- Email: [email protected]
[20] Calcium influx during an action potential
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The full characterization of the frequency dependence of the capacitance at different voltages gives a more detailed description of the voltage dependence of the voltage sensor. The study of the charge movement in voltage-dependent channels is normally done by eliminating all of the linear components of the capacitance. The presence of proteins in the membrane should add quasi-voltageindependent but frequency-dependent capacitance due to the lossy dielectric properties of buried charges and dipoles. Frequency-domain techniques, which have far better resolution than time-domain techniques, may be used to study this voltage-independent but frequency-dependent capacitance added by the expression of the channels to the oocyte membrane.
Acknowledgments We thank Abort Cha for reading and commenting on the manuscript. Supported by NIH grants GM30376 to F.B. and GM52203 and AR38970 to E.S.
[20]
Calcium
By J.
Influx during
an Action Potential
GERARD O. BORST and FRITJOF HELMCHEN
Introduction Action potentials open voltage-sensitive calcium channels in excitable cells, leading to an influx of calcium ions. 1 Calcium ions may control, among others, cell excitability, neurotransmitter release, or gene transcription. This chapter deals with two different methods that can be used to quantify how much Ca > flows into a cell or cell compartment during an action potential. Quantification of Ca 2+ influx may be a first step toward the construction of a model for the calcium dynamics of cells. It may also serve as a reference to study pathological processes such as cell death during ischemia or amyotrophic lateral sclerosis, where increases in calcium influx have generally been implicated. 2'3 I S. Hagiwara and K. 1. Naka, J. Gen. Physiol. 48, 141 (1964). D. W. Choi, "[)'ends Neurosci. 18, 58 (1995). E. Louvel, J. Hugon, and A. Doblc, Trends PharmacoL Sci. 18, 196 (1997).
M E T H O D S IN E N Z Y M O I . O G Y , VOL. 293
(-opyright x, 1998 by Academic Press All tights of reproductioll ill any Ikmn lcserved. 0076 6879/98 $25.00
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The two methods that we compare in this chapter are a voltage-clamp method, in which cells are voltage clamped with an action potential waveform command, and a fluorescence method, in which cells are loaded with a high concentration of a calcium-sensitive fluorescent dye. We apply both methods to a "giant" axosomatic terminal, called the calyx of Held, in a slice preparation of the rat brain stem. Each principal cell in the medial nucleus of the trapezoid body (MNTB) is contacted by a single calyx-type terminal. This synapse is part of a fast auditory pathway that is involved in the localization of s o u n d ) We were interested in the relationship between calcium influx and neurotransmitter release at this glutamatergic synapse. We found that both methods gave similar values for the number of calcium ions that enter the presynaptic terminal during an action potential. We first discuss the action potential waveform voltage-clamp method.
Action Potential Waveform Voltage Clamp Introduction
This method was first used to quantify calcium influx into the squid giant terminal during an action potential. 5 An action potential was first recorded in current clamp and subsequently used as a command template in a voltage-clamp e x p e r i m e n t ) With this paradigm, the voltage-sensitive channels experience the same voltage change as that experienced during a real action potential. If all voltage-sensitive currents, except for the calcium current, are blocked, it becomes possible to record the amplitude and time course of the calcium current in isolation. 5 Integration of this current then gives an estimate for the total calcium influx during an action potential. This method has been used to dissect the contribution of different calcium channel subtypes to the calcium influx during an action potential] l0 to study how the time course of the Ca 2~ influx may shape release, 1~ and to study modulation of the calcium currents by neurotransmitters. 71~ In a 4 R. H. Helfert and A. Aschoff, in "'The Central Audilory System" (G. Ehret and R. Romand, cds.), pp. 193-258. Oxford Univcrsity Press, New York, 1997. 5 R. Llimis, M. Sugimori, and S. M. Simon, Proc. NaIL Acad. Sci. U.S.A. 79, 2415 (1982). ~ M. E. Starzak and R. J. Starzak, I E E E Trans. Biomed. Eng. 2S, 201 (1978) 7 j. Arreola, R. F. Dirksen, R. C. Shieh. D. J. Williford. and S. S. Sheu, Am. J. Physiol. 261, C393 (1991). s R. S. Scroggs and A. P. Fox, .I. Neurosci. 12, 1789 (1992). ') D. P. McCobb and K. G. Beam, Neuron 7, 119 (1991). i~, D. B. Wheeler, A. Randall, and R. W. Tsien, Y. Neurosci. 16, 2226 (1996). t l A. N. Spencer, .1. Przysiezniak, J. AcostaAJrquidi, and T. A. Basarsky, Nature 340, 636 (1989). 12 N. J. Peninglon, J. S. Kelly. and A. P. Fox, Proc. R. Soc. Lond. B 248, 17l (1992),
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variation on this method, only the calcium current is pharmacologically blocked after recording an action potential in current clamp. L3In that case. the current that is needed to maintain the same action potential waveform is the calcium current plus possible calcium-activated currents. For this method to work, a representative template, good voltage control, subtraction of leak and capacitative currents, and the pharmacologic isolation of the calcium currents are needed. The last three points are not specific for this method, but are important whenever calcium currents are recorded. General techniques for recording whole-cell calcium currents have been reviewed in a previous volumeJ 4 We briefly discuss some aspects that are relevant to recording calcium currents in the calyx of Held.
Isolation of Calcium Currents Calcium currents are pharmacologically isolated by blocking sodium channels with tetrodotoxin and potassium currents with external tetraethylammonium and 3,4-diaminopyridine and internal Cs +. We use gluconate or glutamate as the major internal anion in our solution for these experiments. We have not observed a blocking effect of gluconate 15on the calcium current. Peak amplitudes are similar when chloride or methyl sulfate are used as the main anion. Furthermore, transmitter release is not reduced after dialysis of the terminal with solutions containing mixtures of gluconate and glutamate. L<~7A disadvantage of using cesium gluconate, however, is that purified cesium gluconate is not readily available. Commercially available gluconic acid solutions are bulk grade (<95%), making further purification necessary, for example, by repeated precipitation of cesium gluconate in methanol. With these internal and external solutions, an (apparent) reversal potential for the calcium currents more positive than +40 mV is obtained. Additional evidence that there is little contamination by other currents in the physiologically relevant range is the good correspondence of the charges carried by Ca ?+, as obtained with the fluorescence method (see later section), and the calcium current integrals.
Voltage Clamp Good spatial and temporal voltage clamp in the calyx of Held is not easy to obtain. The calcium channels in the calyx of Held gate very fast. Is > T. Doerr, R. Denger, and W. Trautwein, Pfliigers Archiv. 413, 599 (1989). 14 B. P. Bean, Methods Enzymol. 207, 181 (1992). l~ A. A. Velumian, L. Zhang, P. Pennefather, and P. L. Carlem Pfliigers Archiv. 433, 343 (1997). > J . G. G. Borst, F. Hclmchen, and B. Sakmann, J. Physiol. 489, 825 (1995). 17,j. G. G. Borst and B. Sakmann, Nature 383, 431 (1996). lsj. G. G. Borst and B. Sakmann, J. Physiol. 506, 143 (1998).
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If the spatial or temporal voltage clamp is not of sufficient quality, the action potential waveform will be distorted, leading to uninterpretable results. ~) The most important determinant for the quality of the spatial clamp in the calyx of Held is the length of the axon. A long axon often makes voltage clamping impossible. Nevertheless, for short pulses, like an action potential waveform, the problem of poorly clamped axonal calcium channels is much less severe than for long depolarizing voltage steps, as the calcium channels in remote areas will not be activated during short pulses. ~s Because the calyx is a rather thin structure, it is difficult to obtain stable whole-cell recordings with low access resistance. We have circumvented this problem by using two-electrode voltage clamping, in which one patch electrode injects current and the other measures voltage. This configuration makes it possible to compensate a high access resistance (e.g., 4(i) M~Q) with an increase in the voltage-clamp gain. In addition, fortunately, the membrane voltage does not have to change as fast during the action potential waveform as when tail currents are recorded. The current that is needed to force the calcium channels to undergo the same voltage change as during a real action potential consists of an active and a passive component. The active, smaller component is due to the opening of calcium channels. The passive component consists of the current that is needed to charge and discharge the cell capacitance plus the current that flows through the leak resistance of the cell: l=Cm
dVm Vm -- El~,k dt + Rm
(1)
where Cm is membrane capacitance, Vm is voltage, E~,k is the reversal potential of the leak current, and Rm is membrane resistance. The same two strategies that have been used to subtract these linear components of the membrane current signals during voltage steps can also be applied in the case of action potential waveforms. 5 An estimate for the passive currents can be obtained in the presence of a calcium channel blocker. Very stable recordings are needed in that case because the calcium currents are generally much smaller than the passive currents. The other method uses the scaled response to an action potential that is much smaller than the full action potential for subtraction (Fig. 1). The increase in noise can be minimized by averaging many responses with the small action potential before subtraction. The first derivative of the measured voltage matched the passive current well for the action potential waveform (Fig. 1B). This allows an estimate of the capacitance "seen" by the electrode during the waveform, ldeally~ this value is almost as large as the total capacitance, t~>C. M. Armstrong and W. F. Gill)', Methods Enzymol. 2117,100 (1992).
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B
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~
40 mV ]
c
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Fro. 1. Voltage clamping a giant presynaptic terminal with an action potential waveform. (A) Infrared differential interference conlrast video image of a calyx of Held. For twoelectrode voltage clamp, two whole-cell recordings were made. One patch electrode measured voltage and provided a feedback signal for the other electrode, which was used for current injection. [Adapted from J. G. G. Borst and B. Sakmann, Nature 383, 431 434 (1996).] (B) a: Command voltage as measured with the voltage electrode. Also shown is the action potential waveform that has bccn scaled down livefold and that is used R)r subtraction of the passive response. Ten current responses to the smaller action potentials were averaged and scaled up fivefold before subtraction, b: First derivative of the membrane voltage of the full-sized action potential and of the small action potential after scaling, c: Total current. Note the resemblance with the first derivative of the voltage, as cxpected for the passive component. The current associated with the full action potential is larger during the repolarization phase. Subtraction of the passive component gives the calcium current, shown in (C). [Adapted from F. Helmehen, J. G. G. Borst, and B. Sakmann, Biophys. J. 72, 1458 1471 (1997).] (C) Calcium current during an action potential and integral of the calcium current (_)(.~,.All data are from the same experiment. o b t a i n e d f r o m i n t e g r a t i o n o f s t e p r e s p o n s e s . In c a l y c e s w i t h o u t an a x o n , this is i n d e e d t h e case.tS A f t e r s u b t r a c t i o n o f t h e p a s s i v e c u r r e n t , t h e c a l c i u m c u r r e n t r e m a i n e d (Fig. 1C). A s m a l l o u t w a r d c u r r e n t p r e c e d e d t h e i n w a r d c u r r e n t . T h i s c u r r e n t m a y b e d u e to i m p e r f e c t v o l t a g e c l a m p , a l t h o u g h g a t i n g c u r r e n t s m a y also c o n t r i b u t e . I n t e g r a t i o n o f t h e s u b t r a c t e d c u r r e n t y i e l d s t h e t o t a l c a l c i u m influx (Fig. 1C).
