Enzyme assays with boronic acid appended bipyridinium salts

Analytica Chimica Acta 649 (2009) 246–251

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Enzyme assays with boronic acid appended bipyridinium salts Boaz Vilozny a , Alexander Schiller b,∗∗ , Ritchie A. Wessling a , Bakthan Singaram a,∗ a b

Department of Chemistry and Biochemistry, University of California, 1156 High Street, Santa Cruz, CA 95064, USA Friedrich-Schiller-University Jena, Institute for Inorganic and Analytical Chemistry, August-Bebel Str. 2, D-07743 Jena, Germany

a r t i c l e

i n f o

Article history: Received 21 April 2009 Received in revised form 9 July 2009 Accepted 14 July 2009 Available online 22 July 2009 This article is dedicated to the memory of Professor Anthony Fink and his contributions to the field of protein chemistry. Keywords: Boronic acid Saccharide Enzyme assay Fluorescence Viologen

a b s t r a c t In-vitro fluorescent enzyme assays have been developed for sucrose phosphorylase (SPO) and phosphoglucomutase (PGM). These assays make use of a selective carbohydrate sensing system that detects the unlabeled enzymatic products fructose and glucose-6-phosphate. The system comprises 8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt as the reporter unit and boronic acid appended viologens as selective receptors with working ranges from 70 ␮M to 1.0 mM for fructose (SPO) and 190 ␮M to 2.0 mM for glucose-6-phosphate (PGM). The change in fluorescence can be converted into product concentration, allowing initial reaction velocities and Michaelis–Menten kinetics to be calculated. The assays are also carried out in multiwell plate formats, making them suitable for high-throughput screening of enzyme inhibitors. Rapid PGM inhibition screening is demonstrated with EDTA and LiCl. The PGM assay can also be used for enzyme quantification with a detection limit of 50 ng mL−1 . © 2009 Elsevier B.V. All rights reserved.

Many different classes of enzymes, including phosphatases, phosphorylases, mutases, transferases, hydrolases, and isomerases are involved in carbohydrate transformation. Selective regulation by inhibition or activation of key enzymes may lead to the development of new therapeutic drugs [1]. To enable the discovery of new regulating agents, simple and fast methods for continuously monitoring enzyme-catalyzed reactions are essential. Such high-throughput enzyme assays often require special assay formats and modified chromogenic or fluorogenic substrates [2,3]. Carbohydrate reactions represent a challenge for high-throughput screening in that natural enzymatic substrates and products are not chromophoric. Phosphorylases and transferases have been indirectly monitored by the selective detection of cosubstrates [4,5]. Direct detection of substrates can be achieved by the more costly and time intensive methods of HPLC [6] and mass spectrometry [7]. Alternatively, an assay based on product-selective chemical probes provides a detection tool that is rapid, uses the relatively inexpensive colorimetry and fluorime-

∗ Corresponding author. Tel.: +1 831 459 3154; fax: +1 831 459 2935. ∗∗ Corresponding author. Current address: Friedrich-Schiller-University Jena, Institute for Inorganic and Analytical Chemistry, August-Bebel Str. 2, D-07743 Jena, Germany. Tel.: +49 3641 948 113; fax: +49 3641 948 102. E-mail addresses: [email protected] (A. Schiller), [email protected] (B. Singaram). 0003-2670/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2009.07.032

try instrumentation, and is amenable to high-throughput screening [8–12]. To demonstrate the potential of selective fluorescent saccharide probes in enzymatic reactions, we chose the enzymes sucrose phosphorylase (E.C. 2.4.1.7) and phosphoglucomutase (E.C. 5.4.2.2). Phosphoglucomutase (PGM), which converts glucose1-phosphate to glucose-6-phosphate, is found in all organisms including humans. This enzyme is of special interest because of its multiple roles in human health: In addition to its essential role in glycogenesis and glycogenolysis, PGM is also a known target of Li+ at therapeutic concentrations used for treatment of bipolar disorder [13,14]. Furthermore, the enzyme is a factor in the virulence of Pseudomonas aeruginosa, a human pathogen for which there are few effective antibiotics [15,16]. Recently developed assays for PGM include mass spectrometry [17], used to determine enzyme kinetics, and an enzyme-coupled amperometric microsensor [18]. A fluorescent biosensor capable of discriminating saccharides and phosphosaccharides was used to assay several carbohydrate-modifying enzymes, including phosphoglucomutase [19]. Sucrose phosphorylase (SPO) is a glycosyl transferase which catalyzes the conversion of sucrose and phosphate to glucose-1phosphate and fructose. It is commonly found in bacteria, including flora in the human gut, and has been used as a biocatalyst for glycosylation reactions [20,21]. In contrast to information-rich techniques such as mass spectrometry, a simple optical-readout assay is the most common assay

