Potassium and sodium measurements at clinical concentrations using phase-modulation fluorometry

Abstract

We describe the possibility of measuring sodium and potassium at the concentrations present in whole blood using lifetime-based sensing and phase-modulation fluorometry. The probe SBFO was shown to display changes in phase or modulation at sodium concentrations near 100 mM, and to be mostly independent of interfering effects due to potassium. The probe CD222 was found unsuitable for measurements of potassium in blood using intensity-ratio measurements, due to similar spectral changes induced by sodium. However, sodium at blood concentrations near 100 mM causes only a minor change in the lifetime of CD222. Hence, CD222 and lifetime-based sensing can be used to measure blood levels of potassium in the presence of 130 mM sodium. Similarly, sodium causes only a modest change in the lifetime of the potassium probe PBFI, which displays potassium-dependent lifetimes. For both CD222 and PBFI, the presence of blood levels of sodium increases the apparent potassium dissociation constants into the blood physiological range. In total, these results demonstrated the possibility of lifetime-based sensing of sodium and potassium at the extracellular cation concentrations present in blood or blood serum.

1. Introduction

Measurement of potassium in blood is important for hypertensive screening. Optical measurements of blood potassium is difficult due to the large excess of sodium over potassium, 150 and 4.5 mM, respectively, and the chemical similarity of these ions. In the present report we describe a fluorescence method for measuring K⁺ and Na⁺ in blood, each in the presence of the other cation.

Presently used methods for measuring K⁺ and Na⁺ include flame photometry and ion selective electrodes [1–4]_. These mature analytical methods provide the needed accuracy over a wide range of concentrations. However, these methods require handling of blood, which is expensive and is associated with significant health risks to the operator. Hence it is desired to develop optical single-use measurements for blood electrolyte analysis.

The continuing interest in optical clinical chemistry can be seen by the development of optical methods to monitor blood gases (pH_, pCO₂ and pO₂) in whole blood. Optical techniques can be relatively inexpensive and can provide immediate answers for point-of-care testing. Such colorimetric and fluorometric measurements became possible because of discovery of macrocyclic ionophores that posses the property of selectively complexing alkali metal cations [5]. These ionophores are characterized by a cyclic structure with an electron-rich cavity to bind the cation, with the cavity size matching the diameter of the cation to attain binding selectivity. Chromogenic and fluorescent detection of potassium and sodium probes has become feasible because of the development of ionophores that bind metal cations in aqueous solutions with high affinity and specificity [6,7]_. Several chromogenic derivatives of crown ethers have been synthesized which exhibit changes in absorption upon cation binding [8]. This approach has been adapted by Technicon Instruments Corporation using the ChromoLyte reagents for the spectroscopic assay of sodium and potassium in the Technicon RA clinical chemistry analyzer [9].

While colorimetric methods are known for many cations, there is interest in the use of fluorescence which provides high sensitivity detection for the cation-specific fluorescence probes. However, only a limited number of fluorescent probes are available for sodium and potassium. The available probes for sodium include FCryp-2 [10]_, SBFI, SBFO, SBFP [11]_, F221 [12] and Sodium Green [13]_. The available probes for potassium include PBFI [7], CD18 and C18 [14]_, and MCC [15]_.

Most of fluorescence assays for electrolytes are based on the change in fluorescence intensity which occurs in response to the analyte [16]_. While fluorescence intensity measurements are simple and accurate in the laboratory, these are often inadequate in real-world situations. The intensity depends on a number of instrumental factors and on the probe concentration. For instance, the intensity for a given sensor can depend on the details of the optical collection efficiency or on the concentration of fluorophore in the sensor itself. Hence, frequent recalibration is needed for most intensity-based measurements. Wavelength-ratio-metric probes have been developed to make the measurements insensitive to such effects. While this approach has been successful for Ca²⁺ and Mg²⁺, the spectral shifts displayed by the Na⁺ and K⁺ probes are much smaller. Overall, the presently available probes for Na⁺ and K⁺ do not provide spectral changes adequate for their use in clinical chemistry.

