Simultaneous Measurement of Evoked Release and [Ca2+]i in a Crayfish Release Bouton Reveals High Affinity of Release to Ca2+

R. Ravin, H. Parnas, M. E. Spira, N. Volfovsky, and I. Parnas

The Otto Loewi Minerva Center for Cellular and Molecular Neurobiology, Department of Neurobiology, The Hebrew University, Jerusalem 91904, Israel


    ABSTRACT
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Abstract
Introduction
Methods
Results
Discussion
Appendix
References

Ravin, R., H. Parnas, M. E. Spira, N. Volfovsky, and I. Parnas. Simultaneous measurement of evoked release and [Ca2+]i in a crayfish release bouton reveals high affinity of release to Ca2+. The opener neuromuscular junction of crayfish was used to determine the affinity of the putative Ca2+ receptor(s) responsible for evoked release. Evoked, asynchronous release, and steady-state intracellular Ca2+ concentration, [Ca2+]ss, were measured concomitantly in single release boutons. It was found that, as expected, asynchronous release is highly correlated with [Ca2+]ss. Surprisingly, evoked release was also found to be highly correlated with [Ca2+]ss. The quantal content (m) and the rate of asynchronous release (S) showed sigmoidal dependence on [Ca2+]ss. The slope log m/log [Ca2+]ss varied between 1.6 and 3.3; the higher slope observed at the lower [Ca2+]o. The slope log S/log [Ca2+]ss varied between 3 and 4 and was independent of [Ca2+]o. These results are consistent with the assumption that evoked release is controlled by the sum of [Ca2+]ss and the local elevation of Ca2+ concentration near the release sites resulting from Ca2+ influx through voltage-gated Ca2+ channels (Y). On the basis of the above, we were able to estimate Y. We found Y to be significantly <10 µM even for [Ca2+]o = 13.5 mM. The dissociation constant (Kd) of the Ca2+ receptor(s) associated with evoked release was calculated to be in the range of 4-5 µM. This value of Kd is similar to that found previously for asynchronous release.


    INTRODUCTION
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Abstract
Introduction
Methods
Results
Discussion
Appendix
References

The dependence of release of neurotransmitter from nerve terminals on Ca2+ is well established (Augustine et al. 1987; Delaney and Zucker 1990; Dodge and Rahamimoff 1967; Heidelberger et al. 1994; Katz 1969; Llinás et al. 1981; Parnas et al. 1990; Zucker et al. 1991). It has been amply documented that on the arrival of an action potential to the nerve terminal, voltage-gated Ca2+ channels open, Ca2+ flows in, and the intracellular Ca2+ concentration ([Ca2+]i) rises. According to the Ca-voltage hypothesis (review Parnas and Parnas 1994), this rise in intracellular Ca2+ is necessary but insufficient to trigger release; membrane depolarization per se is needed to evoke release of neurotransmitter. In contrast, advocates of the widely acknowledged Ca2+ hypothesis (reviews in Parnas and Parnas 1994; Zucker 1996) suggest that it is the transient elevation of [Ca2+]i, which triggers the onset and termination of neurotransmitter release. It had been suggested that high Ca2+ concentration (~200 µM) is required to trigger release and that thus the putative Ca2+ receptor molecule associated with evoked release has a low affinity for Ca2+ (review Zucker 1996). However, in the absence of direct means to measure the intracellular Ca2+ concentration ([Ca2+]i) in small domains near the release sites, the range of Ca2+ concentration necessary to evoke release under normal physiological conditions (depolarization) remains unknown.

Several experimental attempts have been made to evaluate this concentration in terminals of fast synapses. With the use of a low-affinity Ca2+ indicator, aequorin, it was shown that following a high-frequency train of stimuli, [Ca2+]i reached levels as high as 300 µM for periods of 800 µs in restricted submembraneous domains (Llinás et al. 1992, 1995). These measurements demonstrated that high, localized Ca2+ domains were formed after stimulation. It was not shown, however, that these high concentrations are indeed required for release to occur.

In the absence of a method for measuring [Ca2+]i near the release sites, researchers resolved to calculate this value for small domains near the Ca2+ channel. These calculations resulted in values ranging between 5 and 200 µM. Fogelson and Zucker (1985), Simon and Llinás (1985), Smith and Augustine (1988), Yamada and Zucker (1992), and Naraghi and Neher (1997) calculated that the calcium concentration in the channel mouth or in very close proximity to the channel is as high as 100-200 µM. However, near the release site [Ca2+]i may be lower, depending on the assumed distance of a release site from the channel and the characteristics of the buffers included in the calculations (Naraghi and Neher 1997). Thus, for example, Aharon et al. (1994) calculated that for a brief depolarization, [Ca2+]i is elevated to only 5-10 µM at a distance of 50 nm from the channel mouth.

In view of the inability to directly measure the [Ca2+]i associated with evoked release, and the wide range of values obtained by the theoretical evaluations, we designed a novel approach for estimating the Ca2+ concentration that is actually involved in evoked release.

Although both evoked and asynchronous release depend on the Ca2+ concentration near release sites, asynchronous release is controlled by the steady-state average intracellular Ca2+ concentration ([Ca2+]ss) (Miledi 1973; Rahamimoff et al. 1978; Ravin et al. 1997). Evoked release is controlled by the Ca2+ concentration near the release sites and thus depends on both [Ca2+]ss and on the change in the local Ca2+ concentrations at the release site (termed Y). This transient increase (Y) in calcium concentration depends on the entry of Ca2+ through the voltage-activated Ca2+ channels, the Ca2+ buffers, and the distance between the channels and the release sites.

