Quantal Secretion and Nerve-Terminal Cable Properties at Neuromuscular Junctions in an Amphibian (Bufo marinus)

G. T. Macleod, L. Farnell, W. G. Gibson, and M. R. Bennett

The Neurobiology Laboratory, Institute for Biomedical Research, The Department of Physiology and The School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Macleod, G. T., L. Farnell, W. G. Gibson, and M. R. Bennett. Quantal secretion and nerve-terminal cable properties at neuromuscular junctions in an amphibian (Bufo marinus). The effect of a conditioning depolarizing current pulse (80-200 µs) on quantal secretion evoked by a similar test pulse at another site was examined in visualized motor-nerve terminal branches of amphibian endplates (Bufo marinus). Tetrodotoxin (200 nM) and cadmium (50 µM) were used to block voltage-dependent sodium and calcium conductances. Quantal release at the test electrode was depressed at different distances (28-135 µm) from the conditioning electrode when the conditioning and test pulses were delivered simultaneously. This depression decreased when the interval between conditioning and test current pulses was increased, until, at an interval of ~0.25 ms, it was negligible. At no time during several thousand test-conditioning pairs, for electrodes at different distances apart (28-135 µm) on the same or contiguous terminal branches, did the electrotonic effects of quantal release at one electrode produce quantal release at the other. Analytic and numerical solutions were obtained for the distribution of transmembrane potential at different sites along terminal branches of different lengths for current injection at a point on a terminal branch wrapped in Schwann cell, in the absence of active membrane conductances. Solutions were also obtained for the combined effects of two sites of current injection separated by different time delays. This cable model shows that depolarizing current injections of a few hundred microseconds duration produce hyperpolarizations at ~30 µm beyond the site of current injection, with these becoming larger and occurring at shorter distances the shorter the terminal branch. Thus the effect of a conditioning depolarizing pulse at one site on a subsequent test pulse at another more than ~30 µm away is to substantially decrease the absolute depolarization produced by the latter, provided the interval between the pulses is less than a few hundred microseconds. It is concluded that the passive cable properties of motor nerve terminal branches are sufficient to explain the effects on quantal secretion by a test electrode depolarization of current injections from a spatially removed conditioning electrode.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The motor-nerve terminal in amphibia consists of a number of terminal branches ranging in length from ~20 µm to >100 µm, generally arranged in parallel on the surface of the muscle, and containing tens to hundreds of active zones (Bennett et al. 1986; Katz 1969). The release of transmitter from different sites on these terminal branches by depolarizing pulses applied with an external electrode in the absence of impulses has been used to determine the relationship between the size of the passive membrane depolarization (the electrotonus) (Hodgkin and Rushton 1946) and the resulting number of quanta released (Dudel 1984; Katz and Miledi 1967). In addition, the extent to which transmitter release at a test electrode is modified by prior stimulation at a conditioning electrode placed elsewhere on a terminal branch has been used to analyze possible interactions between the release process at different active zones (Dudel et al. 1993). However, to this time there has been no cable analysis of how an electrotonus is likely to be generated and to propagate in the branches of the terminal, so there is no analytic formulation to guide the interpretation of experimental results. The problem concerns how the electrotonus propagates in a branch that is sealed at both ends and wrapped tightly in a Schwann cell sheath (Heuser and Reese 1977), following the application of current at a chosen site by an external electrode placed on the sheath. Although there has been extensive analysis of the spread of current in dendritic trees following the initiation of a synaptic potential (for a review see Rall et al. 1992), as well as of the propagation of action potentials in branching nerve terminals (Lindgren and Moore 1989; Lüscher and Shiner 1990; Manor et al. 1991), there has been little attention paid to the spread of electrotonus in nerve terminals (Jackson 1993). In the present work, an analytic description is given of the membrane potential changes in a motor-nerve terminal branch, wrapped in Schwann on the surface of a muscle fiber, in response to current injection from one or more external electrodes placed on the branch. This theory is used to interpret the results of how quantal release by an electrotonus at one electrode on a branch can be modified by a preceding electrotonus at another site on the same or a contiguous branch of the motor-nerve terminal.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Experimental