Perhaps the most important factor limiting measurement of Na⁺ and K⁺ at the concentrations present in blood is the cation affinity of currently available probes. These probes were developed for intracellular sodium and potassium concentrations of near 6 and 135 mM, respectively. In contrast, the specified concentrations in blood are 120 to 160 mM for sodium and 2.5 to 6.5 mM for potassium. For clinical measurements the acceptable accuracy is ±3 mM for sodium and ±0.2 mM for potassium [17]_. Hence, the affinities of most fluorophores for sodium and potassium are not suitable for clinical measurements. The difficulties with intensity-based sensing, limited wavelength-ratiometric capabilities of available probes, and inappropriate binding constants appear to be reasons that fluorescence is not in widespread use for the measurements of blood electrolytes. For completeness we note that there have been other approaches to develop optical sensors for K⁺ using the ionophore valinomycin and the inner filter effect [18] or energy transfer [19,20]_. One difficulty with energy transfer sensing is that the extent of energy transfer strongly depends on acceptor concentration, so that the sensor will require frequent calibration. This problem can potentially be circumvented by using covalently linked donors and acceptors. However, few such sensors have appeared due to the difficulties with chemical synthesis.

Based on these considerations, we decided to develop fluorescence methods for sensing sodium and potassium at the concentrations found in whole blood. We looked for probes that display useful changes in lifetime in response to the Na⁺ and K⁺ in the desired cation concentration ranges, for use with lifetime-based sensing [21]_. The probe SBFO was found suitable for measuring sodium at concentrations near 100 mM, and the probes CD222 [22] and PBFI were found suitable for measuring potassium at concentrations near 5 mM. Each cation can be measured in the presence of the other cation. These data show that it is possible to develop lifetime-based fluorescence sensors for sodium and potassium at the concentrations encountered in whole blood.

2. Materials and methods

All sensing fluorophores were obtained from Molecular Probes (Eugene, OR)_. Their chemical structures are shown in Fig. 1. Absorption spectra were measured using a HP 8453 spectrometer. Steady-state intensity measurements were performed using an Aminco-Bowman AB2 spectrofluorometer for SBFO and CD 222, and on SLM 8000 photon counting spectrofluorometer for SBFI and PBFI. Fluorescence intensity decays were measured with frequency-domain instrumentation previously described [23,24]_. The excitation light was a cavity dumped and frequency-doubled pyridine 2 dye laser (Coherent. with the wavelength tunable from 343 to 385 nm. Longer excitation wavelengths (400 nm) were obtained from a frequency-doubled Ti:sapphire laser (Spectra Physics)_. The emission was observed through long wavepass filters which transmitted the probe emission and blocked scattered excitation light.

Fig. 1.

Chemical structures of sodium and potassium fluorescent probes.

Cation-dependent intensities, phase angles and modulations for SBFO and CD222 were measured at several excitation wavelengths because these probes display shifts in their absorption spectra upon cation binding. The samples were freshly prepared before measurement in the buffers, 5 mM Hepes (pH 7.2) for SBFO, SBFI, PBFI, and 30 mM Tris (pH 7.25) for CD 222. The ionic strength of the samples started from 100 mM. The buffers contained 100 mM of tetramethylammonium chloride, TMA(Cl)_. The measurements were carried out at a room temperature of 22°C.

The frequency-domain data were used to determine the intensity decay law using the multi-exponential model [25,26]

$$I\left(t\right)=\sum _{t=1}^n{\alpha }_i{\text{e}}^{-t/{\tau }_i}$$ (1)

where α_i are the preexponential factors (amplitudes)_, τ_i are the decay times, and n the number of exponential components. For the intensity decay measurements, we used magic angle conditions to eliminate the effects of Brownian rotation. The mean decay time ($\overline{\tau }$) and fractional intensities f_i of each component are given by:

$$\overline{\tau }=\sum _i{\alpha }_i{\tau }_i^2/\sum _j{\alpha }_j{\tau }_j=\sum _i{f}_i{\tau }_i$$ (2)

$$f_i={\alpha }_i{\tau }_i/\sum _j{\alpha }_j{\tau }_j.$$ (3)

The intensity decays of SBFI, PBFI and CD 222 were also fitted to a global model in which the decay times were assumed to be independent of the Na⁺ or K⁺ concentration, but the amplitudes of decay times varied to reflect changes in the fractional amounts of each species for various concentrations of Na⁺ or K⁺. Such analyses have been described previously for calcium [27,28] and magnesium probes [29]_.