The Hill coefficient attributed to the dependence of evoked release on intracellular Ca2+ concentrations near the release sites inferred from the dependence of release on extracellular (Dodge and Rahamimoff 1967; Parnas et al. 1982) or on intracellular (Heidelberger et al. 1994; Lando and Zucker 1994) calcium concentration is reported to be 4. If evoked release is measured as a function of only [Ca2+]ss (which is lower than the true Ca2+ concentration associated with evoked release, [Ca2+]ss + Y), the genuine Hill coefficient of 4 will not be obtained. Rather, an "apparent Hill coefficient" smaller than the genuine one (see below in Experimental-theoretical procedure to extract Y from the dependence of m on [Ca2+]ss) will be measured. In the present study we combined experimental data and a theoretical approach to evaluate Y from the deviation of the apparent Hill coefficient from its true value. We found that Y is <10 µM and that the putative Ca2+ receptor for evoked release exhibits high affinity for Ca2+.


    METHODS
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Abstract
Introduction
Methods
Results
Discussion
Appendix
References

Experiments were performed on the opener muscle of the first walking leg (removed by autotomy) of the crayfish Procambarus clarkii. Animals, 3-4 cm long, were purchased from Atchafalaya Biological Supply (Raceland, LA). The preparation was constantly superfused (Gilson minipulse 3, Villiers le bel, France) with Van Harreveld (VH) solution containing (in mM) 220 NaCl, 5.4 KCl, 13.5 CaCl2 (unless otherwise stated), 2.5 MgCl2, and 10 Tris buffer, pH adjusted to 7.4 by adding NaOH. After intra-axonal injection of fura-2, tetrodotoxin (TTX; 5·10-7 M) was added to prevent sodium action potentials. The bath temperature was kept at 11 ± 0.5°C.

For Ca2+ imaging and for recording single quanta events, we used the techniques and calibration methods described by Ravin et al. (1997).

Chemicals

Fura-2 was purchased from Molecular Probes (Eugene, OR). TTX was purchased from Sigma (St. Louis, MO) and RBI (Natick, MA).


    RESULTS
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Abstract
Introduction
Methods
Results
Discussion
Appendix
References

Dependence of evoked and asynchronous release on steady-state Ca2+ concentration

To study the relationship between Ca2+ concentration near the release sites and release, [Ca2+]i was elevated to different levels by trains of depolarizing pulses at different frequencies. The experimental procedure was as follows. Fura-2 was injected into the axon, and then a macropatch electrode was placed over a single bouton under visual control. The electrode was used to depolarize the terminal, by passing trains of constant negative current pulses, and also to monitor quantal events (Dudel 1981) (Fig. 1). For details concerning controls made to ensure that the fura-2 response did not saturate under our experimental conditions and to ensure that the macropatch electrode did not distort the ratio imaging of [Ca2+]ss, see Ravin et al. (1997).



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Fig. 1. Concomitant measurement of [Ca2+]i, evoked release and asynchronous release in a single release bouton. A: [Ca2+]i was raised by electrical stimulation (0.6 ms, -0.7 µA, 700 pulses) at frequencies of 40 Hz (- - - -), 60 Hz (- - -), 80 Hz (- - -), and 100 Hz (----). Small arrow, beginning of stimulation. Lines shown were filtered with a Gaussian low-pass filter using Fourier transform. The plateau level of [Ca2+]i (straight line lowest curve) is defined as [Ca2+]ss (arrow). B: samples of traces from the same experiment (top right). Asterisks denote single quanta events. C: m measured at the same frequencies of stimulation as in A. D: rate of asynchronous release measured 5 ms after each pulse. Frequency of stimulation 60, 80, and 100 Hz. Lines shown in C and D were obtained by using a moving average procedure; 2 points in C and 3 points in D.

For the reader's convenience we present in Fig. 1 the results from Ravin et al. (1997), where the rise in [Ca2+]i was achieved by trains of pulses (0.6 ms, -0.7 µA) at various frequencies of stimulation of 40, 60, 80, and 100 Hz. Figure 1A shows that, at each stimulation frequency, [Ca2+]i reached a plateau (steady-state). The plateaus of [Ca2+]i (denoted [Ca2+]ss) at the frequencies of 40, 60, 80, and 100 Hz were 1.7, 2.4, 2.7, and 3.3 µM, respectively.

Along with monitoring [Ca2+]ss, both evoked release (quantal content, m) and the rate of asynchronous release, S, were measured. As in Ravin et al. (1997), m was measured during the first 5 ms following the depolarizing pulse, and S was measured thereafter. Figure 1C shows that m and [Ca2+]i changed in a similar way (compare Fig. 1, A with C). Figure 1D shows the same behavior for S. At 40 Hz the increase in the rate of asynchronous release was too low to be of significance and is not shown.

Several points shown by the experiments of Fig. 1 should be noted. 1) Small changes in [Ca2+]ss produced significant changes in m. 2) Evoked and asynchronous release share similar qualitative dependence on [Ca2+]ss. 3) These findings indicate that evoked release is determined by the sum of [Ca2+]ss and Y and that they are of the same order of magnitude. Had Y been much larger than [Ca2+]ss, evoked release would show no dependence on [Ca2+]ss (see DISCUSSION for other possible indirect effects of [Ca2+]ss). These experimental results provide the necessary justification for the procedure described below.

