Quantification of Mg2+ extrusion and cytosolic Mg2+-buffering in Xenopus oocytes

ABB Archives of Biochemistry and Biophysics 458 (2007) 3–15 www.elsevier.com/locate/yabbi

Quantification of Mg2+ extrusion and cytosolic Mg2+-buffering in Xenopus oocytes Thomas E. Gabriel b

a,1

, Dorothee Gu¨nzel

a,b,*

a Institut fu¨r Neurobiologie, Heinrich-Heine-Universita¨t, Universita¨tsstr. 1 40225 Du¨sseldorf, Germany Institut fu¨r klinische Physiologie, Charite´, Campus Benjamin Franklin, Hindenburgdamm 30, 12200 Berlin, Germany

Received 16 January 2006, and in revised form 29 May 2006 Available online 4 August 2006

Abstract Intracellular Mg2+ buffering and Mg2+ extrusion were investigated in Xenopus laevis oocytes. Mg2+ or EDTA were pressure injected and the resulting changes in the intracellular Mg2+ concentration were measured simultaneously with Mg2+-selective microelectrodes. In the presence of extracellular Na+, injected Mg2+ was extruded from the oocytes with an estimated vmax and KM of 74 pmol cm2 s1 and 1.28 mM, respectively. To investigate genuine cytosolic Mg2+ buffering, measurements were carried out in the nominal absence of extracellular Na+ to block Mg2+ extrusion, and during the application of CCCP (inhibiting mitochondrial uptake). Under these conditions, Mg2+ buffering calculated after both MgCl2 and EDTA injections could be described by a buffer equivalent with a concentration of 9.8 mM and an apparent dissociation constant, Kd-app, of 0.6 mM together with an [ATP]i of 0.9 mM with a Kd-app 0.12 mM. Xenopus oocytes thus possess highly efficient mechanisms to maintain their intracellular Mg2+ concentration.  2006 Elsevier Inc. All rights reserved. Keywords: Xenopus laevis oocyte; Leech Retzius neuron; Magnesium; ATP; Buffering; Na+/Mg2+ antiport; Membrane transport

Xenopus oocytes are a well established expression system for ion transport proteins (for rev. see [1]), as they exhibit low native transport activity for many ions. Recently, Xenopus oocytes were successfully used by Goytain and Quamme GA [2–4] for the expression and characterization of new potential Mg2+ transport systems. In these studies, the identified transporters were electrogenic and thus could solely be characterized by the resulting changes in oocyte membrane potential. While measurements of changes in the intracellular Mg2+ concentration, [Mg2+]i, were not attempted in these studies, they would be the only means to detect and characterize electroneutral Mg2+ transport systems such as the 1 Mg2+/2 Na+ antiport postulated to exist in numerous systems (for rev. see e.g. [5–7]). *

Corresponding author. Fax: +49 30 8445 4239. E-mail address: [email protected] (D. Gu¨nzel). 1 Present address: Centre for Theoretical and Computational Neuroscience, Portland Square, University of Plymouth, Plymouth, Devon, PL4 8AA, UK. 0003-9861/$ - see front matter  2006 Elsevier Inc. All rights reserved. doi:10.1016/j.abb.2006.07.007

However, measuring changes in [Mg2+]i is complicated by the fact that such changes depend on cytosolic buffering, uptake/release from intracellular stores as well as Mg2+ transport across the cell membrane, processes that together are termed muffling [8]. In oocytes, neither intrinsic Mg2+ transport properties nor cytosolic Mg2+ buffering have yet been investigated. It was therefore the aim of the present study to investigate the mechanisms that dampen the changes in [Mg2+]i caused by uptake of Mg2+ into or loss of Mg2+ from the oocyte. In a previous study on leech neurones [9], iontophoretic injection was employed to determine the intracellular Mg2+ buffer capacity. However, this technique has some serious drawbacks. First, the current necessary for the injection of a cation leads to a considerable depolarisation of the cell membrane. This may cause the opening of voltage-sensitive ion channels, changes in the driving force of electrogenic ion transporters, or it may even damage the cell. Second, depending on the ion motility, only a small fraction of the injected current may be carried by the desired ion,

4

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

making the injection of buffers/chelators with a low ion motility difficult. Moreover, the determination of the transport index (i.e. the percentage of the injection current carried by the desired ion) is tedious. Third, uncharged substances cannot be iontophoretically injected. These difficulties can be avoided by the use of pressure injection. However, pressure injection induces other problems, such as changes in cell volume and the unavoidable injection of a counter-ion. Pressure injection from microcapillaries is a well established technique for the focal application of drugs, for the injection of various substances into single cells (e.g. horseradish peroxidase, fluorescence dyes or caged compounds), or for the injection of RNA or DNA into cells or embryos. When applied to study the buffering capacity of the cytoplasm of a cell for a certain ion species, this technique can be used to inject a solution containing this ion while the increase in the free ion concentration ([Ion]i) is measured simultaneously, e.g. with ion-selective microelectrodes or fluorescence dyes. It can also be used to inject a known amount of additional buffer or chelator into the cell. In consequence, the buffer capacity can be calculated from the observed decrease in [Ion]i [10,11]. Most elegantly, the buffer may be the ion-sensitive fluorescence dye itself [10]. Pressure injection has previously been used to study intracellular Ca2+ buffering [11] and intracellular Mg2+ buffering and diffusion in muscle fibres [12,13]. The major problem of such studies is the quantification of the injected volume. One possibility is the co-injection of another substance that ideally should not be transported across the cell membrane, buffered, or sequestered in cell organelles. Such an approach has been chosen by Schwiening and Thomas [11], who injected CaCl2 into snail neurones and compared the measured changes in the intracellular concentrations of Ca2+ ([Ca2+]i) and Cl ([Cl]i) to estimate intracellular Ca2+ buffering. Their experiments showed, however, that Cl may not be an ideal choice, since Cl is removed from the cytoplasm by cellular transport mechanisms. Another possibility is the co-injection of substances such as lucifer yellow-labelled dextrans [14], TRITC-labelled bovine serum albumin [15] or aequorin [16] and the determination of the injected volume from the resulting fluorescence/ luminescence of the injected cell. Alternative techniques for the determination of the injected volume are reported in the literature [14,15,17], namely direct injection of electrolyte into oil, or the injection of an electrolyte containing a fluorescent marker into an electrolyte droplet of known volume. The direct injection of an electrolyte into oil leads to the formation of small electrolyte droplets, the diameter of which can be measured under a stereo microscope or from photographs allowing estimates of the volume ejected from the capillary. For injection into an electrolyte droplet of known volume, the electrolyte droplet may be kept under oil to prevent evaporation. The fluorescence detected after injection can be used to calibrate the ejected volume.

