in native pKa of the corresponding phenol and the Hammett parameter of the substituent.50, 51 Scheme 1 shows the selected target molecules, assumed to have pKa values that span the pH range from 1-10.

Syntheses of the pH Responsive DAOTA dyes Several of the DAOTA dyes were prepared and characterized previously. N-methyl-N’-(4-aminophenyl)-diazaoxatriangulenium tetrafluoroborate (4a) was prepared en route to DAOTA-bioconjugates,54 while unsubstituted Nmethyl-N’-(2-hydroxyphenyl)-diazaoxatriangulenium hexafluorophosphate (4f) and N-methyl-N’-(3-hydroxyphenyl)-diazaoxatriangulenium hexafluorophosphate (4g) were made to study the effect of the triangulenium core on


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the phenol pKa.53 N-dodecyl-N’-(2-hydroxy-5-methylsulfonylphenyl)-diazaoxatriangulenium hexafluorophosphate (4c) and N-dodecyl-N’-(2-hydroxy-5-trifluoromethylphenyl)-diazaoxatriangulenium hexafluorophosphate (4d) were synthesized to make optical pH sensors.5557 The latter two were revisited here with N-methyl instead of N-dodecyl substituents. All synthetic procedures are available as Supporting Information. The syntheses follow the general synthesis of azaoxatriangulenium dyes shown in Scheme 2.53, 58, 59 The syntheses of the trifluoromethyl substituted derivatives 2d-4d and 2e-4e were obtained in yields similar to those reported for the non-substituted derivatives, when reacting 1 with a slight excess of the appropriate methoxytrifluoromethylaniline.53, 58-60 Under similar conditions, the preparation of nitro-substituted derivatives 4b and 4h proved more difficult. To form the acridinium salts 2b and 2h, longer reaction times were required to obtain full conversion of the tris(2,6-dimethoxyphenyl)methylium tetrafluoroborate (1) starting material. In addition, the purification of 2b and 2h proved to be challenging, due to the extensive formation of various byproduct. If the reaction between 1 and the nitro-substituted anilines was carried out in neat refluxing 2,6-lutidine as reported by Krebs,60 only a slight excess of the nitro substituted anilines were adequate to convert 1 into either 2b and 2h within 90 minutes reaction time. However, the subsequent purifications of 2b and 2h were still found to be difficult, mainly due to the formation of purple byproducts that hampered subsequent recrystallization and co-eluated with the desired product in chromatographic purifications. Using the latter strategy, 2b and 2h were isolated only in low yields without achieving analytical purity despite several chromatographic purifications followed by consecutive recrystallizations. The best conditions for preparation of 2b and 2h were found, when the reactions were performed in a mixture of acetonitrile and 2,6-lutidine at 80 oC for 18 hours using a larger excess of the nitro-substituted anilines. Under these reaction conditions, 2b and 2h were isolated in 56 % and 14 % yields, respectively. The ADOTA+ hexafluorophosphate salts, 3 were prepared through ether cleavage and subsequent intramolecular oxygen ring closure in melted pyridine hydrochloride at approximately 190 oC.58, 59 This gave 3 in isolated yields varying between 3 % and 65 %. The nitro group substituted derivatives 3b and 3h were again challenging to obtain in their pure forms, and were only isolated in 25 % and 3 % yields, respectively. Compound 3b was stable when isolated, while 3h was not. The nitro substituted N-methyl-N’-(2-hydroxy-5-nitrophenyl)-diazaoxatriangulenium hexafluorophosphate salt, 4b, was only isolated in very low yield, while isolation of the N-methylN’-(3-hydroxy-5-nitrophenyl)-diazaoxatriangulenium hexafluorophosphate 4h derivative from 3h was not achieved. The formation of 4h from 2h via a synthetic route involving initial introduction of the second aza-bridge followed by subsequent oxygen ring closure in pyridine hydrochloride was tried.58, 59 According to MALDI-TOF analysis of the

crude reaction mixture only traces of the desired compound was generated, and attempts to isolate and purify 4h remained unsuccessful.

Scheme 2. Synthesis of pH responsive diazaoxatriangulenium dyes 4b, 4d, and 4e. a) Appropriately substituted aminophenol in 2,6-lutidine, acetonitrile, 80 °C, 18 h, then KPF6 (aq). b) Pyr·HCl 180-200 °C, 20 minutes, c) MeNH2 in ethanol, benzoic acid, NMP, 70-80 °C, 18 h.