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method for determining activity of both PGM [22,23] and SPO [24,25]. In this case, the enzymes must be coupled with reductases in order to produce the absorbing species NADH or NADPH. While this method is widely used, it has the disadvantage of relying on multiple cascading enzymatic reactions [26]. Additionally, colorimetry is generally less sensitive than fluorescence, and is limited to the wavelength of NADPH absorbance (340 nm) where there are often interferences due to autofluorescence from biomolecules [27]. In contrast, we report here the continuous monitoring of single enzymatic reactions by selective detection of enzymatic products with green-emitting fluorescent probes. Our laboratory has developed a supramolecular carbohydrate sensing system that comprises fluorescent dyes as reporter units and boronic acid appended viologens as receptors [28–30]. We have shown that these systems are also able to differentiate neutral saccharides, phospho sugars, and nucleotides [31,32]. In what follows, we describe the use of this system in selective enzymatic assays for SPO and PGM, which allows the successful determination of the enzyme kinetics in 24-well plates. The modular sensing ensemble comprises the commercially available fluorescent dye, 8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt (HPTS), and an analyte responsive quencher, either N,N’-bis-(benzyl-2-boronic acid)-4,4’-bipyridinium dibromide (4,4’-o-BBV) or N,N’-bis-(benzyl-2-boronic acid)-3,3’-bipyridinium dibromide (3,3’-o-BBV) (Fig. 1). The quencher and dye are ionically attracted, forming a non-fluorescent ground-state complex in solution. The fluorophore HPTS was selected because it is anionic, water-soluble, and has a high fluorescence quantum yield. While photobleaching can be a problem with powerful excitation sources, the brief and intermittent excitation over 20–30 min of our assay does not appear to affect the fluorescent signal. For longer continuous monitoring applications, a ratiometric method can be used using the two excitation maxima for this dye [33]. The key issue in enzyme assays for SPO and PGM is the selectivity of the BBVs. Using the proper BBV receptor, selective binding of the enzymatic product alters the charge state of the viologen, and hence the fluorescent signal of the probe (Fig. 2). The viologen, 4,4’-o-BBV, is

247

Fig. 1. Selective carbohydrate sensing system of cationic bis-boronic acid appended benzyl viologens (3,3’-o- and 4,4’-o-BBV) and the anionic fluorescent dye, 8hydroxypyrene-1,3,6-trisulfonic acid trisodium salt (HPTS).

used to assay SPO and 3,3’-o-BBV is used to assay the enzymatic reaction of PGM.

1. Materials and methods 1.1. Materials The syntheses of N,N’-bis-(benzyl-2-boronic acid)-4,4’bipyridinium dibromide (4,4’-o-BBV) and N,N’-bis-(benzyl-2boronic acid)-3,3’-bipyridinium dibromide (3,3’-o-BBV) have been reported[29,34] Water was distilled and purified via a MilliQ filtration system (>14 M cm). A detailed list of all reagents and enzymes used is given in the supporting information.

Fig. 2. Enzyme assays for sucrose phosphorylase (SPO) and phosphoglucomutase (PGM) with selective detection of the unlabeled products fructose and glucose-6-phosphate by 4,4’-o-BBV and 3,3’-o-BBV.