PREPARATION AND SOLUTIONS. The iliofibularis muscle of the toad Bufo marinus was used in all experiments. Animals were collected between the months of April and February, measuring between 47 and 73 mm in length, and were killed by pithing. Muscles were pinned on a silicone elastomer (Sylgard) bed in a perspex organ bath of 3 ml capacity. Ringer solution of the following composition was used to perfuse the preparation (in mM): 111.2 NaCl, 2.5 KCl, 1.5 NaH2PO4, 16.3 NaHCO3, 7.8 glucose, and 1.2 MgCl2. CaCl2 was present at 1.8 mM, unless otherwise stated, in both the bath and the electrodes. The Ringer solution was continually bubbled with carbogen gas (95% O2-5% CO2) and maintained at a pH of 7.2-7.4. The temperature was kept between 18 and 20°C. Tetrodotoxin in sodium citrate buffer and cadmium were dissolved directly in water and used at 0.2 and 50 µM, respectively. Nifedipine was used at 10 µM in the presence of 0.02% ethanol.

DODC IODIDE AND FM1-43 FLUORESCENCE. The motor nerve terminal was visualized using epifluorescence following treatment with either the styryl dye N-(3-(triethyl ammonium) propyl)-4-(4-dibutylaminostyryl pyridium), dibromide (FM1-43) (Betz and Bewick 1990; Betz et al. 1992) or 3,3'-diethyloxadicarbocyanine iodide (DODC iodide) (Bennett et al. 1986; Yoshikami and Okun 1984). DODC iodide revealed the position of the axon and Schwann cell nucleus, whereas FM1-43 most accurately defined the extent of the endplate by showing the location of presynaptic vesicle clusters. In some instances the often complex branching of the nerve terminal could only be clarified using FM1-43.

The iliofibularis was exposed to 0.1 µM DODC iodide in 0.001% DMSO in Ringer solution for 40 s and then washed in Ringer solution for 5 min. DODC iodide fluorescence was observed during excitation at 540 nm using an Olympus microscope (BH-2) with fluorescence attachment and rhodamine filter set. An Olympus WPlanFL40XUV water immersion objective (0.7 NA) was used to view the terminals, and the image was displayed on a video monitor (National WV-5470) using a low light TV camera (National WV-1900/B). Images were captured and saved using a Scion Corporation LG3 framegrabber with a 7200/90 Power Macintosh. Terminals were stained with FM1-43 by exposure to 2 µM FM1-43 in a modified Ringer solution (53.7 mM NaCl, 60 mM KCl) for 5 min followed by a minimum of 30 min washing with Ringer solution. FM1-43 fluorescence was observed during excitation using an Olympus fluorescein filter set.

ELECTROPHYSIOLOGICAL RECORDINGS. In each experiment a pair of electrodes was placed on the nerve terminal under direct visual control. Each electrode was capable of passing a stimulating current of up to 2 µA as well as recording evoked release in response to the stimulus. Axon Instruments HS-2A headstages (X10MG) were used with two Axoclamp-2A amplifiers. Recording electrodes were manufactured in the following way. Glass micropipettes were pulled to form tips of 2 µm diam and were then chipped to form a tip with an internal diameter of 15 µm, angled at ~50-60° to the long axis of the pipette. Each pipette was heat polished in a microforge to yield a final tip diameter of ~12 µm. Electrodes were filled with the tissue bathing solution. The position of the electrode tips relative to each other, to the muscle surface, and to the nerve terminal as revealed by staining and epifluorescence was determined by viewing the images on the video monitor. Electrodes were placed directly on selected regions of nerve terminals. Light downward pressure was applied at each electrode site to form a slight seal. Negative pressure was often applied to the solution within the electrodes, equivalent to 100 mm of H2O, to improve the seal. In experiments where the bathing solution contained no added calcium, positive pressure (equivalent to 100 mm of H2O) was applied to the solution within the electrodes that contained calcium (1.8 mM). Particular attention was paid to the level of spontaneous activity that may indicate mechanical irritation. At any pair of sites, the duration of stimulating pulses was the same while the current amplitude was adjusted at each electrode to yield a quantal content close to 0.2. Quantal content was calculated using the method of failures [m = ln(N/N0), where N is number of impulses and N0 is the number of failures] (del Castillo and Katz 1954). If quantal content rose or fell by >25% over the course of a recording trial, the observations were not included in the results. If more than two spontaneous events were observed over the 4.8 s (384 × 12.5 ms) of recorded activity at each site during a trial, the results were discarded. Tetrodotoxin (0.2 µM) was always present in both the bath and the electrodes.