Experimental-theoretical procedure to extract Y from the dependence of m on [Ca2+]ss

The assumed relationship between m or S and [Ca2+]i, near the release sites, is described in Eqs. 1 and 2, respectively. Thus
<IT>m</IT><IT>=</IT><FR><NU><IT><A><AC>m</AC><AC>&cjs1171;</AC></A></IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>n</IT><SUB><IT>m</IT></SUB></SUP><SUB><IT>i</IT></SUB></NU><DE>(<IT>K<SUB>m</SUB></IT><IT>+</IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>i</IT></SUB>)<SUP><IT>n</IT><SUB><IT>m</IT></SUB></SUP></DE></FR> (1a)
Based on the results of Fig. 1, we assume that for evoked release[Ca2+]i is given by
[Ca<SUP>2+</SUP>]<SUB>i</SUB>=<IT>Y</IT><IT>+</IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB> (1b)
In Eq. 1a, <A><AC>m</AC><AC>&cjs1171;</AC></A> stands for the maximal quantal content at high [Ca2+]i, [Ca2+]ss is the measured steady-state intracellular Ca2+ concentration, nm is the genuine Hill coefficient, Km is the analogue of the half saturation constant in the case of Hill coefficient 1, and Y is defined as the increase in Ca2+ concentration above the resting level [Ca2+]ss near the release site. Y is produced by those Ca2+ ions that enter through the voltage-activated Ca2+ channels and reach the release site before or at the time release takes place. Equation 1a is based on the relationship between m and extracellular Ca2+ concentration suggested by Dodge and Rahamimoff (1967) and on the extension of that relationship to depend on intracellular Ca2+ concentration (Parnas and Segel 1981).

The dependence of S on [Ca2+]i is analogous
<IT>S</IT><IT>=</IT><FR><NU><IT><A><AC>S</AC><AC>&cjs1171;</AC></A></IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>n</IT><SUB><IT>s</IT></SUB></SUP><SUB><IT>i</IT></SUB></NU><DE>(<IT>K<SUB>s</SUB></IT><IT>+</IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>i</IT></SUB>)<SUP><IT>n</IT><SUB><IT>s</IT></SUB></SUP></DE></FR> (2a)
where [Ca2+]i for asynchronous release is given by
[Ca<SUP>2+</SUP>]<SUB>i</SUB>=[Ca<SUP>2+</SUP>]<SUB>ss</SUB> (2b)
<A><AC>S</AC><AC>&cjs1171;</AC></A>, Ks, and ns are as in Eq. 1a, but for asynchronous release. The equality in Eq. 2b for asynchronous release was confirmed by Ravin et al. (1997).

Following convention, the genuine Hill coefficient for evoked release, nm, can be obtained from the maximal slope log m/log [Ca2+]i when [Ca2+]i << Km. Under such conditions Eq. 1a becomes
<IT>m</IT><SUB>([<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>i</IT></SUB><IT>≪</IT><IT>K<SUB>m</SUB></IT>)</SUB><IT>=</IT><FR><NU><IT><A><AC>m</AC><AC>&cjs1171;</AC></A></IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>n</IT><SUB><IT>m</IT></SUB></SUP><SUB><IT>i</IT></SUB></NU><DE><IT>K</IT><SUP><IT>n</IT><SUB><IT>m</IT></SUB></SUP><SUB><IT>m</IT></SUB></DE></FR> (3)
and
log <IT>m</IT><SUB>([<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>i</IT></SUB><IT>≪</IT><IT>K<SUB>m</SUB></IT>)</SUB><IT>=log </IT><FR><NU><IT><A><AC>m</AC><AC>&cjs1171;</AC></A></IT></NU><DE><IT>K</IT><SUP><IT>n</IT><SUB><IT>m</IT></SUB></SUP><SUB><IT>m</IT></SUB></DE></FR><IT>+</IT><IT>n<SUB>m</SUB></IT><IT> log </IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>i</IT></SUB> (4)
and the slope of Eq. 4, which is also the maximal slope, is given by
<FR><NU>∂ log <IT>m</IT></NU><DE><IT>∂ log </IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>i</IT><SUB>([<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>i</IT></SUB><IT>≪</IT><IT>K<SUB>m</SUB></IT>)</SUB></SUB></DE></FR><IT>=</IT><IT>n<SUB>m</SUB></IT> (5)
Equation 5 shows that had m been measured as a function of [Ca2+]i, the maximal slope log m/log [Ca2+]i ([Ca2+]i << Km) would equal the genuine Hill coefficient, nm. However, in our experiments, m is measured as a function of only [Ca2+]ss and not as a function of [Ca2+]i (Y + [Ca2+]ss). Hence Eq. 5 must be modified
<FR><NU>∂ log <IT>m</IT></NU><DE><IT>∂ log </IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT><SUB>([<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB><IT>+</IT><IT>Y</IT>)<IT>≪</IT><IT>K</IT><SUB><IT>m</IT></SUB></SUB></SUB></DE></FR><IT>=</IT><IT>n</IT><SUB><IT>app</IT></SUB> (6)
where napp denotes the observed "apparent maximal slope." Solving Eq. 6 for napp yields
<IT>n</IT><SUB><IT>app</IT></SUB><IT>=</IT><FR><NU>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB><IT>·</IT><IT>n<SUB>m</SUB></IT></NU><DE><IT>Y</IT><IT>+</IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB></DE></FR> (6.1)
Examination of Eq. 6.1 immediately shows that napp < nm for Y > 0. For the extreme case where Y >> [Ca2+]ss, m will not depend on [Ca2+]ss and napp will approach zero. For the case where Y approximates [Ca2+]ss, napp < nm and m strongly depends on [Ca2+]ss; it increases as [Ca2+]ss rises (as seen in Fig. 1). Finally, when Y << [Ca2+]ss, napp = nm, as for the case of asynchronous release where Y = 0.

Figure 2 compares the dependencies of S and of m on [Ca2+]ss. The corresponding double logarithmic plots for asynchronous and evoked release are shown in Fig. 2B. As expected (Eq. 6 and foregoing discussion), for the same measured range of low [Ca2+]ss the slope log S/log [Ca2+]ss (3.5) is higher than the slope log m/log [Ca2+]ss (1.1). Furthermore, the slope of ~1 for evoked release at high [Ca2+]o (13.5 mM) suggests that Y is in the range of the measured [Ca2+]ss.