Choice o f Voltage Template A difficult p r o b l e m w i t h this m e t h o d is t h e c h o i c e o f a r e p r e s e n t a t i v e v o l t a g e t e m p l a t e . I d e a l l y , an a c t i o n p o t e n t i a l is first r e c o r d e d in c u r r e n t
[20]
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clamp and played back to the same cell in voltage clamp. However, pharmacologic isolation of the calcium currents is difficult to achieve without internal potassium channel blockers, making it necessary to repatch with a different solution or to use pipette perfusion in whole-cell patch-clamp experiments. Also, many voltage-clamp amplifiers are not suitable for current clamp recordings. 2° The alternative is to select a "typical" action potential and to use this action potential as a voltage template in all subsequent experiments, as was done in Fig. 1. This may also be useful with cells in primary isolation, whose action potential shape may have dramatically changed. An action potential that was recorded in a current clamp experiment in situ may then serve as the template. ~L21 Alternatively, voltage ramps may be used, ~1° which have the advantage that they are more easily reproduced by other authors. In either case, the question of whether the voltage templat e is representative is an important one. In the calyx of Held, action potentials are relatively invariant between cells, making it easier to select a representative template. Once a suitable template has been recorded, the action potential waveform must be provided to the amplifier as a command potential without much distortion. It is important that the interval between points of the action potential waveform command is clearly less than the sample interval at which the template was recorded. Using twice the corner frequency at which the action potential was recorded as the output frequency may not be sufficient because of the gradual rolloff of RC or Bessel filters at higher frequencies, and because of the absence of any interpolation by the digital/ analog (D/A) converter. We use five times the corner frequency to be on the safe side. The software that allows us to use action potential templates is Pulse Control 4.6 (Ref. 22; http://chroma.med.miami.edu/cap/), in combination with I G O R macros (Wavemetrics, Lake Oswego, OR). The flexibility of the macro-based software makes it possible to change the waveform systematically, is as well as to perform analyses on-line. An advantage of the action potential waveform voltage-clamp method is that information about the time course of the calcium current during an action potential is obtained. Alternatively, it may be possible to obtain this information by using cell-attached patch-clamp recordings > or by using the time derivative of the fluorescence signal of a calcium indicator (see later discussion). With the action potential waveform method, time delays in the recorded currents introduced by external filters, or the filter formed by the 21,j. Magistrctti, M. Mantcgazza. E. Guatteo, and E. Wanke, Trends Ne,rosci. 19. 530 (1996). 21 W. J. Song and D. J. Surmcicr, ,l. Neurophysiol. 76, 2290 (1996). "e J. Herrington and R. J. Bookman, in "'Pulse Control V4.0: I G O R XOPs for Patch Clamp Data Acquisition and Capacitance Measurements." University of Miami, Florida. 1994. > M. Mazzanti and L. J. DeFelice, Bi~q~h),s. J. 58, 1059 (1990).
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combination of cell capacitance and access resistance, must be corrected. We have addressed this by making simultaneous current and voltage recordings from the terminal and by using the observation that the action potential in the calyx of Held can be capacitively recorded in the postsynaptic cell. ~¢~24Other methods to estimate the delay between the voltage command and the change in the membrane voltage have been discussed in Ref. 25. After correction for delays, the number of open calcium channels can be estimated at any time during the action potential, if the single-channel conductance of the calcium channel is known. Fluorometric M e a s u r e m e n t of Calcium Influx Introduction
An alternative method to quantify the calcium influx during an action potential is by using a fluorescent calcium indicator. Calcium indicators are generally used to report changes in the intracellular free calcium concentration, [Ca]~. The indicator dyes, which act as exogenous calcium buffers, will distort the time course of the calcium transients if their concentration is not sufficiently small. At very high concentrations the indicator will become the dominant intracellular calcium buffer. In this case, which is referred to as "dye overload," virtually all calcium ions that enter the cytosol are captured by the indicator. Because, in general, the fluorescence change (AF) of an indicator is proportional to the number of dye molecules that have captured a calcium ion, under overload conditions 5 F will be proportional to the total calcium current Q(,~,: 5 F = ,fl..... f lc~, dt - . { i .... Qc~,
(2)
Therefore, with this approach calcium indicators can also be used to measure calcium fluxes. 2¢~'27If the proportionality constant .~..... is known, the total calcium influx can be directly calculated from &F. This method is much simpler and requires fewer assumptions than estimating calcium fluxes from changes in the intracellular calcium concentration. 2s29 One of the advantages of the dye overload technique is that it also is applicable when ions other than Ca 2- are contributing to the currents. Indeed, this method was first used to determine the fractional contribution 24 1. D. Forsythe, .I. Physiol. 479, 381 (1994). 25 F. J. Sigworlh and J. Zhou, Methods Enzymol. 207, 746 (1992). 2, E. Neher and G. J. Augusline. J. Physiol. 450, 273 (1992). 27 E. Neher, Neuropharmacology 34, 1423 (1995). -~'~S. M. Baylor. W. K. Chandler, and M. W. Marshall, J. Physiol. 344, 625 (1983). ~'J D. W. Tank, W. G. Regehr, and K. R. Delaney, .l. Neurosci. 15, 7940 (1995).
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CALCIUM INFLUX DLJRIN(] AN A c r I O N POI'ENTIAI.
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of Ca e- to the current through ligand-gated ion channels. 27"3° 3~ We applied dye overload to measure the total calcium influx during an action potential in the calyx of Held. )-* In Fig. 2A the fluorescence image of a calyx loaded with 1 m M of the high-affinity indicator Fura-2 (Molecular Probes. Eugene, OR) is shown. At this concentration, Fura-2 overrides the endogenous calcium buffers of the terminal (see later discussion). 1~-32With excitation at 380 nm, the fluorescence emission of Fura-2 decreases after calcium binding. A single presynaptic action potential that was evoked by stimulation of the afferent nerve fiber caused a clear decrease in the total Fura-2 fluorescence of the whole terminal (A/~s~; Fig. 2B). Before AF3,s0 can be converted to Qc~,, several conditions have to be met. Normalization and calibration of the fluorescence signal are also required. These aspects arc discussed in the following sections.
Dye Overload Dye overload is reached when the indicator effectively outcompetes the endogenous calcium buffers. This suggests the use of a high-affinity calcium indicator, with a dissociation constant in the same range as the resting intracellular Ca 2+ concentration. So far only Fura-2 has been used. However, in principle, the dye overload technique is not restricted to ratiometric dyes since it requires fluorescence excitation (or collection of fluorescence emission) at a single, calcium-dependent wavelength. Therefore, other high-affinity indicators such as Calcium Green-l, Indo-1, or even E G T A in combination with a pH indicator ~-~ may also be used. How much dye is needed to outcompete the endogenous buffers? An absolute value for the concentration that is needed cannot be given because it depends on the relative calcium-buffering capacities of the indicator and of the endogenous calcium buffers. We illustrate this using the single compartment model introduced by Neher and Augustine. :~' This model describes the competition of an indicator (B) with a pool of rapid endogenous calcium buffers (S). The calcium-buffering capacity of a buffer is given by its calcium-binding ratio27: i~[CaB] _ ~c~ -
i~[Ca]~
K,t (K,, + [Ca]~) 2 [B],,
(3)
s~' R. Schncggcnburger, Z. Zhou. A. Konnerth. and E. Nehcr, Neuron 11, 133 (1993). ~/ Z. Zhou and E. Neher, Pjh'igers Archiv. 425, 511 (1993). ~ ' G. Vcligelebi, K. A. Stadcrman, M. A. Varney. M. Akong, S. D. Hess, and E. C. Johnson, Methods Enzymol. 293, [2], 1998 (this volume). ~" F. Helmchen, J. G. G. Borst, and B. Sakmann, Biw)hys. ,l. '72, 1458 (1997). '~ P. C. Pape, D. S. Jong. and W. K. Chandler, .I. Gen. Physiol. 106, 259 (1995).
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0.02~
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0 0 0 ,o o
0 c,
g 0.01
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-20
I
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t
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D I
~
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-------
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LL
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10 Ca influx Qc~ (pC)
20
FK;. 2. Fluorometric measurement of the total presynaptic calcium influx during an action potential. (A) Wide-field fluorescence image of a calyx of Held lilled with 1 mM Fura-2. The rectangle indicates the subregion from which the total fluorescence signal was collected with the CCD camera. (B) Fura-2 fluorescence decrement at 380-nm excitation ('~F~so) evoked by a single presynaptic action potential, which was elicited orthodromically (arrow). Fluorescence is expressed in bead units (BU). (C) Decrements evoked by single action potentials with the microscope defocused by different amounts. (D) Determination of .[i~,,x. Isolated presynaptic calcium currents (1<~,) were evoked by depolarizing voltage steps and Fura-2 fluorescence decrements were measured simultaneously. The slope of the plot of/k/-'~s0versus the calcium current integral yields./i,,~x, which was 15 BU nC i. [Adapted from J. G. G. Borst and B. Sakmann. Nature 383, 431-434 (1996).]
w h e r e [CAB] is t h e c o n c e n t r a t i o n of t h e b o u n d f o r m , K,t is t h e d i s s o c i a t i o n c o n s t a n t , a n d [B]T is t h e t o t a l c o n c e n t r a t i o n o f t h e b u f f e r . A c c o r d i n g to t h e m o d e l , t h e f l u o r e s c e n c e c h a n g e d i v i d e d by t h e t o t a l c a l c i u m influx ( t h e s o - c a l l e d F/Q ratio, f ) is g i v e n by AF f -
Qc.
K~ - , £ ....
(l + Ks + KB)
(4)
120]
CALCIUM INFLUX DURING AN ACTION POTENTIAl.
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where ./' depends on the relative sizes of the endogenous calcium-binding ratio KS and the exogenous calcium-binding ratio KB. It reaches a saturating value fm,x if KB is much larger than Ks and, in this case, Eq. (4) simplifies to Eq. (2). Thus, dye overload requires KB >> KS. TO choose a dye concentration that fulfills the overload condition, it is useful to have an estimate of Ks. However, this is not strictly necessary. As a simple test one can measure the change in fluorescence that is evoked by a more or less constant calcium influx (e.g., during an action potential) in the presence of different dye concentrations. If the dye concentration is sufficiently high, AF should not change significantly when the dye concentration is doubled. On the other hand, determination of Ks is advantageous because the fraction of the incoming calcium ions that is captured by the indicator can be estimated, and the signal-to-noise ratio can be more readily optimized (see later discussion). For many neurons KS is between 50 and 150. 27 For the calyx of Held we obtained a value of about 40 bv monitoring the effect of Fura-2 on calcium transients evoked by action potentials during Fura-2 loading) 2 Therefore, a concentration of 1 m M Fura-2, which corresponds to a KB of around 2500, is sufficient for overload. According to Eq. (4), more than 98% of the calcium ions will be captured by Fura-2 if KS is 40. In neurons with a higher endogenous calcium-binding ratio, such as cerebellar Purkinje cells) a much higher concentrations of the dye would be needed. One might think that the higher the dye concentration the better. This is not true for two reasons. First, the indicator cannot catch more than 100% of all incoming calcium ions. When the dye concentration is too high, the signal-to-noise ratio will decrease, as discussed further below. Second, the fluorescence intensity in this case may no longer depend linearly on the dye concentration ([B]). Beer's law states that the fluorescence intensity F of a fluorescent layer of thickness d is proportional to 1-10 ~-dlBI where is the extinction coefficient of the dye. The linear approximation F d [B] is only valid if [B] ~ [ln(10) e. d] ~. As an example, we consider a small neuron with a diameter of 10/,m. The extinction coefficient of Fura2 is about 30.000 M ~cm L, therefore, in this case, [B] should be well below 15 mM.
