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Measurements of calcium with a fluorescent probe Rhod-5N: Influence of high ionic strength and pH
Talanta 71 (2007) 437–442
Measurements of calcium with a fluorescent probe Rhod-5N: Influence of high ionic strength and pH Anne-C´ecile Ribou ∗ , Jean-Marie Salmon, Jean Vigo, Catherine Goyet University of Perpignan, BDSI Biophysics and dynamics of Integrated Systems, 52 av. Paul Alduy, 66860 Perpignan, France Received 25 November 2005; received in revised form 4 April 2006; accepted 14 April 2006 Available online 24 May 2006
Abstract We describe a new method for the spectroscopic determination of high calcium concentration using a fluorescent probe Rhod-5N. This method was investigated in order to be utilized in high ionic strength solution, such as seawater. The probe is fluorescent when bound to calcium, LM, but not as the free form L. The dissociation constant of the equilibrium (0.14 mM) was determined at several ionic strengths, i.e. in the absence and in the presence of additional ions (0.7 M NaCl). The influence of pH was studied. In order to correctly model the experimental data, we included a new fluorescent compound: LHM (calcium bound protonated probe). The first acidity constant (0.02 M) and the second dissociation constant (4.5 mM) were calculated. A useful range for the determination of calcium concentration is provided. Such a method is fast and easy to carry out. © 2006 Elsevier B.V. All rights reserved. Keywords: Rhod-5N; Fluorescence; Probe; Calcium; Data analysis; Seawater
1. Introduction Formation and dissolution of calcium carbonate in the ocean are important players in the global carbon cycle and are intimately related to the control of atmospheric CO2 . This gas, one of the most abundant green house gases in the earth’s atmosphere, is thought to be mostly absorbed by the oceans and ultimately neutralized by the reaction with CaCO3 in marine sediments. The precipitation and dissolution of calcium carbonate are a function of [Ca2+ ] and [CO3 2− ] concentrations as well as the calcite and argonite solubility constants. In the open ocean, variations of Ca2+ concentrations are rather small and related with salinity variations. However, a direct determination of [Ca2+ ] can help in the determination of CaCO3 saturation state and in the understanding of the carbon cycle. In 1976, Lebel and Poisson [1] proposed a potentiometric titration of magnesium and calcium ions in seawater. The method uses the differences between ethylenediaminetetraacetic acid (EDTA) and ethyleneglycol bis-(-aminoethyl ether)-NN tetraacetic acid (EGTA) dissociation constants. They obtain, in ideal conditions, a reproducibility of 1/1000. However, this
method is long and demanding. It requires stable environment to avoid erroneous measurements and it cannot be adapted for on board measurements, as a result, it is barely used. Recently, a number of teams attempted to develop new methods using electrophoresis [2], plasma atomic spectrometry [3,4] and nearinfrared spectroscopy [5]. We make use of our knowledge of fluorescent probe to conceive new calcium measurements. Molecular probe, Inc. provides calcium probe with high dissociation constant, the highest belonging to Rhod-5N. Fluorescent measurements are fast and require small volume of seawater (<1 ml). Nowadays, companies can provide small spectrofluorimeter that can be easily brought on boat. In this paper, we described the probe interaction with calcium and proton. We check the influence of high ionic strength on the measurement. We propose a methodology and a model to determine calcium quantity in high ionic strength solution, such as seawater. Finally, we test the reproducibility of the method and give a useful range of optimal utilization. 2. Experimental 2.1. Chemicals
∗
Corresponding author. Tel.: +33 468662113; fax: +33 468662144. E-mail address: [email protected] (A.-C. Ribou).
0039-9140/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.talanta.2006.04.011
CaCl2 , NaCl, HgCl2 and EDTA are of analytical grade and are used as received. A buffer solution of Titrisol at pH 8 is
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A.-C. Ribou et al. / Talanta 71 (2007) 437–442
used. No calcium concentration higher than residual calcium is detected in this solution. Addition of 10% of the buffer, give a stable pH (8.05 ± 0.02). Rhod-5N was purchased from Molecular Probe, Inc. Aliquots of 40 l Rhod-5N at 0.6 mM are kept at −20 ◦ C. Before use, the solution is diluted to the final volume of 1 ml with de-ionized water. The final concentration is tested by recording a fluorescence spectrum for each new solution. Ultrapure de-ionized water was generated by a MilliQ plus system (Millipore).
Table 1 Mean and standard deviation (S.D.) of Rhod-5N fluorescence intensities and calculated calcium concentrations for five identically prepared solutions
2.2. Fluorescence measurements
Mean S.D.
Emission fluorescence spectra are recorded with a spectrofluorimeter (Flx, SAFAS, Monte Carlo, Monaco) after excitation at 551 nm. At this wavelength and at the working concentration, the fluorescence intensity of the probe is more than thousand times higher than the combined intensities of the Raman band and the dissolved organic material in seawater samples. Residual calcium is found in the water used for the experiments. It has to be regularly checked that the residual concentration does not exceed 10 M. The glassware is washed with concentrated solution of acid (HCl) and rinsed with de-ionized water. If required, EDTA solution is used. Three different experiments were performed for Kd determination, for pH variation and for reproducibility of Ca2+ determination.
Correction factor for LH: 1.090 (Section 3.3.3). After addition of 25 l Ca (4 M) to the 1 ml solution. Correction factors: dilution factor (1.025/1) and probe saturation factor: 1.060 (Section 3.2.2). c [NaCl] = 0.07 M, [L] total = 0.48 M and KdLM = 1.4 mM. d γ Ca = 0.409.
2.2.1. Kd determination When the fluorescent spectra of the free probe L and the bound probe LM are different, Kd can be determined studying the evolution of the LM fluorescence spectra in presence of M. Knowing Kd the relation can be used to calculate the concentration of M. For these experiments, the concentration of probe L is chosen constant and we vary the concentration [M]total of calcium. Two solutions are prepared: solution A containing Rhod-5N (0.3–0.6 M), buffer at pH 8 (10%) and residual calcium, and solution B, containing specific calcium concentration in solution A. Varying concentrations of calcium are prepared by mixing different amounts of the two solutions A and B. If necessary, the pH is adjusted with micro-drop of NaOH. The fluorescence spectra are recorded for up to 14 calcium concentrations between 10 M and 20 mM. 2.2.2. pH variation With calcium chelating dyes, protonated and non-protonated probes show two different fluorescent forms [6]. We study the evolution of the LM fluorescent spectra in presence of H+ proton. This was done in order to determine at which pH the non-protonated form exists alone. For these experiments, microvolumes of NaOH or HCl are added to fresh solution B directly in the glass spectrocell. pH is measured with a pH-meter (PHN 81, Tacussel) with an accuracy of 0.01. The fluorescent spectra are recorded for 20 solutions ranging from 4 to 10. 2.2.3. Reproducibility For Ca2+ determination experiments, the reproducibility of the results is checked preparing several solutions of the same
Correcteda ILM (a.u.)