The apparent dissociation constants ($K_{\text{D}}^X$) were calculated with the assumption that the stoichiometry of binding is 1:1,

$$K_{\text{D}}^X=\frac{X_{\text{max}}-X}{X-X_{\text{min}}}\left[{\text{M}}^{+}\right]$$ (4)

where [M⁺] is the ion concentration and X indicates the measured (or calculated) ion-dependent parameter. The apparent dissociation constant is the parameter linking the observable fluorescence to the ion concentrations. It should be noted that only the ion-dependent intensities yield a true dissociation constant reflecting the equilibrium between free and ion-bound forms of probe. The dissociation constants calculated from the ion-dependent time-resolved data (phase angle, modulation or mean decay time) will usually result in higher or lower values than the true value because time-dependent parameters are not proportional to the concentration of the free or ion-bound forms [21]_. The apparent dissociation constants also depend on the choice of excitation wavelengths [21]_. For purposes of chemical sensing, the apparent dissociation constant is the more important parameter because this value defines the useful range of ion concentrations which can be measured using a particular spectral property. The concentration range over which a probe produces an observable response with a chosen parameter is approximately from 0.1 $K_{\text{D}}^X$ to 10 $K_{\text{D}}^X$.

3. Results and discussion

3.1. Intensity measurements of the sodium probe SBFO

SBFO was originally described by Minta and Tsien [11]_. This dye has not been widely used for intracellular Na⁺ measurements because of its high dissociation constant of 50 mM. We are only aware of one report of use SBFO for Na⁺ concentration measurements in lateral intercellular spaces of MDCK cells [30]. However, the weak binding of sodium by SBFO makes it a promising probe for measurement of the higher sodium concentrations present in blood. Absorption and emission spectra of SBFO are shown in Fig. 2. Binding of sodium or potassium to this diazacrown ether causes the blue shift of the absorption spectrum of SBFO with small change in the extinction coefficient. The blue shift upon K⁺ binding is significantly less than that for Na⁺. The relative quantum yield of SBFO increases 3.6-fold and 2.2-fold upon Na⁺ and K⁺ binding, respectively. The 3.6-fold increase corresponds to the reported increase in quantum yield from 0.14 free form. to 0.44 (Na⁺-bound form) [11]_. The change in emission intensity due to cation binding for SBFO depends on the excitation wavelength because of the absorption spectral shift.

Fig. 2.

Absorption and emission spectra of the sodium probe SBFO.

Fig. 3 (top) shows the Na⁺-dependent intensities for SBFO at various excitation wavelengths. The intensity is insensitive to the Na⁺ when SBFO is excited at longer wavelengths. This is because the increased quantum yield of the Na⁺-bound form is compensated by the decreased optical density (lower extinction coefficient)_. The ratio of intensities measured for different excitation wavelengths can be used to measure sodium. Fig. 3 (bottom) shows the respective intensity ratios. To facilitate comparison, the intensity ratios were normalized to 1.0 at the absence of Na⁺ and K⁺. The value of the intensity ratio increases if the second excitation wavelength is longer. It should be pointed out that the intensity at longer excitation wavelengths may be too weak for accurate sensing. The wavelength-ratiometric capability is useful property because it reduces or eliminates the dependence on probe concentration and instrumental factors.

Fig. 3.

Na⁺-dependent fluorescence intensity of SBFO at various excitation wavelengths (top) and excitation intensity ratios (for excitation wavelengths see Fig. 2). Dashed vertical lines illustrate critical concentration range of Na⁺ in the blood.

The sigmoidal titration data in Fig. 3 were analyzed by nonlinear regression to yield an apparent dissociation constant $K_{\text{D}}^{\text{app}}$ using Eq. (4). The true K_D for SBFO for sodium of 63 mM was determined from intensity measurements at 340 nm excitation (Fig. 3, top)_. The apparent dissociation constant $K_{\text{D}}^{\text{app}}$ which describes the ratiometric (or lifetime) data depends on the experimental conditions, including the excitation and emission wavelengths (for details see [21])._. Analysis of the Na⁺-dependent intensity ratios of SBFO (Fig. 3, bottom) resulted in $K_{\text{D}}^{\text{app}}$ values of 56.3, 93.9, and 138.8 mM for the 340/380, 340/390, and 340/400 ratios, respectively. The presence of potassium concentrations below 100 mM had essentially no effect on the intensity ratios of SBFO. Other common components of the blood, including Ca²⁺ (0–10 mM) and Mg²⁺ (0–5 mM)_, and pH (6–8) do not affect the spectral response of SBFO [31]_.