Normalization and Calibration of" Fluorescence Changes The fluorescence intensity that is measured depends on the illumination intensity as well as the photon-detection efficiency. Because these parameters may change with time, intensities should be normalized to a fluorescent standard. Commonly, the fluorescence intensity of fluoresbrite beads (diam34L. Ficrro and I. Llano, J. Physiol. 496, 617 (1996).
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eter 4.5/zm, Polysciences, Warrington, PA) is measured on each experimental day and all intensities are normalized to this value. 2~'273° Fluorescence therefore is expressed in "bead units" (BU; Ref. 30). The intensity of the beads depends on the bandwidths of the excitation and the emission filters. Because maximal emission is at around 470 nm the dichroic mirror should separate below that wavelength. The bead intensity also depends on the solution, which therefore always should be the same. 27 We dilute the beads 1:200 in distilled water, immobilize the beads by drying a drop of this solution on a coverslip, place the coverslip in distilled water under a waterimmersion objective, and subsequently measure the intensity of five beads, each placed in the same region as the terminals. With the CCD camera some pixels could be saturated by the bright beads. This was avoided by slightly defocusing the bead for the measurements. Conversion of the fluorescence changes to total calcium current Qc~, requires the determination of the proportionality factor f ..... (in units of BU nC ~). This is achieved by measuring fluorescence changes evoked by isolated calcium currents, because calcium channels have a very high selectivity for Ca > over other ions under physiologic conditions) ~ We blocked sodium and potassium channels as described earlier, and evoked presynaptic calcium currents with depolarizing voltage steps in voltage clamp. By correlating the decrements in Fura-2 fluorescence with the calcium current integrals we obtained an estimate for.fi..... (Fig. 2D). Usually, the correlation coefficient was very high for depolarizing steps to voltages in the range of - 3 0 to +30 mV (r > 0.99), indicating good pharmacologic isolation of the calcium currents. It is noteworthy that.~ ..... depends on the spectral properties of the experimental setup since the beads and Fura-2 differ with respect to their emission spectrum. 3~ The total calcium influx Qc,, during an action potential is calculated by dividing the fluorescence change through ,/'i..... [Eq. (2)]. Fluorescence Detection
Fluorescence can be detected with a camera, a photomultiplier, or a photodiode. It should be collected with the same efficiency from all cellular compartments that are studied. A region that encloses the relevant structures can be selected as a subregion of the camera (Fig. 2A), with a diaphragm in front of the photomultiplier, or by placement of a small photodiode in the image plane of the microscope (see later discussion). For the determination o f f ..... it is also essential that fluorescence be measured from all structures that contribute to the calcium current measured under voltage ~" B. Hille, in "'Ionic C h a n n e l s of Excitablc Membranes." pp. 1-6(17. Simmer, S u n d e r l a n d , Massachusetts. 1992.
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clamp. Therefore, the calcium influx into cellular structures from which fluorescence is not collected must be considered. For example, the preterminal axon in Fig. 2A is not fully included within the region of measurement. In this case previous measurements, however, have shown that the calcium signal is very small in the axon compared to the terminal, l<' It is also important that the light emitted from structures that are not in focus be collected as well. To test this, fluorescence decrements can be measured at different focal planes. The decrements should not significantly change if the cell is defocused (Fig. 2C). Fluorescent beads may also be helpful for testing this assumption. Actually, the poor spatial resolution in the Zaxis of the wide-field microscope compared to a confocal or a two-photon microscope is an advantage for overload measurements. It may even be possible to measure the total calcium influx in neurons with extensive dendrites, using a low magnification objective with a large field of view. In that case it is important to make sure that the indicator is noi locally saturated 27 and that it outcompetes the endogenous buffers throughout the whole cell, because equilibrating remote processes of a cell with the dye may take a long time. -~(~For such measurements, .~...... would have to be determined in a different cell type under conditions that differ as little as possible from the measurements, because voltage clamping of cells with extensive dendrites is not possible. The same strategy would have to be followed for other possible applications of this method such as m e a s u r e m e n t of calcium influx through low-voltage-activated calcium channels during excitatory postsynaptic potentials, estimation of calcium current densities in dendritic segments, and m e a s u r e m e n t of relative calcium influx into subcellular c o m p a r t m e n t s compared to the whole cell. A n o t h e r approach that can be used to simplify the interpretation of the fluorescence measurements is to allow calcium influx only locally, either by local application of agonists -~7 or by exposing only the structure that is under study to physiologic [Cae+]o.3s C o m p a r i s o n of the V o l t a g e - C l a m p a n d the F l u o r e s c e n c e Method The two methods described gave a similar value of about 0.9 pC (corresponding to around 35 fCpF i ) for the total calcium influx during an action potential in the calyx of Held (23 °, 2 m M [Cae~]<>). This is remarkable since both methods rely on different assumptions. First, the voltage-clamp ~('J. Eilcrs, R. Schneggenburger, and A. Konnerlh, in "'Single-Channel Recording", 2nd Ed. (B. Sakmann and E. Nchcr, eds.), pp. 213-229. Plelmm, New York, 1995. ~: O. Garaschuk, R. Schneggenburger, C Schirra, F. Tcmpia. and A. Konnerth, ]. Physiol. 491,757 (1996). ~s G. J. Augustine. M. P. Charlton, and S. ,1. Smith..I. Ptnsiol. 367, 143 (1985).
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method requires blocking of sodium and potassium channels, whereas the fluorometric measurements can be done in current clamp mode using physiologic external solution. Second, the same action potential waveform was used for voltage clamping the nerve terminals in all experiments. In contrast, action potentials were elicited by orthodromic stimulation in the dye overload experiments and displayed their normal variability with respect to amplitude and time course. Both methods required patch-clamp recordings with relatively low access resistance (R~,cc). For reliable dye loading of the nerve terminal, a low access resistance (-~-15 MI)) during the first 10 rain of recording is needed. 16 As soon as the terminal is loaded, increases in Race are no longer critical. In the voltage-clamp measurements the problem of increases in R .... was circumvented by using two-electrode voltage clamp. We will show later that a single electrode may also be sufficient. The main disadvantage of the overload technique compared to the action potential waveform voltage-clamp technique is that it does not provide information about the time course of the calcium influx. There have been attempts to back calculate the time course of the calcium current by taking the derivative of the fluorescence signal of a calcium indicator [compare Eq. (2)]. 27'28'39'40 However, for this method to work, fluorescence has to be detected with submillisecond time resolution, and the kinetics of the dye have to be fast enough to report the time course of the influx. Therefore, only low-affinity dyes such as MagFura-2 or Magnesium Green may be suitable. According to Eq. (3), it is very difficult for these dyes to outcompete the endogenous buffers, so that they capture only a fraction of the incoming calcium ions. In addition, dye depletion close to the channels may occur during calcium influx. Currently, it does not seem possible to simultaneously obtain quantitative measurements of both amplitude and time course of calcium influx using a fluorometric method.
Measuring Modulation of Calcium Influx With both methods, it becomes possible to study modulation of the calcium influx. To illustrate the possibilities, we show here two simple examples, the dependence of the calcium influx during an action potential in the calyx of Held on extracellular calcium concentration and on temperature (Figs. 3 and 4). A comparison of both methods shows that they give similar values for both manipulations. The signal-to-noise (S/N) ratio is better for the voltage-clamp method than for the fluorescence method, though. The coefficient of variation (standard deviation/mean) was 0.02 for the current integrals during the baseline period shown in Fig. 3B and 0.14 for the fluorescence signals shown in Fig. 3D. In principle, both methods could be 3L)B. L. Sabalini and W. G, Regehr, Nature 384, 170 (1996). 4~S. R. Sinha, L. G. Wu, and P. Saggau, Biophys..I. 72, 637 (1997).
[9,0]
365
CALCIUM INFLUX DURING AN A(TION POTENIIAL
C
A
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F~;. 3. Dependence of the presynaptic calcium influx during an action potential on the external calcium concentration. (A) Calcium currents during action potentials at different external calcium concentrations ([Ca > ],,), as indicated, (B) Time course after break-in of the calcium current integrals during periods with different [Ca2~].. Same experiment as shown in Fig. 1. [Adapted from J. G. G. Borst and B. Sakmann. Nature 383, 431 (1996).] (C) Fluorescence decrements evoked by action potentials with different [Ca-~~1o as indicated (each trace is an average of nine sweeps). (D) Time course after break-in of the total calcium influx during periods with different [Ca "' ],, as measured from the lluorescence decrements. [Adapted from F. Helmchen, J. G. G. Borst, and B. Sakmann, Biophys. ,l. 72, 1458 (1997).]
u s e d to c o r r e l a t e t h e p r e s y n a p t i c c a l c i u m influx d u r i n g a c t i o n p o t e n t i a l s w i t h t h e a m p l i t u d e o f t h e p o s t s y n a p t i c c u r r e n t s in s i m u l t a n e o u s p r e - a n d p o s t s y n a p t i c r e c o r d i n g s . H o w e v e r , a l t h o u g h t h e f l u o r e s c e n c e m e t h o d is t e c h n i c a l l y e a s i e r to p e r f o r m , t h e i n t r o d u c t i o n o f 1 m M F u r a - 2 i n t o t h e t e r m i n a l w o u l d r e d u c e n e u r o t r a n s m i t t e r r e l e a s e significantly. >
Signal-to-Noise Considerations Voltage Clamp. B a s e l i n e n o i s e in w h o l e - c e l l e x p e r i m e n t s d e p e n d s m a i n l y on a c c e s s r e s i s t a n c e a n d m e m b r a n e c a p a c i t a n c e ) t N o i s e d u e to 4~ R. A. Levis and J. L. Rae. Methods E;;zymo/. 207, 14 (1992).
366
ELECTROPHYSIO1.OGY
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,
2
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FK;. 4. Comparison of voltage-clamp and fluorescence measurements of presynaptic calcium influx in the calyx of Held. (A) Dependence of total calcium influx during an action potential on the external calcium concentration [Ca2÷],,. The voltage-clamp method (filled circles) and the fluorescence method (open circles) gave similar results. [Adapted from F. Helmchen, J. G. G. Borst, and B. Sakmann, Biophys. J. 72, 1458 (1997), and from J. G. G. Borst and B. Sakmann, Nature 383, 431 (1996).] (B) Temperature dependence of the total calcium influx with 2 mM [Ca2+]o. Again, the voltage-clamp method (VC) and the fluorescence method (F) gave similar results.
calcium currents will depend, in addition to recording bandwidth, also on open probability, total number of functional calcium channels, and singlechannel current. 42 The large calcium currents in the terminal make it possible to obtain a good S / N ratio (defined as peak amplitude divided by standard deviation of the baseline noise). Even though the noise with the two-electrode voltage clamp is clearly higher than for whole-cell patchclamp recordings, S / N ratios of >20 (at 5 kHz) are easily obtained. A further reduction in baseline noise would permit to do nonstationary noise analysis of the calcium currents during action potentials or to study the contribution of the variance of the calcium currents to the variance of the synaptic currents. Fluorescence. Fluorescence changes evoked by action potentials are relatively small, for example, the signal shown in Fig. 2B corresponds to a relative fluorescence change of only 0.7%. Therefore, the fluorescence noise must be reduced. Noise sources include fluctuations in the output of the light source, vibrational noise, dark noise of the photodetector, and photon 42 S. H. Heinemann and F. Conti, Methods Enz.y'mol. 207, 131 (1992).