Correctedb Imax (a.u.)
(Ca)c (M)
[Ca]d (M)
7461 7414 7697 7471 7662
22699 22086 22738 22746 22777
4.10 × 10−4 4.23 × 10−4 4.29 × 10−4 4.10 × 10−4 4.25 × 10−4
1.00 × 10−3 1.04 × 10−3 1.05 × 10−3 1.00 × 10−3 1.04 × 10−3
7442 180
22600 290
4.19 × 10−4 0.08 × 10−4
1.03 × 10−3 0.02 × 10−3
a
b
calcium concentrations with various NaCl concentrations. In Table 1, 20 l of the probe (24 M), 10% of buffer (pH 8) and 100 l of NaCl (0.7 M) are mixed directly in the glass spectrocell with 100 l of calcium (10 mM). De-ionized water is added to obtain 1 ml final volume. After spectrum recording, 25 l of calcium (4 M) are added to the solution. This is done in order to check the variation of the total probe concentration [L]total . The pH is increased with micro-drops of NaOH to a value between 8.5 and 10. The probe spectrum in the solution with an excess of calcium is then recorded. The temperature is regulated at 25 ± 0.1 ◦ C. 2.3. Data analysis Since LM is the only fluorescent form, LM concentration can be calculated from the experimental data obtained at constant volume: [LM] =
ILM × [L]total Imax
(1)
where [L]total is the total probe concentration and [LM] is the calcium bound probe concentration. ILM is the intensity of LM at the equilibrium and Imax is the intensity if the entire probe is bound to calcium. It was initially determined after addition of an excess of calcium. After analysis of the fluorescence spectra, we obtain an experimental curve of LM concentration as a function of the total calcium concentration (Fig. 1) or as a function of pH (Fig. 2). The total calcium concentration is calculated considering the calcium concentration of solution B and calcium residual in solution A. 2.4. Theoretical model We created a theoretical model in order to model the experimental data. A system of equilibrium equations defines the binding model. Basic hypotheses about individual species involved in these interactions are made as follows.
A.-C. Ribou et al. / Talanta 71 (2007) 437–442
Fig. 1. Concentration of Rhod-5N bound to calcium vs. calcium concentration measured by fluorescence. The X-axis represents calcium concentration in the solution in mol per liter. The Y-axis represents LM concentration in mol per liter. Experimental data are shown as full symbols (), theoretical data obtained with Eq. (3) as full line. The dotted line corresponds to L concentration (free Rhod-5N). (A) [L]total = 0.51 M, [NaCl] = 0 M and (B) [L]total = 0.48 M, [NaCl] = 0.7 M.
2.4.1. Kd determination pH was maintained to 8 in order to avoid the presence of protonated form of the probe. The environment is modeled by the classical equilibrium between M (the calcium) and L (the free probe). We obtain: [L] = KdLM ×
γLM [LM] × γL × γ M [M]
(2)
We find the theoretical Eq. (3) resulting from the conservation of the probe concentration at constant volume [L]total = [L] + [LM]: [LM] =
[L]total (1 + (KdLM /[M]total ) × (γLM /γL × γM ))
(3)
The fluorescent probe concentration [LM] is connected to the total calcium concentration [M]total and total probe concentration [L]total with equilibrium constants KdLM as variable. We assume that [M] is equal to [M]total when [M]total > 100[L]total . In order to compare the experimental and the theoretical curves, the variables are computed with the solver of MS Excel [7]. 2.4.2. pH variation The complex model, presented here, is used to correctly simulate the pH variation experiments. The complex equilibrium system of L, M, H, LM, LMH, LH, LH2 species (L = Rhod-5N and M = calcium and H = proton), when the calcium M binds to
439
Fig. 2. Concentration of Rhod-5N bound to calcium vs. proton concentration measured by fluorescence. The X-axis represents pH value, corrected for the error of the pH-meter. The Y-axis represents LM concentration in mol per liter. Experimental data are shown as full symbols (), and theoretical data as full line (LM + LHM). The different component concentrations in solution calculated by the model are presented as dotted line. The compound name is given next to the respective curves: LM (Rhod-5N bound to calcium); LH (protonated Rhod-5N); LHM (protonated Rhod-5N bound to calcium); L (free probe). (A) [L]total = 0.58 M, [M]total = 0.1 M and (B) [L]total = 0.38 M, [M]total = 0.01 M.
L and to LH, is solved. Four equations for LM, LH, LHM and LH2 have to be solved. We assume that LM and LHM are both fluorescent. The mathematical resolution results from the conservation of the probe concentration [L]total = [LM] + [L] + [LH] + [LHM] + [LH2 ], with [L] defined in Eq. (2) [LH] =
1 γL × × (H) × [L] KaLH γLH
[LHM] = [LH2 ] =
1 KdLHM 1
KaLH2
×
×
γLH × γM × [LH] × [M] γLHM
γLH × (H) × [LH] γLH2
(4)
(5)
(6)
Combining these equations, we obtain second-degree equation to calculate [LM]. [LM] is computed resolving this seconddegree equation, [LHM] is computed with Eqs. (2), (4)–(6). Fluorescent probe concentration ([LM] + [LHM]) is connected to proton activity (H), total calcium concentration [M]total and total probe concentration [L]total with equilibrium constants KdLM , KaLH , KdLHM , KaLH2 as variables. The proton activity (H) is obtained from pH data.
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Fig. 3. Structure of calcium bound Rhod-5N: LM. Atoms in bold letters correspond to the crown ether structure. Global charge of the anion: 1, of the counter ion K+ : 1.
