Calcium-buffering effects of gluconate and nucleotides, as determined by a novel fluorimetric titration method

Abstract

Significantly more Ca²⁺ influx is required for eliciting release of neurotransmitter during whole cell patch clamp recording in the Calyx of Held, when gluconate with 3 mm free ATP is used as pipette filling solution, as compared to a methanesulfonate-based solution with excess Mg²⁺. This reduction in efficiency of Ca²⁺ in eliciting release is due to low-affinity Ca²⁺ binding of both gluconate and ATP²⁻ anions. To study these effects we developed a simple fluorimeteric titration procedure, which reports the dissociation constant, K_D, of a given Ca²⁺ indicator dye, multiplied by 1 plus the sum of Ca²⁺ binding ratios of any anions, which act as low-affinity Ca²⁺ ligands. For solutions without Ca²⁺ binding anions we find K_D values for Fura2FF ranging from 11.5 ± 1.7 to 15.6 ± 7.47 μm depending on the dominant anion used. For Fura6F and KCl-based solutions we find K_D = 17.8 ± 1.3 μm. For solutions with gluconate as the main anion and for solutions that contain nucleotides, such as ATP and GTP, we find much higher values for the product. Assuming that the K_D of the indicator dye is equal to that of KCl-based solutions we calculate the summed Ca²⁺ binding ratios and find a value of 3.55 for a solution containing 100 mm potassium gluconate and 4 mm ATP. Gluconate contributes a value of 1.75 to this number, while the contribution of ATP depends strongly on the presence of Mg²⁺ and varies from 0.8 (with excess Mg²⁺) to 13.8 (in the presence of 3 mm free ATP). Methanesulfonate has negligible Ca²⁺ binding capacity. These results explain the reduced efficiency of Ca²⁺ influx in the presence of gluconate or nucleotides, as these anions are expected to intercept Ca²⁺ ions at short distance.

Introduction

Ca²⁺ binding anions, such as EGTA and BAPTA, are known to reduce the efficiency of Ca²⁺ influx in eliciting neurotransmitter release, if present in the intracellular milieu of presynaptic nerve endings (Adler et al. 1991; Eggermann et al. 2011). In fact, comparison of the differential effects of EGTA (a slow Ca²⁺ binder) and BAPTA (a rapid binder) have been used extensively to infer the spatial relationship between Ca²⁺ channels and Ca²⁺ sensors, as these two chelators intercept inflowing Ca²⁺ ions at very different mean diffusion distances. However, most intracellular solutions in patch clamp studies also contain nucleotides and many protocols use gluconate as the main intracellular anion. Both nucleotides and gluconate are known to display low affinity Ca²⁺ binding (Skibsted & Kilde, 1972), with ATP²⁻ being reported to be among the fastest Ca²⁺ ligands (Hammes & Levison, 1964). The presence of such anions might strongly influence release. However, such effects are difficult to anticipate theoretically, as binding activities depend on the specific composition of solutions and Ca²⁺ binding to ATP²⁻ is antagonized by Mg²⁺ and H⁺. We therefore developed a simple fluorimetic titration procedure, based on the low affinity Ca²⁺ indicator dye Fura2FF, to determine the overall Ca²⁺ binding capacity of solutions, as they are typically used in whole-cell patch clamp recordings (pH 7.2, ionic strength 190 mm and room temperature). The method returns the product of the dissociation constant K_D of the indicator dye and the sum of Ca²⁺ binding ratios of all low-affinity Ca²⁺ binders (incremented by 1). Thus, in the absence of Ca²⁺ binders we obtain the K_D of the dye, which may be used for its calibration as a Ca²⁺ indicator. Changes in K_D upon the inclusion of Ca²⁺ binders can then be used to calculate the Ca²⁺ binding properties of the latter. This type of calibration does not use other Ca²⁺ buffers for reference, but is based exclusively on the Ca²⁺ standard used for titrations.

We examine two low-affinity Ca²⁺ indicator dyes, Fura2FF and Fura6F. For characterizing the influence of anions we determine the Ca²⁺ binding ratio of some of the commonly used pipette-filling solution anions such as isethionate, gluconate, glutamate, methanesulfonate and commonly used nucleotides (ATP and GTP). We point out the role of magnesium regarding the latter and also address the problem of contamination by Ca²⁺ in minimally buffered solutions. Although, in typical pipette solutions, free ATP as well as gluconate were found to contribute only little to the Ca²⁺ binding ratio, their effects on the nanodomain Ca²⁺ may be substantial due to very high Ca²⁺ binding rates. We therefore measured the Ca²⁺ dependence of neurotransmitter release in the Calyx of Held synapse for two variants of nucleotide-containing solutions: one with methanesulfonate as the main anion and an excess of Mg²⁺ over nucleotides and one with gluconate and an excess of ATP²⁻. We find that 2.7 times more Ca²⁺ influx is required for eliciting release of a physiological amount of neurotransmitter when the latter solution is used.

Methods

Theory

The law of mass action for Ca²⁺ binding to an indicator dye with dissociation constant K_D which is present at a total concentration F_t states that the concentration of Ca²⁺-bound dye, [CaF], is given by

(1)

If there are anions present, which bind Ca²⁺ with low affinity, one can rewrite this equation in terms of total Ca²⁺ ([Ca²⁺]′), which is free or else in rapid equilibrium with low affinity Ca²⁺ binders other than the sensor:

(2)

Here ∑κ is the sum of all Ca²⁺ binding ratios. The Ca²⁺ binding ratios are given (in the limit of low Ca²⁺ concentration) as the ratios of total concentrations over their K_D values (Zhou & Neher, 1993). We will refer to [Ca²⁺]′ as ‘apparent free calcium’ in the text below. Inserting eqn (2) into eqn (1) and denoting 1+∑κ by κ′, we obtain

(3)

The fraction of Ca²⁺-bound dye, f_bound, which can be determined experimentally, is given by

(4)

Here, we introduced for simplicity of notation

(5)

where the subscript 0.5 indicates the half point of the titration. Equation (4) shows that f_bound is a function of K_0.5 and does not allow one to separately determine K_D and κ′.

However, in the actual titration we also often include BAPTA to compensate for contamination (see above).