In the present study, several techniques were compared to find a reliable method for determination of the volume ejected from a capillary at a given pressure and duration of pressure application. Pressure injections were then applied to oocytes of the frog, Xenopus laevis and to Retzius neurones of the medicinal leech, Hirudo medicinalis, allowing comparison of the results with data obtained from iontophoretic injections [9]. Part of this work has been published in abstract form [18]. Methods Preparation Experiments were carried out on oocytes of the frog, X. laevis and on Retzius neurones of the leech, H. medicinalis. Frog oocytes were a generous gift from Dr. M.S. Eckmiller (C. & O. Vogt Brain Research Institute, Heinrich-Heine-Universita¨t Du¨sseldorf, Germany). The oocytes were dissociated and defolliculated, following the detailed description by Romero et al. [19]. In brief, freshly dissected ovaries were washed several times in standard saline (composition see below), followed by treatment with 1 mg/ml type A collagenase (Boehringer) for 20–30 min in a nominally Ca2+-free, sterile filtered solution (filter: Nalgene 0.2 lm, room temperature) until follicular membranes were observed to float free. The supernatant was then discarded and the oocytes were rinsed several times before being transferred into a sterile filtered, Ca2+-containing solution, in which they could be kept for more than a week at a temperature of about 10 C. Oocytes were selected to be of similar size. Cell diameters were determined using a stereomicroscope with graded ocular lens and an estimate of the cell volume was calculated assuming a spherical shape of the cells. Oocytes used had an average volume of 0.8 ± 0.08 ll (n = 41). Single oocytes were transferred to an experimental chamber in which the bottom was covered with Sylgard. Five to six insect pins arranged as a palisade prevented the oocyte from being swept away during superfusion. Segmental ganglia from the leech central nervous system were dissected as described by Schlue and Deitmer [20]. Isolated ganglia were transferred to an experimental chamber and fixed ventral side up by piercing the connectives with insect pins. The mean volume of Retzius neurones was estimated from previously determined cell soma diameters (83.2 ± 6.5 lm, n = 14, [9]) to be 307 ± 74 pl (n = 21). During all experiments the experimental chamber (volume 0.2 ml) was continuously superfused with the appropriate saline at room temperature (20–25 C) at a rate of approximately 5 ml/min (25 chamber volumes per minute).

Solutions Standard saline for frog oocytes (modified Barth’s solution) was composed of (mM) NaCl 100, KCl 2, CaCl2 2, MgCl2 1, Hepes 10, pH 7.5 (NaOH). For nominally Ca2+-free saline, CaCl2 was omitted. Standard leech saline (SLS)2 contained (in mM): NaCl 85, KCl 4, MgCl2 1, CaCl2 2, and Hepes 10, pH 7.4 adjusted with approximately 5 mM NaOH, bringing the total Na+ concentration up to 90 mM. Nominally Na+-free saline (frog and leech) was obtained by an equimolar substitution of Na+ with NMDG+ (N-methyl-D-glucamine+; Sigma, Deisenhofen, Germany). To manufacture a Cl-free leech saline, all Cl was replaced by gluconate. To adjust osmolarity and to compensate for the Ca2+ binding of gluconate, concentrations in this solution were increased to (mM):

2 Abbreviations used: SLS, standard leech saline; NMDG+, N-methyl-Dglucamine+; TMA, tetramethylammonium.

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15 Na-gluconate 102, K-gluconate 4.8, Mg-gluconate 2, Ca-gluconate 12, and Hepes 10, pH 7.4 adjusted with approximately 5 mM NaOH.

5

previously described by Gu¨nzel and Schlue [24]. Microelectrodes were used only if their detection limit (as defined by [25]) was below the values recorded during an experiment.

Ion-sensitive microelectrodes Measuring procedure The intracellular free concentrations of Na+ ([Na+]i), Cl ([Cl]i), Mg2+ ([Mg2+]i) and tetramethylammonium ([TMA+]i) were measured using ion-selective microelectrodes based on the neutral carriers ETH 227 (Fluka), Cl Ionophore I (Fluka), ETH 5214 (Fluka) and on the ion-exchanger 477317 (Corning), respectively. Microelectrodes were pulled from borosilicate glass-capillaries (Theta-style, TGC200-15; ‘twisted’ GC150F-15 and GC100F-15, Clark, Reading, GB) and silanized as described by Gu¨nzel et al. [21,22]. After the ion-sensitive barrels had been filled with the appropriate sensors, they were backfilled with 100 mM MgCl2 (Mg2+-selective microelectrodes), 100 mM NaCl (Na+-selective microelectrodes), 0.5 M KCl (Cl-selective microelectrodes) and 100 mM KCl (TMA+-selective microelectrodes). The reference channel was filled with 3 M KCl (Mg2+- and Na+-selective microelectrodes), 3 M LiOAc + 5 mM KCl (TMA+-selective microelectrodes) and 0.5 M K2SO4 + 5 mM KCl (Cl-selective microelectrodes).

Calibration procedure Before and after each experiment, microelectrodes were calibrated in solutions that mimicked the ionic background of intracellular conditions. Mg2+ calibration solutions contained (in mM): KCl 80, NaCl 10, Hepes 10, and 10, 2.5, 0.5, or 0 MgCl2, added from a 1 M-stock solution (Fluka, Buchs, Switzerland), pH 7.3 adjusted with KOH. Na+ calibration solutions were composed of (in mM): KCl 110, MgCl2 0.5, Hepes 10, and 50, 10, 2.5, or 0 NaCl, pH 7.3 adjusted with KOH. In addition, Ca2+ was buffered to a free concentration of about 107 M by adding 0.73 mM CaCl2 and 1 mM EGTA (calculation of CaCl2 and EGTA concentrations based on [23]). In Cl calibration solutions, the concentrations of KCl and K-gluconate were varied (mM): KCl 50, 10 2.5, 0 with K-gluconate 60, 100, 107.5, 110, respectively, over a background of Na-gluconate 10, Mggluconate 0.5, Hepes 10, pH 7.3 adjusted with KOH. TMA+ calibration solutions were composed of (in mM): KCl 80, NaCl 10, Hepes 10, and 10, 2.5, 0.5, or 0 TMA-Cl, pH 7.3 adjusted with KOH. The potential differences between the ion-sensitive channels and the reference channel were plotted against pIon (log[Ion]), and the resulting calibration curves were fitted with the Nicolsky–Eisenman equation as

All potentials were measured against the potential of an extracellular reference electrode (agar bridge containing 3 M KCl and Ag/AgCl cell), using a voltmeter with an input resistance of 1015 X (Institute of Electrochemistry, University of Du¨sseldorf, Germany). The actual ionic signals, i.e. the differences between the potentials of the ion-sensitive channels and the reference channel, were obtained directly by means of the built-in differential amplifier of the voltmeter. The output signals were AD-converted and continuously recorded on a personal computer. Since the values of the transformed ion concentrations were not normally distributed, means ± SD are always given in connection with pIon as suggested by Fry et al. [26]. Mean ion concentrations ([Ion]) were then calculated from the mean pIon values. Statistical analysis was carried out using Student’s t-test.

Pressure injection Changes in [Ion]i were induced by pressure injection of small volumes (0.001–1000 pl) of 100 mM NaCl, 100 mM or 1 M MgCl2, 100 mM EDTA (titrated with KOH or NaOH) or 25 mM TMA-Cl from borosilicate glass capillaries (GC150F-15, Clark, Reading, GB) using a commercial injector (WPI PV830 and a WPI pipette holder MPH6R) to produce pressure pulses of up to 6 bar and 0.2–10 s duration. The capillaries were connected to a voltmeter via a chlorided silver wire to allow confirmation of a successful insertion of the capillary into the cell.