The critical sodium concentration range from 120–160 mM in blood is indicated by vertical lines in Fig. 3. This range is only a small part of Na⁺-sensitive range displayed by SBFO. Measurements with a concentration tolerance of ±3 mM requires intensity measurements with an accuracy of 0.6% and intensity ratio with an accuracy of 0.9%. Such accuracy is difficult to obtain, particularly using one excitation wavelength. When using a single excitation wavelength, Na⁺ measurements will require strict control of excitation drifts and probe concentration. The limited accuracy of Na⁺ measurements in the range from 100 to 200 mM with SBFO using intensity ratios has already been reported [31]_. Sodium measurements based on intensities or intensity ratios of SBFO do not seem feasible for the sodium concentration present in whole blood.

3.2. Lifetime measurements of SBFO

We evaluated SBFO for lifetime-based sensing of sodium. The intensity decay of SBFO was determined from the frequency-domain data (Fig. 4)_. The mean lifetime increased from 1.50 ns for the Na⁺-free form to 2.16 ns for the Na⁺-bound form. The mean lifetime of SBFO was 1.85 ns in presence of 500 mM K⁺. Intensity decays of SBFO were nearly a single exponential. The origin of the Na⁺-dependent lifetime of SBFO appears to be a minor component with a short lifetime near 30 ps (Table 1)_. The major component, with fractional intensity higher than0.98, increased progressively from 1.52 to 2.16 ns with increasing Na⁺ concentration.

Fig. 4.

Frequency-domain intensity decays of SBFO.

Table 1.

Intensity decays of sodium and potassium probes

Probe	Cation (mM)	Decay time (ns)			Fractional intensity			τ (ns)
		τ1	τ2	τ3	f1	f2	f3
SBFO	free	< 0.03 >a	1.52	-	0.016	0.986	-	1.50
	Na+ (1000)	2.16	-	-	1.0	-	-	2.16
	K+ (500)	0.31	1.88	-	0.020	0.980	-	1.85
SBFI	free	< 0.006 >	0.25	0.61	0.215	0.547	0.238	0.29
	Na+ (125)	< 0.006 >	0.25	0.61	0.110	0.196	0.694	0.48
	K+ (120	< 0.006 >	0.25	0.53	0.178	0.391	0.431	0.33
Sodium Green	free	0.09	0.40	2.53	0.106	0.536	0.357	1.13
	Na+ (144)	0.09	0.40	2.53	0.003	0.064	0.933	2.39
	K+ (500)	0.06	0.38	2.38	0.026	0.412	0.562	1.50
CD 222	free	0.04	0.15	0.82	0.424	0.481	0.095	0.17
	K+ (50)	0.04	0.15	0.82	0.014	0.147	0.839	0.71
	Na+ (100)	0.05	0.18	1.39	0.240	0.672	0.088	0.26
PBFI	free	< 0.005 >	0.30	0.83	0.204	0.496	0.300	0.40
	K+ (130)	< 0.005 >	0.30	0.83	0.064	0.111	0.825	0.72
	Na+ (100)	< 0.005 >	0.26	0.69	0.131	0.259	0.610	0.47

^aThe angular brackets indicate this value was held constant in the least square analysis.