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1.2. Solution preparation A glycylglycine buffer (Gly–Gly, pH 7.4, 250 mM), adjusted with sodium hydroxide, was used as the medium for the enzymatic reactions. Stock solutions of BBV/HPTS (2.05 mM and 16.4 ␮M, respectively) were freshly prepared in water immediately before use. A suspension of sucrose phosphorylase (22 ␮g mL−1 ) was prepared using 1.0 mg lyophylized enzyme in 4.5 mL water. A stock solution of 83 ␮g mL−1 phosphoglucomutase was prepared using an ammonium sulfate suspension of the enzyme (6.5 mg mL−1 ) dissolved in water. All other stock solutions used for the enzymatic assay were prepared in water. All manipulations were performed in air and at room temperature (22 ◦ C). A detailed protocol for the assays, including preparation of all solutions, is included in the supporting information. 1.3. Instrumentation and software Fluorescence spectra were measured with a PerkinElmer LS50-B luminescence spectrometer, exciting at 424 nm and measuring the fluorescence intensity from 460 to 600 nm. A 1% attenuation filter was used for excitation, with slit widths for excitation and emission both at 15 nm for sucrose phosphorylase, and with an emission slit width of 7 nm for phosphoglucomutase. Emission spectra were recorded every 30 s with a scan rate of 500 nm min−1 . Absorption spectra were collected using a Hewlett Packard 8452A Diode Array Spectrophotometer. For multiwell fluorescence measurements the fluorescence plate reader Victor® 1420 Multi-label counter from PerkinElmer was used (excitation filter: 420 nm, emission filter: 535 nm, emission aperture: normal, measurement height from the bottom: 6 mm, counting time: 0.1 s). 24-Well plates (Costar® 3526, cell culture cluster, flat bottom with lid, clear polystyrene, sterile) were purchased from Corning Incorporated. Fitting of the data was performed using the Levenberg– Marquardt algorithm in Origin 7.5 from OriginLab, Northampton, MA (USA).

priate medium for each enzymatic reaction. This included all substrates, cofactors, and activators. Each experiment was done in triplicate. Controls were included in each well-plate: dye alone (HPTS 4.0 ␮M) and blank (enzymatic reaction medium). The increase in fluorescence intensity was measured after adding consecutive volumes of 1, 1, 2, 4 ␮L of 0.1 M and 1.2, 2, 4, 12 ␮L of 1.0 M analyte solutions to the BBV/HPTS sensing ensemble. The wellplates were covered with a lid and shaken for 60 s after each analyte addition [35]. Each sample was measured twice with a fluorescence plate reader. After background (matrix effects) subtraction, the relative fluorescence increase F/F0 for each BBV receptor/analyte combination at increasing analyte concentrations was calculated. Plotting the relative fluorescence increase F/F0 against analyte concentration produced the binding curves (Eq. (S1) in supporting information) [36]. Final analyte concentrations were corrected for the volume increase. Note that Eq. (1) is simply the linear portion of the binding curve (Eq. (S1)). F/F0 was converted into product concentration by using Eq. (2), which is derived from the calibration plot of fluorescence intensity ratio (F/F0 ) versus concentration of product. The initial velocity Vi is calculated with Eq. (3). F = 1 + c [A] F0

(1)

F/F0 − 1 c

(2)

[A] = Vi =

[A] t

(3)

F0 is the fluorescence intensity of the quenched dye, F is the fluorescence intensity after the addition of the analyte, [A] is the concentration of the analyte. The unit of c (the calibration factor) is M−1 and t is the time in minutes. Vi is the initial velocity. Enzyme activity can be defined in terms of activity units (U). For our assay, one U of enzyme will convert 1.0 ␮mol of substrate into product(s) per minute at pH 7.4 at 22 ◦ C (1 U mL−1 ≡ 1 mM min−1 ). The analytical detection limit for an analyte is defined as three times the standard deviation of a blank sample.

1.4. Fluorescence enzyme assay procedure

2. Results and discussion

Assays were carried out in triplicate in multiwell plates and measured with a fluorescence plate reader. For the PGM assay, a typical procedure was carried out as follows. Solutions were added to wells in a 24-well plate (2.0 mL total volume) to give final concentrations as follows: Gly–Gly, pH 7.4, 167 mM; Glucose-1phosphate, 5.0 mM; Glucose 1,6-phosphate, 0.020 mM; 3,3’-o-BBV, 0.50 mM; HPTS, 4.0 ␮M; MgCl2 , 30 mM. The reaction was initiated by addition of an aliquot of phosphoglucomutase (13 ␮L) to give a final concentration of 0.54 ␮g mL−1 (0.13 units mL−1 ). Immediately after enzyme addition, the plate was measured for fluorescence at 30 s intervals for 10 min. Controls were measured with no enzyme present, and also with no dye present (background). Fluorescence values were recorded as F/F0 , where F0 is the signal at time zero after background subtraction. A similar procedure was used for the SPO assay, with solutions added to give the following final concentrations. Gly–Gly, pH 7.4, 167 mM; sucrose, 50 mM; KH2 PO4 , 40 mM; 4,4’-o-BBV, 0.50 mM; HPTS, 4.0 ␮M; sucrose phosphorylase, 3.3 ␮g mL−1 (0.15 units mL−1 ). See supporting information for detailed procedures.