2.4.3. Activity coefficients Activity coefficients of each ions in the prepared solutions are calculated from Davies formula (derived from Debye and H¨uckel theory) [8]: √ I 2 √ − 0.3 × I log(γM ) = −A × zi (7) 1+ I The coefficient A varies with temperature; at 25 ◦ C we take 0.509. Notice that the ionic strength change with the ion concentration Ci (I = 1/2 ci z2i ). As long as the calcium concentration is above 0.1 mM we neglect the probe and proton concentrations. Thus, calcium concentrations vary during Kd determination experiments but not for pH variation experiments. It is also true for the activity coefficient of each ion. zi is the global charge of the ions. We assume that the global charge of the probe is equal to 3 for the free probe L, 1 for LM (Fig. 3), 2 for LH, 1 for LH2 and 0 for LHM. 3. Results and discussion The metal chelate LM is shown in Fig. 3. The probe forms a crown ether structure around the calcium ion, the two remaining carboxyl group positioning above and below the central structure. Complexation avoids possible interaction between carboxyl and amino groups due to electrostatic attraction. In the free probe L, the twist due to this interaction makes less favorable the delocalization in the rhodamine moiety. It certainly causes the quenching of the fluorescence of the free probe. 3.1. Rhod-5N emission The probe is fluorescent when bound to calcium, i.e. LM, with an intensity maximum at 574.5 nm. The linearity of the response of the probe fluorescence is verified when totally bounded, within the range 0.1–0.8 M Rhod-5N. After EDTA addition, the probe solution, i.e. L, does not show fluorescence anymore. Without EDTA, in de-ionized water the residual calcium bounds partially to the probe. Increasing the calcium concentration increases the fluorescence intensity of LM, the
Fig. 4. Experimental spectra of Rhod-5N (0.51 M) after excitation at 551 nm obtained for different calcium concentrations. The X-axis represents the emission wavelength in nanometer. The Y-axis represents the fluorescence intensity in arbitrary units. Five spectra were recorded separately and overlaid. The arrows pointed to the respective curves indicate the corresponding calcium concentration. Insert: The fluorescence intensity versus calcium bound probe concentration calculated from the corresponding calcium concentrations.
metal chelate. These results are shown in Fig. 4. The response of the fluorescence signal versus calcium bound probe, LM, concentration is linear (Fig. 4, insert) in all the range tested ([M] = 0.1–10 mM). The fluorescence spectrum shape does not change up to 0.2 M. However, we observe a gradual red-shift when the calcium concentration becomes higher than 0.2 M due to a more complex behavior. It is already known that the fluorescence of the cation probe Mag-Indo-1 changes with increasing calcium concentration [9]. Here, we record spectra below this calcium concentration. Besides, since the unbound probe L is degraded under irradiation, we carefully avoid irradiation before recording the spectrum and reduce the recording-range between 560 and 630 nm. We do not notice any degradation of the calcium bound probe LM. 3.2. Determination of Kd Fig. 1 shows the concentration of the calcium bound probe [LM] versus the total calcium concentration [M]total in absence (Fig. 1A) and in presence (Fig. 1B) of sodium chloride. Experimentally, the calcium concentration is decreased and the pH is kept at 8.0 (see Section 2). Experimental [LM] is calculated (Eq. (1)) from the intensities and the total probe concentration [L]total . Eq. (3) gives the theoretical [LM]. In Fig. 1A, only calcium and Rhod-5N are present in solution. The equilibrium between L and LM depends on the equilibrium constant, with KdLM the only variable in the equation to be computed with the solver of MS Excel. For each point, [M]total is calculated using the calcium concentration of solution B and calcium residual in solution A. This concentration varies from one experiment to the other. It is calculated from the fluorescence intensity of solution A and we use it as an additional variable in the model. We compute the dissociation constant (0.14 ± 0.03 mM) and the residual calcium concentration. KdLM is lower than the dissociation given by Molecular Probe (0.32 mM). The residual calcium (13 M) was exceptionally high in our first experiment. The correction for residual calcium is not necessary in this case, but improved
A.-C. Ribou et al. / Talanta 71 (2007) 437–442
the fit of experimental and modeled curves at lower calcium concentrations. 3.2.1. Addition of NaCl Seawater is a complex medium. If the calcium is present at about 10 mM, the other ions increase the global ionic concentrations. Salinity 35 is equivalent to a sodium chloride concentration of 0.7 M. To confirm the validity of our model and to test KdLM value, we decided to reproduce the experiments replacing the de-ionized water by a solution of 0.7 M NaCl. The experimental data and the model (Eq. (3)) is shown in Fig. 1B. The ionic strength of our solutions (0.69–0.72) is slightly higher than the limit recommended by Davies formula (I > 0.5). However, we obtain a reasonable good similarity between the experimental and theoretical data with identical KdLM value (0.14 mM) and residual calcium concentration of 1.2 mM. This high concentration is probably due to a calcium impurity in the commercially obtained NaCl. As expected, after NaCl addition, the probe binding is delayed. After addition of 20 mM of calcium the probe is not fully bound anymore. 3.2.2. Imax calculation To calculate the experimental [LM] with Eq. (1), we need to obtain Imax , the intensity when the entire probe is bound to calcium. Generally (Fig. 1), the employed calcium concentration is not sufficient to entirely bind the probe especially for high ionic strength solutions. We perform a correction to obtain a realistic value of Imax . Moreover, calcium concentration higher than 0.2 M cannot be used without changing the probe binding. From the theoretical model, we calculate Imax . For example, with initial [M]total = 0.02 M, [L]total = 0.48 M and [NaCl] = 0.7 M (Fig. 1B) we used a probe saturation factor of 1.198 (4.800/4.006). After correction we obtained Imax = 22,300 a.u., the intensity of the first recorded spectrum (higher calcium concentration) was only of 18,600 a.u. 3.3. pH variation Accurate results require careful control of pH value since the binding equilibrium is strongly dependent on pH. Molecular Probes advises to work at pH above 6 [10]. LH is a nonfluorescent form of the probe. However, the fluorescent probe LM concentration will depend on LH deprotonation. To confirm that at pH 8 no LH is present, we perform pH variation experiments. Fig. 2 shows the experimental data obtained for constant calcium concentrations, [M]total = 0.1 M (Fig. 2A) and for [M]total = 0.01 M (Fig. 2B). The latter concentration corresponds to the calcium concentration in seawater. At these concentrations even for high pH values, the probe is not totally bound to calcium (94% and 91%, respectively). The ionic strength (I = 0.3 and 0.03, respectively) is not dependent on the proton concentration. Therefore, the ion activities are constant. To model these experimental data, the equilibrium of LM and LH alone cannot be used. The shape of the curve is too complex. To correctly model these data, we use the second-degree equation described in Section 2.