Therefore, we have to consider the equation

(6)

where [CaB] is the Ca²⁺-bound form of BAPTA, for which equations in analogy to eqns (1) and (3) hold. Therefore

(7)

To calculate a prediction of f_bound from eqn (4) for a given K_0.5 and Ca²⁺ contamination (assumed as free parameters in the subsequent least squares fit), [Ca²⁺]′ must be calculated through an iterative procedure similar to that used by standard chelator programs, such as MaxChelator (Bers et al. 1994). As starting values we used [Ca²⁺]′ = Ca_t, and adjusted [Ca²⁺]′ in subsequent steps by a fraction of the difference between the calculated value for Ca_t and the target value. Using 0.01 as the fraction value, the procedure is repeated until it converges on a pair of [Ca²⁺]′ and Ca_t values consistent with eqn (7). We then used [Ca²⁺]′ and the estimates for K_0.5 and Ca²⁺ contamination to evaluate the sum of the square difference between the f_bound predicted by eqn (4) and the experimental data. This process was repeated with updated estimates of K_0.5, Ca²⁺ contamination and [Ca²⁺]′ until a least squares fit of eqn (4) to the titration data was achieved. The figures show measured values of f_bound, together with the fits plotted against [Ca²⁺]′, as determined by the fits.

The calculations outlined above require an estimate of the K_0.5,B of BAPTA. For most solutions we used a value of 0.22 μm (Zhou & Neher, 1993). This is, of course, not correct for solutions with κ′>>1. In a few cases we therefore repeated the least square fit with κ′, as obtained in the first run, entering K_0.5,B = κ′·0.22 μm. Applying this procedure iteratively, the K_0.5 of the indicator dye generally decreased by about 5% while the fitted contamination decreased by about 10%.

Solution preparation

For calcium titration measurements, 4 mm calcium solutions were prepared for all pipette solutions outlined in Table1 using 1 m stock calcium solution (VWR International BVBA, Leuven, Belgium). Adjustment of added calcium to 2, 3, 5, 10, 15, 25, 50, 100, 250, 1000 and 2000 μm was performed through dilution of the 4 mm calcium solutions with the corresponding calcium-free solutions. Fura2FF (TEFLabs, Austin, TX, USA) or Fura6F (Molecular Probes, Eugene, OR, USA) was added to all solutions at a final concentration of 5 μm and 20–100 μm BAPTA was added to all solutions to chelate any contaminating calcium. In all solutions the KCl (or otherwise CsCl content) was adjusted to obtain the required ionic strength (190.9 or 150.9 mm, see Table2). For calcium contamination measurements, all base solutions with 200 μm BAPTA were prepared from 100 mm BAPTA stock (Molecular Probes). Solutions with 5, 10, 20, 30, 50 and 100 μm BAPTA were prepared through dilution of the high BAPTA solution with the zero BAPTA base solutions. For the potassium isethionate-based solution an initial 750 μm BAPTA solution was prepared from 100 mm BAPTA stocks and dilutions to 500, 200, 100, 50, 30, 20, 10 and 5 μm were performed. Chemicals used in the preparation of potassium gluconate, potassium glutamate, potassium isethionate and caesium methanesulfonate-based solutions were obtained from Sigma (St Louis, MO, USA). Caesium gluconate was made by titrating gluconic acid with CsOH to pH 7.0 (Sigma). Cold methanol (−20°C) was added to the mixture until the solution turned slightly opaque. For crystallization, the solution was stored overnight at 4°C. The next day, the crystals were filtered off, dissolved in a minimum amount of water and treated with activated charcoal. The mixture was filtered through a fluted filter and the resulting clear liquid was mixed with methanol and again crystals were precipitated. The caesium gluconate salt was filtered and dried overnight at 40°C in a drying oven. All other chemicals were obtained from Sigma, and Merck (Darmstadt, Germany). All solutions were prepared in plastic vessels to prevent leaching of ions from glass vessels. To prepare solutions for titration experiments, substances were dissolved with ultrapure Millipore water in plastic containers and adjusted to the required pH by adding 1 m KOH or 1 m HCl except that 1 m CsOH was used for caesium-based solutions.

Table 1.

Solution composition and K_0.5 values

Solution	IS	pH	Nucleotides	Chemical composition	K0.5 (± 95% CI)
iKCl w Hepes	150.9	7.2	—	147.9 KCl, 10 Hepes	9.8 ± 1.1
iKCl w Hepes	190.9	7.2	—	187.9 KCl, 10 Hepes	13.8 ± 1.1
iKCl w Hepes	190.9	6.0	—	187.9 KCl, 10 Hepes	15.9 ± 1.3
iKCl w Hepes	190.9	5.0	—	187.9 KCl, 10 Hepes	72.6 ± 2.5
iKCl w Hepes w nucleotide	190.9	7.2	+	160.0 KCl, 10 Hepes, 5 Na2-phosphocreatine, 4 ATP-Mg, 0.3 Na2-GTP	27.9 ± 1.7
Potassium gluconate, IS150	150.9	7.2	+	20 KCl, 100 potassium gluconate, 10 Hepes, 5 Na2-phosphocreatine, 4 ATP-Mg, 0.3 Na2-GTP	48.4 ± 2.1
Potassium gluconate, IS150	150.9	7.2	+	60 KCl, 60 potassium gluconate, 10 Hepes, 5 Na2-phosphocreatine, 4 ATP-Mg, 0.3 Na2-GTP	41.1 ± 2.5
Potassium gluconate	190.9	7.2	+	60 KCl, 100 potassium gluconate, 10 Hepes, 5 Na2-phosphocreatine, 4 ATP-Mg, 0.3 Na2-GTP	62.8 ± 3.4
Potassium gluconate w/o nucleotide	190.9	7.2	—	87.9 KCl, 100 potassium gluconate, 10 Hepes	37.9 ± 1.7
Caesium gluconate	190.9	7.2	+	30 CsCl, 100 caesium gluconate, 30 TEA-Cl, 10 Hepes, 5 Na2-phosphocreatine, 4 ATP-Mg, 0.3 Na2-GTP	65.5 ± 3.2
Caesium gluconate, EX ATP	190.9	7.2	+	15 CsCl, 100 caesium gluconate, 30 TEA-Cl, 10 Hepes, 1 MgCl2 5 Na2-phosphocreatine, 4 Na2-ATP, 0.3 Na2-GTP	229.2 ± 3.9
Caesium gluconate, EX Mg	190.9	7.2	+	24 CsCl, 100 caesium gluconate, 30 TEA-Cl, 10 Hepes, 5 Na2-phosphocreatine, 4 ATP-Mg, 0.3 Na2-GTP, 2 MgCl2	49.0 ± 2.3
Potassium glutamate w/o nucleotide	190.9	7.2	—	87.9 KCl, 100 potassium glutamate, 10 Hepes	14.8 ± 1.4
Potassium isethionate w/o nucleotide	190.9	7.2	—	87.9 KCl, 100 potassium isethionate, 10 Hepes	15.6 ± 7.4
Caesium methanesulfonate w/o nucleotide	190.9	7.2	—	57.9 CsCl, 100 caesium methanesulfonate, 30 TEA-Cl, 10 Hepes	11.5 ± 1.7
Caesium methanesulfonate EX Mg	190.9	7.2	+	24.0 CsCl, 100 caesium methanesulfonate, 30 TEA-Cl, 10 Hepes, 5 Na2-phosphocreatine, 4 ATP-Mg, 0.3 Na2-GTP, 2 MgCl2	ND