Optical Spectroscopy DAOTA is a highly emissive yellow fluorescent dye.61, 62 The absorption maxima of the DAOTA derivatives 4a-4g lie at 552-557 nm and the emission maxima lie at 585-592 nm


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(Figure 2 and Table 1). DAOTA dyes without PeT quenching substituents have fluorescence quantum yields (φfl) of 51-58 % and fluorescence lifetimes (τfl) of 17-20 ns in acetonitrile solution.62

Figure 2. Emission spectra of the sol-gel solubilized diazaoxatriangulenium DAOTA fluorophores 4a and 4c-4g in water at high and low pH (low and high intensity spectra, respectively), defined as the first and the last spectrum when obtaining the response curves; excitation at 505 nm.

Introduction of a phenol does not change the photophysical properties compared to DAOTA dyes without PeT quenching substituents; while the DAOTA fluorescence is completely quenched at high pH values where the phenolate form dominates.53 This is illustrated by the spectra shown in Figure 2. Cursory inspection of Figure 2 shows that while the fluorescence of 4d-g are fully quenched by the phenolate substituent, the fluorescence of the methylsulfonyl substituted DAOTA 4c and the aniline substituted derivative 4a are not completely quenched at high pH. The single point fluorescence quantum yields included in Table 1 also show that the nitro derivatives behave differently from the other compounds. In 4b, the phenol acts as a partial quencher and the phenolate does not fully quench the fluorescence. In contrast, the trifluoromethane substituted DAOTAs 4d-e are as fluorescent as the parent molecule and are efficiently quenched by intramolecular PeT at high pH (Table 1 and Figure 2).53 Thus, 4b is excluded from further studies, and we move onto investigate the pH response exhibited by the fully responsive phenol/phenolate based DAOTA dyes 4c-g and the anilinium/aniline based DAOTA dye 4a. Table 1. Absorption and fluorescence properties of 4b, 4d, and 4e measured in 1 vol% DMSO in PBS solution at pH 2 and pH 12. Compound 4b 4d 4e

pH 2 pH 12 pH 2 pH 12 pH 2 pH 12

absa

emb

flc

nm 552 556 553 557 554 556

nm 586 591 585 585 587 587

0.20 0.49 0.51 -

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at the maximum absorbance of the S 0  S1 absorption envelope. at the maximum fluorescence intensity. cSingle point fluorescence quantum yield. Rhodamine 6G as reference. aWavelength

bWavelength

Figure 3. Emission spectra of sol-gel solubilized diazaoxatriangulenium dyes at different pH. Sol-gel with 4f was dissolved in 0.010 M Britton-Robinson buffer, at different pH values. The spectra have been normalized with respect to the spectrum measured at pH 5.20. Excitation at 505 nm, slits 10 nm. Emission 550-700 nm, slits 5 nm.

Figure 3 shows a representative series of emission spectra upon varying pH. As seen, the fluorescence is partly quenched at pH-values between 6 and 10 defining the operational range of the sensor.

pH Response Curves The pH response of the dyes can be visualized by plotting either their fluorescence intensities at a single wavelength or as the integrated emission intensities as a function of pH. The result is in both cases a response curve. Fitting a suitable function to the response data yields the calibration curve or formally the calibration function F. Response data and calibration curves from the six investigated DAOTA dyes solubilized by a sol gel are shown in Figure 4. Note that the dyes and sol-gel material are fully dissolved and the samples studied are all homogeneous. A response curve is generated when the change in a molecular property is read from a sensor. The sensor consists of the responsive DAOTA dye in a cuvette and a fluorescence Cary Eclipse spectrometer, see SI for details.55, 57, 63-65 The responsive DAOTA molecule responds to a chemical input x and the sensor converts the change to a sensor signal y.18, 39, 66-74 Here, a change in pH (x) induced a change in the fraction of protonated and thus fluorescent DAOTA dye, which is read as change in emission intensity (y). The relation between x and y—between pH and emission intensity—is given by the calibration function F. If the sensor is to be used to determine x, a dedicated software and sensor calibration is needed to convert the sensor signal y to the reported value x’ by using the inverse of the calibration function F–1, also denoted the evaluation function.75-77 When using a conventional pH meter, the proton activity


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x is determined from an electrochemical potential (y in mV) that in turn is converted into a reported pH (x’).78 In sensor development these facts are often overlooked, but when developing a functional sensor response, calibration, and evaluation curves must all be considered.79 With the chemical input as pH (x = pH) and the sensor signal, y, defined as the integrated emission intensity in the range from 580 nm to 630 nm, the response curve can be plotted. The symbols in Figure 4 show the response curves recorded from the pH responsive DAOTA dyes. As the dyes show limited solubility in water, all experiments were performed on dyes solubilized in a sol-gel, see Supporting Information for details.