Each trial consisted of 384 stimulation pulses delivered at the rate of 1 Hz to each electrode. The order and delay of current pulses delivered to different sites on the terminal by the two electrodes was varied using a three-phase cycle, and this cycle was repeated 128 times. Figure 1 shows a cycle in a typical trial: 1) a pair of pulses delivered simultaneously at each site (zero delay); 2) a pulse delivered at electrode 1 ~4 ms before a pulse at electrode 2 (4-ms delay); 3) a pulse delivered at electrode 2 ~4 ms before a pulse at electrode 1. This alternating system of stimuli was used to avoid any problems relating to nonstationarity as the conditioning pulses in the second and third pairs could be used as the unconditioned references for the test pulses. In the case of the first pair of pulses in Fig. 1, where pulses were delivered simultaneously to each site, referring to one electrode as the test electrode and the other as the conditioning electrode is done for ease of explanation only. Where there is zero delay between pulses, either electrode can be regarded as the test electrode or the conditioning electrode and mT/m at zero delay can be calculated for both sites, where mT/m refers to the measure of spatial facilitation or depression (Dudel et al. 1993), as the average quantal content measured at the test site when a pulse at the test site is preceded by a pulse at the conditioning site (mT), divided by the average quantal content produced by a pulse at the test site in the absence of any stimulus at the conditioning site (m).



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Fig. 1. Stimulation of the nerve terminal and evoked responses. Three consecutive pairs of traces from the start of a train of 384 pairs of pulses delivered at 1 Hz. Pulses of 80 µs duration were used in this example, and the delay between the start of the conditioning pulse and the start of the test pulse was set at 4 ms in pairs number 2 and number 3.

Data were collected using a MacLab/4s data acquisition system.

Theoretical

This section contains only a summary of the theoretical model; a detailed account can be found in Bennett et al. (1999).

A motor-nerve terminal branch is modeled as a one-dimensional cable with external resistance and leakage to earth (see Fig. 1C in Bennett et al. 1999). The extracellular longitudinal resistance is primarily the resistance to longitudinal current flow between the nerve-terminal and its associated Schwann-cell sheath, whereas the resistance to earth is primarily that provided by the tortuosities in the Schwann-cell sheath. Let Vi be the intracellular potential, Vo the extracellular potential, and Vm = Vi - Vo the membrane potential. In the continuum limit these satisfy the differential equations
<FR><NU>∂<IT>V</IT><SUB><IT>m</IT></SUB></NU><DE><IT>∂</IT><IT>T</IT></DE></FR><IT>+</IT><IT>V</IT><SUB><IT>m</IT></SUB><IT>=</IT><FR><NU><IT>∂<SUP>2</SUP></IT><IT>V</IT><SUB><IT>i</IT></SUB></NU><DE><IT>∂</IT><IT>X</IT><SUP><IT>2</IT></SUP></DE></FR> (1)

<FR><NU>∂<IT>V</IT><SUB><IT>m</IT></SUB></NU><DE><IT>∂</IT><IT>T</IT></DE></FR><IT>+</IT><IT>V</IT><SUB><IT>m</IT></SUB><IT>=</IT>− <FR><NU><IT>1</IT></NU><DE><IT>&kgr;</IT></DE></FR> <FR><NU><IT>∂<SUP>2</SUP></IT><IT>V</IT><SUB><IT>o</IT></SUB></NU><DE><IT>∂</IT><IT>X</IT><SUP><IT>2</IT></SUP></DE></FR><IT>+&mgr;</IT><IT>V</IT><SUB><IT>o</IT></SUB><IT>−&ngr;</IT><IT>I</IT><SUB><IT>in</IT></SUB>(<IT>T</IT>)<IT>&dgr;</IT>(<IT>X</IT>) (2)
where kappa  = ro/ri, µ = rm/re, nu  = <RAD><RCD><IT>r</IT><SUB>m</SUB><IT>r</IT><SUB>i</SUB></RCD></RAD>, X = <RAD><RCD><IT>r</IT><SUB>i</SUB>/<IT>r</IT><SUB>m</SUB></RCD></RAD>, T = t/tau m, tau m = rmcm. The quantities ro, ri, rm, re, cm, and tau m are defined in Table 1; x (µm) is distance along the cable, and t (ms) is time. The injected current is Iin(T) and the delta-function delta (X) indicates that injection takes place at the point X = 0. 