ND, not determined.

Table 2.

Contamination values

Solution	IS	pH	Added BAPTA (μm)	Fitted contamination (μm)
iKCl	190.9	7.2	20	9.16
iKCl	190.9	6.0	20	9.83
iKCl	190.9	5.0	20	22.8
iKCl	150.9	7.2	20	9.35
iKCl + nucleotides	190.9	7.2	20	15.0
Potassium gluconate	190.9	7.2	20	17.5
Potassium gluconate	150.9	7.2	20	18.0
Potassium gluconate – nuc	190.9	7.2	20	15.7
Caesium gluconate	190.9	7.2	50	48.6
Caesium gluconate +ATP	190.9	7.2	50	56.5
Caesium gluconate +Mg	190.9	7.2	50	46.1
Potassium glutamate	190.9	7.2	20	15.7
Potassium isethionate	190.9	7.2	100	71.4
Caesium methanesulfonate	190.9	7.2	15	12.3

Fluorescence spectroscopy

Excitation spectra were measured using 5 μl of sample solution placed in a 1 mm path-length quartz cuvette (uCuvette G1.0, Eppendorf, Hamburg, Germany) using a Fluoromax2 spectrofluorometer (Horiba Jobin Yvon Inc., Edison, NJ, USA). Excitation wavelength was scanned from 260 to 450 nm in 2 nm increments while emission was collected at 510 nm with a slit width of 10 nm and 0.5 s integration. Reference excitation spectra for free and bound Fura2FF were measured from solutions with 200 μm BAPTA and 50 mm added calcium, respectively. All titrations were performed in triplicate at room temperature (22–24°C).

Evaluation of inner filter effect

To evaluate the presence of an inner filter effect (Lakowicz, 2006) within the 1 mm path-length cuvette used in the titration experiments, a series of solutions with increasing Fura2FF concentration were prepared in the calcium-free iKCl base solution (see Table1). Samples with Fura2FF concentration ranging from 0 to 20 μm in 2.5 μm increments were prepared through serial dilution of the 20 μm solution with the dye-free solution. Excitation spectra were measured as outlined above and the peak excitation intensity was evaluated as a function of dye concentration. The peak intensity was found to be proportional to the concentration through 10 μm Fura2FF, only above which was quenching due to the inner filter effect observed.

Data analysis

To correct for small differences in sensor concentration all spectra were normalized to the intensity of emission with excitation at the isobestic point of Fura2FF, 354 nm. The free and bound sensor fractions within a given sample were determined through linear unmixing of the excitation spectra with the free and bound reference spectra. The bound fraction was then fit as a function of apparent total calcium, along with information of the added BAPTA and sensor concentrations, to determine the K_0.5, the apparent free calcium concentrations, [Ca²⁺]′, and calcium contamination present in the sample (see Theory). The 95% confidence intervals for a given set of fitted parameters were determined as previously described (Bates & Watts, 2008; Bonate, 2011) using the root mean square error of the fit, the t-value for 95% confidence limit, and the variance–covariance matrix determined from the QR decomposition of the Jacobian matrix (partial derivatives of the fitted function evaluated at a given set of fitted parameters). All analysis was performed using Matlab 7.12 (The MathWorks, Natick, MA, USA).

Electrophysiology

Brainstem slices were prepared from juvenile (postnatal day 9–11) Wistar rats of either sex in accordance with national and institutional guidelines as previously described (Lin et al. 2012). After decapitation, the whole brain was immediately immersed into ice-cold low Ca²⁺ artificial cerebrospinal fluid (aCSF) containing the following (in mm): 125 NaCl, 2.5 KCl, 3 MgCl₂, 0.1 CaCl₂, 10 glucose, 25 NaHCO₃, 1.25 NaH₂PO₄, 0.4 ascorbic acid, 3 myo-inositol and 2 sodium pyruvate, pH 7.3. The brainstem was glued onto the stage of a VT1000S vibratome (Leica, Wetzlar, Germany), and 200 μm-thick coronal slices containing the medial nucleus of the trapezoid body were collected. Slices were equilibrated for 30 min at 35°C in the same aCSF solution, except that the CaCl₂ and MgCl₂ concentrations were 2 and 1 mm, respectively. Thereafter, slices were kept at room temperature (22–24°C) for up to 4 h.

Patch clamp recordings were made from Calyx of Held terminals using an EPC-10 amplifier controlled by Pulse software (HEKA Elektronik, Lambrecht/Pfalz, Germany). Sampling intervals and filter settings were 20 μs and 4.5 kHz, respectively. Cells were visualized by differential interference contrast microscopy through a 60× water-immersion objective (numerical aperture 1.0; Olympus) using an upright Axioskop FS microscope (Zeiss, Oberkochen, Germany). All experiments were performed at room temperature. Patch pipettes were prepared from borosilicate glass (Science Products, Hofheim, Germany) and pulled on a P-97 micropipette puller (Sutter Instruments, Novato, CA, USA) with an open tip resistance ranging from 4 to 5 MΩ. Pipettes were coated with dental wax to minimize fast capacitive transients during voltage clamp experiments and to reduce stray capacitance. Access resistance (R_s) values were ≤20 MΩ. R_s compensation was set to 60–70% (2 μs delay).