[20]
367
CAI_CIIJM INFLUX DURING AN ACTION POTENTIAL
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FI(;. 5. Signal-to-noisc ratio of fluorescence changes cw)ked by action potentials. (A) The fraction of calcium ions that bind to Fura-2 is plotted as a function of the Fura-2 calciumbinding ratio Kl~. Around half of the calcium ions bind to Fura-2 when t% equals the endogenous calcium-binding ratio KS, which was assumed to be 40. One mM Fura-2 corresponds to a calcium-binding ratio of about 2500. (B) Signal-to-noise ratio of action potential evoked Fura 2 fluorescence decrements versus gl~. The S/N ratio is defined as AF divided by the standard deviation of the prestimulus fluorescence trace. Data points were obtaincd at Fura-2 concentra tions of ~20 IxM, 50 IxM, 100 ffM, and 1 mM. respectively. A curve according to Eq. (6) was scaled to lit the three first points (C 22{I, KS = 40). [Adapted from F. Helmcben. ,1. G. G. Borsl. and B. Sakmann, Bioph3s. ,I. 72, 1458 1470 (1997),]
shot noise. 43 Because the signals are so small, it may be important to lind the dye concentration that yields the highest S/N ratio. We define the S/N ratio as the fluorescence change k F divided by the standard deviation of the baseline fluorescence oT. The percentage of calcium ions captured by the indicator is given by f/f, ..... [Eq. (4)]. It is shown in Fig. 5A as a function of the exogenous calcium-binding ratio KB. The endogenous calcium-binding ratio Ks was assumed to be 4 0 . 32 in the best case of a shotnoise-limited optical recording the variance of the fluorescence signal is proportional to the number of measured photons. However, in brain slices the autofluorescence of endogenous fluorophores > results in a relatively high background fluorescence. For example, at our setup the background ltuorescence is equivalent to the fluorescence of a terminal loaded with 100 ffM Fura-2, corresponding to K~ ~ 220. Assuming that background and dye fluorescence are independent, the variance of the total fluorescence is proportional to the sum of the background fluorescence and the indicator fluorescence F, where F is proportional to [B],r, which for small perturbations of [Ca]i from the resting level itself is proportional to Kl~ [Eq. (3)]. Therefore the variance is proportional to: ~ (C + ~t~)
(5)
4~ j._y. Wu and L. B. Cohen, in "Fluorescent and Lumincsccnt Probes for Biological Activity" (W. T. Mason. ed.), pp. 389 4()4. Academic Press, London, 1993.
368
ELECFROPHYSIOLOGY
[20]
where C is a constant representing the binding ratio that the indicator would have if its fluorescence were equal to the background fluorescence. Neglecting other noise sources, it follows that: AF KB S/N ratio - - - oc o-v (1 + K s + K B ) ~ / C + K B
(6)
As seen in Fig. 5B, the actual S/N ratios that we obtained with the CCD camera using different concentrations of Fura-2 are reasonably well described by this relationship. For high dye concentrations, KB > KS, the S/N ratio decreases proportional to (C + KB) ~/2 [Eq. (6)]. This decrease occurs because &F saturates (the indicator cannot bind more calcium ions than enter the cell) but the noise still increases with increasing dye concentrations. To obtain the exogenous calcium-binding ratio K0 for which the S/N ratio is maximal, Eq. (6) can be differentiated with respect to KB, yielding: (1 +Ks)
1+
+8
(7)
Thus, if background fluorescence can be neglected (C - 0), the highest S/N ratio is obtained if cells are loaded with a dye concentration that is equivalent to KB -- K0 -- 1 + KS. In this situation, which has been referred to as "balanced loading, ''44 only 50% of the calcium ions are captured by the indicator. With higher background fluorescence, more dye is needed for the best S/N ratio; for example, with a C equivalent to Ks, the optimal dye concentration is already twice as large. By definition, KB >> Ks during overload, so unless C is much larger than Ks, the S/N ratio will be clearly suboptimal. To increase the S/N ratio one may choose to work with a lower dye concentration so that only a fraction of the calcium ions is captured and the total calcium influx is calculated from Eq. (4) using an estimate of Ks. However, Ks may vary between cells, leading to uncertainties in this calculation.
Simple Photodetector Another possibility for increasing the S/N ratio of the fluorescence measurements is to use a photodetector with a high quantum efficiency. Because spatial resolution is not needed, an alternative to a CCD camera is a photodiode. Advantages are their low cost, ease of operation and high bandwidth. C o m p a r e d to photomultipliers, photodiodes have a larger dark current but this is not critical in our case because of the high dye concentrations used. Photodiodes have been widely used to measure calcium signals 44 Z. Z h o u and E. Neher. J. Physiol. 469, 245 (1993).
[20]
369
CAI~CIUM INFLUX DURING AN ACTION POTENI'IA[,
power supply preamplifiel image plane of microscope
PD1 u PD2
=0.5pF
3hotodiodes
$2386-18K J- J-
[--1.,71" .~[.[.~[T] i~ k~~
microscopeadapter ~ J Fl¢;. 6. A simple photodetector to measure calcium influx during an action potential. (Left) Schematic diagram of the photodiode system. The metal box contains the preamplilicr. Two silicon photodiodes ($2386-18K, H a m a m a t s u l'hotonics, Japan) are located in the image plane of thc microscope's camera output port. Active area of the photodiodes is 1.1 × 1.1 mm, corresponding to 27.5 × 27.5 p,m in the focal plane of a Zeiss 40× water immersion objective. The q u a n t u m efficiency of the photodiode used is 84% at 560 nm. (Right) Diagram of the photodiode preamplifier, consisting of an O P A l ll (Burr-Brown, Tucson, A Z ) current-tow)ltage converter and a Max4fl0 (Maxim Inlcgrated Products, Sunnyvale, CA) differential amplilier that provides a gain of 21. Feedback resistor is 10 ( ; ~ . Stray capacitance is around 0.5 pF, giving a corner lYcquency of around 300 Hz, as measured from the rise time of the photodiode signal to an L E D light source.
from pools of labeled terminals. 45'4~We have constructed a simple photodiode to measure calcium signals from small cell compartments such as the calyx of Held (Fig. 6). Light is collected by the photodiode from a region of similar size as the subregion of the camera shown in Fig. 2A. Simultaneous measurement of a background region is possible using a second neighboring photodiode, although this is not necessary when total influx is measured. With this simple device fluorescence decrements evoked by single action potentials can be resolved using 1 mM Fura-2 for overload (Fig. 7). Simultaneous Voltage-Clamp and Fluorescence Measurements To illustrate the use of this photodiode we have simultaneously measured calcium influx during an action potential with both methods (Fig. 7). A terminal was voltage clamped using an action potential waveform, as shown in Fig. 1, except continuous whole-cell voltage clamp with a single electrode was used and fluorescence was monitored at the same lime with the photodiode. To be able to voltage clamp the terminals with a single electrode, it was important to select terminals with short axons and to keep 45 L.-G. W u and P. Saggau, J. Neurosci. 14, 645 (1994). 4~, W. G. Regehr and D. W. Tank, N e u r o n 7, 451 (1991).
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I201
A
lnA I B
Qoa-.
C
0.5 pC
0.5 ms
50 ms
Fu;. 7. Simultaneous recording of calcium current during an action potential using the voltage-clamp and fluorescence methods. A terminal was loaded wilh Fura-2 and w)ltage clamped with an action potential waveform to compare the calcium influx oblained with both methods. Determination of./i ..... could be done in this case within the same experiment by construction of a current-w)ltage relation, as shown in Fig. 2D. Conlmuous single electrode voltage clamp was used. The outputs of the patch-clamp amplifier and the photodiode amplifier were simultaneously digitized with a 16-bit A/D converter (ITC-16 Instrutech, Great Neck, NY) at 50 kHz: thc photodiode voltages were decimated to 1 kHz to reduce memory require ments. Access resistance was 8 Mr!, compensated to 90%. Total capacitance was 33 pF. Axon length was around 100/*m. (A) Calcium currenis. Filtered at 5 kHz. (B) Integral of response shown in part (A). ((7) Fluorescence measurements. Photodiode signal was digitally filtered to 20 Hz. Calibration bar is shown in pC, ().5 pC corresponded to 0.0056 BU and 73 fA photodiode current. Responses are the average of 2().
the access resistance after electronic compensation below 2 MtL Both m e t h o d s g a v e s i m i l a r v a l u e s f o r t h e c a l c i u m influx. T h e S / N r a t i o w a s a g a i n better for the voltage-clamp method than for the fluorescence method.
Conclusions We have compared two methods to detect the influx of calcium ions during single action potentials and found that they gave similar results in a g i a n t s y n a p t i c t e r m i n a l o f t h e r a t b r a i n s t e m . B o t h m e t h o d s h a v e advantageous features. The main advantages of the voltage-clamp method
[21]
WHOLE (TELL AND SINGLE CHANNEL CURRENT MEASUREMENT
371
are that it provides information about the time course of the calcium influx, that it can be used in the presence of physiologic intracellular calcium buffer concentrations, that a systematic manipulation of the action potential waveform is possible, and that it gives a better S/N ratio than the dye overload technique. The main advantages of the fluorometric method are that it is relatively simple, that measurements arc done in current clamp in physiological external solutions, and that it can in principle be used to quantify fluxes in small subcellular compartments.
Acknowledgments Wc thank Dr. B. Sakmann for continuous support, R. Rodc l and K. Schmidt for o:mstruction of the pholodiode amplilier and Dr. T. D. Parsons for comments on an earlier version of this manuscript. J. G. (]. B. was supported by the E. U. (TMR program).
[21] C o m b i n e d W h o l e - C e l l a n d S i n g l e - C h a n n e l C u r r e n t M e a s u r e m e n t w i t h Q u a n t i t a t i v e C a 2+ I n j e c t i o n o r F u r a - 2 M e a s u r e m e n t o f C a 2-
By L.
D O N A L D P A R T R I D ( i E , H A N N S ULRI(TH Z E I L H O F E R ,
and
D I E T E R SWANDUL1.A
Introduction Intracellular free Ca 2- is an important second messenger in most cell types and cytoplasmic Ca 2+ concentration, [CaX~]i, is tightly controlled by cytoplasmic buffering and regulation of influx and efflux pathways. In excitable cells, cytoplasmic Ca 2+ couples electrical events with a broad range of effector functions. Voltage-dependent calcium channels provide a direct means for this coupling, while postsynaptic ligand-gated channels provide additional regulated pathways for Ca 2- entry. In addition to its welldescribed roles in excitation-contraction coupling and excitation-secretion coupling, cytoplasmic Ca 2~ is responsible for excitation-gating coupling for several important classes of ion channels. The broad class of CaZ+-regulated channels includes Ca2--activated potassium, nonselective (CAN) and chloride channels, and Ca2+-inactivated calcium channels. In addition, these and other channels can be modulated by metabolic processes that depend o n C a 2 +.
Established techniques are available to measure membrane currents in cells voltage clamped with either intracellular microelectrodes or with patch
N'II-rtI()DS IN ENZYMOLOGY, VOL 293
('opyright i 1998by AcadcmicPress All rightsof teploductionin any Iilrm reserved. 0076-0879/9h $2500
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The full characterization of the frequency dependence of the capacitance at different voltages gives a more detailed description of the voltage dependence of the voltage sensor. The study of the charge movement in voltage-dependent channels is normally done by eliminating all of the linear components of the capacitance. The presence of proteins in the membrane should add quasi-voltageindependent but frequency-dependent capacitance due to the lossy dielectric properties of buried charges and dipoles. Frequency-domain techniques, which have far better resolution than time-domain techniques, may be used to study this voltage-independent but frequency-dependent capacitance added by the expression of the channels to the oocyte membrane.