2.1. Fluorescent response to enzymatic products The basis of our proposed assay is the selective recognition by the probe of the enzymatic products fructose (for SPO) and glucose6-phosphate (for PGM). The binding characteristics of the BBV/HPTS combination with fructose and glucose-6-phosphate have been reported [29,36]. However, the criteria for the selectivity of the BBVs toward an analyte is not always determined by the binding constant, but by the signal modulation (F/F0 ). As shown in the calibration curves, the products fructose and glucose-6-phosphate produce a strong signal even in the presence of excess amounts of their respective analyte precursors (Figures S2 and S3) [36]. The calibration curve for fructose gave a slope of 462 ± 22 M−1 using 4,4’-o-BBV, and the curve for glucose-6-phosphate gave a slope of 192 ± 6 M−1 using 3,3’-o-BBV. The analytical detection limit for fructose is 70 ␮M with a linear working curve up to 1.0 mM, while for glucose-6-phosphate the working range is 190 ␮M to 2.0 mM. No binding with the BBV receptors was observed with the substrates sucrose and ␣-d-glucose-1-phosphate in the concentration range from 0.5 to 10 mM [37].

1.5. Calibration of enzyme assay to determine initial reaction rates (Vi )

2.2. General fluorescent response to enzymatic reactions

Mixed solutions of BBV and HPTS (BBV 0.50 mM, HPTS 4.0 ␮M) were placed in 24-well plates (2.0 mL in each well) in the appro-

As described in Fig. 2, the fluorescent probe ensemble is expected to produce a signal during the production of either

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Fig. 3. Real-time fluorescence assay for SPO (A) and PGM (B) showing the different selectivity of the BBV/HPTS probes. The enzymatic reactions are both followed with 3,3’-o-BBV () and 4,4’-o-BBV (䊉). Background with no enzyme () using either 4,4’-o-BBV (SPO) and 3,3’-o-BBV (PGM) as the receptor. See Section 1 for reaction conditions.

glucose-6-phosphate from glucose-1-phosphate (PGM reaction) or fructose from sucrose (SPO reaction). After profiling the response of the fluorescent probe to the products of the enzyme-catalyzed reaction, evolution of the fluorescent signal was observed by performing the enzymatic reaction in a cuvette in the presence of the appropriate dye/receptor system. Both enzymatic reactions show immediately increasing fluorescence over time, with no incubation period (Figure S1). During the enzymatic reactions no changes in the fluorescence spectra were observed, indicating that the chemical identity of the signaling unit (HPTS) is not altered. It should be noted that the reaction of SPO, monitored with 4,4’-oBBV/HPTS, results in a two-fold increase in fluorescence intensity during the 5-min reaction time. This reaction is considerably more sensitive than the PGM reaction using 3,3’-o-BBV. This is consistent with the calibration results, in which the sensing system for fructose is roughly twice as sensitive as that for glucose-6phosphate. This difference is partially due to the greater quenching of HPTS by 4,4’-o-BBV, resulting in a lower initial fluorescence. After showing that the enzymatic reaction could be continuously monitored by fluorimetry, we then focused on adapting this assay to a multiwell plate format and quantitatively characterizing the reactions.

values are in acceptable agreement with the activity rates given by Sigma–Aldrich of 0.15 and 0.13 U mL−1 [38]. Thus, the boronic acid appended viologens at 0.5 mM concentration did not significantly inhibit the activity of the two enzymes [39]. Comparable activities were also demonstrated using the traditional colorimetric assays for detecting the absorbance of NADPH [36]. For both enzymatic reactions, increasing the enzyme concentration resulted in increased initial velocity, indicating that the enzymatic reactions were the rate-limiting process and not the kinetics of the two-component sensing ensemble BBV/HPTS (Figure S6 and S7). 2.4. Determination of kinetic parameters for sucrose phosphorylase The SPO assay was used to determine the kinetic Michaelis–Menten parameters (Fig. 4) [40]. The values of Km = 8.7 ± 1.9 mM and Vmax = 0.34 ± 0.03 mM min−1 for sucrose phosphorylase are in good agreement to values found in the literature [41–43]. While the exact conditions have varied among previous examples, reported values for Km range from 1.7 to 5.3 mM. A comparison of kinetic parameters is shown in Table 1.