Eqn. (1) is fitted to the measured fluorescence intensities recorded at different pH values. The results of the fits are shown in Figure 4 and the essential data are compiled in Table 2. The pKa values determined for the dyes are significantly lower than that of the corresponding free phenols stated in Scheme 1. This lowering of the pKa is to a large extend due to the positive charge on the DAOTA fluorophore which acts as an inductive electron withdrawing group.53 While 4a responds in the acidic range and 4g responds in the alkaline range, compounds 4c-f all respond in the physiologically relevant pH range. The determined k values are with an average of 2.13 slightly lower than the ideal value of 2.30. This stretches the sigmoidal function and increases the operational range. The values of a and y0 are proportional to the fluorescence quantum yield when the dye is protonated and deprotonated, respectively. Cursory inspection of the data in Figure 2 and Table 2 show that this is indeed the case. Table 2 shows a high y0 for 4a and 4c; the two dyes with clearly defined spectra at high pH values in Figure 2. Table 2. Fitting parameters found to describe the variation of the emission intensities as function of pH for the diazaoxatriangulenium derivatives 4a and 4c-4g.

Figure 4: Individual calibration curves for sol-gel solubilized dyes 4a and 4c-g measured in 0.01 M Britton-Robinson buffer. After subtraction of baseline signal y0, the integrated fluorescence emission in the range 580-630 nm is normalized with regards to the span, a, and plotted vs. observed pH measured in the solution for all six dyes: 4a: (●) pKa = 1.85, 4c: (×) pKa = 5.38, 4d: (■) pKa = 6.05, 4e: (▼) pKa = 7.68, 4f: (▲) pKa = 8.10, 4g: (*) pKa = 9.14.

Calibration Curve for One Dye: Individual response data for the pH responsive dyes 4a and 4c-g are shown in Figure 4. To generate calibration functions (calibration curves) these were fitted to a sigmoidal function relating the optical sensor signal, y, to the pH, x. 𝑦 = 𝐹𝑠𝑖𝑔𝑚𝑜𝑖𝑑𝑎𝑙 (𝑥) = 𝑦0 +

𝑎

(1)

1+𝑒 𝑘(x−p𝐾𝑎 )

where y0 is the base line signal, a is the signal span, k is a material specific shape factor of the curve. The sigmoidal function (Eqn. 1) is achieved by re-writing the HendersonHasselbalch equation:80 pH = pKa + log([A-]/[HA]),

(2)

using the fact that the optical signal y is directly proportional to the fraction of the responsive dye in acid form, α, so that: α = (y-y0)/a = [HA]/([HA] + [A-]).

(3)

Combining Eq. 2 and Eq. 3, and isolation of y yields: y = 𝑦0

𝑎

+ 1+10(pH−p𝐾𝑎)

(4)

In ideal systems e.g. when dyes in solution are fully described by the Henderson-Hasselbalch equation, k is simply the conversion of logarithm base k = ln(10) = 2.3026. For responsive dyes in complex media k is typically lower.36 To determine the calibration function F and the characteristic pKa value for each dye, a sigmodal curve described by

a

Compound

pKa

pH rangea

kb

a∙10-4 c

y0∙10-4 c

4a

1.85

1.0-2.7

2.26

138

18.1

4c

5.38

4.5-6.3

2.20

284

21.6

4d

6.05

5.1-7.0

2.12

387

4.97

4e

7.68

6.7-8.7

2.05

302

4.05

4f

8.10

7.1-9.1

2.04

409

2.98

4g

9.14

8.2-10.0

2.13

206

2.08

Calculated as 4/k. b Average k is 2.13. c Given in counts

The pKa value defines the pH region in which the dye has high sensitivity, and thus the operational range of the sensor. The width of the operational pH range is defined by k. Following the IUPAC recommendation of limit of detection,40 optical sensors containing one dye have an operational range of 4/k pH units (see Supporting Information for details). The operational ranges for each dye are included in Table 2. Although Figure 4 shows that the six dyes span the pH scale from pH ~1 to pH ~10, when adhering to the IUPAC definition the broadest span of a pH sensor made from this series of dyes is from pH = 4.5 to pH =10. Note that when the dyes are immobilized in an ORMOSIL matrix, we have previously observed a k-value of 1.5,81 which would allow a sensor to be made from the DAOTA dyes 4a and 4c-g that covers the range from pH ~0.5 to pH ~10.5.