Acknowledgments We thank Abort Cha for reading and commenting on the manuscript. Supported by NIH grants GM30376 to F.B. and GM52203 and AR38970 to E.S.
[20]
Calcium
By J.
Influx during
an Action Potential
GERARD O. BORST and FRITJOF HELMCHEN
Introduction Action potentials open voltage-sensitive calcium channels in excitable cells, leading to an influx of calcium ions. 1 Calcium ions may control, among others, cell excitability, neurotransmitter release, or gene transcription. This chapter deals with two different methods that can be used to quantify how much Ca > flows into a cell or cell compartment during an action potential. Quantification of Ca 2+ influx may be a first step toward the construction of a model for the calcium dynamics of cells. It may also serve as a reference to study pathological processes such as cell death during ischemia or amyotrophic lateral sclerosis, where increases in calcium influx have generally been implicated. 2'3 I S. Hagiwara and K. 1. Naka, J. Gen. Physiol. 48, 141 (1964). D. W. Choi, "[)'ends Neurosci. 18, 58 (1995). E. Louvel, J. Hugon, and A. Doblc, Trends PharmacoL Sci. 18, 196 (1997).
M E T H O D S IN E N Z Y M O I . O G Y , VOL. 293
(-opyright x, 1998 by Academic Press All tights of reproductioll ill any Ikmn lcserved. 0076 6879/98 $25.00
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CALCIUM INFLUX DURING AN ACTION POTENTIAL
353
The two methods that we compare in this chapter are a voltage-clamp method, in which cells are voltage clamped with an action potential waveform command, and a fluorescence method, in which cells are loaded with a high concentration of a calcium-sensitive fluorescent dye. We apply both methods to a "giant" axosomatic terminal, called the calyx of Held, in a slice preparation of the rat brain stem. Each principal cell in the medial nucleus of the trapezoid body (MNTB) is contacted by a single calyx-type terminal. This synapse is part of a fast auditory pathway that is involved in the localization of s o u n d ) We were interested in the relationship between calcium influx and neurotransmitter release at this glutamatergic synapse. We found that both methods gave similar values for the number of calcium ions that enter the presynaptic terminal during an action potential. We first discuss the action potential waveform voltage-clamp method.
Action Potential Waveform Voltage Clamp Introduction
This method was first used to quantify calcium influx into the squid giant terminal during an action potential. 5 An action potential was first recorded in current clamp and subsequently used as a command template in a voltage-clamp e x p e r i m e n t ) With this paradigm, the voltage-sensitive channels experience the same voltage change as that experienced during a real action potential. If all voltage-sensitive currents, except for the calcium current, are blocked, it becomes possible to record the amplitude and time course of the calcium current in isolation. 5 Integration of this current then gives an estimate for the total calcium influx during an action potential. This method has been used to dissect the contribution of different calcium channel subtypes to the calcium influx during an action potential] l0 to study how the time course of the Ca 2~ influx may shape release, 1~ and to study modulation of the calcium currents by neurotransmitters. 71~ In a 4 R. H. Helfert and A. Aschoff, in "'The Central Audilory System" (G. Ehret and R. Romand, cds.), pp. 193-258. Oxford Univcrsity Press, New York, 1997. 5 R. Llimis, M. Sugimori, and S. M. Simon, Proc. NaIL Acad. Sci. U.S.A. 79, 2415 (1982). ~ M. E. Starzak and R. J. Starzak, I E E E Trans. Biomed. Eng. 2S, 201 (1978) 7 j. Arreola, R. F. Dirksen, R. C. Shieh. D. J. Williford. and S. S. Sheu, Am. J. Physiol. 261, C393 (1991). s R. S. Scroggs and A. P. Fox, .I. Neurosci. 12, 1789 (1992). ') D. P. McCobb and K. G. Beam, Neuron 7, 119 (1991). i~, D. B. Wheeler, A. Randall, and R. W. Tsien, Y. Neurosci. 16, 2226 (1996). t l A. N. Spencer, .1. Przysiezniak, J. AcostaAJrquidi, and T. A. Basarsky, Nature 340, 636 (1989). 12 N. J. Peninglon, J. S. Kelly. and A. P. Fox, Proc. R. Soc. Lond. B 248, 17l (1992),
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variation on this method, only the calcium current is pharmacologically blocked after recording an action potential in current clamp. L3In that case. the current that is needed to maintain the same action potential waveform is the calcium current plus possible calcium-activated currents. For this method to work, a representative template, good voltage control, subtraction of leak and capacitative currents, and the pharmacologic isolation of the calcium currents are needed. The last three points are not specific for this method, but are important whenever calcium currents are recorded. General techniques for recording whole-cell calcium currents have been reviewed in a previous volumeJ 4 We briefly discuss some aspects that are relevant to recording calcium currents in the calyx of Held.
Isolation of Calcium Currents Calcium currents are pharmacologically isolated by blocking sodium channels with tetrodotoxin and potassium currents with external tetraethylammonium and 3,4-diaminopyridine and internal Cs +. We use gluconate or glutamate as the major internal anion in our solution for these experiments. We have not observed a blocking effect of gluconate 15on the calcium current. Peak amplitudes are similar when chloride or methyl sulfate are used as the main anion. Furthermore, transmitter release is not reduced after dialysis of the terminal with solutions containing mixtures of gluconate and glutamate. L<~7A disadvantage of using cesium gluconate, however, is that purified cesium gluconate is not readily available. Commercially available gluconic acid solutions are bulk grade (<95%), making further purification necessary, for example, by repeated precipitation of cesium gluconate in methanol. With these internal and external solutions, an (apparent) reversal potential for the calcium currents more positive than +40 mV is obtained. Additional evidence that there is little contamination by other currents in the physiologically relevant range is the good correspondence of the charges carried by Ca ?+, as obtained with the fluorescence method (see later section), and the calcium current integrals.
Voltage Clamp Good spatial and temporal voltage clamp in the calyx of Held is not easy to obtain. The calcium channels in the calyx of Held gate very fast. Is > T. Doerr, R. Denger, and W. Trautwein, Pfliigers Archiv. 413, 599 (1989). 14 B. P. Bean, Methods Enzymol. 207, 181 (1992). l~ A. A. Velumian, L. Zhang, P. Pennefather, and P. L. Carlem Pfliigers Archiv. 433, 343 (1997). > J . G. G. Borst, F. Hclmchen, and B. Sakmann, J. Physiol. 489, 825 (1995). 17,j. G. G. Borst and B. Sakmann, Nature 383, 431 (1996). lsj. G. G. Borst and B. Sakmann, J. Physiol. 506, 143 (1998).
[20]
CAI.Cn;M INFLUX DURING AN ACTION POTENTIAL
355
If the spatial or temporal voltage clamp is not of sufficient quality, the action potential waveform will be distorted, leading to uninterpretable results. ~) The most important determinant for the quality of the spatial clamp in the calyx of Held is the length of the axon. A long axon often makes voltage clamping impossible. Nevertheless, for short pulses, like an action potential waveform, the problem of poorly clamped axonal calcium channels is much less severe than for long depolarizing voltage steps, as the calcium channels in remote areas will not be activated during short pulses. ~s Because the calyx is a rather thin structure, it is difficult to obtain stable whole-cell recordings with low access resistance. We have circumvented this problem by using two-electrode voltage clamping, in which one patch electrode injects current and the other measures voltage. This configuration makes it possible to compensate a high access resistance (e.g., 4(i) M~Q) with an increase in the voltage-clamp gain. In addition, fortunately, the membrane voltage does not have to change as fast during the action potential waveform as when tail currents are recorded. The current that is needed to force the calcium channels to undergo the same voltage change as during a real action potential consists of an active and a passive component. The active, smaller component is due to the opening of calcium channels. The passive component consists of the current that is needed to charge and discharge the cell capacitance plus the current that flows through the leak resistance of the cell: l=Cm
dVm Vm -- El~,k dt + Rm
(1)
where Cm is membrane capacitance, Vm is voltage, E~,k is the reversal potential of the leak current, and Rm is membrane resistance. The same two strategies that have been used to subtract these linear components of the membrane current signals during voltage steps can also be applied in the case of action potential waveforms. 5 An estimate for the passive currents can be obtained in the presence of a calcium channel blocker. Very stable recordings are needed in that case because the calcium currents are generally much smaller than the passive currents. The other method uses the scaled response to an action potential that is much smaller than the full action potential for subtraction (Fig. 1). The increase in noise can be minimized by averaging many responses with the small action potential before subtraction. The first derivative of the measured voltage matched the passive current well for the action potential waveform (Fig. 1B). This allows an estimate of the capacitance "seen" by the electrode during the waveform, ldeally~ this value is almost as large as the total capacitance, t~>C. M. Armstrong and W. F. Gill)', Methods Enzymol. 2117,100 (1992).
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ELECIROPHYSIOLOGY
A
B
[20]
C
~
40 mV ]
c
0.5 ms \ Ioa
0.5 ms
Fro. 1. Voltage clamping a giant presynaptic terminal with an action potential waveform. (A) Infrared differential interference conlrast video image of a calyx of Held. For twoelectrode voltage clamp, two whole-cell recordings were made. One patch electrode measured voltage and provided a feedback signal for the other electrode, which was used for current injection. [Adapted from J. G. G. Borst and B. Sakmann, Nature 383, 431 434 (1996).] (B) a: Command voltage as measured with the voltage electrode. Also shown is the action potential waveform that has bccn scaled down livefold and that is used R)r subtraction of the passive response. Ten current responses to the smaller action potentials were averaged and scaled up fivefold before subtraction, b: First derivative of the membrane voltage of the full-sized action potential and of the small action potential after scaling, c: Total current. Note the resemblance with the first derivative of the voltage, as cxpected for the passive component. The current associated with the full action potential is larger during the repolarization phase. Subtraction of the passive component gives the calcium current, shown in (C). [Adapted from F. Helmehen, J. G. G. Borst, and B. Sakmann, Biophys. J. 72, 1458 1471 (1997).] (C) Calcium current during an action potential and integral of the calcium current (_)(.~,.All data are from the same experiment. o b t a i n e d f r o m i n t e g r a t i o n o f s t e p r e s p o n s e s . In c a l y c e s w i t h o u t an a x o n , this is i n d e e d t h e case.tS A f t e r s u b t r a c t i o n o f t h e p a s s i v e c u r r e n t , t h e c a l c i u m c u r r e n t r e m a i n e d (Fig. 1C). A s m a l l o u t w a r d c u r r e n t p r e c e d e d t h e i n w a r d c u r r e n t . T h i s c u r r e n t m a y b e d u e to i m p e r f e c t v o l t a g e c l a m p , a l t h o u g h g a t i n g c u r r e n t s m a y also c o n t r i b u t e . I n t e g r a t i o n o f t h e s u b t r a c t e d c u r r e n t y i e l d s t h e t o t a l c a l c i u m influx (Fig. 1C).