2.3. Fluorescent assay in multiwell plate format The enzyme assays for SPO and PGM were prepared by mixing the reagents in aqueous glycylglycine buffer in 24-well plates. The reactions were initiated by the addition of the corresponding enzyme in solution, and real-time product formation was observed by the fluorescence increase at fixed time intervals for approximately 10 min. In the SPO assay, 4,4’-o-BBV gave a nearly linear response, while 3,3’-o-BBV began to saturate after 6 min (Fig. 3A). In contrast, 4,4’-o-BBV showed no response in the PGM assay and 3,3’o-BBV gave a nearly linear response (Fig. 3B). This can be explained by the different selectivity of the BBV/HPTS probes for enzymatic products [36]. Initial velocities Vi were calculated from ex situ calibration curves (Figures S2 and S3). Specifically, the linear portion of the calibration curve was used to convert fluorescent signal into product concentration for the first several minutes of the enzymatic assay. This was then converted into initial reaction velocity using Eq. (3). For SPO and PGM, an initial velocity of Vi = 0.25 ± 0.01 mM min−1 and Vi = 0.14 ± 0.01 mM min−1 , respectively, was calculated. These

Fig. 4. Fluorescence response of the SPO assay at different sucrose concentrations of 0.5 (), 5 (), 10 (), and 50 (䊉) mМ with enzyme concentration of 3.3 ␮g mL−1 (0.15 U mL−1 ). Background with no SPO (). Inset: plot of initial velocity Vi against sucrose concentration fitted with Michaelis–Menten equation (Eq. (S2)) [36].

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Table 1 Comparison of Michaelis–Menten kinetics for sucrose phosphorylase from the literature and current work. Source

pH

Temperature (◦ C)

Km (mM)

Vmax (␮mol min−1 U −1 )a

Method

Current work Ref. [41] Ref. [42] Ref. [43]

7.4 7.0 7.0 7.0

22 30 37 20

8.7 ± 1.9 2 5.31 1.66

2.2 ± 0.2 1.4 NDb NDb

Fluorescent probe for fructose Colorimetric assay for NADPH with enzyme-coupled reaction Colorimetric assay for NADH with enzyme-coupled reaction Colorimetric assay for NADPH with enzyme-coupled reaction

a b

Vmax is normalized to account for the quantity of enzyme in the reaction. ND (not determined).

Fig. 5. Fluorescence response of the PGM assay with different EDTA concentrations of 0 (䊉), 1.0 (), 2.0 (), and 4.0 () mM EDTA along with a blank () containing no enzyme. Reaction conditions: enzyme 0.54 ␮g mL−1 (0.13 U mL−1 ), 3,3’-o-BBV 0.50 mM, HPTS 4.0 ␮M, glucose-1-phosphate 5.0 mM, glucose-1,6-diphosphate 0.02 mM, MgCl2 2.0 mM, Gly–Gly 175 mM, pH 7.4, 22 ◦ C. Inset: initial velocity Vi against EDTA concentration [36].

2.5. Inhibition of PGM reaction The PGM assay was tested for the ability to screen for enzyme inhibitors in a high-throughput format. Known inhibitors, ETDA [44] and lithium ions [14], were taken to demonstrate the rapid screening possibilities with the new PGM assay. The results of the enzymatic assay in the presence of 2 mM Mg2+ and varying amounts of EDTA are shown in Fig. 5. Importantly, the chelator showed little effect on the system at concentrations below 2 mM, but reduced enzyme activity at concentrations equal to or above that of magnesium. The EDTA inhibition experiment, which was done in a 24-well