For measuring membrane capacitance (ΔC_m), pipettes were filled with solutions containing either caesium gluconate with 3 mm excess ATP, caesium gluconate with 2 mm excess Mg²⁺ or caesium methanesulfonate with 2 mm excess Mg²⁺ (see Table1). Pipette solutions were supplemented with 50 μm EGTA to compensate for any Ca²⁺ contamination. The bath solution was supplemented with 1 μm TTX, 1 mm 4-aminopyridine, and 40 mm tetraethylammonium chloride to suppress voltage-gated Na⁺ and K⁺ currents. C_m was measured and ΔC_m was estimated as described previously (Lin et al. 2011). Offline analysis was done with Igor Pro (WaveMetrics, Lake Oswego, OR, USA). Electrophysiological data are given as mean ± SEM.

Results

Fluorimetric titration of low-affinity Ca²⁺ dyes without the use of Ca²⁺ buffers

Traditionally, calibration of Ca²⁺ indicator dyes is performed with the help of calibration buffers. Varying the ratio of Ca²⁺-bound to free form of the calibration buffer (such as BAPTA or EGTA), defined concentrations of free Ca²⁺ ([Ca²⁺]) are established. Measurements of fluorescence ratio for a range of solutions with different free [Ca²⁺] then allow one to obtain and analyse a calibration curve, for example for determining the dissociation constant of the indicator dye. This procedure meets with two problems when applied to indicator dyes with dissociation constants in the range 10–20 μm: (1) relatively high concentrations of low-affinity calibration buffers are required to overcome the effects of Ca²⁺ binding to the indicator dye; and (2) the properties of the calibration buffers have to be known for the specific composition of the given solution, which in turn may require a calibration of that buffer in that solution.

Since our aim is to measure free Ca²⁺ in the presence of relatively high concentrations of anions, and to determine whether these anions have some low-affinity Ca²⁺ binding capacity, we would have to titrate such anions in a second step after calibrating the indicator dye. It turns out that there is a straightforward way to obtain the same information in a single titration run without resorting to a calibration buffer. As shown in the Methods, one can readily obtain an apparent dissociation constant K_0.5 from the midpoint of a fluorimetric titration, which is the product of the actual concentration-based K_D and the Ca²⁺ binding ratio κ_P of the low-affinity anions in the solution (subscript P for ‘pipette’ solution). In this titration defined amounts of Ca²⁺ are added, using a calibrated Ca²⁺ standard. The accuracy of the resulting K_0.5 values depends only on the accuracy of that standard, on the accuracy of pipetting and of fluorescence readings. Problems of Ca²⁺ contamination of the solution will be addressed below.

Figure1A shows the result of three such titrations using ‘isotonic’ KCl (iKCl) (three different pH values) and 5 μm Fura2FF (for exact composition of the solutions see Table1). The solution also contained 20 μm BAPTA for compensation of contaminating Ca²⁺. The ‘apparent free Ca²⁺’ (see eqn (6) extends from 100 nm to 10 mm. The ordinate is the ‘Ca²⁺ -bound fraction’ of the indicator dye, as defined in the Methods. A least-squares fit of eqn (4) to the pH 7.2 data points yields a value for K_0.5 of 13.8 μm. Independent measurements comparing solutions with 10 and 1 mm Hepes under tight observation of pH showed that 10 mm Hepes did not influence the result. Assuming, then, that Cl⁻ does not bind Ca²⁺ we adopt the value of 13.8 μm for the dissociation constant of Fura2FF at pH 7.2 in a KCl-based medium.

Figure 1. Effects of pH and ionic strength on the K_0.5 of Fura2FF.

A, calcium titrations of three solutions of isotonic KCl solutions with 5 μm Fura2FF and pH values of 7.2 (circles), 6.0 (squares) and 5.0 (diamonds) were performed after initially chelating contaminating calcium with 20 μm BAPTA. The bound fraction of Fura2FF was plotted against the apparent free calcium. The least-squares fit of the bound fraction of Fura2FF from three measurements of pH 7.2 solution (continuous line) yielded a value for K_0.5 of 13.8 μm with initial Ca²⁺ contamination of 9.16 μm. Fitting the bound fractions from titrations of the pH 6.0 (dashed line) and pH 5.0 (dotted line) solutions yielded respective K_0.5 values of 15.9 ± 1.3 and 72.6 ± 2.5 μm and calcium contamination values of 9.8 and 22.8 μm. The insert shows a plot of K_0.5 versus pH with a theoretical curve according to: . B, titrations of two solutions of isotonic KCl with 5 μm Fura2FF, pH 7.2, and different ionic strengths (IS) were performed. Fitting the bound fraction of Fura2FF as a function of added calcium for the solution with ionic strength of 190.9 mm (continuous line black) yielded a K_0.5 of 13.8 ± 1.1 μm, while decreasing the ionic strength to 150.9 mm (dashed black line) decreased the K_0.5 to 9.8 ± 1.1. Similar measurements were performed with potassium gluconate-based solutions and show a decrease in K_0.5 from 62.8 ± 3.4 to 41.1 ± 2.5 μm for the IS190 (solid grey line) and IS150 (dashed grey line) solutions, respectively. The insert shows a plot of K_0.5 of chloride-based solutions versus ionic strength with a theoretical curve according to Bers et al. (1994), constrained to pass through the data point at 0.19 mm. The theoretical curve is well approximated by K_0.5 = −6.891 × 10⁻⁶ + 1.09 × 10⁻⁴ I, where I is the ionic strength.

Dependence of the dissociation constant on pH and ionic strength

Figure1A also contains data for two additional pH values. Slight acidification to pH 6 has little effect. However, switching to pH 5 increases the K_0.5 by a factor of 5.26. The inset in Fig.1A plots the K_D values together with a fit to the equation K_0.5 = K_D*·(1+[H⁺]·K_H), assuming competition between Ca²⁺ binding and H⁺ binding to the doubly deprotonated form of Fura2FF only, with values for K_D* = 13 μm and K_H = 3.23 × 10⁵ m⁻¹. Here, [H] was calculated according to (the offset of 0.13 corrects for the activity coefficient of H⁺, according to Martell & Smith, 1974).