441
3.3.1. Model We assume that calcium can bind LH. The new complex LHM is fluorescent and shows a spectrum identical to the one of LM. Since the structure of LHM is very similar to the one of LM (i.e. no interaction between carboxyl and amino groups) there is no reason for a spectral change. But, we expect the affinity of LH to calcium to be smaller than that of L since only three carboxyl groups are present. The new dissociation constant is KdLHM . Thus, the addition of a fourth equilibrium (for the formation of LH2 in competition with LHM) with a second acidity constant (KaLH2 ) is necessary. The addition of subsequent LH3 and LH2 M forms of the probe was not required as our model already correctly fit the experimental data. Moreover, the affinity of LH2 for calcium must be highly reduced. We were able to model the two sets of data with the same set of constants after a careful search for the global charge of the probe complexes. We make simple hypotheses as followed: carboxyl groups: four negative charges and amino group: one positive charge (global charge of L: 3). After addition of Ca2+ , the global charge of LM is 1 (Fig. 3). After reaction of one carboxyl group with a proton, the global charge of LH is 2 and that of LHM is 0. 3.3.2. Dissociation and acidity constants The simulation of the experimental data with a model with four constants allows for many possible solutions for the four values. To obtain the new constants with reliability, we set KdLM to 0.14 mM. This enabled us to find for the two experiments (Fig. 2A and B), the following set of constants: dissociation, KdLHM = 4.5 mM and acidity, KaLH = 0.02 M and KaLH2 = 15 M. The presence of a second calcium-probe equilibrium can explain the difference found between the dissociation constant given by Molecular Probe (0.32 mM) and our dissociation constants (0.14 and 4.5 mM). The value of pKaLH is 7.7. 3.3.3. Working pH In Fig. 2, we can observe that the protonated forms of the probe, LH and LHM; are present, among others, between pH 6 and 8. From the theoretical model established for the pH variation, we can extrapolate the pH value from which these two protonated forms disappeared. In Fig. 2B ([Ca2+ ] = 0.01 M), at pH 8, less than 2% of the probe are bound to proton. For [Ca2+ ] = 0.001 M, 9% of the probe are bound to protons. This will restrict the use of Eq. (3) for measurements of calcium at this pH and lower one. However, a mathematical correction of the probe concentration can be simply obtained from the theoretical model. This will allow working at a chosen pH. 3.4. Useful range of utilization and reproducibility The method is tested for the determination of calcium concentration by multiple replicate measurements. Different manipulation conditions are tested and compared (replacement of titrisol solution by NaOH, pH 9). We have also tested the potential interactions of other cations with Rodh-5N to mimic the complexity of seawater. We have checked the effect of the addition of MgCl2 (Mg2+ being the main cation in seawater after Na+ ) and of the
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addition of HgCl2 (1 l/1 ml, an inhibitor of biological development that is added to the sea sample for technical reason). We did not see changes of the spectrum shape or changes of fluorescence intensities after addition of HgCl2 or MgCl2 . In order to obtain an optimal utilization range, we make the hypothesis that we obtain a reliable evaluation of calcium concentration between pKd −1 and pKd + 1. In this case the intensity ratio, ILM /Imax , is between 0.1 and 0.9. In theory, this is related to a calcium concentration between 0.14 M and 1.4 mM. However, in this calcium concentration domain, the ionic strength effect is not negligible. If we calculate with our model the ionic strength effect due to calcium alone (i.e. without [NaCl]), the domain ranges from [Ca] = 20 M to 7 mM. Considering that domain and the calcium concentrations usually found in seawater, we should dilute a seawater sample tenfold. In this case, we have to consider the presence of other ions in the diluted sample. Thus, for NaCl = 0.07 M, we obtain the domain for calcium concentrations ranging from 0.2 to 40 mM. With this approach, we will be able to adapt the domain of measurements depending upon the experimental conditions. The results obtained for one set of measurements ([Ca] = 1 mM and [NaCl] = 0.07 M) are shown in Table 1. The calcium activities are calculated from Eqs. (1) and (3) after correction of the presence of LH around pH 8. The correction factor for LH, 1.090 for pH 8.05 was obtained from the theoretical model. Within the variation range of pH (±0.02 after addition of 1/10 of the titrisol solution, pH 8), this correction factor varies only 1/1000th fold. NaCl concentration (0.07 M) was used to evaluate the ionic strength value using our model. We obtained after iterative calculation, a ionic strength of 0.073 for
the experimental solution, allowing us to calculate an activity coefficient of 0.409 for calcium. We obtained the mean calcium activity and the mean concentration of 0.419 and 1.03 mM, respectively (Table 1). The reproducibility is expressed as the standard deviation of the five samples (S.D. = 0.02 mM for calcium concentration). We are now testing if this accuracy (<2%) is sufficient to measure calcium concentration variations in seawater collections. The spectroscopic determination of calcium concentrations in high ionic strength solutions constitutes a very rapid method. The new method described here was successfully tested on seawater collected from 3000 m depth to surface Pacific Ocean water and we intend to develop automated measurements. This will increase the accuracy of data acquisition and will allow us to perform the measurements directly on board oceanographic ships just after sampling. References [1] J. Lebel, A. Poisson, Mar. Chem. 4 (1976) 321. [2] T. Wang, H.L. Hian, S.F.Y. Li, J. Liq. Chromatogr. R. T. 21 (1998) 2485. [3] G. Abbasse, G. Ouddane, J.-C. Fischer, J. Anal. Atom. Spectrom. 17 (2002) 1354. [4] K. Mitko, M. Bebek, Atom. Spectrosc. 21 (2000) 77. [5] J.Y. Chen, R. Mastsunaga, K. Ishikawa, H. Zhang, Appl. Spectrosc. 57 (2003) 1399. [6] A.-C. Ribou, J. Vigo, P.M. Viallet, J.-M. Salmon, Biophys. Chem. 81 (2000) 179. [7] Microsoft Windows 98 Microsoft Excel 97 SR-2. [8] C.W. Davies, Ion Dissociation, Butterworths, London, 1962, p. 41. [9] J. Pesco, J.-M. Salmon, J. Vigo, P. Viallet, Anal. Biochem. 290 (2001) 221. [10] Molecular Probe, www.probes.com/handbook, section 20.3.