                              
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Table 1. Values of parameters used in the calculations

In the case of no earth leakage (µ = 0), Eqs. 1 and 2 can be combined to give a single equation for the membrane potential
(&kgr;+1)<FENCE><FR><NU>∂<IT>V</IT><SUB><IT>m</IT></SUB></NU><DE><IT>∂</IT><IT>T</IT></DE></FR><IT>+</IT><IT>V</IT><SUB><IT>m</IT></SUB></FENCE><IT>=</IT><FR><NU><IT>∂<SUP>2</SUP></IT><IT>V</IT><SUB><IT>m</IT></SUB></NU><DE><IT>∂</IT><IT>X</IT><SUP><IT>2</IT></SUP></DE></FR><IT>−&ngr;&kgr;</IT><IT>I</IT><SUB><IT>in</IT></SUB>(<IT>T</IT>)<IT>&dgr;</IT>(<IT>X</IT>) (3)
which is just the standard cable equation and is readily soluble for a range of inputs and boundary conditions. However, for µ not equal  0, Eqs. 1 and 2 do not uncouple, and their solution is more difficult. For the infinite cable, some analytic solutions are possible (Bennett et al. 1999), but for the finite cable, which is the case of interest here, it is best to proceed straight to a numerical solution. A numerical method previously employed to solve similar equations describing a bidomain model of smooth muscle tissue (Henery et al. 1997) was adapted to the present case (again, details are in Bennett et al. 1999). This allows the solution of the present cable model with sealed ends and current injection at arbitrary positions at arbitrary times.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Experimental

The evoked quantal release at a test stimulating electrode on a terminal branch as a result of injecting current with a conditioning electrode on the same or a contiguous terminal branch, at different test-conditioning intervals, was determined. Tetrodotoxin was always present to block voltage-dependent sodium conductance changes and cadmium sometimes present to block voltage-dependent calcium conductance changes.

Two stimulating/recording electrodes were placed in the loose-patch mode at different positions along the length of a single terminal branch that had previously been visualized with either DODC iodide or FM1-43. The electrode proximal to the site of nerve entry was used to deliver a conditioning impulse at an interval before determination of the quantal release produced by a test impulse at the distal site (mtd). This was compared with the quantal release evoked at the distal site in the absence of a conditioning stimulus at the proximal site (md), so giving mtd/md. Data from the reverse stimulating protocol (conditioning stimulus at a distal site and the test stimulus at a proximal site) was also available from the same recording trial and allowed calculation of mtp/mp. The three phase alternating cycle of stimuli illustrated in Fig. 1 allows calculation of mtd/md and mtp/mp for delays of between 0 and 4 ms. Pulses were either 80 or 200 µs in duration. The extent to which release was evoked from sites beyond the rim of the stimulating electrode was checked by stimulating with the loose-patch electrode and simultaneously recording all the quantal release from the nerve terminal using an intracellular electrode. It was found that all releases recorded with the intracellular electrode were accompanied by negative-going signs of quantal release at the loose-patch electrode (data not shown).

The values of mtd/md and mtp/mp observed for different conditioning-test delays when both electrodes were placed on the same motor-nerve terminal branch are shown in Fig. 2. Results have been pooled for 11 different terminal branches in which the distance between the 2 stimulating/recording electrodes varied between 28 and 85 µm and the branch length from 57 to 154 µm. The average value of mtp/mp at zero delay was 0.56 ± 0.06 (mean ± SE, n = 9); and mtd/md was 0.38 ± 0.08 (n = 11; Fig. 2D); in both cases no depression in release was observed when the delay between stimuli was 2 or 4 ms. The average quantal content at the proximal electrode was 0.33 ± 0.06 (n = 9) and at the distal electrode 0.21 ± 0.03 (n = 11). Experiments were also carried out when each of the two stimulating/recording electrodes were placed on different terminal branches. Figure 3A shows the results when each of these branches belong to the same motor-nerve terminal. Depression in the average release of quanta by a test impulse at one electrode following a conditioning impulse at the other electrode when the delay was zero occurred in much the same way as that observed when both electrodes were on the same terminal branch (compare Fig. 3A with Fig. 2D); this occurred independently of which electrode produced the conditioning stimulus. These results indicate that the electrotonus generated in one terminal branch can propagate to a contiguous terminal branch.