Figure1B compares two titration curves, both at pH 7.2 for two different values of ionic strength, which cover the range of ionic strengths typically used for whole cell patch clamp experiments. The dissociation constant decreases (by 29%) when decreasing ionic strength by 40 mm. The inset plots K_D values together with a fit according to eqns (11)–(14) of Bers et al. (1994), which are based on the electrochemical theory of dilute electrolytes (Harned & Owen, 1958; Harrison & Bers, 1989). The data conform to the theory quite well, but the low range of ionic strength values prevents any further conclusions. Combining the fits of Fig.1A and B, one arrives at an approximate dependence of K_0.5 on pH and ionic strength (I, in mol l⁻¹) according to

(8)

The underlying data were obtained at room temperature (22°C), and need to be corrected for temperature differences. Using eqn (10) of Bers et al. (1994) and an enthalpy of 4.04 kcal m⁻¹, as reported for dibromoBAPTA, we predict a 1.4-fold decrease in K_0.5 when changing to physiological temperature.

Apparent Ca²⁺ affinity of Fura2FF for solutions with a variety of major anions

The binding of a cation to an anionic ligand (such as a Ca²⁺ indicator dye) is influenced not only by ionic strength, but also by the nature of the major ions in solution (Bockris & Reddy, 1973). These effects are generally represented by activity coefficients in the sense that activity of an ion (for which physiochemical laws, such as the law of mass action, hold strictly) is assumed to be the product of the stoichiometric concentration and an activity coefficient. Since our titrations are based on concentrations, the ‘stoichiometric K_D’ which we obtain is actually a product of the true dissociation constant (K_D) – the Ca²⁺ binding ratios (see above) – and a term representing activity coefficients of the participating ions. The latter vary with ionic strength and also somewhat with the nature of the dominant anions and cations. Therefore, we expect the measured K_0.5 to vary somewhat between solutions with different main anions. Mean molal activity coefficients for simple sodium salts at 200 mm ionic strength vary typically by about 10–20% (Robinson & Stokes, 1959). Therefore, we expect K_0.5 (which is a product of K_D and κ_P, see above) to vary to that degree, even in the absence of Ca²⁺ binding to any of the anions present. Any deviations larger than that are interpreted as Ca²⁺ binding.

Figure2A shows titration curves for solutions similar to those of Fig.1A, except that 100 mm KCl was replaced by either 100 mm potassium isethionate, potassium glutamate, or caesium methanesulfonate (all at pH 7.2). Values for K_0.5 are 15.6 ± 7.4, 14.8 ± 1.4 and 11.5 ± 1.7 μm, respectively (see Table1 for a summary of results, shown as ± the 95% confidence limits). We consider the differences between these three anions and chloride to be within the range, which can be attributed to activity effects (see also Discussion).

Figure 2. Effects of different dominant anions and nucleotides on the K_0.5 of Fura2FF.

A, titration curves for solutions with 100 mm potassium glutamate, potassium isethionate or caesium methanesulfonate are indicated by the solid, dashed and dotted lines, respectively. Fitting the calcium-bound fraction of Fura2FF from three measurements of each solution yielded K_0.5 values of 14.8 ± 1.4 μm for the glutamate-based solution, 15.6 ± 7.5 μm for the isethionate solution and 11.5 ± 1.7 μm for the methanesulfonate solution. B, titrations of KCl and potassium gluconate-based solutions with and without nucleotides were performed. Fitting the bound fraction of Fura2FF in the iKCl solution without nucleotides (solid black line) present yielded a K_0.5 value of 13.8 ± 1.1 μm, while the presence of nucleotides (dashed black line) increased K_0.5 to 27.9 ± 1.7 μm. The fitted K_0.5 value for the potassium gluconate-based solution without nucleotides (solid grey line) was 37.9 ± 1.7 μm, while the presence of nucleotides (dashed grey line) increased K_0.5 to 62.8 ± 3.4 μm.

Anions with low-affinity Ca²⁺ binding

Potassium gluconate is often used as major anion in whole cell patch clamp experiments. However, Christoffersen and Skibsted (1975) reported an apparent K_D for Ca²⁺ binding of gluconate⁻ of 15.5 mm (Christoffersen & Skibsted, 1975). This would imply that 100 mm potassium gluconate in a pipette solution would contribute 100/15.5 = 6.46 to its κ_P value. Likewise, most pipette solutions contain nucleotides, such as ATP²⁻ and GTP²⁻, which have Ca²⁺ and Mg²⁺ binding capacity. We therefore measured K_0.5 for solutions containing these anions.

First, we considered solutions, which again are very similar to that of Fig.1A. In one solution, iKCl + nucleotides, 27.9 mm KCl is replaced by 5 mm Na₂phosphocreatine, 4 mm MgATP plus 0.3 mm Na₂GTP. In the other two solutions, potassium gluconate and potassium gluconate + nucleotides, 100 mm KCl of each corresponding iKCl solution is replaced by potassium gluconate. Calcium titrations of these solutions are plotted in Fig.2B and show that both replacements shift the curves rightwards. In the KCl solutions the K_0.5 is increased by a factor of 2.02 as a result of the presence of nucleotides and in the case of gluconate it is increased by a factor of 2.75. These changes are much larger than expected for merely electrostatic interactions and probably reflect low-affinity binding of Ca²⁺ to these anions (see Discussion).

We also tested the effect of ionic strength on K_0.5 in potassium gluconate-based solutions by lowering KCl for a total change in ionic strength from 190.9 to 150.9 mm. We did so in two different ways, once reducing KCl content from 60 to 20 mm and once reducing both KCl and potassium gluconate content proportionally. As in the case of the chloride-based solution, the K_0.5 decreased, as expected by theory.

Caesium-based solutions

The measurement of Ca²⁺ currents in nerve terminals requires the blockade of all other current components. Replacement of K⁺ by Cs⁺ is often used as an effective blocker of K⁺ channels. We therefore tested several solutions, which are exactly those used in patch clamp experiments, with caesium gluconate as the main constituent and nucleotides, Na⁺-phosphocreatine and Hepes added (see Table1 for exact composition). We were also interested in how far Mg²⁺ binding to ATP²⁻ would change the properties of the solutions. Therefore, we compared three cases: (1) the nucleotide composition, as used above for the potassium-based solution with an estimated free [ATP²⁻] of about 1 mm, (2) a solution with excess ATP²⁻ with free [ATP²⁻] of about 3.3 mm and (3) a solution with 1.7 mm excess Mg²⁺, resulting in free [ATP²⁻] < 0.38 mm (assuming K_D,Mg = 0.02 mm; Moisescu & Thieleczek, 1979).