Choice o f Voltage Template A difficult p r o b l e m w i t h this m e t h o d is t h e c h o i c e o f a r e p r e s e n t a t i v e v o l t a g e t e m p l a t e . I d e a l l y , an a c t i o n p o t e n t i a l is first r e c o r d e d in c u r r e n t
[20]
CALCIUM INFLUX DURING AN ACTION POTENTIAL
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clamp and played back to the same cell in voltage clamp. However, pharmacologic isolation of the calcium currents is difficult to achieve without internal potassium channel blockers, making it necessary to repatch with a different solution or to use pipette perfusion in whole-cell patch-clamp experiments. Also, many voltage-clamp amplifiers are not suitable for current clamp recordings. 2° The alternative is to select a "typical" action potential and to use this action potential as a voltage template in all subsequent experiments, as was done in Fig. 1. This may also be useful with cells in primary isolation, whose action potential shape may have dramatically changed. An action potential that was recorded in a current clamp experiment in situ may then serve as the template. ~L21 Alternatively, voltage ramps may be used, ~1° which have the advantage that they are more easily reproduced by other authors. In either case, the question of whether the voltage templat e is representative is an important one. In the calyx of Held, action potentials are relatively invariant between cells, making it easier to select a representative template. Once a suitable template has been recorded, the action potential waveform must be provided to the amplifier as a command potential without much distortion. It is important that the interval between points of the action potential waveform command is clearly less than the sample interval at which the template was recorded. Using twice the corner frequency at which the action potential was recorded as the output frequency may not be sufficient because of the gradual rolloff of RC or Bessel filters at higher frequencies, and because of the absence of any interpolation by the digital/ analog (D/A) converter. We use five times the corner frequency to be on the safe side. The software that allows us to use action potential templates is Pulse Control 4.6 (Ref. 22; http://chroma.med.miami.edu/cap/), in combination with I G O R macros (Wavemetrics, Lake Oswego, OR). The flexibility of the macro-based software makes it possible to change the waveform systematically, is as well as to perform analyses on-line. An advantage of the action potential waveform voltage-clamp method is that information about the time course of the calcium current during an action potential is obtained. Alternatively, it may be possible to obtain this information by using cell-attached patch-clamp recordings > or by using the time derivative of the fluorescence signal of a calcium indicator (see later discussion). With the action potential waveform method, time delays in the recorded currents introduced by external filters, or the filter formed by the 21,j. Magistrctti, M. Mantcgazza. E. Guatteo, and E. Wanke, Trends Ne,rosci. 19. 530 (1996). 21 W. J. Song and D. J. Surmcicr, ,l. Neurophysiol. 76, 2290 (1996). "e J. Herrington and R. J. Bookman, in "'Pulse Control V4.0: I G O R XOPs for Patch Clamp Data Acquisition and Capacitance Measurements." University of Miami, Florida. 1994. > M. Mazzanti and L. J. DeFelice, Bi~q~h),s. J. 58, 1059 (1990).
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combination of cell capacitance and access resistance, must be corrected. We have addressed this by making simultaneous current and voltage recordings from the terminal and by using the observation that the action potential in the calyx of Held can be capacitively recorded in the postsynaptic cell. ~¢~24Other methods to estimate the delay between the voltage command and the change in the membrane voltage have been discussed in Ref. 25. After correction for delays, the number of open calcium channels can be estimated at any time during the action potential, if the single-channel conductance of the calcium channel is known. Fluorometric M e a s u r e m e n t of Calcium Influx Introduction
An alternative method to quantify the calcium influx during an action potential is by using a fluorescent calcium indicator. Calcium indicators are generally used to report changes in the intracellular free calcium concentration, [Ca]~. The indicator dyes, which act as exogenous calcium buffers, will distort the time course of the calcium transients if their concentration is not sufficiently small. At very high concentrations the indicator will become the dominant intracellular calcium buffer. In this case, which is referred to as "dye overload," virtually all calcium ions that enter the cytosol are captured by the indicator. Because, in general, the fluorescence change (AF) of an indicator is proportional to the number of dye molecules that have captured a calcium ion, under overload conditions 5 F will be proportional to the total calcium current Q(,~,: 5 F = ,fl..... f lc~, dt - . { i .... Qc~,
(2)
Therefore, with this approach calcium indicators can also be used to measure calcium fluxes. 2¢~'27If the proportionality constant .~..... is known, the total calcium influx can be directly calculated from &F. This method is much simpler and requires fewer assumptions than estimating calcium fluxes from changes in the intracellular calcium concentration. 2s29 One of the advantages of the dye overload technique is that it also is applicable when ions other than Ca 2- are contributing to the currents. Indeed, this method was first used to determine the fractional contribution 24 1. D. Forsythe, .I. Physiol. 479, 381 (1994). 25 F. J. Sigworlh and J. Zhou, Methods Enzymol. 207, 746 (1992). 2, E. Neher and G. J. Augusline. J. Physiol. 450, 273 (1992). 27 E. Neher, Neuropharmacology 34, 1423 (1995). -~'~S. M. Baylor. W. K. Chandler, and M. W. Marshall, J. Physiol. 344, 625 (1983). ~'J D. W. Tank, W. G. Regehr, and K. R. Delaney, .l. Neurosci. 15, 7940 (1995).
[20]
CALCIUM INFLUX DLJRIN(] AN A c r I O N POI'ENTIAI.
359
of Ca e- to the current through ligand-gated ion channels. 27"3° 3~ We applied dye overload to measure the total calcium influx during an action potential in the calyx of Held. )-* In Fig. 2A the fluorescence image of a calyx loaded with 1 m M of the high-affinity indicator Fura-2 (Molecular Probes. Eugene, OR) is shown. At this concentration, Fura-2 overrides the endogenous calcium buffers of the terminal (see later discussion). 1~-32With excitation at 380 nm, the fluorescence emission of Fura-2 decreases after calcium binding. A single presynaptic action potential that was evoked by stimulation of the afferent nerve fiber caused a clear decrease in the total Fura-2 fluorescence of the whole terminal (A/~s~; Fig. 2B). Before AF3,s0 can be converted to Qc~,, several conditions have to be met. Normalization and calibration of the fluorescence signal are also required. These aspects arc discussed in the following sections.
Dye Overload Dye overload is reached when the indicator effectively outcompetes the endogenous calcium buffers. This suggests the use of a high-affinity calcium indicator, with a dissociation constant in the same range as the resting intracellular Ca 2+ concentration. So far only Fura-2 has been used. However, in principle, the dye overload technique is not restricted to ratiometric dyes since it requires fluorescence excitation (or collection of fluorescence emission) at a single, calcium-dependent wavelength. Therefore, other high-affinity indicators such as Calcium Green-l, Indo-1, or even E G T A in combination with a pH indicator ~-~ may also be used. How much dye is needed to outcompete the endogenous buffers? An absolute value for the concentration that is needed cannot be given because it depends on the relative calcium-buffering capacities of the indicator and of the endogenous calcium buffers. We illustrate this using the single compartment model introduced by Neher and Augustine. :~' This model describes the competition of an indicator (B) with a pool of rapid endogenous calcium buffers (S). The calcium-buffering capacity of a buffer is given by its calcium-binding ratio27: i~[CaB] _ ~c~ -
i~[Ca]~
K,t (K,, + [Ca]~) 2 [B],,
(3)
s~' R. Schncggcnburger, Z. Zhou. A. Konnerth. and E. Nehcr, Neuron 11, 133 (1993). ~/ Z. Zhou and E. Neher, Pjh'igers Archiv. 425, 511 (1993). ~ ' G. Vcligelebi, K. A. Stadcrman, M. A. Varney. M. Akong, S. D. Hess, and E. C. Johnson, Methods Enzymol. 293, [2], 1998 (this volume). ~" F. Helmchen, J. G. G. Borst, and B. Sakmann, Biw)hys. ,l. '72, 1458 (1997). '~ P. C. Pape, D. S. Jong. and W. K. Chandler, .I. Gen. Physiol. 106, 259 (1995).
360
ELECTROPHYSIOLOGY
A
C
[20]
[
0.02~
O, o o
0 0 0 ,o o
0 c,
g 0.01
I
-20
I
I
t
I
-I0 0 10 20 Amount of defocus (pro)
D I
~
AF38o
B 0 mV .......... 5 ms
I
0.2 s
0.1s
80 mV ..........
-------
m
0.2
LL
0.0 I
I
I
0
10 Ca influx Qc~ (pC)
20
FK;. 2. Fluorometric measurement of the total presynaptic calcium influx during an action potential. (A) Wide-field fluorescence image of a calyx of Held lilled with 1 mM Fura-2. The rectangle indicates the subregion from which the total fluorescence signal was collected with the CCD camera. (B) Fura-2 fluorescence decrement at 380-nm excitation ('~F~so) evoked by a single presynaptic action potential, which was elicited orthodromically (arrow). Fluorescence is expressed in bead units (BU). (C) Decrements evoked by single action potentials with the microscope defocused by different amounts. (D) Determination of .[i~,,x. Isolated presynaptic calcium currents (1<~,) were evoked by depolarizing voltage steps and Fura-2 fluorescence decrements were measured simultaneously. The slope of the plot of/k/-'~s0versus the calcium current integral yields./i,,~x, which was 15 BU nC i. [Adapted from J. G. G. Borst and B. Sakmann. Nature 383, 431-434 (1996).]
w h e r e [CAB] is t h e c o n c e n t r a t i o n of t h e b o u n d f o r m , K,t is t h e d i s s o c i a t i o n c o n s t a n t , a n d [B]T is t h e t o t a l c o n c e n t r a t i o n o f t h e b u f f e r . A c c o r d i n g to t h e m o d e l , t h e f l u o r e s c e n c e c h a n g e d i v i d e d by t h e t o t a l c a l c i u m influx ( t h e s o - c a l l e d F/Q ratio, f ) is g i v e n by AF f -
Qc.
K~ - , £ ....
(l + Ks + KB)
(4)
120]
CALCIUM INFLUX DURING AN ACTION POTENTIAl.
361
where ./' depends on the relative sizes of the endogenous calcium-binding ratio KS and the exogenous calcium-binding ratio KB. It reaches a saturating value fm,x if KB is much larger than Ks and, in this case, Eq. (4) simplifies to Eq. (2). Thus, dye overload requires KB >> KS. TO choose a dye concentration that fulfills the overload condition, it is useful to have an estimate of Ks. However, this is not strictly necessary. As a simple test one can measure the change in fluorescence that is evoked by a more or less constant calcium influx (e.g., during an action potential) in the presence of different dye concentrations. If the dye concentration is sufficiently high, AF should not change significantly when the dye concentration is doubled. On the other hand, determination of Ks is advantageous because the fraction of the incoming calcium ions that is captured by the indicator can be estimated, and the signal-to-noise ratio can be more readily optimized (see later discussion). For many neurons KS is between 50 and 150. 27 For the calyx of Held we obtained a value of about 40 bv monitoring the effect of Fura-2 on calcium transients evoked by action potentials during Fura-2 loading) 2 Therefore, a concentration of 1 m M Fura-2, which corresponds to a KB of around 2500, is sufficient for overload. According to Eq. (4), more than 98% of the calcium ions will be captured by Fura-2 if KS is 40. In neurons with a higher endogenous calcium-binding ratio, such as cerebellar Purkinje cells) a much higher concentrations of the dye would be needed. One might think that the higher the dye concentration the better. This is not true for two reasons. First, the indicator cannot catch more than 100% of all incoming calcium ions. When the dye concentration is too high, the signal-to-noise ratio will decrease, as discussed further below. Second, the fluorescence intensity in this case may no longer depend linearly on the dye concentration ([B]). Beer's law states that the fluorescence intensity F of a fluorescent layer of thickness d is proportional to 1-10 ~-dlBI where is the extinction coefficient of the dye. The linear approximation F d [B] is only valid if [B] ~ [ln(10) e. d] ~. As an example, we consider a small neuron with a diameter of 10/,m. The extinction coefficient of Fura2 is about 30.000 M ~cm L, therefore, in this case, [B] should be well below 15 mM.