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Fig. 2. Degree of depression of quantal release at a test site following stimulation at a conditioning site. A: schematic diagram showing placement of 2 electrodes ( and open circle ) on a single branch of a nerve terminal for which data are shown in B-D. B: abscissa shows the time delay between the start of the conditioning pulse and the start of the test pulse. Ordinate gives the ratio of the average quantal content at the test-site electrode following a conditioning pulse (mtp or mtd) to the average quantal content at the test-site electrode without a conditioning pulse (mp or md); because the results were pooled, the ordinate is labeled mT/m. Individual estimates of mT/m from every recording trial at each of 11 different motor-nerve terminals are included. Each point represents an estimate of mT/m at either a proximal or distal site for a single set of sites. Two estimates of mT/m are gained from each pair of sites because of the alternating but symmetrical stimulus paradigm (Fig. 1). , test electrode positioned proximally to the site of axon entry relative to the conditioning electrode; open circle , test electrode more distal. Recording trials were not included where m was <0.05. C: average results for each of the 11 different motor-nerve terminals. Each average estimate was derived from between 1 and 4 recording trials at a set of sites. D: average estimates of mT/m for all sets of sites on the same terminal branch. Estimates of mT/m gained from up to 4 recording trials at a particular motor-nerve terminal were given equal weighting as those gained from a single trial (a train of 384 paired pulses) at another motor-nerve terminal. Vertical bars, means ± SE. All pulses were of 80 or 200 µs duration and delivered at 1 Hz.



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Fig. 3. Degree of depression with different electrode configurations. A: average value of mT/m when the 2 electrodes are on different branches of the same motor-nerve terminal. Estimates of mT/m from sites on both branches were combined when calculating the average at each delay (n = 25 when delay was 0). B: average value of mT/m when the 2 electrodes are on different motor-nerve terminals on the same muscle fiber (n = 14 when delay was 0). C: estimates of mT/m when the test electrode is placed on a motor-nerve terminal branch and the conditioning electrode is placed either directly on the muscle surface (open circle ), or the conditioning electrode is placed above the same motor-nerve terminal branch out of direct contact () as shown in the insets. Where the conditioning electrode was placed directly on the muscle surface, the distance between the electrodes was 65 µm with the electrode on the muscle displaced from the end of the terminal branch by ~40 µm. D: averages of data shown in C.

Although the loose-patch electrodes were placed visually on the same or contiguous terminal branches, further checks were made to ensure that current injection from the electrodes only gave rise to an electrotonus in the injected branch(s). When muscle fibers that received a polyneuronal innervation were observed, the stimulating/recording electrodes were placed on different branches, one belonging to one motor-nerve terminal and the other to the second terminal (Fig. 3B). In this case no depression was observed in the average release of quanta evoked by a test impulse at one electrode when delivered at zero delay following a conditioning impulse at the other electrode. The average distance between the two electrodes (Fig. 3B) was 81 µm, whereas electrodes on the same branch (Fig. 3) were an average of 52 µm apart, and electrodes on separate branches of the same terminal were on average 70 µm apart (Fig. 3, A and B). In another series of experiments, one electrode was placed in the loose-patch mode on a terminal branch and the other electrode on the underlying muscle fiber, ~65 µm away, as shown schematically in Fig. 3C (top panel). A conditioning impulse on the muscle fiber had no affect on quantal release at the test electrode on the nerve terminal (Fig. 3, C and D). Alternatively, one electrode was placed on a terminal branch in the loose-patch mode, and the other was displaced 70 mm vertically above the same terminal branch so that it was no longer in direct contact with the branch. Again there was no effect of a conditioning pulse on quantal release by a test pulse at the electrode in loose-patch mode on the motor nerve terminal branch (Fig. 3, C and D). The current injection is then restricted to the terminal branch(s) on which the electrodes are placed.