Figure3 plots titration curves for these three cases. In the case of ‘normal’ nucleotides the K_0.5 of 65.5 ± 3.2 μm is close to that of the equivalent potassium gluconate-based solution. Depleting free [ATP²⁻] by excess Mg²⁺ decreases this slightly to 49.0 ± 2.3 μm. However, increasing free ATP²⁻ increases K_0.5 to 229.2 ± 3.9 μm, which is 4.7 times higher than the value for depleted [ATP²⁻] and 16.7 times higher than the value for KCl-based solutions. This indicates that the contribution of 3 mm free ATP to κ_P is about 16 (see Discussion).

Figure 3. Effects of excess ATP²⁻ and Mg²⁺ on the K_0.5 of Fura2FF.

Titration curves for solutions with 100 mm caesium gluconate under normal conditions as well as in the presence of excess ATP or Mg²⁺ are indicated by the solid, dashed and dotted lines, respectively. Fitting the bound fraction of Fura2FF from three measurements of each solution yielded K_0.5 values of 65.5 ± 3.2 μm for the normal solution, 229.2 ± 3.9 μm for the solution with excess ATP and 49.0 ± 2.3 μm for the solution with excess Mg²⁺.

The influence of free [ATP²⁻] on Ca²⁺ sensitivity of neurotransmitter release

Given the strong effect of [ATP²⁻] on the Ca²⁺ binding ratio of pipette filling solutions, we studied neurotransmitter release in the Calyx of Held synapse using three solutions with different Ca²⁺ binding ratios. These included a caesium methanesulfonate-based solution with negligible Ca²⁺ binding, as well as two solutions with extreme differences in [ATP²⁻] (solution ‘caesium methanesulfonate ExMg’, ‘caesium gluconate ExATP’, and ‘caesium gluconate ExMg’, Table1). This was of interest, as estimates for the basal Ca²⁺ binding ratio of fixed Ca²⁺ buffers in the Calyx of Held range from 25 to 40 (Neher & Taschenberger, 2013), which indicates that the presence of 3 mm [ATP²⁺] and gluconate changes the Ca²⁺ binding ratio of dialysed cytosol substantially. Also, free [ATP²⁻] is known as a very fast Ca²⁺ binder (Hammes & Levison, 1964), which should be very potent in interfering with Ca²⁺ binding to the Ca²⁺ sensors of the neurotransmitter release apparatus. Indeed, when measuring capacitance changes in response to action potential-like stimuli, we observed substantial differences between the three solutions. The amount of Ca²⁺ influx during 3 ms ramp depolarizations was varied by varying the amplitudes of the depolarizations (Fig.4A–C).

Figure 4. A pronounced shift in the capacitance – presynaptic Ca²⁺ charge relationship in the presence of excess free ATP.

A, a series of AP-like voltage ramps (−80 to 50, 10 and 0 mV with depolarization phase, 1 ms and repolarization phase 2 ms) were applied to calyx terminals. B and C, averaged capacitance traces and Ca²⁺ currents were obtained from 10, 8 and 10 terminals with Ex ATP (black), Ex Mg (grey) and methanesulfonate (not shown in A–C for clarity of display), respectively. D, changes in capacitance as functions of presynaptic Ca²⁺ charge. The smooth black lines represent fits to the data using a Hill equation with midpoint at 1.18 pC (methanesulfonate), 1.97 pC (Ex Mg) and 3.16 pC (Ex ATP). The maximum for the Hill-fit was fixed to 202.2 fF, which is the mean of responses to 10 mV step depolarizations to 0 mV (257.9 fF for methanesulfonate, 169.4 fF for gluconate with excess Mg²⁺ and 180.2 fF for gluconate with excess ATP). The inset figure presents the relationship with double-logarithmic scale. Note the clear shifts along the x-axis between the three curves.

Figure4D plots the observed capacitance changes, which are proportional to the number of vesicles released, as a function of the integral of the Ca²⁺ current transients. Maximum responses, depleting the whole rapidly releasing pool of vesicles, were obtained by 10 ms depolarizations to 0 mV (Lin et al. 2011). The data for the three solutions were fitted by Hill curves. The Hill coefficients were set to 2.6, which resulted in sigmoid-shaped curves, as is characteristic for the Ca²⁺ dependence of neurotransmitter release (Dodge & Rahamimoff, 1967). We used the Hill fits to calculate the Ca charge required to elicit a 20 fF response, which is close to what is released by an action potential. The resulting numbers were 0.5 pC for the caesium methanesulfonate-based solution, 0.84 pC for the gluconate-based solution with excess Mg²⁺, and 1.35 pC for the gluconate-based solution with excess ATP²⁻.

The handling of Ca²⁺ contamination

Titrating an indicator dye with a K_D around 15 μm requires solutions with free [Ca²⁺] ranging from about 1 μm to several hundred micromoles. Unfortunately solutions, even when prepared very carefully, have Ca²⁺ contamination in the range of a few to some tens of micromoles (Bers et al. 1994). At the low end these contaminations can be handled by using the (unknown) concentration of contamination as a free parameter in the fitting of titration curves (see Methods). For contaminations above 5 μm, however, the fitting becomes quite unreliable, as there are no low concentration points included in the fits. We therefore estimated contamination for all solutions used by a preliminary titration with BAPTA. We then added the required amount of BAPTA, thus determined, to ‘neutralize’ the contamination. Since the K_D of BAPTA is about 100 times smaller than the K_D of Fura2FF, BAPTA acts like ‘negative Ca²⁺’, and the remaining difference between BAPTA and contamination can be readily handled in the fitting routine (see Methods). We would like to point out, however, that for in vivo experiments, neutralization of contaminating Ca²⁺ should be achieved with EGTA (and not BAPTA) to avoid effects on the Ca²⁺ nanodomain in the case of slight overcompensation. We found that our K⁺-based solutions have typically 10–15 μm contamination, whereas caesium gluconate, for instance, has up to 50 μm contamination. Values for contamination are given in Table2. In caesium gluconate solutions the apparent fraction of bound Ca²⁺ at saturating total Ca²⁺ stayed below the value typically observed for other solutions. We attribute this to the likely presence of metal ions other than Ca²⁺, which may have higher affinity than Ca²⁺, but lower fluorescence yield. To test this assumption we titrated caesium gluconate in the presence of 4 mm Ca²⁺ with TPEN, a chelator with very high affinity for heavy metal ions (Arslan et al. 1985), and found only a slight increase in maximum fluorescence compatible with the presence of about 2–5 μm heavy metals.