Measurements of calcium with a fluorescent probe Rhod-5N: Influence of high ionic strength and pH Anne-C´ecile Ribou ∗ , Jean-Marie Salmon, Jean Vigo, Catherine Goyet University of Perpignan, BDSI Biophysics and dynamics of Integrated Systems, 52 av. Paul Alduy, 66860 Perpignan, France Received 25 November 2005; received in revised form 4 April 2006; accepted 14 April 2006 Available online 24 May 2006
Abstract We describe a new method for the spectroscopic determination of high calcium concentration using a fluorescent probe Rhod-5N. This method was investigated in order to be utilized in high ionic strength solution, such as seawater. The probe is fluorescent when bound to calcium, LM, but not as the free form L. The dissociation constant of the equilibrium (0.14 mM) was determined at several ionic strengths, i.e. in the absence and in the presence of additional ions (0.7 M NaCl). The influence of pH was studied. In order to correctly model the experimental data, we included a new fluorescent compound: LHM (calcium bound protonated probe). The first acidity constant (0.02 M) and the second dissociation constant (4.5 mM) were calculated. A useful range for the determination of calcium concentration is provided. Such a method is fast and easy to carry out. © 2006 Elsevier B.V. All rights reserved. Keywords: Rhod-5N; Fluorescence; Probe; Calcium; Data analysis; Seawater
1. Introduction Formation and dissolution of calcium carbonate in the ocean are important players in the global carbon cycle and are intimately related to the control of atmospheric CO2 . This gas, one of the most abundant green house gases in the earth’s atmosphere, is thought to be mostly absorbed by the oceans and ultimately neutralized by the reaction with CaCO3 in marine sediments. The precipitation and dissolution of calcium carbonate are a function of [Ca2+ ] and [CO3 2− ] concentrations as well as the calcite and argonite solubility constants. In the open ocean, variations of Ca2+ concentrations are rather small and related with salinity variations. However, a direct determination of [Ca2+ ] can help in the determination of CaCO3 saturation state and in the understanding of the carbon cycle. In 1976, Lebel and Poisson [1] proposed a potentiometric titration of magnesium and calcium ions in seawater. The method uses the differences between ethylenediaminetetraacetic acid (EDTA) and ethyleneglycol bis-(-aminoethyl ether)-NN tetraacetic acid (EGTA) dissociation constants. They obtain, in ideal conditions, a reproducibility of 1/1000. However, this
method is long and demanding. It requires stable environment to avoid erroneous measurements and it cannot be adapted for on board measurements, as a result, it is barely used. Recently, a number of teams attempted to develop new methods using electrophoresis [2], plasma atomic spectrometry [3,4] and nearinfrared spectroscopy [5]. We make use of our knowledge of fluorescent probe to conceive new calcium measurements. Molecular probe, Inc. provides calcium probe with high dissociation constant, the highest belonging to Rhod-5N. Fluorescent measurements are fast and require small volume of seawater (<1 ml). Nowadays, companies can provide small spectrofluorimeter that can be easily brought on boat. In this paper, we described the probe interaction with calcium and proton. We check the influence of high ionic strength on the measurement. We propose a methodology and a model to determine calcium quantity in high ionic strength solution, such as seawater. Finally, we test the reproducibility of the method and give a useful range of optimal utilization. 2. Experimental 2.1. Chemicals
∗
Corresponding author. Tel.: +33 468662113; fax: +33 468662144. E-mail address: [email protected] (A.-C. Ribou).
0039-9140/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.talanta.2006.04.011
CaCl2 , NaCl, HgCl2 and EDTA are of analytical grade and are used as received. A buffer solution of Titrisol at pH 8 is
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A.-C. Ribou et al. / Talanta 71 (2007) 437–442
used. No calcium concentration higher than residual calcium is detected in this solution. Addition of 10% of the buffer, give a stable pH (8.05 ± 0.02). Rhod-5N was purchased from Molecular Probe, Inc. Aliquots of 40 l Rhod-5N at 0.6 mM are kept at −20 ◦ C. Before use, the solution is diluted to the final volume of 1 ml with de-ionized water. The final concentration is tested by recording a fluorescence spectrum for each new solution. Ultrapure de-ionized water was generated by a MilliQ plus system (Millipore).
Table 1 Mean and standard deviation (S.D.) of Rhod-5N fluorescence intensities and calculated calcium concentrations for five identically prepared solutions
2.2. Fluorescence measurements
Mean S.D.
Emission fluorescence spectra are recorded with a spectrofluorimeter (Flx, SAFAS, Monte Carlo, Monaco) after excitation at 551 nm. At this wavelength and at the working concentration, the fluorescence intensity of the probe is more than thousand times higher than the combined intensities of the Raman band and the dissolved organic material in seawater samples. Residual calcium is found in the water used for the experiments. It has to be regularly checked that the residual concentration does not exceed 10 M. The glassware is washed with concentrated solution of acid (HCl) and rinsed with de-ionized water. If required, EDTA solution is used. Three different experiments were performed for Kd determination, for pH variation and for reproducibility of Ca2+ determination.
Correction factor for LH: 1.090 (Section 3.3.3). After addition of 25 l Ca (4 M) to the 1 ml solution. Correction factors: dilution factor (1.025/1) and probe saturation factor: 1.060 (Section 3.2.2). c [NaCl] = 0.07 M, [L] total = 0.48 M and KdLM = 1.4 mM. d γ Ca = 0.409.
2.2.1. Kd determination When the fluorescent spectra of the free probe L and the bound probe LM are different, Kd can be determined studying the evolution of the LM fluorescence spectra in presence of M. Knowing Kd the relation can be used to calculate the concentration of M. For these experiments, the concentration of probe L is chosen constant and we vary the concentration [M]total of calcium. Two solutions are prepared: solution A containing Rhod-5N (0.3–0.6 M), buffer at pH 8 (10%) and residual calcium, and solution B, containing specific calcium concentration in solution A. Varying concentrations of calcium are prepared by mixing different amounts of the two solutions A and B. If necessary, the pH is adjusted with micro-drop of NaOH. The fluorescence spectra are recorded for up to 14 calcium concentrations between 10 M and 20 mM. 2.2.2. pH variation With calcium chelating dyes, protonated and non-protonated probes show two different fluorescent forms [6]. We study the evolution of the LM fluorescent spectra in presence of H+ proton. This was done in order to determine at which pH the non-protonated form exists alone. For these experiments, microvolumes of NaOH or HCl are added to fresh solution B directly in the glass spectrocell. pH is measured with a pH-meter (PHN 81, Tacussel) with an accuracy of 0.01. The fluorescent spectra are recorded for 20 solutions ranging from 4 to 10. 2.2.3. Reproducibility For Ca2+ determination experiments, the reproducibility of the results is checked preparing several solutions of the same
Correcteda ILM (a.u.)