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Fig. 2. Dependence of m and S on [Ca2+]ss. A: [Ca2+]ss was raised by stimulation at frequencies of 20, 40, 60, 80, and 100 Hz (0.6 ms, -0.6 µA, 700 pulses). , m; black-triangle, S. B: double logarithmic plots of the data of A. Slope of 1.1 for evoked release and 3.5 for asynchronous release.

Conducting 12 experiments of the type shown in Fig. 2, we found that the average napp for evoked release at [Ca2+]o = 13.5 mM was 1.6 ± 0.4. For comparison we note that Ravin et al. (1997) found the average slope for asynchronous release to be 3.3 ± 0.84 (n = 22).

As mentioned in the INTRODUCTION, the true Hill coefficient for evoked release is considered to be 4 (Dodge and Rahamimoff 1967, in the frog; Parnas et al. 1982; Lando and Zucker 1994, in the crayfish; Heidelberger et al. 1994, in retinal bipolar cells). Therefore the smaller than four apparent slope napp obtained for evoked release, when measured as a function of [Ca2+]ss, may be used to extract Y.

Equation 6.1 for napp, the source equation for evaluating Y, describes partial  log [Ca2+]ss for any particular value of [Ca2+]ss. In principle, Y may be obtained by simple inversion of Eq. 6.1, i.e.
<IT>Y</IT><IT>=</IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB><FENCE><FR><NU><IT>n<SUB>m</SUB></IT></NU><DE><IT>n</IT><SUB><IT>app</IT></SUB></DE></FR><IT>−1</IT></FENCE> (6.1a)
However, experimentally only the average of napp, <OVL><IT>n</IT><SUB>app</SUB></OVL>, over a range of [Ca2+]ss is measured. Thus we actually obtain Y(<OVL><IT>n</IT><SUB>app</SUB></OVL>) experimentally. Therefore the procedure for estimating Y(<OVL><IT>n</IT><SUB>app</SUB></OVL>) from the experimental data consists of two steps. First, Eq. 6.1 is averaged over the experimental range of [Ca2+]ss, and then Y(<OVL><IT>n</IT><SUB>app</SUB></OVL>) is solved for using the experimental value of <OVL><IT>n</IT><SUB>app</SUB></OVL>. Avergaing Eq. 6.1, we obtain (see APPENDIX for derivations and definitions)
<OVL><IT>n</IT><SUB><IT>app</IT></SUB></OVL><IT>=</IT><IT>n<SUB>m</SUB></IT><IT>−</IT><FR><NU><IT>n<SUB>m</SUB>Y</IT></NU><DE><IT>&Dgr;</IT>[<IT>Ca</IT><SUB><IT>ss</IT></SUB>]</DE></FR><IT> ln </IT><FENCE><FR><NU>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>max</IT></SUP><SUB><IT>ss</IT></SUB><IT>+</IT><IT>Y</IT></NU><DE>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>min</IT></SUP><SUB><IT>ss</IT></SUB><IT>+</IT><IT>Y</IT></DE></FR></FENCE> (6.2)
Y(<OVL><IT>n</IT><SUB>app</SUB></OVL>) can be evaluated numerically from Eq. 6.2. However, the results of Fig. 2 indicate that a simpler expression for Y(<OVL><IT>n</IT><SUB>app</SUB></OVL>) can be obtained.

Figure 2 reveals that for any [Ca2+]ss within the measured range of [Ca2+]ss, napp is very well approximated by its average value, <OVL><IT>n</IT><SUB>app</SUB></OVL>.

Thus, extracting Y from Eq. 6.1 and substituting napp = <OVL><IT>n</IT><SUB>app</SUB></OVL>, we obtain
<IT>Y</IT><IT>=</IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB><FENCE><FR><NU><IT>n<SUB>m</SUB></IT></NU><DE><OVL><IT>n</IT><SUB><IT>app</IT></SUB></OVL></DE></FR><IT>−1</IT></FENCE> (6.3)
Y in Eq. 6.3 is still defined for any specific [Ca2+]ss, but averaging this expression over the experimental range of [Ca2+]ss yields Y(<OVL><IT>n</IT><SUB>app</SUB></OVL>)
<IT>Y</IT>(<OVL><IT>n</IT><SUB><IT>app</IT></SUB></OVL>)<IT>=</IT><OVL>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB></OVL><FENCE><FR><NU><IT>n<SUB>m</SUB></IT></NU><DE><IT>n</IT><SUB><OVL><IT>app</IT></OVL></SUB></DE></FR><IT>−1</IT></FENCE> (6.4)
where [Ca2+]ss is the average concentration in the range used experimentally to measure napp.

For simplicity, we will use in the following napp instead of <OVL><IT>n</IT><SUB>app</SUB></OVL> and Y instead of Y(<OVL><IT>n</IT><SUB>app</SUB></OVL>).

Taking the data of Fig. 2 and evaluating Y according to Eq. 6.4, we find that Y = 3.8 µM. We repeated such evaluations in 12 experiments and found the average Y to be 2.73 ± 1.2 µM.

Y can be evaluated also in a less formal and a more intuitive way. Equation 4, where [Ca2+]i is substituted by Y + [Ca2+]ss (Eq. 1b), shows that Y is the exact [Ca2+] (constant for different [Ca2+]ss in each experiment), which must be added to the various levels of [Ca2+]ss to obtain a slope of 4 in the double logarithmic plots of log m/log [Ca2+]ss. Evaluating Y from the data of Fig. 2 in this way yields Y = 3.4 µM, a value that is rather similar to the one obtained by solving Eq. 6.4 (3.8 µM). The average Y (12 experiments) that was needed to bring each individual slope (log m/log [Ca2+]ss) to four was 2.43 ± 1 µM, a value similar to the average Y obtained by solving Eq. 6.4 (2.73 ± 1.2 µM).