Comparison between Fura2FF and Fura6F

Several studies on [Ca²⁺] in nerve terminals have used Fura6F. Estimates for its K_D range from 5.3 μm (Life Technologies) to 15 μm (Müller et al. 2007). Fura6F is no longer available commercially and will probably be replaced by Fura2FF in future studies, as the K_D values of the two indicator dyes are very similar. We therefore considered it as important to compare the K_0.5 values of the two dyes, using the same method. We performed titrations on those solutions, which had actually been used in patch clamp experiments (KCl-based, potassium gluconate-based and caesium gluconate-based). We found a K_0.5 value for Fura6F in KCl-based solution of 17.8 μm. Values in gluconate⁻-based solution including nucleotides were 56.2 and 84.5 μm for K⁺ and Cs⁺, respectively. Measurements with Fura6F confirmed the conclusion regarding contamination as obtained with Fura2FF.

Discussion

Here we characterize the Ca²⁺ binding properties of electrolyte solutions, as they are typically used in pipettes during whole cell patch clamp experiments on brain slices and neuronal cultures (adjusted to an ionic strength of 190 mm, pH7.2, and at 22°C). We also determine stoichiometric (or concentration-based) dissociation constants for the Ca²⁺ indicator dyes Fura2FF and Fura6F.

The fluorimetric titrations presented do not rely on known dissociation constants of other Ca²⁺ buffers, only on the accuracy of a commercially available Ca²⁺ standard. In our measurements, we find that the K_0.5 of Fur2FF varies somewhat, depending on the major anion used, as expected from the physical chemistry of electrolyte solutions (Harned & Owen, 1958). These variations range from 10 to 20% for chloride, glutamate, methanesulfonate and isethionate (see Table1). Gluconate-based solutions, however, have K_0.5 values that are higher by about a factor of 2–3. Since our method measures the product of the actual K_D and the combined Ca²⁺ binding ratio, κ, of all low-affinity Ca²⁺ ligands present, we interpret the higher values for gluconate-based solutions in terms of low-affinity Ca²⁺ binding of the glutamate anion (Christoffersen & Skibsted, 1975). Furthermore, we find that nucleotides, such as ATP²⁻ and GTP²⁻, also contribute to the Ca²⁺ binding capacity. This contribution varies strongly with the presence of magnesium, which competes for nucleotide binding.

Together, the contributions of gluconate and nucleotides to κ (the ratio of total Ca²⁺ over free Ca²⁺) may range from 1.5 to 15. This can have substantial effects on Ca²⁺ buffering, given estimates for total Ca²⁺ binding ratio, κ_s, of fixed low-affinity buffers in the cytoplasm of Calyx nerve terminals ranging from 25 to 40 and considering the high Ca²⁺ binding rate of ATP^2– (>10⁹ m⁻¹ s⁻¹; theoretical 8 × 10⁹ m⁻¹ s⁻¹ (Hammes & Levison, 1964)). In fact, we find that Ca²⁺ influx is 2.7 times less efficient in triggering neurotransmitter release in Calyx of Held nerve terminals with a caesium gluconate solution with 3 mm free [ATP²⁻] than with a caesium methanesulfonate-based solution with negligible Ca²⁺ binding capacity. As ATP²⁻ and Mg²⁺ may vary widely in the cytoplasm, depending on the metabolic state of the cells (Veech et al. 1979), this demonstrates that their balance needs careful consideration.

Comparison with literature data

Our value of K_D for Fura2FF in KCl-based solutions without nucleotides (13.8 ± 1.1 μm) does not compare favourably with 5 μm reported by Xu-Friedman & Regehr (1999) and 4.18 μm by Aponte et al. (2008). Values for both dyes are also quite different from those given by the suppliers (LifeTech: Fura6F K_D = 5.30 μm, TefLabs: Fura2FF K_D = 35 μm). This discrepancy is probably due to differences in ionic strength and assumptions about the K_D of calibration buffers. However, when extrapolating our K_D to an ionic strength of 100 mm, (K_0.5 = −6.891 × 10⁻⁶ + 1.09 × 10⁻⁴ I) a more comparable K_D is estimated (∼3.58 μm). Our K_D of 17.8 ± 1.3 μm for Fura6F data is in rather good agreement with the 15 μm reported by Müller et al. (2007).

We confirm that gluconate has some Ca²⁺ binding capacity. At a concentration of 100 mm, its contribution to the Ca²⁺ binding ratio (1.75) suggests a K_D of 57 mm, which is much higher than the reported 15.5 mm (Skibsted & Kilde, 1972). However, a more recent study reported K_D values of 32.3 and 71.4 mm from calcium electrode-based measurements and iodometric titrations in 0.2 m NaCl, respectively (Vavrusova et al. 2013). Likewise, the increase in K_0.5 by 13.85 μm for the iKCl solution with 3.3 mm free nucleotides indicates a K_D for Ca²⁺ binding to ATP²⁻ of 0.24 mm, which is very close to the 0.2 mm reported by Schoenmakers et al. (1992). The K_0.5 measured for the glutamate solution was found to be only slightly greater than the K_D of the calcium indicator, and thus we cannot confirm significant Ca²⁺ binding to glutamate⁻, as reported by Davies & Waind (1950).

Comparison with other calibration methods

The method for calibrating Ca²⁺ indicator dyes, described here, has the advantage that it does not rely on any other Ca²⁺ buffer and can be readily performed with solutions actually used for filling patch clamp pipettes. Its disadvantage is that it does not discriminate between loose electrostatic interactions and specific, low-affinity binding. We have to infer the latter by the assumption that the true dissociation constant of the indicator dye in the presence of a given Ca²⁺ binding anion is the same as that in the presence of a similar anion without Ca²⁺ binding properties.