Normalization and Calibration of" Fluorescence Changes The fluorescence intensity that is measured depends on the illumination intensity as well as the photon-detection efficiency. Because these parameters may change with time, intensities should be normalized to a fluorescent standard. Commonly, the fluorescence intensity of fluoresbrite beads (diam34L. Ficrro and I. Llano, J. Physiol. 496, 617 (1996).
362
ELECTROPHYSIOLO(}Y
[201
eter 4.5/zm, Polysciences, Warrington, PA) is measured on each experimental day and all intensities are normalized to this value. 2~'273° Fluorescence therefore is expressed in "bead units" (BU; Ref. 30). The intensity of the beads depends on the bandwidths of the excitation and the emission filters. Because maximal emission is at around 470 nm the dichroic mirror should separate below that wavelength. The bead intensity also depends on the solution, which therefore always should be the same. 27 We dilute the beads 1:200 in distilled water, immobilize the beads by drying a drop of this solution on a coverslip, place the coverslip in distilled water under a waterimmersion objective, and subsequently measure the intensity of five beads, each placed in the same region as the terminals. With the CCD camera some pixels could be saturated by the bright beads. This was avoided by slightly defocusing the bead for the measurements. Conversion of the fluorescence changes to total calcium current Qc~, requires the determination of the proportionality factor f ..... (in units of BU nC ~). This is achieved by measuring fluorescence changes evoked by isolated calcium currents, because calcium channels have a very high selectivity for Ca > over other ions under physiologic conditions) ~ We blocked sodium and potassium channels as described earlier, and evoked presynaptic calcium currents with depolarizing voltage steps in voltage clamp. By correlating the decrements in Fura-2 fluorescence with the calcium current integrals we obtained an estimate for.fi..... (Fig. 2D). Usually, the correlation coefficient was very high for depolarizing steps to voltages in the range of - 3 0 to +30 mV (r > 0.99), indicating good pharmacologic isolation of the calcium currents. It is noteworthy that.~ ..... depends on the spectral properties of the experimental setup since the beads and Fura-2 differ with respect to their emission spectrum. 3~ The total calcium influx Qc,, during an action potential is calculated by dividing the fluorescence change through ,/'i..... [Eq. (2)]. Fluorescence Detection
Fluorescence can be detected with a camera, a photomultiplier, or a photodiode. It should be collected with the same efficiency from all cellular compartments that are studied. A region that encloses the relevant structures can be selected as a subregion of the camera (Fig. 2A), with a diaphragm in front of the photomultiplier, or by placement of a small photodiode in the image plane of the microscope (see later discussion). For the determination o f f ..... it is also essential that fluorescence be measured from all structures that contribute to the calcium current measured under voltage ~" B. Hille, in "'Ionic C h a n n e l s of Excitablc Membranes." pp. 1-6(17. Simmer, S u n d e r l a n d , Massachusetts. 1992.
[201
CALCIUM INFLUXDURING AN ACTIONPOTKNTIAI.
363
clamp. Therefore, the calcium influx into cellular structures from which fluorescence is not collected must be considered. For example, the preterminal axon in Fig. 2A is not fully included within the region of measurement. In this case previous measurements, however, have shown that the calcium signal is very small in the axon compared to the terminal, l<' It is also important that the light emitted from structures that are not in focus be collected as well. To test this, fluorescence decrements can be measured at different focal planes. The decrements should not significantly change if the cell is defocused (Fig. 2C). Fluorescent beads may also be helpful for testing this assumption. Actually, the poor spatial resolution in the Zaxis of the wide-field microscope compared to a confocal or a two-photon microscope is an advantage for overload measurements. It may even be possible to measure the total calcium influx in neurons with extensive dendrites, using a low magnification objective with a large field of view. In that case it is important to make sure that the indicator is noi locally saturated 27 and that it outcompetes the endogenous buffers throughout the whole cell, because equilibrating remote processes of a cell with the dye may take a long time. -~(~For such measurements, .~...... would have to be determined in a different cell type under conditions that differ as little as possible from the measurements, because voltage clamping of cells with extensive dendrites is not possible. The same strategy would have to be followed for other possible applications of this method such as m e a s u r e m e n t of calcium influx through low-voltage-activated calcium channels during excitatory postsynaptic potentials, estimation of calcium current densities in dendritic segments, and m e a s u r e m e n t of relative calcium influx into subcellular c o m p a r t m e n t s compared to the whole cell. A n o t h e r approach that can be used to simplify the interpretation of the fluorescence measurements is to allow calcium influx only locally, either by local application of agonists -~7 or by exposing only the structure that is under study to physiologic [Cae+]o.3s C o m p a r i s o n of the V o l t a g e - C l a m p a n d the F l u o r e s c e n c e Method The two methods described gave a similar value of about 0.9 pC (corresponding to around 35 fCpF i ) for the total calcium influx during an action potential in the calyx of Held (23 °, 2 m M [Cae~]<>). This is remarkable since both methods rely on different assumptions. First, the voltage-clamp ~('J. Eilcrs, R. Schneggenburger, and A. Konnerlh, in "'Single-Channel Recording", 2nd Ed. (B. Sakmann and E. Nchcr, eds.), pp. 213-229. Plelmm, New York, 1995. ~: O. Garaschuk, R. Schneggenburger, C Schirra, F. Tcmpia. and A. Konnerth, ]. Physiol. 491,757 (1996). ~s G. J. Augustine. M. P. Charlton, and S. ,1. Smith..I. Ptnsiol. 367, 143 (1985).
364
ELECTROPHYSIOLOGY
[20]
method requires blocking of sodium and potassium channels, whereas the fluorometric measurements can be done in current clamp mode using physiologic external solution. Second, the same action potential waveform was used for voltage clamping the nerve terminals in all experiments. In contrast, action potentials were elicited by orthodromic stimulation in the dye overload experiments and displayed their normal variability with respect to amplitude and time course. Both methods required patch-clamp recordings with relatively low access resistance (R~,cc). For reliable dye loading of the nerve terminal, a low access resistance (-~-15 MI)) during the first 10 rain of recording is needed. 16 As soon as the terminal is loaded, increases in Race are no longer critical. In the voltage-clamp measurements the problem of increases in R .... was circumvented by using two-electrode voltage clamp. We will show later that a single electrode may also be sufficient. The main disadvantage of the overload technique compared to the action potential waveform voltage-clamp technique is that it does not provide information about the time course of the calcium influx. There have been attempts to back calculate the time course of the calcium current by taking the derivative of the fluorescence signal of a calcium indicator [compare Eq. (2)]. 27'28'39'40 However, for this method to work, fluorescence has to be detected with submillisecond time resolution, and the kinetics of the dye have to be fast enough to report the time course of the influx. Therefore, only low-affinity dyes such as MagFura-2 or Magnesium Green may be suitable. According to Eq. (3), it is very difficult for these dyes to outcompete the endogenous buffers, so that they capture only a fraction of the incoming calcium ions. In addition, dye depletion close to the channels may occur during calcium influx. Currently, it does not seem possible to simultaneously obtain quantitative measurements of both amplitude and time course of calcium influx using a fluorometric method.
Measuring Modulation of Calcium Influx With both methods, it becomes possible to study modulation of the calcium influx. To illustrate the possibilities, we show here two simple examples, the dependence of the calcium influx during an action potential in the calyx of Held on extracellular calcium concentration and on temperature (Figs. 3 and 4). A comparison of both methods shows that they give similar values for both manipulations. The signal-to-noise (S/N) ratio is better for the voltage-clamp method than for the fluorescence method, though. The coefficient of variation (standard deviation/mean) was 0.02 for the current integrals during the baseline period shown in Fig. 3B and 0.14 for the fluorescence signals shown in Fig. 3D. In principle, both methods could be 3L)B. L. Sabalini and W. G, Regehr, Nature 384, 170 (1996). 4~S. R. Sinha, L. G. Wu, and P. Saggau, Biophys..I. 72, 637 (1997).
[9,0]
365
CALCIUM INFLUX DURING AN A(TION POTENIIAL
C
A
AF380
0.005 BU 0.33 pC
2 mM [Ca2*]o-- - V 0.5 ms
2 mM
0.2s
D
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1 mM
~" 1.0
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60
F~;. 3. Dependence of the presynaptic calcium influx during an action potential on the external calcium concentration. (A) Calcium currents during action potentials at different external calcium concentrations ([Ca > ],,), as indicated, (B) Time course after break-in of the calcium current integrals during periods with different [Ca2~].. Same experiment as shown in Fig. 1. [Adapted from J. G. G. Borst and B. Sakmann. Nature 383, 431 (1996).] (C) Fluorescence decrements evoked by action potentials with different [Ca-~~1o as indicated (each trace is an average of nine sweeps). (D) Time course after break-in of the total calcium influx during periods with different [Ca "' ],, as measured from the lluorescence decrements. [Adapted from F. Helmchen, J. G. G. Borst, and B. Sakmann, Biophys. ,l. 72, 1458 (1997).]
u s e d to c o r r e l a t e t h e p r e s y n a p t i c c a l c i u m influx d u r i n g a c t i o n p o t e n t i a l s w i t h t h e a m p l i t u d e o f t h e p o s t s y n a p t i c c u r r e n t s in s i m u l t a n e o u s p r e - a n d p o s t s y n a p t i c r e c o r d i n g s . H o w e v e r , a l t h o u g h t h e f l u o r e s c e n c e m e t h o d is t e c h n i c a l l y e a s i e r to p e r f o r m , t h e i n t r o d u c t i o n o f 1 m M F u r a - 2 i n t o t h e t e r m i n a l w o u l d r e d u c e n e u r o t r a n s m i t t e r r e l e a s e significantly. >
Signal-to-Noise Considerations Voltage Clamp. B a s e l i n e n o i s e in w h o l e - c e l l e x p e r i m e n t s d e p e n d s m a i n l y on a c c e s s r e s i s t a n c e a n d m e m b r a n e c a p a c i t a n c e ) t N o i s e d u e to 4~ R. A. Levis and J. L. Rae. Methods E;;zymo/. 207, 14 (1992).
366
ELECTROPHYSIO1.OGY
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[9.0]
B Room temn
1.0
6
.=_=
Phw¢it~lnnie~l ~mp
1.0
0 0.5
==
o
0.5
o
0.0
,
0
1 [Ca2+]o (mM)
,
2
0.0
VC
F
VC
F
FK;. 4. Comparison of voltage-clamp and fluorescence measurements of presynaptic calcium influx in the calyx of Held. (A) Dependence of total calcium influx during an action potential on the external calcium concentration [Ca2÷],,. The voltage-clamp method (filled circles) and the fluorescence method (open circles) gave similar results. [Adapted from F. Helmchen, J. G. G. Borst, and B. Sakmann, Biophys. J. 72, 1458 (1997), and from J. G. G. Borst and B. Sakmann, Nature 383, 431 (1996).] (B) Temperature dependence of the total calcium influx with 2 mM [Ca2+]o. Again, the voltage-clamp method (VC) and the fluorescence method (F) gave similar results.
calcium currents will depend, in addition to recording bandwidth, also on open probability, total number of functional calcium channels, and singlechannel current. 42 The large calcium currents in the terminal make it possible to obtain a good S / N ratio (defined as peak amplitude divided by standard deviation of the baseline noise). Even though the noise with the two-electrode voltage clamp is clearly higher than for whole-cell patchclamp recordings, S / N ratios of >20 (at 5 kHz) are easily obtained. A further reduction in baseline noise would permit to do nonstationary noise analysis of the calcium currents during action potentials or to study the contribution of the variance of the calcium currents to the variance of the synaptic currents. Fluorescence. Fluorescence changes evoked by action potentials are relatively small, for example, the signal shown in Fig. 2B corresponds to a relative fluorescence change of only 0.7%. Therefore, the fluorescence noise must be reduced. Noise sources include fluctuations in the output of the light source, vibrational noise, dark noise of the photodetector, and photon 42 S. H. Heinemann and F. Conti, Methods Enz.y'mol. 207, 131 (1992).