Sodium concentrations can be determined from the phase and modulation values measured at a single light modulation frequency (Fig. 5)_. SBFO displayed useful changes in phase angle and modulation, approximately an 11-degree change in phase and a 16% change in the modulation. Useful changes were observed from 50 to 200 MHz. The Na⁺-sensitive range can be adjusted by the choice of the excitation wavelength. For example, the apparent dissociation constants calculated from the phase angle using Eq. (4), are 18.5 mM (345 nm)_, 81 mM (380 nm)_, and 154 mM (400 nm)_. The Na⁺-sensitive range using modulation is shifted toward lower Na⁺ concentrations (Fig. 5, bottom)_, which is typical with phase-modulation sensing [21]_. The values of $K_{\text{D}}^{\text{app}}$ from the modulation data (Fig. 5, bottom) are 10 mM (345 nm)_, 49 mM (380 nm)_, and 157 mM (400 nm)_. The best Na⁺ sensitivity for the narrow clinical range of Na⁺ concentrations (dashed lines) can be obtained for excitation wavelengths from 380–400 nm. The needed accuracy of ±3 mM Na⁺ requires measurements of phase angle and modulation with an accuracy of 0.06 degrees and 0.09% (at 380 nm excitation)_. Such accuracy may be achievable with a dedicated single modulation frequency instrument using present optoelectronic technology. For instance, a commercially available phase-modulation instruments with wide range of modulation frequencies provides measurements with an accuracy of 0.1–0.2 degrees and 0.3–0.5% for phase angle and modulation, respectively. Hence, it will be challenging to perform phase and modulation measurements with the accuracy required for clinically useful measurements of sodium. There is still a need for improved fluorescent probes for sodium.

Fig. 5.

Na⁺-dependent phase angles (top) and modulations (bottom) of SBFO at several excitation wavelengths.

3.3. Intensity and lifetime properties of sodium probe SBFI

SBFI is regarded as a useful excitation wavelength ratio probe for intracellular sodium measurements [32–37]_, but its affinity for sodium is too high for use at blood levels of sodium. The shapes and wavelengths of absorption and emission spectra of SBFI are similar to those of SBFO. SBFI undergoes a small shift in the absorption spectrum to shorter wavelengths and an increase in the extinction coefficient on cation binding (Fig. 6, top)_. Fig. 6 (bottom) shows the excitation intensity ratios for SBFI. The choice of excitation wavelength is usually similar to that of the calcium probe fura-2, 340/380 nm and the emission maximum of 500 to 520 nm. The exact ratio is dependent on the wavelengths selected and instrumentation used. The 340/380 excitation intensity ratio of SBFI (at 500 nm) changes substantially (about 3.5-fold) for Na⁺, resulting in an apparent dissociation constant of 9.6±0.4 mM (Na⁺ only)_. In the presence of K⁺, with the total concentration [Na⁺]+[K⁺] constant at 135 mM (approximately the physiological concentration)_, the apparent K_D for sodium is 16.5±2.0 mM. The important intracellular [Na⁺]_i and extracellular [Na⁺]_e concentration ranges are marked in Fig. 6. Hence, SBFI will usually be completely saturated at sodium concentrations above 100 mM.

Fig. 6.

Top: Absorption and emission (Exc. 345 nm) spectra of SBFI. Bottom: Excitation intensity ratios of SBFI at different solution compositions. Dashed lines mark the important intracellular [Na⁺]_i and extracellular [Na⁺]_e concentrations.

We have also measured the intensity decays of SBFI at various Na⁺ (Fig. 7, top) and K⁺ (not shown) concentrations. The fluorescence intensity decays were found to be multi-exponential. Global analysis resulted in three decay times, 6 ps, 0.25 ns, and 0.61 ns with amplitudes dependent on Na⁺ concentration (Table 1)_. The mean lifetime increased from 0.29 ns (Na⁺-free form)_, to 0.48 ns (Na⁺_- bound form)_, resulting in a substantial change in phase angle and modulation. SBFI may be a moderately useful lifetime probe for sodium at intracellular concentrations, but will be completely saturated at extracellular sodium concentrations.

Fig. 7.

Top: Frequency-domain intensity decays of SBFI. Bottom: ion-dependent phase angle of SBFI for 292.3 MHz.

For measurement of sodium in blood, it will be necessary for the probe to discriminate against potassium. Unfortunately, binding of K⁺ also affects the lifetime of SBFI. Fig. 7 (bottom) shows the Na⁺- and K⁺-dependent phase angles for SBFI. The presence of 135 mM of K⁺ significantly decreases the phase angle (lifetime) change in response to Na⁺. This observation is somewhat unexpected since the intensity ratio (Fig. 6) showed good discrimination against potassium. Nonetheless, in cases where the K⁺ concentration is low (e.g., less than 10 mM)_, lifetime-based (phase-modulation) sensing of Na⁺ with SBFI can be an alternative to the ratiometric method. However, because of the high affinity of SBFI for Na⁺, only lower sodium concentrations below 10 mM can be measured using this probe. Other reports have shown that non-ratio-metric sodium probe Sodium Green displays an excellent lifetime sensitivity and selectivity to Na⁺ [13]_. However, Sodium Green also displays a high affinity for sodium, and is only useful for concentrations below 10 mM.