In our analysis we decomposed the excitation spectra, measured from the titration samples using a spectrofluorometer, as linear combinations of spectra from Ca²⁺-free and Ca²⁺-saturated samples of the dye. The corresponding fractional contributions are equated with the free and bound fractions of dye, respectively. Alternatively, one may perform calibrations under the fluorescence microscope with glass capillaries with short path lengths (e.g. 350 μm), in which it is more practical to perform measurements with two excitation wavelengths, and analyse data according to

(9)

as originally described by Grynkiewicz et al. (1985). This uses calibration parameters R_min (ratio at zero [Ca²⁺]), R_max (ratio at saturating [Ca²⁺]) and an effective K′_eff.

When using Ca²⁺-indicator dyes, such as Fura2FF or Fura6F on the microscope, one has to calibrate the dye for ratiometric use. Given the knowledge of the actual (instrument-independent) value of the K_D (e.g. for iKCl), we propose the following strategy to render the ratiometric calibration consistent with K_D.

• Determine R_min and R_max using a medium dye concentration of 200 μm and either in vitro or in vivo calibration procedures, as described previously (Helmchen, 2005; Neher, 2005; Schneggenburger, 2005).

• Determine the value of α (iso-coefficient), for which F₁+αF₂ (F₁ and F₂ being fluorescence values at excitation wavelengths 1 and 2, respectively) does not change during a [Ca²⁺] transient (Zhou & Neher, 1993).

From this, an estimate of K_eff of the indicator dye can be obtained using the equation

(10)

to be used for ratiometric measurements eqn (9). Alternatively, a full ratiometric calibration with three or more calibration solutions (see, for instance, Schneggenburger, 2005) yields values for R_min, R_max and K_eff. Determining the isocoefficient then allows one to calculate K_D from eqn (10). This value should agree with the one determined by the spectroscopic calibration (for KCl-based solutions without nucleotides). Deviations between the two values may be due to procedural errors, incorrect assumptions about the K_D of the buffer used, or differences between the in vitro situation and the intracellular environment during an in vivo calibration (for details see Helmchen, 2005; Neher, 2005). We compared the K_D values of our ‘spectroscopic’ calibration of Fur6F in isotonic KCl with that of an in vivo calibration of the same dye in caesium gluconate-based solution and found K_D,spec = 17.8 ± 1.3 μm and K_D,in-situ = 12.9 ± 0.1 μm. For the in vivo calibration we used DPTA as a calibration buffer (Schneggenburger, 2005) assuming a K_D of 80 μm. The small discrepancy is expected, given the range of K_D values observed in vitro for different anions and given the fact that the ionic milieu in the crowded environment of the cytoplasm is definitely not the same as that of a relatively dilute aqueous solution (Poenie, 1990).

Choice of anions in whole cell patch clamp experiments

We find that gluconate adds 1.75 to the Ca²⁺ binding capacity of the pipette solution and nucleotides (4 mm MgATP + 0.3 mm NaGTP) add another 1.8 to this number. The combined effect is negligible for many situations, given the intrinsic fixed buffer capacity of most neurons ranging from 20 to hundreds. On the other hand, little is known about mobile endogenous Ca²⁺ binding molecules, which may include Ca²⁺ binding proteins, nucleotides and other low molecular-weight substances that may be replaced by constituents of the pipette solution (Müller et al. 2007). If endogenous mobile Ca²⁺ buffers are scarce, the apparent diffusion coefficient of Ca²⁺ may change several fold (Wagner & Keizer, 1994; Neher, 1998) when pipette-delivered mobile buffers compete with fixed buffers and thereby mobilize Ca²⁺. Also, calculations of microdomain Ca²⁺ signals are expected to be strongly influenced by low-affinity binding of ATP²⁻ or gluconate. Given the high concentrations of these reagents, the binding product (product of anion concentration and Ca²⁺ binding rate constant, k_on) may be very high. Although no data seem to be available for k_on of gluconate, a typical value of 10⁸ m⁻¹ s⁻¹ combined with a concentration of 0.1 m will result in 10⁷ s⁻¹. This, together with a diffusion coefficient D_Ca of 220 μm² s^–1 results in a length constant for diffusional equilibration of (Neher, 1998). This implies that within 10 nm of a Ca²⁺ source, free Ca²⁺ will be equilibrated with gluconate. Given the Ca²⁺ binding ratio of the solution discussed, the free [Ca²⁺] will be reduced by a factor of 2.75 by gluconate and by a factor of 4.55 for the combined effect of gluconate and nucleotides. Given the steep dependence of neurotransmitter release on [Ca²⁺], this should have dramatic consequences on release at synapses with very tight coupling between channels and Ca²⁺ sensors. Release at synapses with weaker coupling should not be influenced as much by the choice of anions, since slower buffers with higher affinity are expected to control [Ca²⁺] at larger distances (Naraghi & Neher, 1997). The relatively modest effects observed in our measurements at the Calyx of Held are consistent with larger coupling distances, as reported for this preparation (Wang et al. 2008). In this sense, comparisons of release between methanesulfonate and gluconate or else while varying the Mg²⁺/ATP ratio should be good indicators for very tight coupling between release-ready vesicles and Ca²⁺ channels, such as those found at cochlear hair cells (Wong et al. 2014).

Key points

• The efficiency of neurotransmitter release is influenced by the presence of Ca²⁺ binding molecules.

• In this study we show that the use of gluconate as the dominant anion in pipette filling solutions, together with the presence of ATP and GTP, influences the efficiency of Ca²⁺-mediated release during whole cell patch clamp measurements in the Calyx of Held.

• We introduce a novel fluorimetric titration procedure for low-affinity calcium dyes, such as Fura2FF, that allows us to determine the calcium binding ratios of several commonly used pipette solutions.

• These results explain the influence of gluconate and nucleotides on neurotransmitter release, provide guidelines for calibrating pipette solutions and calcium indicators, and may provide a basis for studying the coupling between calcium sensors and sources.

Additional information

Competing interests

The authors have no conflicts of interest to declare.

Author contributions

A.W., K.H.L. and E.N. conceived and designed the research; A.W. and K.H.L. performed the experiments; A.W., K.H.L. and E.N. analysed the data; A.W. and E.N. wrote the manuscript. All authors approved the final version.

Funding

This work was funded in part by the Cluster of Excellence and DFG Research Center Nanoscale Microscopy and Molecular Physiology of the Brain and a grant from the European Commission (EuroSPIN) (to E.N.).