Dependence of Y on [Ca2+]o

Entry of Ca2+ during a pulse depends on the extracellular concentration of Ca2+. In most theoretical models, the change in intracellular Ca2+ concentration below the Ca2+ channel pore and in its vicinity does not take changes in extracellular Ca2+ concentration into account (Fogelson and Zucker 1985; Simon and Llinás 1985; Yamada and Zucker 1992). Aharon et al. (1994, Fig. 6) calculated that the ratio between two levels of intracellular Ca2+ obtained 50 nm away from the channel following a brief (1 ms) pulse to 0 mV will correlate with the ratio of the corresponding [Ca2+]o.

Therefore it is expected that the ratio between Y obtained at 13.5 mM [Ca2+]o to that obtained at 3 mM [Ca2+]o should be about 4. Figure 3 shows that this was indeed the case. Evoked and asynchronous releases were measured in the same bouton, at 13.5 and 3 mM [Ca2+]o. For asynchronous release, very similar slopes log S/log [Ca2+]ss were obtained at the two extracellular Ca2+ concentrations. The slope was 4.3 for 13.5 mM [Ca2+]o (black-triangle), and it was 3.7 for 3 mM [Ca2+]o (black-lozenge ). By contrast, for evoked release the slope log m/log [Ca2+]ss was 2 for [Ca2+]o = 13.5 mM () and 3.3 for [Ca2+]o = 3 mM (). The corresponding Ys were 1.37 µM for [Ca2+]o = 13.5 mM and 0.3 µM for [Ca2+]o = 3 mM.



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Fig. 3. Different napp are obtained at different [Ca2+]o. [Ca2+]ss was raised by a train of 800 pulses (1 ms, -0.7 µA) at frequencies of 20, 40, 60, 80, and 100 Hz. black-triangle, log S/log [Ca2+]ss in [Ca2+]o = 13.5 mM, slope = 4.3; black-lozenge , log S/log [Ca2+]ss in [Ca2+]o = 3 mM, slope = 3.7; , log m/log [Ca2+]ss in [Ca2+]o = 13.5 mM, slope = 2; , log m/log [Ca2+]ss in [Ca2+]o = 3 mM, slope = 3.3.

In 12 such experiments, the average slope for 13.5 mM [Ca2+]o was 1.6 ± 0.41, and the corresponding average Y was 2.73 ± 1.2 µM. The average slope for [Ca2+]o = 3 mM was significantly higher; it was 2.7 ± 0.32. The corresponding average Y was 0.88 ± 0.4 µM (n = 5). The ratio of the estimated Ys at the two Ca2+ concentrations is in the range predicted by Aharon et al. (1994).

Evaluation of <A><AC>m</AC><AC>&cjs1171;</AC></A> and Km

The results presented thus far indicate that Y is in the same range as the measured [Ca2+]ss; i.e., a few micromolars. Concerning Km (Eq. 1a), had it been much larger than a few micromolars, m would be insensitive to the low levels of [Ca2+]ss measured experimentally. Because m varied significantly with changes in [Ca2+]ss, Km, like Ks (the Kd for asynchronous release) (Ravin et al. 1997), is likely to be in the micromolar range.

Ravin et al. (1997) established the maximal rate of asynchronous release, <A><AC>S</AC><AC>&cjs1171;</AC></A>, and extracted Ks from these measurements, finding it to be in the range of 2-4 µM. The same procedure, however, cannot be used for evoked release. This is because in order to achieve high [Ca2+]ss to support maximal release, long pulses of ~5 ms must be applied (Ravin et al. 1997). Evoked release in response to such long pulses cannot be measured because most of it occurs during the pulse itself when measurements are not possible owing to the stimulus artifact. Ravin et al. (1997) found that when S and Ks were measured directly or evaluated from Eq. 2 subjected to rearrangements, similar values were obtained. Therefore, by analogy to asynchronous release, we rearranged Eq. 1a and used it to evaluate m and Km. Rearrangement of Eq. 1a gives
<FR><NU>1</NU><DE><SUP><IT>n<SUB>m</SUB></IT></SUP><RAD><RCD><IT>m</IT></RCD></RAD></DE></FR><IT>=</IT><FR><NU><IT>k<SUB>m</SUB></IT></NU><DE><SUP><IT>n<SUB>m</SUB></IT></SUP><RAD><RCD><IT><A><AC>m</AC><AC>&cjs1171;</AC></A></IT></RCD></RAD></DE></FR><IT>·</IT><FR><NU><IT>1</IT></NU><DE><IT>Y</IT><IT>+</IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB></DE></FR><IT>+</IT><FR><NU><IT>1</IT></NU><DE><SUP><IT>n<SUB>m</SUB></IT></SUP><RAD><RCD><IT><A><AC>m</AC><AC>&cjs1171;</AC></A></IT></RCD></RAD></DE></FR> (7)
Equation 7 shows that plotting 1/nm<RAD><RCD><IT>m</IT></RCD></RAD> as a function of 1/Y + [Ca2+]ss will generate a straight line with a slope of km/nm<RAD><RCD><IT><A><AC>m</AC><AC>&cjs1171;</AC></A></IT></RCD></RAD>, where intersection with the y-axis provides 1/nm<RAD><RCD><IT><A><AC>m</AC><AC>&cjs1171;</AC></A></IT></RCD></RAD>.