Correctedb Imax (a.u.)
(Ca)c (M)
[Ca]d (M)
7461 7414 7697 7471 7662
22699 22086 22738 22746 22777
4.10 × 10−4 4.23 × 10−4 4.29 × 10−4 4.10 × 10−4 4.25 × 10−4
1.00 × 10−3 1.04 × 10−3 1.05 × 10−3 1.00 × 10−3 1.04 × 10−3
7442 180
22600 290
4.19 × 10−4 0.08 × 10−4
1.03 × 10−3 0.02 × 10−3
a
b
calcium concentrations with various NaCl concentrations. In Table 1, 20 l of the probe (24 M), 10% of buffer (pH 8) and 100 l of NaCl (0.7 M) are mixed directly in the glass spectrocell with 100 l of calcium (10 mM). De-ionized water is added to obtain 1 ml final volume. After spectrum recording, 25 l of calcium (4 M) are added to the solution. This is done in order to check the variation of the total probe concentration [L]total . The pH is increased with micro-drops of NaOH to a value between 8.5 and 10. The probe spectrum in the solution with an excess of calcium is then recorded. The temperature is regulated at 25 ± 0.1 ◦ C. 2.3. Data analysis Since LM is the only fluorescent form, LM concentration can be calculated from the experimental data obtained at constant volume: [LM] =
ILM × [L]total Imax
(1)
where [L]total is the total probe concentration and [LM] is the calcium bound probe concentration. ILM is the intensity of LM at the equilibrium and Imax is the intensity if the entire probe is bound to calcium. It was initially determined after addition of an excess of calcium. After analysis of the fluorescence spectra, we obtain an experimental curve of LM concentration as a function of the total calcium concentration (Fig. 1) or as a function of pH (Fig. 2). The total calcium concentration is calculated considering the calcium concentration of solution B and calcium residual in solution A. 2.4. Theoretical model We created a theoretical model in order to model the experimental data. A system of equilibrium equations defines the binding model. Basic hypotheses about individual species involved in these interactions are made as follows.
A.-C. Ribou et al. / Talanta 71 (2007) 437–442
Fig. 1. Concentration of Rhod-5N bound to calcium vs. calcium concentration measured by fluorescence. The X-axis represents calcium concentration in the solution in mol per liter. The Y-axis represents LM concentration in mol per liter. Experimental data are shown as full symbols (), theoretical data obtained with Eq. (3) as full line. The dotted line corresponds to L concentration (free Rhod-5N). (A) [L]total = 0.51 M, [NaCl] = 0 M and (B) [L]total = 0.48 M, [NaCl] = 0.7 M.
2.4.1. Kd determination pH was maintained to 8 in order to avoid the presence of protonated form of the probe. The environment is modeled by the classical equilibrium between M (the calcium) and L (the free probe). We obtain: [L] = KdLM ×
γLM [LM] × γL × γ M [M]
(2)
We find the theoretical Eq. (3) resulting from the conservation of the probe concentration at constant volume [L]total = [L] + [LM]: [LM] =
[L]total (1 + (KdLM /[M]total ) × (γLM /γL × γM ))
(3)
The fluorescent probe concentration [LM] is connected to the total calcium concentration [M]total and total probe concentration [L]total with equilibrium constants KdLM as variable. We assume that [M] is equal to [M]total when [M]total > 100[L]total . In order to compare the experimental and the theoretical curves, the variables are computed with the solver of MS Excel [7]. 2.4.2. pH variation The complex model, presented here, is used to correctly simulate the pH variation experiments. The complex equilibrium system of L, M, H, LM, LMH, LH, LH2 species (L = Rhod-5N and M = calcium and H = proton), when the calcium M binds to
439
Fig. 2. Concentration of Rhod-5N bound to calcium vs. proton concentration measured by fluorescence. The X-axis represents pH value, corrected for the error of the pH-meter. The Y-axis represents LM concentration in mol per liter. Experimental data are shown as full symbols (), and theoretical data as full line (LM + LHM). The different component concentrations in solution calculated by the model are presented as dotted line. The compound name is given next to the respective curves: LM (Rhod-5N bound to calcium); LH (protonated Rhod-5N); LHM (protonated Rhod-5N bound to calcium); L (free probe). (A) [L]total = 0.58 M, [M]total = 0.1 M and (B) [L]total = 0.38 M, [M]total = 0.01 M.
L and to LH, is solved. Four equations for LM, LH, LHM and LH2 have to be solved. We assume that LM and LHM are both fluorescent. The mathematical resolution results from the conservation of the probe concentration [L]total = [LM] + [L] + [LH] + [LHM] + [LH2 ], with [L] defined in Eq. (2) [LH] =
1 γL × × (H) × [L] KaLH γLH
[LHM] = [LH2 ] =
1 KdLHM 1
KaLH2
×
×
γLH × γM × [LH] × [M] γLHM
γLH × (H) × [LH] γLH2
(4)
(5)
(6)
Combining these equations, we obtain second-degree equation to calculate [LM]. [LM] is computed resolving this seconddegree equation, [LHM] is computed with Eqs. (2), (4)–(6). Fluorescent probe concentration ([LM] + [LHM]) is connected to proton activity (H), total calcium concentration [M]total and total probe concentration [L]total with equilibrium constants KdLM , KaLH , KdLHM , KaLH2 as variables. The proton activity (H) is obtained from pH data.
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Fig. 3. Structure of calcium bound Rhod-5N: LM. Atoms in bold letters correspond to the crown ether structure. Global charge of the anion: 1, of the counter ion K+ : 1.