Determination of capillary tip radii Inner tip radii (r) of the glass capillaries for pressure injection were determined by the air bubble method [27–30]. This method is based on the linear correlation between the logarithm of the tip diameter of a capillary and the logarithm of the minimum pressure (PC-min) necessary to form air bubbles at a capillary tip immersed in a solution of known surface tension. As derived in the Appendix A Eqs. (1)–(6), PC-min solely depends on the tip diameter (radius) and the surface tension, r, between the medium within the capillary (e.g. air) and the medium surrounding the tip (e.g. ethanol, see also [27]). Using Eq. (6), tip radii

Fig. 1. Capillary parameters (A) Capillary tip radii as determined by the bubble method. For r > 0.24 lm there was excellent agreement between values determined in water and ethanol (). For 0.076 lm < r < 0.24 lm, values could only be determined in ethanol (s). (B) There was good correlation between the tip radii of the glass capillaries and the electrolyte volume injected into water-saturated paraffin oil for tip radii >0.3 lm (j). At smaller tip radii volumes were one to two orders of magnitude lower than expected from this correlation so that this method did not allow an accurate calibration of the injected volume for tip radii <0.3 lm. In a few cases debris was clinging to the capillary tips, rendering them useless for pressure injection (h). Injection pressure, 6 bar; duration, 10 s; continuous line, linear regression.

6

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

in the present study were calculated as r = 2 r/PC-min with rair–ethanol = 22.8 mN/m (20 C, [31]). To verify these data, the experiments were repeated with the tips of the capillaries immersed in water. Due to the higher surface tension (rair–water = 72.8 mN/m, 20 C, [31]), considerably higher pressures had to be used under these conditions. For the smaller tip radii (<0.24 lm) the maximum pressure of our system (6 bar = 60,000 N/m2) was insufficient to elicit air bubble ejection in water. For all radii above this value, however, there was an excellent correlation between radii determined with the tips immersed in ethanol and in water, respectively (Fig. 1A). Subsequently, these tip radii were used to estimate the interfacial tension between water and water-saturated paraffin oil, by determining PC-min necessary to inject oil droplets into water or water droplets into oil. Under these conditions rwater–oil amounted to 20.8 ± 3.0 mN/m (n = 10).

Determination of intracellular ATP concentrations ATP in single oocytes was determined using a luciferase based bioluminescent assay (FL-AAM, Sigma) as previously described [32]. The diameter of the oocytes was determined using a stereomicroscope with a graded ocular, to allow calculation of the oocyte volume and thus of intracellular ATP concentrations ([ATP]i).

Results Resting Em, [Mg2+]i and [ATP]i in Xenopus oocytes In 46 Xenopus oocytes investigated, the mean Em was 47.2 ± 14.2 mV (all values means ± SD). In these oocytes, a mean intracellular pMg-value of 3.53 ± 0.26 was found. This value is equivalent to an average [Mg2+]i of 0.30 mM (95% confidence limit 0.25–0.34 mM). Oocyte [Mg2+]i values were thus very similar to the values previously found in leech Retzius neurons (e.g. 0.32 mM, [9], 0.37 mM [33]). In contrast, [ATP]i values in oocytes amounted to only 0.9 ± 0.17 mM (n = 10) and were thus considerably lower than values previously found in leech Retzius neurons (in the order of 5 mM [9]). The oocytes, and for some control experiments leech Retzius neurons, were subsequently used for the determination of intracellular Mg2+ buffering properties, by pressure injecting either Mg2+- or EDTA-containing solutions. It was therefore a major objective of the present study, to establish a reliable method for the routine determination of the volume ejected from the glass capillaries into the cells. Pressure injection into oil As a first approach, an attempt was made to calibrate the volume ejected from a capillary at a given pressure and duration as described by Corson and Fein [17]. Capillary tips were immersed in paraffin oil (Sigma) that had been water-saturated to prevent water loss from the droplet into the surrounding oil. Pressure (2–6 bars) was then applied for various durations (2–10 s), resulting in the ejection of electrolyte droplets. The droplet diameters were determined, using a stereomicroscope with graded ocular lens, and the volumes were calculated assuming a spherical shape. However, it was found that especially in capillaries

which produced small droplets there was no linear relationship between droplet volume and injection duration at a given pressure, or droplet volume and pressure at a given duration, respectively. This prompted us to look further into the relationship between tip radius and ejected volume. Correlation between tip radius and ejected volume Injections into oil were repeated with capillaries of known tip radius (tip radii determined by the air bubble technique as described above). In these experiments, there was good correlation between ejected volume (pressure, 6 bar; duration, 10 s) and tip radius (Fig. 1B, R2 = 0.90) for tip radii >0.3 lm. At smaller tip radii, however, no useful correlation was found. Furthermore, even small impurities at the tips considerably reduced the ejected volume (Fig. 1B) so that tip radii alone could not be used to accurately predict the volume ejected from a capillary at a given pressure and duration. At a constant pressure of 6 bar, only rather blunt capillaries (Fig. 2A, mean inner tip radius 1.25 lm) showed a linear relationship between droplet volume and the duration of pressure application. At smaller tip radii, the relationship deviated significantly from the expected proportionality (Fig. 2B, mean inner tip radius 0.4 lm; Fig. 2C, mean inner tip radius 0.14 lm). Conversely, the relationship between droplet volume and applied pressure (at a constant duration of pressure application of 10 s) was linear only for mean capillary tip radii of 1.25 lm while it was increasingly pressure dependent at mean tip radii of 0.34 and 0.15 lm (Fig. 2D). Attempts to fit the relationship between the droplet volume/duration of pressure application shown in Fig. 2A–C using Eq. (10) (Appendix A) showed, that for small tip radii this was only possible if the direct pressure dependence of the apparent hydrodynamic resistance Gh derived from Fig. 2D was assumed. Such a pressure dependence of Gh has previously been described by van Dongen [34] and explained by adhesion forces between the electrolyte and the inner glass surface of the capillary. Volume calibration by MgCl2 or EDTA injection into electrolyte droplets In order not to be restricted to very blunt capillaries, an attempt was made to calibrate ejected volumes by pressure injection of solutions containing either MgCl2 or EDTA into electrolyte droplets and simultaneously measuring the resulting changes in Mg2+ concentration within the droplet ([Mg2+]dr) with Mg2+-selective microelectrodes. To this end, 1 ll of the appropriate electrolyte was pipetted (Eppendorf Varipette 4710, 0.5–10 ll, calibration verified by weighing) onto Parafilm covered with water-saturated paraffin oil (Sigma). As previously described [22], such droplets can be treated like cells, i.e. ion-selective microelectrodes and injection electrodes can be inserted into the droplets and thus ion changes can be monitored during

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

7

Fig. 2. Time and pressure dependence of the ejected volume (A–C). Time dependence of the electrolyte volume injected into paraffin oil (injection pressure, 6 bar). At mean tip radii of 1.25 lm (A) and 0.4 lm (B) the ejected volume was proportional to the duration of pressure application. Thus, surface tension effects were negligible. At the smallest mean tip radii of 0.14 lm (C), however, the ejected volume was not proportional to the duration of pressure application. Values could only be fitted [Eq. (10), Appendix A] if surface tension and pressure dependence of Gh were taken into account (continuous line). During injections into cells/electrolyte droplets, no surface tension effects have to be considered and hence larger injected volumes are expected (dotted line). (D) Pressure dependence of Gh increased with decreasing tip radii. The relatively strong pressure dependence that had to be used to fit the values in C (continuous line, see arrow) could not be measured directly, as the low pressure was insufficient to elicit measurable droplet formation at very fine tips.

microinjections. In these experiments the droplets were grounded by connecting the pressure injection electrode directly to ground. For injections of MgCl2, the electrolyte droplets were nominally Mg2+-free (composition: 0 mM Mg2+ calibration solution), for EDTA injections they contained 2.5 mM Mg2+ (2.5 mM Mg2+ calibration solution). The recording of such an experiment is shown in Fig. 3A. For direct comparison, the same capillary was used to inject directly into oil and measure the diameter of the resulting droplet before and after each experiment. From the measured volumes, the expected changes in [Mg2+]dr were calculated (dotted lines in Fig. 3A) and compared to the measured values. It was found that the measured changes in [Mg2+]dr were up to twice the expected changes calculated from direct injections into oil (mean factor, 1.73), indicating again that interface tension between oil and the electrolyte solution opposed droplet formation at small tip radii. This hypothesis was supported by the finding that selection of blunt capillaries (tip radius >1.25 lm) resulted in considerably better agreement of calculated vs. measured values, reducing the ratio between the measured and expected [Mg2+]i changes to about 1.3 (Fig. 3B; s in Fig. 4F).