Linear Approximation of Calibration Curves Describing the sigmoidal calibration curves shown in Figure 4 by a linear function of the type: 𝑦 = 𝐹𝑙𝑖𝑛𝑒𝑎𝑟 (𝑥) = 𝑠 𝑥 + 𝑏 (5) can be useful, since a two-point calibration then is sufficient for calibration of sensors. Linear calibration curves only require the determination of two parameters, while a four-point calibration is required to determine a sigmoidal


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calibration curve. For the linear approximation given in Eqn. (5), s is the slope i.e. the sensitivity, and 𝑏 corresponds to the signal at pH = 0. Using the coefficients determined in Eqn. (5), an estimated pH can be determined, x’: 𝑥′ =

𝑦−𝑏

range if a linear approximation of the calibration curve is used. The mean error 𝜀̅, the maximum error εmax and the sensitivity are given in Table 3 as function of k. With typical values of k = 2, the mean error will be 0.005 with a maximum error of 0.02 in a range of 1 pH unit. For most applications in life sciences and biotechnology, this would be fully acceptable if the pKa is centered on the relevant pH. For any purpose where pH ranges of 2-3 units are required, sensors with multiple dyes are required if a linear approximation of the calibration curve is used. The same is true if a higher precision is required. The alternative is to do a four-point calibration to determine the sigmoidal calibration curve, or alternatively, if some parameters in the sigmoidal function are so robust that they can be fixed prior to calibration, fewer calibration points may be used.

(6)

𝑠

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and the error, ε, calculated as: 𝜀 = |𝑥′ − x| (7) The error in pH obtained when the sigmoidal calibration curve is approximated by a linear curve is reported in Table 3 for different pH ranges. For a sensor with k = 2.3026, the valid pH range for obtaining errors below 0.02 pH units is ~1 pH unit. In case k = 1.5, the analogue pH range is ~2 pH units. It follows that optical pH sensors based on one single dye with a performance comparable to well-established potentiometric methods can only be useful in a narrow pH

Table 3: Correlation between pH range, given in terms of k, and error ε in pH and sensitivity A obtained when the sigmoidal calibration curve is approximated as linear. One dye, n = 1 Mean pH error, 𝜀̅

pH range

Two dyes n = 2; pKa distance = 2.6339/k Max 𝜀max

pH

error,

Sensitivity, A (% per 0.01

Mean pH error, 𝜀̅

Max 𝜀max

pH) b

pH

error,

Sensitivity, A (% per 0.01 pH)

1/k

0.0013/k

0.0042/k

0.247 k

2.2×10–5/k

1.1×10–4/k

0.167 k

2/k

0.010/k

0.032/k

0.239 k

6.5×10–4/k

0.0031/k

0.166 k

3/k

0.032/k

0.096/k

0.226 k

0.0044/k

0.020/k

0.165 k

4/k a

0.071/k

0.20/k

0.212 k

0.016/k

0.065/k

0.163 k

6/k

0.20/k

0.50/k

0.181 k

0.079/k

0.28/k

0.152 k

8/k

0.38/k

0.86/k

0.154 k

0.21/k

0.62/k

0.138 k

a pH

b

range as recommended by IUPAC for one dye sensor. Sensitivity is the slope of the line approximated the sigmoidal curve.

Calibration Curve from a Sensor Containing n Indicators We claim that the calibration curve of an optical sensor containing multiple responsive dyes based on the same fluorophore can be represented as the sum of the individual sigmoidal calibration curves weighted by the molar ratios of the dyes. The calibration curve for a sensor with an equimolar ratio of n responsive dyes is thus described by: 𝑦=

𝑛−𝑑𝑦𝑒𝑠 𝐹𝑠𝑖𝑔𝑚𝑜𝑖𝑑𝑎𝑙 (𝑥)

= 𝑦0 + 𝑎 ∑𝑛𝑖=1

1/𝑖 1+𝑒 𝑘(p𝐾𝑎𝑖 −𝑥)

(8)

where pKai is the characteristic pKa value of the ith dye. Determining the calibration curve for this sensor requires that n times four parameters are determined. This is not feasible. One solution is to use a linear approximation of the calibration curve. To do so, the optimal separation between pKa values was determined to be described by Eqn. (9), see Supporting Information for details. 2 𝑘

ln(

1 2−√3

) ≈ 2.6339/𝑘

4.6/k, see Supplementary Information. This is in agreement with results reported without considering the dependency in k.82 Thus, the optimal separation between pKa values of two dyes in order to achieve a sensor with the best approximation of a linear response is 1.6-2.4 pH units depending on k.