3.4. Intensity measurements using the potassium probe CD 222

CD 222 is a new fluorescent probe for potassium and has recently become available from Molecular Probes. Its synthesis and spectral properties are described by Crossley et al. [22]_. Absorption and emission spectra of CD222 are shown in Fig. 8. CD222 can be excited at longer wavelengths than the other potassium-sensitive fluorophore PBFI, and CD22 displays a large absorption shift upon binding potassium. The absorption spectrum displays a 30 nm blue shift upon binding either of K⁺ or Na⁺ (dashed line) with a decreasing extinction coefficient above 350 nm. The emission spectra show a minor blue shift on cation binding. The quantum yield of CD 222 increases3.7-fold for the K⁺-bound form and only 1.4-fold for the Na⁺-bound form. The K_D of CD 222 for K⁺ determined from the intensity is 0.8 mM in the absence of Na⁺. This value is in close agreement with reported values of 1.0 [22] and 0.9 mM [38]_. At first glance the potassium affinity of CD222 appears to be too high for measurement of blood concentrations of potassium. However, we will show below that sodium binds competitively to CD222, raising its apparent potassium dissociation constant to the useful range near 5 mM.

Fig. 8.

Absorption and emission spectra of CD222 at various K⁺ concentrations. Emission spectra were taken for 365 nm excitation. CD 222 concentration was 2.7 μM. Respective spectra of CD 222 in the presence of 100 mM of Na⁺ are presented by the dashed lines.

Fig. 9 (top) shows the K⁺-dependent intensities of CD222 at various excitation wavelengths in the presence of 135 mM Na⁺. This concentration of Na⁺ was used to mimic that found in whole blood. For excitation wavelengths from 365–395 nm the intensities of CD 222 display a good sensitivity to the K⁺, but above the desired of 2.5–6.5 mM range. This is because the binding constant for K⁺ (K_D =0.8 mM) is strongly affected by Na⁺, increasing it to 54 mM for the average value from the data for 365 and 395 nm excitation. The respective intensity ratios in the presence of 135 mM Na⁺ (Fig. 9, bottom) display no sensitivity to K⁺ for 365/410 nm and a modest sensitivity for the 365/395 nm ratio. These results indicate that intensity-based and wavelength-ratiometric sensing of K⁺ in the blood are not promising using the probe CD 222. Measurements with a concentration tolerance of ±0.2 mM will require the intensity measurements (excitation at 365 nm) to be accurate to 0.7%. Such an accuracy is difficult to obtain in a well controlled cuvette measurements, and is not likely to be obtainable in a turbid and colored sample like blood.

Fig. 9.

K⁺-dependent fluorescence intensity of CD 222 in the presence of 135 mM Na⁺ at various excitation wavelengths (see Fig. 6) (upper panel) and respective excitation intensity ratios (lower panel. Dashed vertical lines illustrate critical concentration range of K⁺ in the blood.

3.5. Lifetime measurements of CD222

Since intensity based measurements of K⁺ in blood using CD222 did not seem possible, we examined CD222 in a lifetime-based probe. We measured the frequency-domain intensity data of CD 222 with various concentrations of K⁺ and Na⁺ (Fig. 10)_. Global analysis of the intensity decays of CD 222 resulted in three decay times, 0.04, 0.15, and 0.82 ns (Table 1). The mean lifetime of CD 222 increased from 0.17 ns for the free form to 0.71 ns for the K⁺-bound form. In the presence of 100 mM Na⁺, the mean lifetime is 0.26 ns. Hence, the increase in mean lifetime due to the binding of Na⁺ to CD 222 is much smaller than the increase in lifetime due to K⁺. This result suggests the possibility using CD 222 to measure K⁺ in the presence of high concentrations of Na⁺.

Fig. 10.

Frequency-domain intensity decays of CD 222 for various K+ concentrations. Dashed lines represent intensity decay at the presence of 100 mM Na⁺. Excitation wavelength was 380 nm and emission above 440 nm.