Volume calibration by co-injection of various ions in cells As an alternative approach calibration of the injected volume was attempted by the co-injection and simultaneous measurement of the concentration of various ions which intracellularly remain unbuffered. The initial choice was the tetramethylammonium ion, TMA+, because it is not actively extruded from Retzius neurones [35] and intracellular TMA+ concentrations can easily be measured with ion-selective microelectrodes. In keeping with the results obtained in electrolyte droplets, injection of TMA+ into Retzius neurones resulted in stable increases in [TMA+]i (Fig. 4A) that were 1.65 times larger than the value calculated from the size of droplets injected directly into oil (R2 = 0.55, n = 26). Increases were thus similar to those found in electrolyte droplets. However, TMA+ was found to interfere at the Mg2+-selective microelectrode and therefore could not be used for the present purpose. Injection of Mg2+ and EDTA inevitably is coupled to the injection of a counter-ion, in our case Cl and Na+, respectively (EDTA titrated with NaOH). As suggested by Schwiening and Thomas [10], it was therefore attempted to directly monitor the injected volume by measuring

8

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

Fig. 3. (A) Ion injections into droplets. Recordings of Mg2+ injections into a droplet. Arrows and numbers indicate time point and duration of ion injections, dotted lines denote expected values for the free Mg2+ concentration within the droplet ([Mg2+]dr). At capillary tip radii 60.14 lm, [Mg2+]dr increased about 70% (here: 100%) more than calculated from the size of droplets injected directly into oil. (B) Relationship between the expected and the actually measured increase in [Mg2+]dr. Due to the effects of interfacial tension between electrolyte and oil during calibration, the actually measured values were by a factor of 1.3 larger than expected.

intracellular Cl or Na+ concentrations. In control experiments, either MgCl2 or NaCl were injected into Retzius neurones while the preparation was kept in SLS and the resulting changes in [Cl]i and [Na+]i, respectively, were measured. However, impalement with two separate electrodes by itself often caused an increase in the intracellular concentrations of these ions which superimposed the increases due to pressure injection. The experiments were therefore repeated in nominally Cl-free and Na+-free bath solutions, respectively. The recording of such an experiment (injection of NaCl) is shown in Fig. 4B. In this and 11 equivalent experiments, [Na+]i in Retzius neurones increased considerably less than expected from the amount injected ( in Fig. 4F). Increases were always transient, indicating that the injected Na+ was rapidly extruded from the cells. Similar results were obtained for [Cl]i ([ ] in Fig. 4F). Results from oocytes were qualitatively similar. Thus, neither [Cl]i increases nor [Na+]i increases could be used as an internal calibration signal for the injected volume. Mg2+ injections into Xenopus oocytes All further experiments were carried out on Xenopus oocytes using blunt injection capillaries (tip radius about 1.25 lm). Injected volumes were calibrated by directly injecting into oil before and/or after each experiment and correcting the calculated droplet volume by the factor 1.3 evaluated above. Fig. 4C shows the recording of an experiment during which a Mg2+-containing solution was repeatedly injected into Xenopus oocytes and the resulting changes in [Mg2+]i were determined with Mg2+-selective microelectrodes. [Mg2+]i changes were considerably smaller than expected (dotted line in Fig. 4C; see in Fig. 4F and Fig. 5A), indicating substantial intracellular Mg2+ muffling. After each Mg2+ injection [Mg2+]i decreased with an average rate of 25 lM/min (0.019 ± 0.009 pMg units/

•

min). As shown in Fig. 4D, this decrease was inhibited in the absence of extracellular Na+. It was therefore attributed to active Mg2+ extrusion from the oocyte presumably by Na+/Mg2+ antiport. In the absence of extracellular Na+, [Mg2+]i increases after Mg2+ injection were larger than in the presence of extracellular Na+, indicating that Na+/ Mg2+ antiport contributed to Mg2+ muffling in Xenopus oocytes. To quantify intracellular Mg2+ buffering, the expected changes in [Mg2+]i ([Mg2+]i-theor) were recalculated using Eq. (11), the [ATP]i value of 0.9 mM determined with a luciferin/luciferase assay, and the apparent dissociation constant, Kd-ATP, for the binding of Mg2+ and ATP of 0.117 mM [36]. The best fit for values obtained in the presence of extracellular Na+ was obtained for a buffer equivalent with a concentration [Bu]t of 10.2 mM and a Kd-Bu of 0.6 mM. For values obtained in the absence of extracellular Na+ the best fit was obtained with a [Bu]t of 9.8 mM and a Kd-Bu of 0.6 mM (Fig. 5B). These values appeared to indicate that extracellular Na+ had no influence on intracellular Mg2+ muffling. However, restriction of the calculation to those experiments during which both Na+-containing and Na+-free solutions had been applied and which therefore allowed a direct comparison of the two conditions, resulted in the following values: [Bu]t of 11.3 mM and Kd-Bu of 0.7 mM in the presence of extracellular Na+, [Bu]t of 9.0 mM and Kd-Bu of 0.6 mM in the absence of extracellular Na+ (Fig. 5C and D). Thus, under the conditions of the present study, Na+/Mg2+ antiport accounts for about 20% of total muffling. EDTA injections into Xenopus oocytes EDTA-containing solutions were injected into Xenopus oocytes and the resulting decreases in [Mg2+]i were determined with Mg2+-selective microelectrodes. The recording of such an experiment is shown in Fig. 4E. Again,