Figure 4 shows results from 19 experiments. In Fig. 4A, m is plotted against Y + [Ca2+]ss. For each individual experiment a different Y was added, namely, the Y calculated from Eq. 6.4 for that particular experiment. In Fig. 4B the results of Fig. 4A are presented according to Eq. 7. <A><AC>m</AC><AC>&cjs1171;</AC></A> was obtained from the point of intersection of the regression line with the y-axis. Taking the true Hill coefficient, nm, to be four (see justification above), <A><AC>m</AC><AC>&cjs1171;</AC></A> was found to be 9.13, and Km was found to be 4.9 µM.



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Fig. 4. Dependence of evoked release on (Y + [Ca2+]ss), pooled results of 19 experiments. For each individual experiment, a different Y was added; the Y calculated from Eq. 6.4 for that particular experiment. A: m as a function of Y + [Ca2+]ss. B: data of A plotted according to Eq. 7. The straight line is obtained by a linear regression. <A><AC>m</AC><AC>&cjs1171;</AC></A>, of 9.13 was obtained from the intersection of the straight line with the y-axis. Km of 4.9 µM was obtained from the slope of the straight line.


    DISCUSSION
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Abstract
Introduction
Methods
Results
Discussion
Appendix
References

The single most important experimental result in this study is that evoked release correlates strongly with [Ca2+]ss. Based on this finding, we assumed that the intracellular Ca2+ concentration near the release sites, i.e., the Ca2+ concentration on which evoked release depends, is the sum of [Ca2+]ss and Y. The following experimental results are consistent with this assumption: 1) both evoked and asynchronous release depend profoundly and in a similar manner on [Ca2+]ss; 2) the slope log release/log [Ca2+]ss is close to 4 for asynchronous release, and it is between 1 and nearly 4 for evoked release; 3) for evoked release this slope depends on the extracellular Ca2+ concentration, and it becomes higher (approaches 4) as extracellular Ca2+ concentration declines; 4) for both evoked release under a given [Ca2+]o and asynchronous release, the maximal slope log release/log [Ca2+]ss occurs at low [Ca2+]ss. For asynchronous release, where it could be measured, the slope declines at a higher [Ca2+]ss (Ravin et al. 1997).

From the experimental results analyzed in view of the above assumption, we reached two fundamental conclusions. The Kd for evoked release (Km) is similar to the Kd for asynchronous release (Ks), both in the range of a few micromolar. The second conclusion is that under physiological conditions Y is in the range of a few micromolars.

Possible sources of error in evaluating Y

To evaluate Y, we specifically assumed that (Y + [Ca2+]ss) << Km. How justified is this assumption in view of our finding that Km is in the range of a few micromolars? For low [Ca2+]o, Y was estimated to be a fraction of a micromolar, and the above assumption is fully justified. For [Ca2+]o = 13.5 mM, Y was estimated to be in the range of a few micromolars, and the above assumption could potentially introduce a certain degree of inaccuracy; when (Y + [Ca2+]ssapprox  Km, the slope log m/log [Ca2+]ss will be smaller than nm, and hence Y will be somewhat overestimated (see Eq. 6.4).

Another factor that affects the estimation of Y is the value attributed to nm. We as many others (see INTRODUCTION) took nm to be 4. Our present experimental results support this value (see Fig. 3). Nevertheless, had we taken nm to be 5, Y would acquire 30-50% higher levels (see Eq. 6.4). Thus the estimated Y would still remain in the range of a few micromolars.

Basic assumption, [Ca2+]i = Y + [Ca2+]ss

A major concern is the validity of our basic assumption that evoked release relates to Y + [Ca2+]ss, that is Y and [Ca2+]ss act on a common site to promote release (denoted as model 1).

[Ca2+]ss could potentially act via a site different from that which Y acts on. Specifically, [Ca2+]ss could increase <OVL><IT>m</IT></OVL> (denoted model 2), or it could increase the affinity of the release machinery to Ca2+ (denoted model 3). Model 2 correlates with the suggestion of Llinás et al. (1991), according to which [Ca2+]ss increases the number of vesicles ready for release. Model 3 examines the possibility that Km depends on [Ca2+]ss [a possible interpretation of a suggestion made by Wright et al. (1996)].

Figure 5 shows the equations and predictions of each of the three models concerning several key experimental results. The equations describing the various models for evoked release are depicted on the left. Following convention, the equation for asynchronous release is common to all three models and is provided in model 1 (see equation for S).



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Fig. 5. Examination of 3 mathematical models for their ability to predict the experimental results. Model 1: the assumed role of [Ca2+]ss is to add to Y and the sum of the two (Y + [Ca2+]ss) determines m. Parameters: <A><AC>m</AC><AC>&cjs1171;</AC></A> = 10; Km = 4 µM; nm = 4; Y = 4 µM (- - - - -), Y = 0.3 µM (---). The equation for asynchronous release (S) is common to all 3 models and is provided in model 1. <A><AC>S</AC><AC>&cjs1171;</AC></A> = 700 s-1, Ks = 4 µM; ns = 4. Model 2: the assumed role of [Ca2+]ss is to increase <A><AC>m</AC><AC>&cjs1171;</AC></A>, but it is also added to Y as in model 1. The lowest value of <A><AC>m</AC><AC>&cjs1171;</AC></A>, <A><AC>m</AC><AC>&cjs1171;</AC></A>(min) = 10; alpha  = 8; Kss = 2 µM; Km = 250 µM; nm = 4; Y = 700 µM (- - - - -), Y = 50 µM (---). Model 3: the assumed role of [Ca2+]ss is to decrease Km, hence to increase the affinity of the release system for Ca2+. In addition, [Ca2+]ss is added to Y as for model 1. <A><AC>m</AC><AC>&cjs1171;</AC></A> = 10; Km(max) = 250 µM; Kss = 2 µM, beta  = 95; nm = 4; Y = 700 µM (- - - - -), Y = 50 µM (---).