2.4.3. Activity coefficients Activity coefficients of each ions in the prepared solutions are calculated from Davies formula (derived from Debye and H¨uckel theory) [8]: √ I 2 √ − 0.3 × I log(γM ) = −A × zi (7) 1+ I The coefficient A varies with temperature; at 25 ◦ C we take 0.509. Notice that the ionic strength change with the ion concentration Ci (I = 1/2 ci z2i ). As long as the calcium concentration is above 0.1 mM we neglect the probe and proton concentrations. Thus, calcium concentrations vary during Kd determination experiments but not for pH variation experiments. It is also true for the activity coefficient of each ion. zi is the global charge of the ions. We assume that the global charge of the probe is equal to 3 for the free probe L, 1 for LM (Fig. 3), 2 for LH, 1 for LH2 and 0 for LHM. 3. Results and discussion The metal chelate LM is shown in Fig. 3. The probe forms a crown ether structure around the calcium ion, the two remaining carboxyl group positioning above and below the central structure. Complexation avoids possible interaction between carboxyl and amino groups due to electrostatic attraction. In the free probe L, the twist due to this interaction makes less favorable the delocalization in the rhodamine moiety. It certainly causes the quenching of the fluorescence of the free probe. 3.1. Rhod-5N emission The probe is fluorescent when bound to calcium, i.e. LM, with an intensity maximum at 574.5 nm. The linearity of the response of the probe fluorescence is verified when totally bounded, within the range 0.1–0.8 M Rhod-5N. After EDTA addition, the probe solution, i.e. L, does not show fluorescence anymore. Without EDTA, in de-ionized water the residual calcium bounds partially to the probe. Increasing the calcium concentration increases the fluorescence intensity of LM, the
Fig. 4. Experimental spectra of Rhod-5N (0.51 M) after excitation at 551 nm obtained for different calcium concentrations. The X-axis represents the emission wavelength in nanometer. The Y-axis represents the fluorescence intensity in arbitrary units. Five spectra were recorded separately and overlaid. The arrows pointed to the respective curves indicate the corresponding calcium concentration. Insert: The fluorescence intensity versus calcium bound probe concentration calculated from the corresponding calcium concentrations.
metal chelate. These results are shown in Fig. 4. The response of the fluorescence signal versus calcium bound probe, LM, concentration is linear (Fig. 4, insert) in all the range tested ([M] = 0.1–10 mM). The fluorescence spectrum shape does not change up to 0.2 M. However, we observe a gradual red-shift when the calcium concentration becomes higher than 0.2 M due to a more complex behavior. It is already known that the fluorescence of the cation probe Mag-Indo-1 changes with increasing calcium concentration [9]. Here, we record spectra below this calcium concentration. Besides, since the unbound probe L is degraded under irradiation, we carefully avoid irradiation before recording the spectrum and reduce the recording-range between 560 and 630 nm. We do not notice any degradation of the calcium bound probe LM. 3.2. Determination of Kd Fig. 1 shows the concentration of the calcium bound probe [LM] versus the total calcium concentration [M]total in absence (Fig. 1A) and in presence (Fig. 1B) of sodium chloride. Experimentally, the calcium concentration is decreased and the pH is kept at 8.0 (see Section 2). Experimental [LM] is calculated (Eq. (1)) from the intensities and the total probe concentration [L]total . Eq. (3) gives the theoretical [LM]. In Fig. 1A, only calcium and Rhod-5N are present in solution. The equilibrium between L and LM depends on the equilibrium constant, with KdLM the only variable in the equation to be computed with the solver of MS Excel. For each point, [M]total is calculated using the calcium concentration of solution B and calcium residual in solution A. This concentration varies from one experiment to the other. It is calculated from the fluorescence intensity of solution A and we use it as an additional variable in the model. We compute the dissociation constant (0.14 ± 0.03 mM) and the residual calcium concentration. KdLM is lower than the dissociation given by Molecular Probe (0.32 mM). The residual calcium (13 M) was exceptionally high in our first experiment. The correction for residual calcium is not necessary in this case, but improved
A.-C. Ribou et al. / Talanta 71 (2007) 437–442
the fit of experimental and modeled curves at lower calcium concentrations. 3.2.1. Addition of NaCl Seawater is a complex medium. If the calcium is present at about 10 mM, the other ions increase the global ionic concentrations. Salinity 35 is equivalent to a sodium chloride concentration of 0.7 M. To confirm the validity of our model and to test KdLM value, we decided to reproduce the experiments replacing the de-ionized water by a solution of 0.7 M NaCl. The experimental data and the model (Eq. (3)) is shown in Fig. 1B. The ionic strength of our solutions (0.69–0.72) is slightly higher than the limit recommended by Davies formula (I > 0.5). However, we obtain a reasonable good similarity between the experimental and theoretical data with identical KdLM value (0.14 mM) and residual calcium concentration of 1.2 mM. This high concentration is probably due to a calcium impurity in the commercially obtained NaCl. As expected, after NaCl addition, the probe binding is delayed. After addition of 20 mM of calcium the probe is not fully bound anymore. 3.2.2. Imax calculation To calculate the experimental [LM] with Eq. (1), we need to obtain Imax , the intensity when the entire probe is bound to calcium. Generally (Fig. 1), the employed calcium concentration is not sufficient to entirely bind the probe especially for high ionic strength solutions. We perform a correction to obtain a realistic value of Imax . Moreover, calcium concentration higher than 0.2 M cannot be used without changing the probe binding. From the theoretical model, we calculate Imax . For example, with initial [M]total = 0.02 M, [L]total = 0.48 M and [NaCl] = 0.7 M (Fig. 1B) we used a probe saturation factor of 1.198 (4.800/4.006). After correction we obtained Imax = 22,300 a.u., the intensity of the first recorded spectrum (higher calcium concentration) was only of 18,600 a.u. 3.3. pH variation Accurate results require careful control of pH value since the binding equilibrium is strongly dependent on pH. Molecular Probes advises to work at pH above 6 [10]. LH is a nonfluorescent form of the probe. However, the fluorescent probe LM concentration will depend on LH deprotonation. To confirm that at pH 8 no LH is present, we perform pH variation experiments. Fig. 2 shows the experimental data obtained for constant calcium concentrations, [M]total = 0.1 M (Fig. 2A) and for [M]total = 0.01 M (Fig. 2B). The latter concentration corresponds to the calcium concentration in seawater. At these concentrations even for high pH values, the probe is not totally bound to calcium (94% and 91%, respectively). The ionic strength (I = 0.3 and 0.03, respectively) is not dependent on the proton concentration. Therefore, the ion activities are constant. To model these experimental data, the equilibrium of LM and LH alone cannot be used. The shape of the curve is too complex. To correctly model these data, we use the second-degree equation described in Section 2.