To check that the modifications in quantal release at the test electrode due to current injection at the conditioning electrode were due to passive propagation of an electrotonus, checks were made to ensure that there were no voltage-dependent calcium conductances involved, the sodium ones having been eliminated with tetrodotoxin. The effect of decreasing [Ca2+] in the bathing solution on test quantal secretion was therefore examined. Pulses of 500 µs duration were used when calcium was not added to the bath, because under these circumstances it is difficult to evoke quanta with current pulses of 80 or 200 µs durations. In experiments where electrodes were either on the same branch or on different branches of the same terminal, the average value of mT/m at zero delay when 500-µs pulses were used with 1.8 mM [Ca2+] in both the bath and electrodes was 0.62 ± 0.18 (n = 8; Fig. 4A). If calcium was not added to the bathing Ringer solution but calcium was maintained at 1.8 mM in both electrodes, then mT/m was 0.76 ± 0.10 (n = 10; Fig. 4B), so that the depression in release was not contingent on a propagating potential dependent on voltage-dependent conductance changes. A further check on this was made by introducing 50 µM cadmium into the normal bath solution. The depression in mT/m when a zero delay was used was not affected by cadmium (0.49 ± 0.08, n = 4) compared with 0.56 ± 0.05 (n = 35; Fig. 4C). Nifedipine (10 µM) also had little effect (Fig. 4D).



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Fig. 4. Effect of pulse duration and of Ca2+, cadmium, and nifedipine on depression. A: average values of mT/m for different values of pulse duration. Abscissa gives the pulse duration used for both conditioning and test pulses with 1.8 mM [Ca2+] in the bath and electrodes (n = 35, 14, 8, and 2, respectively). B: average values of mT/m using 500 µs duration pulses in the presence of Ca2+ (1.8 mM) (triangle ) and in its absence (black-triangle, n = 10, 10, and 4) while maintaining 1.8 mM [Ca2+] in the electrodes. C: average values of mT/m when 50 µM cadmium is present in both the bath and electrodes (, n = 4) and when it is not (, n = 4). D: average values of mT/m when 10 µM nifedipine is present in both the bath and electrodes (black-lozenge , n = 8, 7, and 8) and when it is not (diamond , n = 8). Diagrams show the arrangement of the electrodes in each case.

Theoretical

The cable model was used to determine the effects of injecting a depolarizing current pulse of 200 µs duration with an external electrode at the middle of terminal branches of different length. The resulting membrane potential changes were then determined for branches of length 2,000, 400, 300, and 200 µm. Figure 5A shows that the spatial distribution of the depolarization just before the end of the current pulse extends, in the case of a cable 200 µm long, for a distance of ~30 µm on either side of the electrode, before passing into a hyperpolarization that extends out much greater distances to reach the end of the branches for all but the longest branch considered. The time courses of the potential changes at different distances along the length of branches of different lengths, shown in Fig. 5, B-D, indicate that the membrane potential change close to the site of current injection (within ~30 µm for the 200-µm-long cable) is always in the depolarizing direction, but that at further distances out the initial depolarization changes to a hyperpolarization that outlasts the time course of the current pulse of 200 µs duration by periods that are longer than the pulse duration.



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Fig. 5. Electrotonic potentials in the cable model of a terminal branch following injection of a current pulse of duration 200 µs and magnitude 15 nA at the midpoint. Aa-Ad: spatial distribution of the membrane potential displacement at the end of the current pulse for branches of different total lengths, as indicated; the horizontal broken line is zero potential. B-D: temporal changes in the membrane potential at the 3 positions indicated by the vertical dotted lines in the corresponding graph in A.

The cable model was next used to determine the effects of injecting depolarizing currents pulses of 200 µs duration simultaneously with two external electrodes placed at different distances apart but symmetrically in the middle of terminal branches of different length. The spatial distributions of the membrane potential change just before the end of the current pulse when the electrodes are 60 µm apart are shown in Fig. 6A for terminal branches of different length. The membrane is depolarized between the electrodes and for some distance beyond on either side of them at all branch lengths, but then passes into a hyperpolarization that reaches to the end of the branches. Determination of the time course of membrane potential change at one electrode due to current injection alone at the other shows how the potential changes from being predominantly a depolarization to a hyperpolarization as the length of the branch is decreased (Fig. 6B). On the other hand, determination of the time course of the membrane potential change at one electrode due to current injection alone at that electrode shows that this is of course always a depolarization, but of smaller amplitude as the length of the branch decreases (Fig. 6C), due to the end effects caused by the termination of the branch. The result is that the time course and amplitude of the membrane potential change at an electrode when both electrodes inject current simultaneously is due to the interaction of the propagating electrotonus from the other electrode as well as the current flow from the electrode in question in relation to the end of the branch (Fig. 6D).