plate, provides further evidence that the assay is effectively reporting the conversion of glucose-1-phosphate to glucose-6-phosphate. The Mg2+ chelator EDTA disrupts the activity of PGM by removing the Lewis acidic metal center from the active site. In contrast, lithium ions inhibit the PGM reaction by a competitive displacement of the Mg2+ ions from the active sites. The velocity of the reaction shows a marked response to 1 mM lithium chloride; in contrast, sodium chloride and potassium chloride had little effect. (Fig. 6A). Plotting the reaction rate [45] as a function of inhibitor concentration gives an IC50 value of about 1.5 mM for LiCl (Fig. 6B). This is consistent with a previous example (measured using the colorimetric enzyme-coupled method detecting NADPH) in which 4 mM Li+ caused 50% inhibition of the enzyme in the presence of 4 mM Mg2+ [46]. This is especially relevant given that the therapeutic concentration of lithium is 0.6–1.2 mM [13], while magnesium concentrations are up to 1 mM in the cytosol [14]. Overall, the sensitivity of the fluorescent probe to these agents indicates that it can be used to find new, more potent inhibitors of PGM for the treatment of bipolar disorder or as anti-microbial agents. 2.6. Detection limit for PGM After observing an increase in sensitivity after reducing the magnesium chloride concentration in the PGM assay [36], we used those conditions to find whether the assay could be used to quantify enzyme concentration. To find the detection limit for phosphoglucomutase, the fluorescence signal (F/F0 ) was recorded after 5 and 120 min, measured from the time of addition of varying amounts of enzyme. As shown in Fig. 7, the response is linear after 5 min with a slope of 1.2 ± 0.02 × 10−3 ng mL−1 , and gives a detection limit of 50 ng mL−1 or 0.013 U mL−1 PGM. Even with the modest signal increase achieved after only 5 min reaction time, the sensitivity of the assay is as good as that from an amperometric biosensor for phosphoglucomutase [18]. Measuring after 120 min gave a greater

Fig. 6. Inhibition of PGM activity with 0.54 ␮g mL−1 (0.13 U mL−1 ) enzyme and 2 mM Mg2+ . (A) Fluorescence increase measured at 30 s intervals in the presence of 1 mM chloride salts of sodium (䊉), potassium (), and lithium (). The control () contains no added salts. (B) Initial rate (fluorescence intensity increase per minute) of enzymatic reaction in the presence of increasing salt concentrations [36].

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References

Fig. 7. Determination of PGM concentration. Fluorescence was measured after 5 min () and 120 min (䊉) of initiation with varying amounts of enzyme. For the signal at 5 min, the slope is 1.12 ± 0.02 × 10−3 mL ng−1 (R2 > 0.999). Error bars reflect the standard deviation among four separate trials [36].

signal with a non-linear plot, and also a much lower degree of precision. The reproducibility over four replicates, as measured by relative standard deviation, gave an average of 1.2% for a 5 min incubation time and 4.6% after 120 min. 3. Conclusion and outlook We have introduced a new method for the label-free monitoring of carbohydrate-modifying enzymes based on the two-component sensing ensemble BBV/HPTS. The saccharide receptors 4,4’-o-BBV and 3,3’-o-BBV were used to achieve product-selectivity in the two enzyme assays. This method requires no substrate/dye conjugate, radio-labeling, or sophisticated equipment for detection. It is also notable that 0.5 mM viologen quencher did not interfere with enzyme function or activity. The inexpensive fluorescent assays are suitable for high-throughput screening of potential inhibitors. For example, we anticipate that enzymatic reactions of sucrase, invertase, phosphodiesterases or mannitol and sorbitol dehydrogenases can also be followed with our versatile sensing ensemble in multiwell formats. In addition, phosphopentomutases, which catalyze the transfer of phosphate between the one and five positions of ribose or deoxyribose for the synthesis pool of nucleotides, can be assayed. We anticipate that the detection limit of the sensing ensemble can be further reduced by using boronic acid appended bis-viologens as carbohydrate receptors [47]. Studies to demonstrate this are currently in progress. Acknowledgements We thank GluMetrics, Inc., participating in the UC BioStar Industry–University Cooperative Research program (grant bio0410458), for continual financial support. We thank Dr. Mary Wessling for her helpful discussion and the ETOX Laboratory (UCSC) for providing the fluorescence plate reader. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.aca.2009.07.032.

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