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

9

Fig. 4. (A–E) Ion injections into cells. Recordings of ion injections into, leech neurones (A and B) and oocytes (C–E). Arrows indicate time point and duration of ion injections. Dotted lines, expected values for the free [Ion]. (A) When TMA+ was injected into leech Retzius neurones, [TMA+]i increased considerably more than calculated from the size of droplets injected directly into oil. (B) Na+ injections into leech Retzius neurones could not be used as internal calibrations for the injected volume, as Na+ was rapidly removed from these cells. (C) For Mg2+ injections into frog oocytes, capillaries with large tip radii P0.4 lm could be used to minimise an underestimation of the injected volume due to surface tension effects. Under these conditions [Mg2+]i in oocytes increased considerably less than expected, indicating strong cytosolic buffering. After each injection, [Mg2+]i decreased towards its original value. (D) This [Mg2+]i decrease was inhibited in nominally Na+-free bath. [Mg2+]i increases under these conditions were larger than in the presence of extracellular Na+, reflecting the contribution of Na+ dependent Mg2+ transport towards Mg2+ muffling. (E) EDTA injections into frog oocytes, caused [Mg2+]i in oocytes to decrease. As summarized in Fig. 5 A, these decreases were considerably smaller than expected from the amount of EDTA injected, indicating strong cytosolic buffering. [Mg2+]i remained at the low levels reached after each EDTA injection. (F) Summary of injection experiments in droplets, Retzius neurones and oocytes. The measured increase in the free ion concentration ([Ion]) is plotted against the expected increase calculated from the injected amount. Injection of Mg2+ into electrolyte droplets resulted in measured [Mg2+]dr-values that were larger than the expected values (s, above dashed line), indicating that injections into oil underestimate the amount of electrolyte ejected from a capillary. Similar results were obtained, if TMA+ was injected into Retzius neurones (not shown). In contrast, if [Cl]i ([ ]) and [Na+]i () were injected into Retzius neurons, increases were considerably smaller than expected (values below dashed line), probably due to active extrusion from these cells. Similarly, [Mg2+]i increases (d) elicited by Mg2+ injections into oocytes indicate strong muffling which is predominantly due to cytosolic buffering, as effects of active removal from the cell or uptake into mitochondria could be ruled out (compare Fig. 5). (continuous lines, linear regression).

[Mg2+]i changes elicited by EDTA injections into frog oocytes were considerably smaller than expected from calculations using Eq. (12) and an apparent Kd-EDTA of 2 lM, calculated from the constants given by Caldwell [37] for

EDTA (see • in Fig. 5A), indicating substantial intracellular Mg2+ muffling. Intracellular Mg2+ buffering was estimated using Eq. (11). The best fit for the data was obtained at a [Bu]t of 9.8 mM and

10

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

Fig. 5. Mg2+ buffering in oocytes (A–C) Mg2+ injections into frog oocytes in Na+-free bath solution () or in Na+-containing bath solution (j); Mg2+ + CCCP (carbonyl cyanide 3-chlorophenylhydrazone) injections (d), EDTA injections (). (A) Expected changes in [Mg2+]i (D[Mg2+]i-theor) without cytosolic Mg2+ buffering are plotted against measured changes in [Mg2+]i (D[Mg2+]i). Without any Mg2+ buffering, the values would have been expected to fall onto the continuous line. (B) As in (A), but using Eq. (11) to calculate D[Mg2+]i-theor for the Mg2+ injections in the nominal absence of extracellular Na+ and for the EDTA injections, assuming an additional cytosolic Mg2+ buffer with a total concentration, [Bu]t, of 9.8 mM and an apparent dissociation constant, Kd-Bu, of 0.6 mM. As judged by the good agreement of the values obtained during inhibition of Mg2+ uptake into mitochondria (d), dissipation of the mitochondrial membrane potential with CCCP this process did not appear to contribute to Mg2+ muffling. (C and D) Comparison of values obtained in the presence and absence of extracellular Na+ within the same cell. In (C), D[Mg2+]i-theor for all values were calculated with a [Bu]t, of 9.0 mM and a Kd-Bu of 0.6 mM (best fit for values obtained in the nominal absence of extracellular Na+, ). In (D), D[Mg2+]i-theor for values obtained in the presence of extracellular Na+ (j) were recalculated using a [Bu]t, of 11.3 mM and a Kd-Bu of 0.7 mM, resulting in a considerably better fit for these values.

a Kd-Bu of 0.6 mM (Fig. 5B). It is notable, that Mg2+ increases in the absence of extracellular Na+ and Mg2+ decreases during the injection of EDTA can be described by the same parameters. Under both conditions Na+/Mg2+ antiport does not affect the observed changes in [Mg2+]i. Mg2+ injections in the presence of the mitochondrial uncoupler CCCP To examine a possible contribution of Mg2+ uptake into mitochondria towards intracellular Mg2+ muffling, the uncoupler CCCP was either bath-applied or co-injected during Mg2+ injections into oocytes. Under these conditions a [Bu]t of 10.6 mM and Kd-Bu of 0.7 mM was obtained by applying Eq. (11). CCCP thus had no measurable effect on intracellular Mg2+ muffling (Fig. 5B). Discussion Intracellular buffering has been widely studied with respect to H+ and Ca2+, but literature on intracellular

Mg2+ is still comparatively sparse (for rev. see [38]). A fundamental difference between the buffering of H+ and Ca2+, and the buffering of Mg2+ is, that the free intracellular concentrations of Ca2+ ([Ca2+]i) and H+ are in the range of 100 nM while the free intracellular concentration of Mg2+ ([Mg2+]i) is 3–4 orders of magnitude higher, i.e. about 0.1–1 mM. In the case of Ca2+, buffer concentrations in the range of some 100 lM are sufficient to yield a buffering ratio (the change in the total intracellular ion concentration divided by the change in free intracellular ion concentration) of 200–500. An example is the Ca2+-binding protein parvalbumin which, in muscle, has been found at a concentration of 0.43 mM [12] and which has an apparent Kd of some 50 nM [39]. Assuming [Ca2+]i to be 100 nM, about 50% of the parvalbumin is associated with Ca2+ under resting conditions. This is in contrast to Mg2+. A major intracellular Mg2+ buffer is believed to be ATP, which has a Kd-ATP of about 0.12 mM [36] and a concentration in the millimolar range, i.e. only about 10 times higher than [Mg2+]i. Thus, ATP is about 70–90% Mg2+ saturated and therefore acts as a

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

Mg2+ store rather than as a buffer, i.e. it protects the cells against Mg2+ loss but not against an overload of Mg2+ [36]. In a previous study on Mg2+ muffling in leech Retzius neurones [9], Mg2+ was iontophoretically injected into single cells. In these experiments the injection current could be used as a direct measure for the amount of Mg2+ injected into the cell, since the relationship between the current used for injection and the amount of Mg2+ leaving the capillary (transport index) could be established from injections into electrolyte droplets. The main drawback of this method is the need to use depolarising currents during Mg2+ injections and the impossibility of injecting electrically uncharged substances. In the present study, an attempt was made to circumvent these problems inherent in iontophoretic injections by using pressure injection into single cells as a method to determine intracellular Mg2+ muffling. The main difficulty of pressure injection, however, was the exact determination of the volume ejected from a capillary into the cell. Effects of surface/interfacial tension Based on the theoretical considerations derived in the Appendix A, it could be demonstrated that the difficulties in the exact determination of the volume ejected from a capillary arose mainly from interfacial tension effects at the tip of the capillary. Eq. (10) demonstrates that the lack of proportionality between the ejected volume and the duration of pressure application during the injection of an electrolyte into oil may be explained by an initial retardation of droplet formation (at h 6 r; see Fig. 6).