Each model was tested for its predictions concerning the dependence of m on [Ca2+]ss under two values of Y (middle column, dashed line corresponds to high Y and continuous line to low Y). The values of the various parameters are provided in the legends. For both models 2 and 3, the sites where [Ca2+]ss acts exhibit a high affinity for Ca2+ with a Kd taken to be 2 µM. In contrast, in these two models, the site where Y acts exhibits a low affinity for Ca2+, Km being 250 µM in model 2 and the initial Km(max) = 250 µM in model 3.

Examination of the predictions of the three models reveals that none of the experimental findings (points 1-4 above) can be accounted for by models 2 and 3. Specifically, in contrast to experiments, the dependence of evoked release and asynchronous release on [Ca2+]ss differs. Also, the maximal slope log m/log [Ca2+]ss is achieved at high [Ca2+]ss. At low [Ca2+]ss, this slope is close to zero. Exactly the opposite is seen in the experiments where the maximal slope is achieved at low [Ca2+]ss. The value of the maximal slope (1.6 in model 2 and 1.3 in model 3) bears no resemblance to the Hill coefficient assumed in these models (nm = 4). An additional discrepancy concerns the dependence of evoked release on [Ca2+]o. The experiments clearly showed that at low [Ca2+]ss the slope log m/log [Ca2+]ss was much higher at low [Ca2+]o, where it approached the genuine Hill coefficient of 4 (see Fig. 5). In contrast, models 2 and 3 predict that at the relevant range of low [Ca2+]ss there is virtually no difference in the slopes at the two Ys (reflecting [Ca2+]o) examined. Both for Y = 700 µM and for Y = 50 µM the slope log m/log [Ca2+]ss at low [Ca2+]ss approached zero (the ratio between the low and high Y was the same in all 3 models).

All the fundamental discrepancies mentioned above stem from the same source. They result from the assumption made in models 2 and 3 that Y and Km are high. As a direct result of this assumption, using the terminology of some of the investigators cited above, the "site" responsible for evoked release does not sense the low levels of [Ca2+]ss. Consequently, when [Ca2+]ss is elevated, but is still low in comparison with Y, the behavior of m reflects the properties of the site that is sensitive to [Ca2+]ss (<A><AC>m</AC><AC>&cjs1171;</AC></A> in model 2 and Km in model 3) and not the properties of the site that is sensitive to Y.

We must conclude that our experimental results can be explained best by model 1.

How do our experimental results and conclusions relate to other work in this field? Our experimental finding that low concentrations of Ca2+ in the micromolar range are sufficient to promote release differ from those of Heidelberger et al. (1994), but resemble those of Mulkey and Zucker (1993) and Delaney et al. (1989), which nevertheless reached conclusions different from ours (see below).

Heidelberger et al. (1994) found in goldfish retinal bipolar cells that half-maximal release was obtained at [Ca2+]i of 194 µM. In their work, [Ca2+]i was raised to different concentrations by flash photolysis of DM nitrophen and not by the natural depolarizing stimulus. The synapse of bipolar cells releases tonically, and it may differ in some aspects from other fast synapses (Zucker 1996). In any event, if the depolarizing natural stimulus affects release in addition to the opening of Ca2+ channels as suggested by the Ca2+-voltage hypothesis (review Parnas and Parnas 1994), it is possible that without membrane depolarization higher concentrations of Ca2+ are required for release.

Delaney et al. (1989) and Mulkey and Zucker (1993), based on the residual Ca2+ hypothesis for synaptic facilitation and their experimental results, calculated [Ca2+]i at the release site after action potential to be in the range of few micromolars. These authors rejected their own experimentally based calculations because such low concentrations of Ca2+ would contradict the "calcium domain hypothesis" that demands much higher [Ca2+]i to promote release. As a result, they also claimed that the residual Ca2+ hypothesis is inadequate to account for facilitation.

Such conclusions, which do not emerge directly from the findings themselves, are motivated by the established view that high concentrations of Ca2+ (in the hundreds micromolar range) are necessary to evoke release. It should be remembered, however, that this view is mainly based on reasoning and less on direct experimental evidence (see INTRODUCTION). The Ca-voltage hypothesis circumvents the difficulties that prompted the advocacy of the "high calcium domain" hypothesis and is supported by a body of experimental findings (review Parnas and Parnas 1994).

What of our assumption that [Ca2+]ss and Y act at the same site to promote release? This question relates to the ongoing debate whether evoked release and facilitation share a common mechanism. Our model 1 represents the view that residual Ca2+ (analogous to [Ca2+]ss) governs facilitation, and hence, [Ca2+]ss and Y act at the same site (Arechiga et al. 1990; Connor et al. 1986; Dudel et al. 1982; Hochner et al. 1991; Katz and Miledi 1968; Kretz et al. 1982; Magleby and Zengel 1982; Miledi and Thies 1971; Rahamimoff 1968; Rahamimoff et al. 1980; Zucker 1988). Other investigators postulated that facilitation, in its different forms, results from Ca2+ binding to a high-affinity site different from the one associated with evoked release (Balnave and Gage 1977; Kamiya and Zucker 1994; Winslow et al. 1994; Wright et al. 1996; Yamada and Zucker 1992; Zucker 1996).

A similar and related unresolved debate concerns the question of whether evoked and asynchronous release share a common mechanism. Goda and Stevens (1994) suggested for asynchronous and evoked release high- and low-affinity sites for Ca2+ binding, respectively. Their results, however, can be interpreted in more than one way as pointed out by the authors themselves: "We favor the 'two Ca2+-sensor' hypothesis, although we cannot exclude the other alternative" (Goda and Stevens 1994).