Direct Calibration of Sensors Containing n Indicators Figure 5 shows the measured pH response determined from a 1:1 binary mixture of 4d and 4e. The model described by Eqn. (8) with n = 2 was fitted to the data to determine the calibration curve. pKa values of 6.16 and 7.67 for respectively 4d and 4e were determined by this model. The values determined from the binary mixture are in good agreement with the individually determined values.

(9)

Table 3 compares the precision for a sensor with one (n = 1) and two (n = 2) dyes. For two dyes, the region where the linear approximation can be applied is expanded. With typical values of k = 2, the operational range with errors below 0.02 is now 2 pH units, compared to 1 pH unit with a single dye. However, pKa separations larger than 2.6339/k improves the precision of the sensor when using the linear approximation. Thus, a minimum in 𝜀̅ is found at separations in pKa of 3.7/k and a minimum in εmax is found at


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ACS Sensors two pKa values is ~1.5 pH units, which is close to the optimal pKa separation of 3.7/k. This means that 4d and 4e may form a calibration curve with good linearity in the region pH = 5.1 to pH = 8.7 and errors below 0.02 pH units if calibrated using a linear approximation of the calibration function. Note that the 1:1 ratio was confirmed by the fit.

Figure 5: Response and calibration curve of a 1:1 binary mixture of 4d and 4e. Measured response data (filled symbols), determined calibration function (full line) modelled using Eqn. (8), and contributions from the individual dyes to the calibration curve (dashed lines). The grey shaded areas indicate the range of operation according to IUPAC definition.

Table 4 summarizes the number of parameters varied for each fit and the associated estimated precision given as: 𝜒2 = ∑

(𝑥−𝑥 ′ )2 𝑥′

=∑

𝜀2

(10)

𝑥′

Table 4: Number of parameters (p) varied for each fit and the associated estimated precision (2) Number of parameters varied

Number of fixed parameters

Precision, χ2, in operational range

Binary (p = 8); pH range = 5.1-8.7 yo and k common

6

0

0.0067

Fixed pKa

4

2

0.0073

3

3

0.0084

Fixed (1:1)

ratio

Figure 6: Calibration curve of 3:3:1:1 (top) and 1:1:3:3 (bottom) quaternary mixtures of 4a, 4c, 4f, and 4g. Measured response data (filled symbols), determined calibration function (full line) modelled using Eqn. (8) with individual spans, ai, and contributions from the individual dyes to the calibration curve (dashed lines). The grey shaded areas indi-

Quaternary (p = 16); pH range = 0.9-10.1

3:3:1:1

1:1:3:3

yo and k common

10

0

0.025

0.072

Fixed pKa

6

4

0.052

0.094

Fixed using exp ratio

3

7

0.319

0.515

Fixed using fitted ratio

3

7

0.090

0.093

If the pKa values are fixed at the values determined from the individual response curves (Table 2), the estimated precision decreases from 0.0067 to 0.0073 pH values. A small difference that fully justifies that pKa values can be kept fixed once properly determined. The separation of the

cate the range of operation according to IUPAC definition.

Figure 6 shows the response curve from quaternary mixtures of 4a, 4c, 4e, and 4g as function of pH. The solution containing dyes were mixed in two different ratios, targeting distributions of 3:3:1:1 and 1:1:3:3. These ratios were chosen to test if the response is linear in concentration. This is the case, since the response from the quaternary mixture can be described by a weighted sum of response curves of the individual dyes, but when four dyes are included, the uncertainty in the concentration of the individual dyes increases. Creating a calibration function using fixed values of the ratios and refining one overall span parameter resulted in a poor precision of 0.3-0.5 pH units. This is very likely due to poor accuracy in the dye loading, but may also