11

As interfacial tension effects obviously do not occur during injections into cells or into large electrolyte droplets, the amount of electrolyte injected into oil was considerably smaller than the amount injected into a cell. The discrepancy increases with decreasing tip radius and has to be taken into account when using injections into oil for calibration. Consequently, increases in [TMA+]i during TMA+ injections into Retzius neurones were found to be approximately 1.65 times the values estimated from injections into oil. In theory, this might be attributed to the fact that not all of the cellular volume is accessible to the injected ion. However, Mg2+ injections into electrolyte droplets yielded a strikingly similar value of 1.73 times the amount expected. It must therefore be concluded that the error does indeed lie within the method of calibration by an injection of electrolyte directly into oil. The discrepancy decreases with increasing tip radius e.g. to a factor of 1.3 in the blunter capillaries used for frog oocytes, but nevertheless it had always to be taken into account when using this technique for calibration. The alternative solution, namely a calibration of the ejected volume by injections into electrolyte droplets before/after every injection experiment, was found to be too time consuming to be routinely carried out. Cytosolic Mg buffering Mg buffering/muffling in the present study was quantified by calculating an equivalent buffer concentration [Bu] with an apparent dissociation constant, Kd-Bu, as suggested by Gu¨nzel et al. [9]. The advantage of this concept is that it takes into consideration that buffering varies not only with

Fig. 6. (A and B) Model of the initial phase of bubble/droplet formation at the tip of a capillary. Depending on how a bubble/droplet attaches to the tip of a capillary, Eq. (6) should yield inner (A) or outer (B) tip radii. (C) The application of a pressure, PC, to a capillary generates bubble/droplet formtion at the tip of the capillary. Surface/interfacial tension, r, at the interface between the bubble/droplet and the surrounding medium causes an opposing pressure, Pr. The growing bubble/droplet can be described as a calotte with increasing height, h, and constant radius, r (inner or outer tip radius of the capillary).

12

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

the total amount of injected ion or buffer, but also with the initial degree of intracellular buffer saturation. A further advantage is that effects of buffers of known concentration and apparent Kd, such as ATP, can be evaluated separately. In the present study, for example, [ATP]i in frog oocytes was found to be 0.9 mM and thus somewhat lower than the 2.3 mM reported by Gribble et al. [40]. Using the [Bu]t of 9.8 mM and Kd-Bu, of 0.6 mM estimated in the present study and the lower [ATP]i-value of 0.9 mM, the combined effects of these two buffer systems can be illustrated by the following calculations: to obtain a 0.2 mM increase in [Mg2+]i from its resting value of 0.3 mM to a value of 0.5 mM, the total intracellular Mg2+ concentration ([Mg]t) has to be increased by 1.47 mM. A decrease in [Mg2+]i by the same amount to a value of 0.1 mM would require a decrease in [Mg]t of 2.30 mM. Using the higher [ATP]i value of 2.3 mM reported by Gribble et al. [40] increases the necessary [Mg]t changes to 1.6 and 2.66 mM, respectively. The calculated [Mg]t changes at the different [ATP]i values are only minor, indicating that Mg2+ buffering in oocytes is governed by non-ATP buffers. In contrast, previously determined non-ATP Mg2+ buffering in leech Retzius neurones was considerably smaller and amounted to 4.2 mM with a Kd-Bu of 0.1 mM [9], while the ATP concentrations in Retzius neurones were considerably higher, i.e. in the order of 5 mM. Thus, the total buffer concentration in Retzius neurones and frog oocytes was similar, but due to the greater contribution of ATP towards total intracellular Mg2+ buffering, [Mg2+]i in Retzius neurones should vary considerably with changes in ATP concentration. As an example, a total ATP depletion in frog oocytes should result in an increase in [Mg2+]i from 0.3 to 0.38 mM (initial [ATP]i 0.9 mM) or to 0.55 mM (initial [ATP]i 2.3 mM), while in Retzius neurons [Mg2+]i should increase from 0.32 to 3.1 mM. Indeed, such a dependence of [Mg2+]i on the ATP concentration has been utilized by Koss et al. [41] and Grubbs and Walter [42] to estimate intracellular Mg2+ buffering in cardiomyocytes and in the smooth muscle cell line BC3H-1, respectively. In contrast, in cells with a low proportion of ATP-dependent Mg2+ buffering, such as Xenopus oocytes, [Mg2+]i is almost independent of the energetic status of the cell. Apart from ATP or other nucleotides, a great variety of intracellular compounds is able to bind Mg2+, such as organic acids (e.g. citrate or malate), inorganic anions (e.g. phosphate, sulfate), phosphate containing compounds such as phospholipids, phosphocreatin or 2,3 bisphosphoglycerate, and a large variety of proteins, including actin, troponin, myosin and parvalbumin [5,9,12,33,38,41–43]. Thus, Mg2+ buffers are an extremely heterogeneous group and concentrations of the various components often differ greatly between different cell types. Attempts to estimate intracellular Mg2+ buffering simply by adding up known Mg2+ buffers, as e.g. recently endeavoured by Tursun et al. [43] are therefore likely to result in underestimates.

Mg2+ sequestration Mitochondria have been demonstrated to act as intracellular Mg2+ stores [44]. The main driving force for Mg2+ movement across the mitochondrial membrane is the mitochondrial membrane potential, which, under physiological conditions, would favour an uptake of Mg2+. In the present study, an attempt was made to collapse the mitochondrial membrane potential by the application of CCCP and thus to completely block Mg2+ uptake into this compartment. However, CCCP had no detectable effect on Mg2+ buffering in oocytes. Furthermore, Mg2+ buffering in frog oocytes was symmetrical, i.e. the same values were obtained during Mg2+ and EDTA injection. As it cannot be expected that the injection of EDTA induced considerable changes in the driving force across the mitochondrial membrane, this also suggests that Mg2+ uptake into mitochondria should not play a major role in Mg2+ muffling. The reason for this lack of contribution of oocyte mitochondria towards Mg2+ muffling is assumed to be due to the small proportion of the total mitochondrial volume relative to the whole oocyte volume. The size of an oocyte mitochondrium had been reported to be 2 lm in length and 0.2 lm in diameter [45], the number of mitochondria per oocyte was estimated to be about 107 [46], yielding a total mitochondrial volume of only 0.1–0.2% of the total oocyte volume. Na+-dependent Mg2+ extrusion In Retzius neurones, about 50% of the non-ATP Mg2+ muffling observed in Na+-containing bath solutions could be attributed to the activity of the Na+/Mg2+ antiport present in these cells. In contrast, active Mg2+ extrusion initially did not appear to play a major role in the short term ’muffling’ of [Mg2+]i changes in oocytes. In oocytes the effects of Mg2+ extrusion could, however, be visualized if injections in the presence and absence of extracellular Na+ were carried out within the same experiment (see Fig. 4D). As shown in Fig. 5C and D, the average effect amounted to about 20% of the overall Mg2+ muffling. The respective values for cytosolic Mg2+ buffering and for the average rate of [Mg2+]i decrease (oocytes, 25 lM/ min; Retzius neurons, values from [33] at 20 C, 0.035 ± 0.007 pMg units/min, equivalent to 0.6 lM/min) in Xenopus oocytes and leech Retzius neurons can be used to estimate and compare the changes in [Mg]t and, knowing the respective cell diameters, the rates of net Mg2+ efflux across the plasma membranes of these cells. Calculations of the Na+ dependent decreases in [Mg]t resulted in very similar values for both cell types: 94 lM/min in oocytes and 89 lM/min in Retzius neurons. However, due to the differences in surface/volume ratio between oocytes and Retzius neurones, the calculated Mg2+ flux per unit membrane area differed greatly. In a more detailed analysis shown in Fig. 7A, decreases in [Mg]t were plotted