In contrast, our results confirm earlier suggestions (Bain and Quastel 1992; Dodge and Rahamimoff 1967; Narita et al. 1983; Parnas and Segel 1981; Quastel and Saint 1988) that evoked and asynchronous release share a basic common mechanism, where the dependence on Ca2+ is concerned, and differ only quantitatively. According to the Ca-voltage hypothesis (review Parnas and Parnas 1994), the maximal level of evoked release (<A><AC>m</AC><AC>&cjs1171;</AC></A>), but not that of asynchronous release (<A><AC>S</AC><AC>&cjs1171;</AC></A>) (providing that it is measured at resting potential), increases with the rise in the level of depolarization (Lustig et al. 1989). The qualitative similarity between evoked and asynchronous release in their dependence on [Ca2+]ss, shown here and in Ravin et al. (1997), does not rule out the possibility that the two differ in other aspects. Indications for possible differences in the mechanism of the two come from knockout experiments (Geppert et al. 1994). However, even if some aspects in the mechanism of the two modes of release do differ, the two main conclusions of the present work remain: the affinity of the putative Ca2+ receptor associated with evoked release is high, in the range of a few micromolars, and the level of Ca2+ needed at release sites to evoke release after an action potential is also in the range of a few micromolar.


    APPENDIX
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Abstract
Introduction
Methods
Results
Discussion
Appendix
References

This section is concerned with calculating the average of napp over the range of [Cass] where napp was measured
<OVL><IT>n</IT><SUB><IT>app</IT></SUB></OVL><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>&Dgr;</IT>[<IT>Ca</IT><SUB><IT>ss</IT></SUB>]</DE></FR> <LIM><OP>∫</OP><LL>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>min</IT></SUP><SUB><IT>ss</IT></SUB></LL><UL>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>max</IT></SUP><SUB><IT>ss</IT></SUB></UL></LIM> <IT>n</IT><SUB><IT>app</IT></SUB><IT>d</IT>[<IT>Ca</IT><SUB><IT>ss</IT></SUB>] (A1)
where Delta [Cass] = [Ca2+]ssmax - [Ca2+]ssmin, [Ca2+]ssmax and [Ca2+]ssmin being the highest and lowest [Ca2+]ss, respectively, where napp was measured.

Our task here is to evaluate this integral using Eq. 6.1
<IT>n</IT><SUB>app</SUB><IT>=</IT><IT>n<SUB>m</SUB> </IT><FR><NU>[Ca<SUB>ss</SUB>]</NU><DE>[Ca<SUB>ss</SUB>]<IT> + Y</IT></DE></FR>
To simplify the calculation, it is advantageous to rewrite this result in the form
<IT>n</IT><SUB><IT>app</IT></SUB><IT>=</IT><IT>n<SUB>m</SUB></IT><FENCE><IT>1−</IT><FR><NU><IT>Y</IT></NU><DE>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB><IT>+</IT><IT>Y</IT></DE></FR></FENCE> (A2)
Thus
<OVL><IT>n</IT><SUB><IT>app</IT></SUB></OVL><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>&Dgr;</IT>[<IT>Ca</IT><SUB><IT>ss</IT></SUB>]</DE></FR> <LIM><OP>∫</OP><LL>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>min</IT></SUP><SUB><IT>ss</IT></SUB></LL><UL>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>max</IT></SUP><SUB><IT>ss</IT></SUB></UL></LIM> <IT>n<SUB>m</SUB></IT><FENCE><IT>1−</IT><FR><NU><IT>Y</IT></NU><DE>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB><IT>+</IT><IT>Y</IT></DE></FR></FENCE><IT>d</IT>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUB><IT>ss</IT></SUB>

=<IT>n<SUB>m</SUB></IT><IT>−</IT><FR><NU><IT>n<SUB>m</SUB>Y</IT></NU><DE><IT>&Dgr;</IT>[<IT>Ca</IT><SUB><IT>ss</IT></SUB>]</DE></FR><IT> ln </IT><FENCE><FR><NU>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>max</IT></SUP><SUB><IT>ss</IT></SUB><IT>+</IT><IT>Y</IT></NU><DE>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>min</IT></SUP><SUB><IT>ss</IT></SUB><IT>+</IT><IT>Y</IT></DE></FR></FENCE> (A3)
Finally, using the definitions of Delta [Cass], we can rewrite this result as
<OVL><IT>n</IT><SUB><IT>app</IT></SUB></OVL><IT>=</IT><IT>n<SUB>m</SUB></IT><FENCE><IT>1−</IT><FR><NU><IT>Y</IT></NU><DE><IT>&Dgr;</IT>[<IT>Ca</IT><SUB>ss</SUB>]</DE></FR></FENCE><IT> ln </IT><FENCE><FR><NU><IT>1+&Dgr;</IT>[<IT>Ca</IT><SUB><IT>ss</IT></SUB>]</NU><DE>[<IT>Ca</IT><SUP><IT>2+</IT></SUP>]<SUP><IT>min</IT></SUP><SUB><IT>ss</IT></SUB><IT>+</IT><IT>Y</IT></DE></FR></FENCE> (A4)


    ACKNOWLEDGMENTS

This research was supported by United States-Israel Binational Science Foundation (BSF) Grant 93-00308/1 to H. Parnas, I. Parnas, and G. Augustine. We are grateful to the Goldie-Anna fund for continuous support. M. E. Spira is the Jacomo De Viali Professor for Neurobiology. I. Parnas is the Greenfield Professor for Neurobiology. The APPENDIX was derived by A. R. Tzafriri.


    FOOTNOTES

Address for reprint requests: I. Parnas, Dept. of Neurobiology, Institute of Life Sciences, Hebrew University, Jerusalem 91904, Israel.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 23 April 1998; accepted in final form 8 October 1998.


    REFERENCES
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Abstract
Introduction
Methods
Results
Discussion
Appendix
References

0022-3077/99 $5.00 Copyright © 1999 The American Physiological Society