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be due to cross talk between the different DAOTA derivatives in the system. Letting the calibration determine the dye ratios in the two mixtures gave the following results: 2.71:3.10:0.94:1.26 and 0.74:0.98:3.14:3.13. These values were then used to generate the calibration function. Although the ratios of the dyes are far from ideal, the precision of the two sensors was determined to be 0.02 and 0.07 for 3:3:1:1 and 1:1:3:3 ratios of 4a, 4c, 4e, and 4g over a pH range from 0.9 to 10.1. The precision was achieved by using a full fit of all parameters to generate the calibration function. The 3:3:1:1 sensor performs better over the broader range, as the sensitivity for this mixing ratio is more evenly spaced over the entire range. The pKa values determined by the fit are in good agreement with the individually determined values, see Supplementary Information. The number of parameters varied in the fit can be decreased by fixing of the pKa values. Here slightly worse precision is obtained, but the precision is still below 0.1 pH units typically required in most applications of broad range pH sensors. Note that the pKa spacing in this example is not ideal, and there are regions of poor sensitivity in the operational window. These regions correspond to the white regions in Figure 6. A proper broad range sensor can be designed to operate over a range of 7-9 pH units, but that requires 4-6 different dyes with pKa values spaced by ~1.5 pH units. The modelling of the complex mixtures show that with carefully controlled dye ratios, the number of parameters required to describe a reliable calibration curve can be reduced from 4 × n to 3: the background y0, the sensor material specific parameter, k, and overall span a. Note that all pKa values can be fixed when known. The result is a broad range pH sensor that with a calibration of three parameters gives a precision of ~0.1 pH units.

CONCLUSIONS Several DAOTA dyes with different PeT quenching motifs were synthesized and investigated, and it was shown that variation in pKa for the fluorophore follows the Hammett relationship. By recording fluorescence spectra as a function of pH, it was shown that using PeT to generate pH responsive fluorescent DAOTA dyes gives rise to a perfect sigmoidal response. The response curves from single dyes, and binary and quaternary mixtures of dyes were recorded, and calibration curves were generated using linear and sigmoidal functions. The former only has two variable parameters, while the latter has 4 × n parameters, where n is the number of dyes. The precision of the resulting evaluation functions was considered for each method and for a varying number of fixed parameters in the sigmoidal function. While simple and easily applicable, the linear approximation of the response has a limiting precision of 0.02 pH units and a narrow range of operation. Therefore, we conclude that the best approach is to use a sigmoidal calibration function

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and locking stable parameters such as dye concentration a and dye pKa. In the binary and quaternary systems studied here, this allows for an extended operational range and high precision. We conclude that broad range optical sensors can be generated from mixtures of responsive molecules that consist of a single fluorophore functionalized with different PeT receptor motifs. Yet we conclude that the sigmoidal response of this type of sensors gives rise to complications when calibrating sensors. Complications that can be overcome either by a linear approximation of response or by robust sensor chemistry that allows for locking one or more calibration parameters. The former is ideal for sensors that only need a small operational window, while the latter is needed for any type of colorimetric broad range sensor.

ASSOCIATED CONTENT Supporting Information Supporting Information Available: The following files are available free of charge. SI_Paper09_v5.pdf. Synthetic procedures and compound characterization, spectroscopic methods and data, and theoretical treatment of multiparameter calibration.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID Thomas Just Sørensen: 0000-0003-1491-5116 Bo W. Laursen: 0000-0002-1120-3191 Funding Sources The authors thank Lundbeckfonden (grant#2013-12793), Novo Nordisk Fonden (grant#4096), the Danish Council of Independent Research (Grant# DFF-6111-00483, DFF–1337-00005 and DFF–1335-00773), Carlsbergfondet, Villum Fonden (grant#14922), BIOPRO, Innovationsfonden (grant#517900914B), UpX and the University of Copenhagen.

Notes The authors declare the following competing financial interest(s): TJS and BWL are founders and current owners of FRS-systems ApS, a University of Copenhagen Spin-Out company commercializing the optical pH sensors investigated in this manuscript.

ACKNOWLEDGMENTS The authors thank Lundbeckfonden (grant#2013-12793), Novo Nordisk Fonden (grant#4096), Carlsbergfonden, Villum Fonden (grant#14922), BIOPRO, Innovationsfonden (grant#5179-00914B), the Danish Council of Independent


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Research (Grant# DFF – 1337-00005 and DFF – 1335-00773), UpX and the University of Copenhagen.

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TOC graphic 64x32mm (300 x 300 DPI)


Tuning the pKa of a pH Responsive Fluorophore and the

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