441
3.3.1. Model We assume that calcium can bind LH. The new complex LHM is fluorescent and shows a spectrum identical to the one of LM. Since the structure of LHM is very similar to the one of LM (i.e. no interaction between carboxyl and amino groups) there is no reason for a spectral change. But, we expect the affinity of LH to calcium to be smaller than that of L since only three carboxyl groups are present. The new dissociation constant is KdLHM . Thus, the addition of a fourth equilibrium (for the formation of LH2 in competition with LHM) with a second acidity constant (KaLH2 ) is necessary. The addition of subsequent LH3 and LH2 M forms of the probe was not required as our model already correctly fit the experimental data. Moreover, the affinity of LH2 for calcium must be highly reduced. We were able to model the two sets of data with the same set of constants after a careful search for the global charge of the probe complexes. We make simple hypotheses as followed: carboxyl groups: four negative charges and amino group: one positive charge (global charge of L: 3). After addition of Ca2+ , the global charge of LM is 1 (Fig. 3). After reaction of one carboxyl group with a proton, the global charge of LH is 2 and that of LHM is 0. 3.3.2. Dissociation and acidity constants The simulation of the experimental data with a model with four constants allows for many possible solutions for the four values. To obtain the new constants with reliability, we set KdLM to 0.14 mM. This enabled us to find for the two experiments (Fig. 2A and B), the following set of constants: dissociation, KdLHM = 4.5 mM and acidity, KaLH = 0.02 M and KaLH2 = 15 M. The presence of a second calcium-probe equilibrium can explain the difference found between the dissociation constant given by Molecular Probe (0.32 mM) and our dissociation constants (0.14 and 4.5 mM). The value of pKaLH is 7.7. 3.3.3. Working pH In Fig. 2, we can observe that the protonated forms of the probe, LH and LHM; are present, among others, between pH 6 and 8. From the theoretical model established for the pH variation, we can extrapolate the pH value from which these two protonated forms disappeared. In Fig. 2B ([Ca2+ ] = 0.01 M), at pH 8, less than 2% of the probe are bound to proton. For [Ca2+ ] = 0.001 M, 9% of the probe are bound to protons. This will restrict the use of Eq. (3) for measurements of calcium at this pH and lower one. However, a mathematical correction of the probe concentration can be simply obtained from the theoretical model. This will allow working at a chosen pH. 3.4. Useful range of utilization and reproducibility The method is tested for the determination of calcium concentration by multiple replicate measurements. Different manipulation conditions are tested and compared (replacement of titrisol solution by NaOH, pH 9). We have also tested the potential interactions of other cations with Rodh-5N to mimic the complexity of seawater. We have checked the effect of the addition of MgCl2 (Mg2+ being the main cation in seawater after Na+ ) and of the
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addition of HgCl2 (1 l/1 ml, an inhibitor of biological development that is added to the sea sample for technical reason). We did not see changes of the spectrum shape or changes of fluorescence intensities after addition of HgCl2 or MgCl2 . In order to obtain an optimal utilization range, we make the hypothesis that we obtain a reliable evaluation of calcium concentration between pKd −1 and pKd + 1. In this case the intensity ratio, ILM /Imax , is between 0.1 and 0.9. In theory, this is related to a calcium concentration between 0.14 M and 1.4 mM. However, in this calcium concentration domain, the ionic strength effect is not negligible. If we calculate with our model the ionic strength effect due to calcium alone (i.e. without [NaCl]), the domain ranges from [Ca] = 20 M to 7 mM. Considering that domain and the calcium concentrations usually found in seawater, we should dilute a seawater sample tenfold. In this case, we have to consider the presence of other ions in the diluted sample. Thus, for NaCl = 0.07 M, we obtain the domain for calcium concentrations ranging from 0.2 to 40 mM. With this approach, we will be able to adapt the domain of measurements depending upon the experimental conditions. The results obtained for one set of measurements ([Ca] = 1 mM and [NaCl] = 0.07 M) are shown in Table 1. The calcium activities are calculated from Eqs. (1) and (3) after correction of the presence of LH around pH 8. The correction factor for LH, 1.090 for pH 8.05 was obtained from the theoretical model. Within the variation range of pH (±0.02 after addition of 1/10 of the titrisol solution, pH 8), this correction factor varies only 1/1000th fold. NaCl concentration (0.07 M) was used to evaluate the ionic strength value using our model. We obtained after iterative calculation, a ionic strength of 0.073 for
the experimental solution, allowing us to calculate an activity coefficient of 0.409 for calcium. We obtained the mean calcium activity and the mean concentration of 0.419 and 1.03 mM, respectively (Table 1). The reproducibility is expressed as the standard deviation of the five samples (S.D. = 0.02 mM for calcium concentration). We are now testing if this accuracy (<2%) is sufficient to measure calcium concentration variations in seawater collections. The spectroscopic determination of calcium concentrations in high ionic strength solutions constitutes a very rapid method. The new method described here was successfully tested on seawater collected from 3000 m depth to surface Pacific Ocean water and we intend to develop automated measurements. This will increase the accuracy of data acquisition and will allow us to perform the measurements directly on board oceanographic ships just after sampling. References [1] J. Lebel, A. Poisson, Mar. Chem. 4 (1976) 321. [2] T. Wang, H.L. Hian, S.F.Y. Li, J. Liq. Chromatogr. R. T. 21 (1998) 2485. [3] G. Abbasse, G. Ouddane, J.-C. Fischer, J. Anal. Atom. Spectrom. 17 (2002) 1354. [4] K. Mitko, M. Bebek, Atom. Spectrosc. 21 (2000) 77. [5] J.Y. Chen, R. Mastsunaga, K. Ishikawa, H. Zhang, Appl. Spectrosc. 57 (2003) 1399. [6] A.-C. Ribou, J. Vigo, P.M. Viallet, J.-M. Salmon, Biophys. Chem. 81 (2000) 179. [7] Microsoft Windows 98 Microsoft Excel 97 SR-2. [8] C.W. Davies, Ion Dissociation, Butterworths, London, 1962, p. 41. [9] J. Pesco, J.-M. Salmon, J. Vigo, P. Viallet, Anal. Biochem. 290 (2001) 221. [10] Molecular Probe, www.probes.com/handbook, section 20.3.