We used data for a modulation frequency of 286 MHz to determine the K⁺-dependent phase angles and modulations in presence of 135 mM of Na⁺ (Fig. 11)_. The choice of modulation frequency of 286 MHz is of course arbitrary. One may choose a frequency higher than 500 MHz, but this may require a faster detector than standard photo-multiplier tube (PMT)_, such as a microchannel plate PMT which is an expensive device, or a photodiode which is typically less sensitive.

Fig. 11.

Cation-dependent phase angles (top) and modulations (bottom) of CD 222 for various solution compositions.

The phase angles of CD 222 displays a good sensitivity to K⁺ and only modest sensitivity to Na⁺. The apparent dissociation constants from the phase angles are 0.54 mM for K⁺ and 1.74 mM for Na⁺, and 0.35 mM for K⁺ and 1.3 mM for Na⁺ from the modulation data, respectively. More important are changes in the phase angle and modulation in the presence of both cations. These changes are 32.4 degrees in phase and 29.8% in modulation for K⁺ binding, and only of 3.4 degrees and 4.9% for Na⁺ binding to the CD 222 at 286 MHz. The K⁺ induced changes in the phase angle and modulation are suitable for measurements of K⁺, particularly at frequencies higher than 200 MHz. The dynamic range for K⁺ is somewhat decreased by the presence of sodium, but the range of phase and modulation values is still adequate for lifetime-based sensing of K⁺.

These phase and modulation data indicate that Na⁺ binding does not cause a significant change in the lifetime of CD 222. This is an important observation because almost entire dynamic range in the phase and modulation remains available for K⁺ sensing. However, the presence of sodium in the solution has a large impact on binding of K⁺. The K⁺-sensitive range is dramatically shifted toward higher K⁺ concentration in the presence of 135 mM Na⁺, resulting in an apparent dissociation constants for K⁺ of 34.2 mM and 15.5 mM from phase and modulation, respectively. This means that the apparent binding affinity for K⁺ decreased 63-fold from phase angle and 44-fold from modulation. In spite of decrease of K⁺ affinity, the phase angle and modulation data for CD 222 are promising parameters for K⁺ sensing in the blood. Measurements with an accuracy of 0.12 degree in phase and 0.2% in modulation are sufficient to fulfill the required tolerance of ±0.2 mM in the range from 2.5 to 6.5 mM of K⁺ concentration. Such accuracy for phase and modulation measurements can be obtained with commercial frequency-domain instruments. The accuracy can be improved if an excitation wavelength shorter than 380 nm can be used.

3.6. Intensity measurements of the potassium probe PBFI

PBFI is chemically and spectroscopically similar to SBFI (Fig. 1) and was introduced at the same time as SBFI and SBFO [11]_. In contrast to SBFI, there are only few reports of using PBFI to measure K⁺ concentrations and K⁺ transport through membranes [38–42]_. This is because the spectral shifts in absorption (Fig. 12, top) are much less than observed for SBFI, with only minor change in the extinction coefficient. The 340/380 excitation ratios for PBFI are shown in Fig. 12, bottom. It is surprising that the 340/380 ratio changes more for Na⁺ (circles) than for K⁺ (triangles)_. These data indicate that PBFI is poor potassium probe for intracellular as well for extracellular K⁺ measurements. Intracellular K⁺ concentrations (120–140 mM) will saturate the intensity signal because of the low dissociation constant of 6 mM [11]_. Extracellular K⁺ concentrations (2.5–6.5 mM) need to be measured with a high background of Na⁺ (about 140 mM)_, which also will saturate the intensity change of PBFI. Hence, we examined the cation-dependent intensity decays of PBFI.

Fig. 12.

Absorption and emission (Exc. 345 nm) spectra of PBFI (top) Excitation intensity ratios of PBFI at several solution compositions (bottom).