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

13

Fig. 7. Kinetics of Mg2+ extrusion (A) KM and vmax for Mg2+ extrusion from Retzius neurones and Xenopus oocytes were estimated by fitting the experimental data assuming Michaelis–Menten kinetics (v = vmax * [Mg2+]i)/(KM + [Mg2+]i) using a least squares approach. (B) For clarity, values are linearized in a double-reciprocal plot (Lineweaver–Burk diagram). v, rate of decrease in the total intracellular Mg2+ concentration after Mg2+ loading of a cell, calculated from the rate of [Mg2+]i decrease and the cytosolic buffering. (j) Oocytes; (s) Retzius neurons.

against the corresponding [Mg2+]i values and fitted assuming Michaelis–Menten kinetics, using a least squares approach to estimate vmax and KM. For clarity, the data are linearized in a Lineweaver–Burk diagram in Fig. 7B. vmax and KM were estimated for Mg2+ extrusion from oocytes as 74 pmol cm2 s1 and 1.28 mM, and from Retzius neurones as 12 pmol cm2 s1. and 0.52 mM, respectively. For comparison, Tashiro et al. [47] report a vmax of 0.2–0.4 pmol cm2 s1 and a KM of 1.51 mM in rat ventricular myocytes. These values indicate that KM is similar in these three preparations, while vmax increases with a decreasing surface/volume ratio. As Tashiro et al. [47] point out, differences in vmax may simply reflect the carrier density per unit surface area which would thus be more than a factor 200 higher in oocytes than in heart myocytes. This estimate clearly demonstrates the difficulties that may arise, if it were attempted to express mammalian Na+/Mg2+ antiport in Xenopus oocytes and to detect its effects over the background activity of the native oocyte transport.

if the transport system is electroneutral, as has been suggested for many vertebrate Na+/Mg2+ antiport systems (for rev. see [5–7]).

Conclusions

Initially, bubble or droplet formation at the tip of a capillary can be described by a calotte with a constant radius r (r being identical to the tip radius of the capillary) and an increasing height h (see Fig. 5C). The following equations apply for the volume, V, and the surface area, S, of the bubble/droplet:  p  V ¼ h 3r2 þ h2 ; ð1Þ 6  2  ð2Þ S ¼ p r þ h2

In conclusion, pressure injection is a reliable technique for the determination of intracellular ion buffering only in large cells. Indeed, in this context, it has so far been applied only to skeletal muscle fibres and giant snail neurones [11–13]. In smaller cells, it will be useful only, if a reliable means of volume calibration (i.e. injection of dyes as suggested by [14–16]) can be combined with the measurement of the free ion concentration. In terms of physiology it could be shown that Mg2+ in the oocyte cytosol is well buffered and that excess Mg2+ is removed by a highly active Na+ dependent Mg2+ transport system. It is therefore concluded that oocytes are not a preferable expression system for investigations on Mg2+ transport,

Acknowledgments We thank M. Weischenberg for technical assistance, Dr. G.R. Dubyak (Case Western Reserve University Cleveland, OH, USA) for carrying out ATP measurements, Dr. M.S. Eckmiller (C. & O. Vogt Brain Research Institute, Heinrich-Heine-Universita¨t Du¨sseldorf, Germany) for the gift of Xenopus oocytes and Dr. E. Gu¨nzel (Landsberg/ Lech, Germany) for invaluable help in the derivation of Eq. (10). This work was supported by the DFG (GU 447/6-1). Appendix A Theoretical aspects of bubble/droplet formation at capillary tips

and  dV p ¼ r 2 þ h2 ; dh 2 dS ¼ 2ph dh

ð3Þ ð4Þ

14

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

If a pressure, P, is applied to increase the volume of a droplet at the tip of a capillary, energy has to be spent to increase the surface area of the droplet. Energy conservation implies that PdV = rdS (r, surface or interfacial tension) and thus with Eqs. (3) and (4): 4rh P¼ 2 : ð5Þ r þ h2 Differentiation of this equation (dP/dh) shows that pressure is maximal at r = h. Maximum pressure, Pr-max can, therefore, be calculated from P rmax ¼ 2r=r:

ð6Þ

The pressure applied to the capillary during pressure injection has to be larger than Pr-max to overcome interfacial tension and allow the formation of an electrolyte droplet at the electrode tip. In case of the bubble method for the determination of capillary tip radii, the minimum capillary pressure, PC-min, necessary to start bubble formation is determined. Ideally, PC-min is equal to Pr-max and therefore only dependent on r of the media involved (i.e. air and ethanol) and on the tip radius r. In the literature there is no consensus on whether r represents the inner (e.g. [28]) or outer [27] tip radius (compare Fig. 5A and B). Data by Schnorf et al. [29], however, appear to be in somewhat better agreement with the inner tip diameter. Time course of droplet formation For the calculation of the time course of droplet formation in oil it was initially assumed that dV/dt is proportional to PC  Pr. In analogy to van Dongen [34], the apparent hydrodynamic conductance, Gh , of the capillaries was defined as Gh ¼

ðdroplet volumeÞ ; so that the following equation was ðpressureÞ  ðtimeÞ obtained :

dV ¼ Gh  ðP C  P r Þ: dt

ð7Þ

Incidentally, assuming laminar flow [34], the law of Hagen– Poiseuille applies: V pr4 ¼ DP ðl; effective capillary length;g; viscosityÞ; t 8gl pr4 : i:e: Gh ¼ 8gl

ð8Þ

Thus Gh depends on the fourth power of r and is therefore extremely sensitive to any debris adhering to the capillary tip. With Eqs. (3) and (5), Eq. (7) can be written as:    p 2 4rh 2 dh  r þh ¼ Gh P C  2 or 2 dt r þ h2 dh 2G P C 8G rh ¼  2 h 2    h 2 : dt p r þ h p r 2 þ h2

To obtain h as a function of t (or rather t as a function of h), this equation has to be integrated, for the solution of which we are indebted to Dr. E. Gu¨nzel (Landsberg/Lech, Germany):   1 3 E 2 1 E2 2 h þ 2h þ þr h t¼ 3D D D2 2D   E3   þ 4 ln h2  2Yh þ r2  ln r2 2D    

E 3 ðY  X Þ ðh  Y Þ Y þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi arctg pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  arctg pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D4 r2  Y 2 r2  Y 2 r2  Y 2 ð10Þ P r D E C where D ¼ 2  Gh  E ¼ 8  Gh  X ¼ r2 Y ¼ : p p E 2D Using this equation to fit the data shown in Fig. 2A–C, it was found for small tip diameters that a proper fit was possible only if Gh was assumed to be pressure-dependent. As previously shown by van Dongen [34] and as comfirmed in the present study (Fig. 2D), this is indeed the case. Calculation of Mg2+ muffling Intracellular Mg2+ muffling was calculated as suggested by Gu¨nzel et al. [9], assuming that intracellular Mg2+ binds to ATP and, in addition, is affected by processes such as binding to unspecified intracellular binding sites, extrusion or sequestration. The sum of these ATP-independent processes is described by a buffer equivalent, Bu. From the following equations: ½ATPt ¼ ½ATPi þ ½MgATP ½But ¼ ½Bui þ ½MgBu   ½Mgt ¼ Mg2þ i þ ½MgATP þ ½MgBu   K d-ATP ¼ Mg2þ i  ½ATPi =½MgATP   K d-Bu ¼ Mg2þ i  ½Bui =½MgBu ([ATP]t, [Bu]t, [Mg]t, total concentrations; [ATP]i, [Bu]i, [Mg2+]i, free concentrations; [MgATP], [MgBu], concentrations of the complexes between Mg2+ and ATP or Bu; Kd-ATP, Kd-Bu, apparent dissociation constants of the binding between Mg2+ and ATP or Bu) [Mg2+]i can be calculated as the positive, real solution of the cubic equation:  2þ  3   2   Mg i þ A  Mg2þ i þ B  Mg2þ i þ C ¼ 0 ð11Þ with A ¼ K app-ATP þ K app-Bu þ ½ATPt þ ½But  ½Mgt B ¼ K app-ATP  K app-Bu þ ½ATPt  K app-Bu þ ½But  K app-ATP  ½Mgt  K app-ATP  ½Mgt  K app-Bu C ¼ ½Mgt  K app-ATP  K app-Bu