[20]
367
CAI_CIIJM INFLUX DURING AN ACTION POTENTIAL
B
A
2O
o~ 1 0 0 -
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6
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2000
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Ca-binding
ratio KB
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2000 Ca-binding ratio ~(B
FI(;. 5. Signal-to-noisc ratio of fluorescence changes cw)ked by action potentials. (A) The fraction of calcium ions that bind to Fura-2 is plotted as a function of the Fura-2 calciumbinding ratio Kl~. Around half of the calcium ions bind to Fura-2 when t% equals the endogenous calcium-binding ratio KS, which was assumed to be 40. One mM Fura-2 corresponds to a calcium-binding ratio of about 2500. (B) Signal-to-noise ratio of action potential evoked Fura 2 fluorescence decrements versus gl~. The S/N ratio is defined as AF divided by the standard deviation of the prestimulus fluorescence trace. Data points were obtaincd at Fura-2 concentra tions of ~20 IxM, 50 IxM, 100 ffM, and 1 mM. respectively. A curve according to Eq. (6) was scaled to lit the three first points (C 22{I, KS = 40). [Adapted from F. Helmcben. ,1. G. G. Borsl. and B. Sakmann, Bioph3s. ,I. 72, 1458 1470 (1997),]
shot noise. 43 Because the signals are so small, it may be important to lind the dye concentration that yields the highest S/N ratio. We define the S/N ratio as the fluorescence change k F divided by the standard deviation of the baseline fluorescence oT. The percentage of calcium ions captured by the indicator is given by f/f, ..... [Eq. (4)]. It is shown in Fig. 5A as a function of the exogenous calcium-binding ratio KB. The endogenous calcium-binding ratio Ks was assumed to be 4 0 . 32 in the best case of a shotnoise-limited optical recording the variance of the fluorescence signal is proportional to the number of measured photons. However, in brain slices the autofluorescence of endogenous fluorophores > results in a relatively high background fluorescence. For example, at our setup the background ltuorescence is equivalent to the fluorescence of a terminal loaded with 100 ffM Fura-2, corresponding to K~ ~ 220. Assuming that background and dye fluorescence are independent, the variance of the total fluorescence is proportional to the sum of the background fluorescence and the indicator fluorescence F, where F is proportional to [B],r, which for small perturbations of [Ca]i from the resting level itself is proportional to Kl~ [Eq. (3)]. Therefore the variance is proportional to: ~ (C + ~t~)
(5)
4~ j._y. Wu and L. B. Cohen, in "Fluorescent and Lumincsccnt Probes for Biological Activity" (W. T. Mason. ed.), pp. 389 4()4. Academic Press, London, 1993.
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where C is a constant representing the binding ratio that the indicator would have if its fluorescence were equal to the background fluorescence. Neglecting other noise sources, it follows that: AF KB S/N ratio - - - oc o-v (1 + K s + K B ) ~ / C + K B
(6)
As seen in Fig. 5B, the actual S/N ratios that we obtained with the CCD camera using different concentrations of Fura-2 are reasonably well described by this relationship. For high dye concentrations, KB > KS, the S/N ratio decreases proportional to (C + KB) ~/2 [Eq. (6)]. This decrease occurs because &F saturates (the indicator cannot bind more calcium ions than enter the cell) but the noise still increases with increasing dye concentrations. To obtain the exogenous calcium-binding ratio K0 for which the S/N ratio is maximal, Eq. (6) can be differentiated with respect to KB, yielding: (1 +Ks)
1+
+8
(7)
Thus, if background fluorescence can be neglected (C - 0), the highest S/N ratio is obtained if cells are loaded with a dye concentration that is equivalent to KB -- K0 -- 1 + KS. In this situation, which has been referred to as "balanced loading, ''44 only 50% of the calcium ions are captured by the indicator. With higher background fluorescence, more dye is needed for the best S/N ratio; for example, with a C equivalent to Ks, the optimal dye concentration is already twice as large. By definition, KB >> Ks during overload, so unless C is much larger than Ks, the S/N ratio will be clearly suboptimal. To increase the S/N ratio one may choose to work with a lower dye concentration so that only a fraction of the calcium ions is captured and the total calcium influx is calculated from Eq. (4) using an estimate of Ks. However, Ks may vary between cells, leading to uncertainties in this calculation.
Simple Photodetector Another possibility for increasing the S/N ratio of the fluorescence measurements is to use a photodetector with a high quantum efficiency. Because spatial resolution is not needed, an alternative to a CCD camera is a photodiode. Advantages are their low cost, ease of operation and high bandwidth. C o m p a r e d to photomultipliers, photodiodes have a larger dark current but this is not critical in our case because of the high dye concentrations used. Photodiodes have been widely used to measure calcium signals 44 Z. Z h o u and E. Neher. J. Physiol. 469, 245 (1993).
[20]
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CAI~CIUM INFLUX DURING AN ACTION POTENI'IA[,
power supply preamplifiel image plane of microscope
PD1 u PD2
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microscopeadapter ~ J Fl¢;. 6. A simple photodetector to measure calcium influx during an action potential. (Left) Schematic diagram of the photodiode system. The metal box contains the preamplilicr. Two silicon photodiodes ($2386-18K, H a m a m a t s u l'hotonics, Japan) are located in the image plane of thc microscope's camera output port. Active area of the photodiodes is 1.1 × 1.1 mm, corresponding to 27.5 × 27.5 p,m in the focal plane of a Zeiss 40× water immersion objective. The q u a n t u m efficiency of the photodiode used is 84% at 560 nm. (Right) Diagram of the photodiode preamplifier, consisting of an O P A l ll (Burr-Brown, Tucson, A Z ) current-tow)ltage converter and a Max4fl0 (Maxim Inlcgrated Products, Sunnyvale, CA) differential amplilier that provides a gain of 21. Feedback resistor is 10 ( ; ~ . Stray capacitance is around 0.5 pF, giving a corner lYcquency of around 300 Hz, as measured from the rise time of the photodiode signal to an L E D light source.
from pools of labeled terminals. 45'4~We have constructed a simple photodiode to measure calcium signals from small cell compartments such as the calyx of Held (Fig. 6). Light is collected by the photodiode from a region of similar size as the subregion of the camera shown in Fig. 2A. Simultaneous measurement of a background region is possible using a second neighboring photodiode, although this is not necessary when total influx is measured. With this simple device fluorescence decrements evoked by single action potentials can be resolved using 1 mM Fura-2 for overload (Fig. 7). Simultaneous Voltage-Clamp and Fluorescence Measurements To illustrate the use of this photodiode we have simultaneously measured calcium influx during an action potential with both methods (Fig. 7). A terminal was voltage clamped using an action potential waveform, as shown in Fig. 1, except continuous whole-cell voltage clamp with a single electrode was used and fluorescence was monitored at the same lime with the photodiode. To be able to voltage clamp the terminals with a single electrode, it was important to select terminals with short axons and to keep 45 L.-G. W u and P. Saggau, J. Neurosci. 14, 645 (1994). 4~, W. G. Regehr and D. W. Tank, N e u r o n 7, 451 (1991).
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ELECrROPHYSIOLOGY
I201
A
lnA I B
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C
0.5 pC
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50 ms
Fu;. 7. Simultaneous recording of calcium current during an action potential using the voltage-clamp and fluorescence methods. A terminal was loaded wilh Fura-2 and w)ltage clamped with an action potential waveform to compare the calcium influx oblained with both methods. Determination of./i ..... could be done in this case within the same experiment by construction of a current-w)ltage relation, as shown in Fig. 2D. Conlmuous single electrode voltage clamp was used. The outputs of the patch-clamp amplifier and the photodiode amplifier were simultaneously digitized with a 16-bit A/D converter (ITC-16 Instrutech, Great Neck, NY) at 50 kHz: thc photodiode voltages were decimated to 1 kHz to reduce memory require ments. Access resistance was 8 Mr!, compensated to 90%. Total capacitance was 33 pF. Axon length was around 100/*m. (A) Calcium currenis. Filtered at 5 kHz. (B) Integral of response shown in part (A). ((7) Fluorescence measurements. Photodiode signal was digitally filtered to 20 Hz. Calibration bar is shown in pC, ().5 pC corresponded to 0.0056 BU and 73 fA photodiode current. Responses are the average of 2().
the access resistance after electronic compensation below 2 MtL Both m e t h o d s g a v e s i m i l a r v a l u e s f o r t h e c a l c i u m influx. T h e S / N r a t i o w a s a g a i n better for the voltage-clamp method than for the fluorescence method.
Conclusions We have compared two methods to detect the influx of calcium ions during single action potentials and found that they gave similar results in a g i a n t s y n a p t i c t e r m i n a l o f t h e r a t b r a i n s t e m . B o t h m e t h o d s h a v e advantageous features. The main advantages of the voltage-clamp method
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WHOLE (TELL AND SINGLE CHANNEL CURRENT MEASUREMENT
371
are that it provides information about the time course of the calcium influx, that it can be used in the presence of physiologic intracellular calcium buffer concentrations, that a systematic manipulation of the action potential waveform is possible, and that it gives a better S/N ratio than the dye overload technique. The main advantages of the fluorometric method are that it is relatively simple, that measurements arc done in current clamp in physiological external solutions, and that it can in principle be used to quantify fluxes in small subcellular compartments.
Acknowledgments Wc thank Dr. B. Sakmann for continuous support, R. Rodc l and K. Schmidt for o:mstruction of the pholodiode amplilier and Dr. T. D. Parsons for comments on an earlier version of this manuscript. J. G. (]. B. was supported by the E. U. (TMR program).
[21] C o m b i n e d W h o l e - C e l l a n d S i n g l e - C h a n n e l C u r r e n t M e a s u r e m e n t w i t h Q u a n t i t a t i v e C a 2+ I n j e c t i o n o r F u r a - 2 M e a s u r e m e n t o f C a 2-
By L.
D O N A L D P A R T R I D ( i E , H A N N S ULRI(TH Z E I L H O F E R ,
and
D I E T E R SWANDUL1.A
Introduction Intracellular free Ca 2- is an important second messenger in most cell types and cytoplasmic Ca 2+ concentration, [CaX~]i, is tightly controlled by cytoplasmic buffering and regulation of influx and efflux pathways. In excitable cells, cytoplasmic Ca 2+ couples electrical events with a broad range of effector functions. Voltage-dependent calcium channels provide a direct means for this coupling, while postsynaptic ligand-gated channels provide additional regulated pathways for Ca 2- entry. In addition to its welldescribed roles in excitation-contraction coupling and excitation-secretion coupling, cytoplasmic Ca 2~ is responsible for excitation-gating coupling for several important classes of ion channels. The broad class of CaZ+-regulated channels includes Ca2--activated potassium, nonselective (CAN) and chloride channels, and Ca2+-inactivated calcium channels. In addition, these and other channels can be modulated by metabolic processes that depend o n C a 2 +.
Established techniques are available to measure membrane currents in cells voltage clamped with either intracellular microelectrodes or with patch
N'II-rtI()DS IN ENZYMOLOGY, VOL 293
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