3.7. Lifetime measurements of PBFI

Frequency-domain intensity decays of PBFI are shown in Fig. 13, top. The fluorescence intensity decays are complex. A triple exponential decay with decay times of 5 ps, 0.30 ns, and 0.83 ns satisfactorily describes the intensity decays of PBFI at each K⁺ concentration (Table 1)_. The mean lifetime increased from 0.40 to 0.72 ns upon K⁺ binding, resulting in useful changes in phase angle and modulation over a wide range of modulation frequencies. For a modulation frequency of 289.7 MHz these changes are of 25.2 degrees and 26.7% in phase and modulation, respectively (Fig. 13, bottom)_. The most important observation is that lifetime of PBFI is much less sensitive to Na⁺ than was observed from intensity, allowing measurement of K⁺ in the presence of a high Na⁺ concentration. The ion-dependent phase angle of PBFI (Fig. 13, bottom) are similar to those observed for CD 222 shown in Fig. 11 (top)_. However, the presence of Na⁺ affects the binding affinity for K⁺ much less than for CD 222. For instance, apparent K_D of PBFI for K⁺ in the absence of Na⁺ is 1.7 mM and in the presence of Na⁺+K⁺=135 mM is 17.5 mM. This means the affinity of binding K⁺ decreased about 10-fold for PBFI, as compared to 63-fold for CD 222 in the presence of 135 mM Na⁺. It should be noted that the probes contain different chelators, PBFI contains a diazacrown, and CD 222 contains a [2.2.2] cryptand.

Fig. 13.

Frequency-domain intensity decays of PBFI (top). Cation-dependent phase angles of PBFI for different solution compositions (bottom).

In our earlier report about phase fluorometric sensing of K⁺ using a PBFI we concluded that optical sensing of K⁺ was a borderline possibility [43]_. At that time we did not use TMA (Cl) to maintain a high ionic strength of solutions and we were not aware that a small amount of K⁺ may significantly change the lifetime of PBFI. Therefore, the reported mean lifetime for free form of PBFI was 0.53 ns [43]_. Other laboratories have studied the binding of K⁺ to PBFI in the ground and excited states [44]_. The reported decay times for PBFI of 0.27–0.32 ns and 0.75–0.90 ns are similar to our own values. The short component of about 5 ps has not been reported, presumably because of instrument resolution of about 6 ps per channel [44]_.

4. Conclusions

Fluorescent sensors for Na⁺ and K⁺ were characterized with the goal of measuring sodium and potassium at the concentrations present in blood. Two sensing methods were tested, wavelength-ratiometric and lifetime-based sensing. It should be noted that the clinical concentration ranges of Na⁺ and K⁺ in blood are narrow compared with the usual 100-fold range of fluorescent sensors. In addition, extracellular K⁺ measurements need to be performed in presence of large amount of Na⁺ (about 135 mM)_. The phase and modulation data for the potassium probes PBFI and CD 222 show very good sensitivity to K⁺ and discrimination against the Na⁺. In contrast, the excitation intensity ratiometric data displayed very poor sensitivity to K⁺ in the presence of Na⁺. The overall changes in phase and modulation are modest, but it should be possible to measure K⁺ in the presence of Na⁺, and vice versa. Apparently it is possible for the potassium probes to bind sodium without displaying a cation-induced change in lifetime. These observations suggest the synthesis of additional probes for potassium without regard for the wavelength-ratiometric capabilities or high discrimination against Na⁺. Using fluorophores with higher quantum yields, longer excitation wavelengths, and longer fluorescence lifetimes will enhance the usefulness of the probes. Cation probes based on metal-ligand complexes containing rhenium, ruthenium, osmium, or a lanthanide, should also be considered.

Sodium probes with larger dissociation constants and more importantly, with a larger change in lifetime than SBFO, are desirable for accurate measurement of Na⁺ in the blood. The clinical range of sodium concentration in the blood is much narrower than for potassium. The discrimination against K⁺ for sodium probes is much less of a problem because of the crown ether for Na⁺ has a smaller binding cavity. Also, the K⁺ concentration in the blood is much lower than that of sodium. Overall, lifetime-based sensing using available probes, SBFO, PBFI, and CD 222 can provide measurements of sodium and potassium at the concentrations found in blood or blood serum.

Abbreviations:

CD 222

coumarin diacid cryptand w2.2.2x

MCC

6,7-(4-methyl.coumaro-w2.2.2x cryptand

SBFI

sodium binding benzofuran isophtalate

SBFO

sodium binding benzofuran oxazole

SBFP

sodium binding benzofuran phtalatel

PBFI

potassium binding benzofuran isophtalate

TMA(Cl)

tetramethylammonium (chloride)