ð9Þ

The effect of EDTA injections were calculated using the following equation

T.E. Gabriel, D. Gu¨nzel / Archives of Biochemistry and Biophysics 458 (2007) 3–15

  ½Mgt ¼ Mg2þ i       þ Mg2þ i  ½ATPt = K d-ATP þ Mg2þ i       þ Mg2þ i  ½But = K d-Bu þ Mg2þ i       þ Mg2þ i  ½EDTAt = K d-EDTA þ Mg2þ i ð12Þ with [EDTA]t being the total amount of EDTA injected and Kd-EDTA being the apparent dissociation constant of 2 lM (calculated from the constants given by [37]). References [1] C.A. Wagner, B. Friedrich, I. Setiawan, F. Lang, S. Broer, Cell Physiol. Biochem. 10 (2000) 1–12. [2] A. Goytain, G.A. Quamme, Br. Med. Chem. Genomics 6 (2005) 48. [3] A. Goytain, G.A. Quamme, Biochem. Biophys. Res. Commun. 330 (2005) 701–705. [4] A. Goytain, G.A. Quamme, Physiol. Genomics 22 (2005) 382–389. [5] P.W. Flatman, Annu. Rev. Physiol. 53 (1991) 259–271. [6] K.W. Beyenbach, Magnes. Trace Elem. 9 (1990) 233–254. [7] A.M. P Romani, A. Scarpa, Front. Biosci. 5 (2000) d720–d734. [8] R.C. Thomas, J.A. Coles, J.W. Deitmer, Nature 350 (1991) 564. [9] D. Gu¨nzel, F. Zimmermann, S. Durry, W.-R. Schlue, Biophys. J. 80 (2001) 1298–1310. [10] E. Neher, Neuropharmacol. 34 (1995) 1423–1442. [11] C.J. Schwiening, R.C. Thomas, J. Physiol. 491 (1996) 621–633. [12] H. Westerblad, D.G. Allen, J. Physiol. 453 (1992) 413–434. [13] J.C. Bernengo, C. Collet, V. Jacquemond, Biophys. Chem. 89 (2001) 35–51. [14] G.M. Lee, J. Cell Sci. 94 (1989) 443–447. [15] G. Minaschek, J. Bereiter-Hahn, G. Bertholdt, Exp. Cell Res. 183 (1989) 434–442. [16] A.L. Grosvenor, C.L. Crofcheck, K.W. Anderson, D.L. Scott, S. Daunert, Anal. Chem. 69 (1997) 3115–3118. [17] D.W. Corson, A. Fein, Biophys. J. 44 (1983) 299–304. [18] D. Gu¨nzel, T. Gabriel, W.-R. Schlue, Pflu¨gers Arch. 445 (2003) S58. [19] M.F. Romero, Y. Kanai, H. Gunshin, M.A. Hediger, Methods Enzymol. 296 (1998) 17–52. [20] W.-R. Schlue, J.W. Deitmer, J. Exp. Biol. 87 (1980) 23–43. [21] D. Gu¨nzel, S. Durry, W.-R. Schlue, Pflu¨gers Arch. 435 (1997) 65–73. [22] D. Gu¨nzel, A. Mu¨ller, S. Durry, W.-R. Schlue, Electrochim. Acta 44 (1999) 3785–3793.

15

[23] H.A. Pershadsingh, J.M. McDonald, J. Biol. Chem. 255 (1980) 4087– 4093. [24] D. Gu¨nzel, W.-R. Schlue, J. Physiol. 491 (1996) 595–608. [25] D. Ammann, Ion-Selective Microelectrodes. Principles, Design and Application, Springer Verlag, Berlin, 1986. [26] C.H. Fry, S.K. Hall, L.A. Blatter, J.A.S. McGuigan, Exp. Physiol. 75 (1990) 187–198. [27] S. Mittman, D.G. Flaming, D.R. Copenhagen, J.H. Belgum, Neurosci. Meth. 22 (1987) 161–166. [28] N. Hagag, M. Viola, B. Lane, J.K. Randolph, Biotechniques 9 (1990) 401–406. [29] M. Schnorf, I. Potrykus, G. Neuhaus, Exp. Cell Res. 210 (1994) 260–267. [30] C.L. Bowman, A.M. Ruknudin, Cell Biochem. Biophys. 31 (1999) 185–206. [31] G.W.C. Kaye, T.H. Laby, Tables of physical and chemical constants and some mathematical functions, 14th ed., Longman Group Ltd., London, 1973. [32] R.D. Beigi, G.R. Dubyak, J. Immunol. 165 (2000) 7189–7198. [33] D. Gu¨nzel, K. Hintz, S. Durry, W.-R. Schlue, J. Neurophysiol. 94 (2005) 441–453. [34] P.A.W. van Dongen, J. Neurosci. Methods 10 (1984) 281–291. [35] S. Neumann, P.W. Dierkes, W.-R. Schlue, Electrochim. Acta 47 (2001) 309–317. [36] D. Lu¨thi, D. Gu¨nzel, J.A.S. McGuigan, Exp. Physiol. 84 (1999) 231–252. [37] P.C. Caldwell, in: A.W. Cuthbert (Ed.), Calcium and Cellular Function, MacMillan and Co. Ltd., London, 1970, pp. 10–16. [38] R.D. Grubbs, Biometals 15 (2002) 251–259. [39] S.H. Lee, B. Schwaller, E. Neher, J. Physiol. 525 (2000) 419–432. ¨ mma¨la¨, F.M. Ashcroft, J. Physiol. [40] F.M. Gribble, R. Ashfield, C. A 498 (1997) 87–98. [41] K.L. Koss, R.W. Putnam, R.D. Grubbs, Am. J. Physiol. 264 (1993) C1259–C1269. [42] R.D. Grubbs, A. Walter, Mol. Cell. Biochem. 136 (1994) 11–22. [43] P. Tursun, M. Tashiro, M. Konishi, Biophys. J. 88 (2005) 1911–1924. [44] T. Kubota, Y. Shindo, K. Tokuno, H. Komatsu, H. Ogawa, S. Kudo, Y. Kitamura, K. Suzuki, K. Oka, Biochim. Biophys. Acta 1744 (2005) 19–28. [45] E. Marinos, F.S. Billett, J. Embryol. Exp. Morphol. 62 (1981) 395–409. [46] E. Marinos, Cell Differ. 16 (1985) 139–143. [47] M. Tashiro, P. Tursun, M. Konishi, Biophys. J. 89 (2005) 3235–3247.