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Fig. 6. Electrotonic potentials in the cable model of a terminal branch following synchronous current injection by 2 electrodes (E1 and E2) at 2 sites symmetrically placed on the branch. Each injection is a pulse of duration 200 µs and magnitude 15 nA. Aa-Ad: spatial distribution of the membrane potential displacement at the end of the current pulses, for branches of the total lengths indicated, when there is simultaneous injection from E1 and E2 at the positions indicated by the vertical dotted lines; the horizontal broken line is zero potential. B: time course of the membrane potential at E2 when there is current injection at E1 only. C: time course of the membrane potential at E2 when there is current injection at E2 only. D: time course of the membrane potential at E2 when there is current injection at both electrodes. In each case, results are given for the 4 cable lengths in A.

The changes in amplitude of the membrane potential at one of these two electrodes near the end of the 200-µs pulse for simultaneous current injections from the electrodes at different distances apart on branches of different length are shown in Fig. 7A. As the separation between the electrodes increases, there is at first a substantial decrease in the amplitude of the membrane potential change beneath an electrode due to the increasing hyperpolarizing effects produced by current flow from the other electrode. With further separation, the membrane potential change increases as the effects of current flow from the electrode on the ends of the branch become important. The changes in amplitude of the membrane potential at one of the two electrodes near the end of the 200-µs pulse when current is injected from the electrode alone at different positions on branches of different length is given in Fig. 7B. This shows clearly the effects of current flowing into the ends of the branch, gradually increasing the size of the potential at the electrode as it approaches the end of the branch.



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Fig. 7. Spatial distribution of the peak amplitude of the electrotonic potentials in the cable model of a terminal branch following synchronous current injection by 2 electrodes (E1 and E2) at sites symmetrically placed on the branch. Each injection is a pulse of duration 200 µs and magnitude 15 nA. A: amplitude of the membrane potential at E2 as a function of the electrode separation when there is simultaneous injection of current at E1 and E2 for the 3 terminal lengths indicated. B: amplitude of the membrane potential at E2 as a function of the electrode separation when current is injected only at E2. The 4 curves are for terminal branches of lengths 2,000, 200, 160, and 120 µm, as indicated.

The effects of asynchronous injection of current pulses from two electrodes on the cable model of a terminal branch were also investigated. In this case, current injection with a pulse of 200 µs duration at one electrode (the conditioning electrode) was followed by a 200-µs pulse at the other electrode (the test electrode) at different intervals. The spatial distribution of the membrane potential at different positions along the length of branches of different length at the end of the second pulse when the interval between the beginning of one pulse and that of the other is 200 µs is shown in Fig. 8A. In this case the depolarization at the test electrode is still affected by the propagating hyperpolarization from the conditioning electrode 60 µm away for all terminal lengths. This can be seen to be the case by reference to Fig. 8, B-D, which shows the time course of the propagating electrotonus from the conditioning electrode to the test electrode, the size of the depolarization at the test electrode when it alone injects current, and the cumulative effects of both when current is injected asynchronously from both electrodes, respectively. Clearly, the time course of the propagating electrotonus from the conditioning electrode is such that it can still effect the depolarization at the test electrode when this occurs at the end of the conditioning depolarization.



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Fig. 8. Electrotonic potentials in the cable model of a terminal branch following asynchronous current injection by 2 electrodes (E1 and E2) at 2 sites 60 µm apart symmetrically placed on the branch. Each injection is a pulse of duration 200 µs and magnitude 15 nA. Aa-Ad: spatial distribution of the membrane potential displacement at the end of 400 µs, for branches of the different total lengths indicated, when there is a current pulse of 200 µs at E1 followed immediately by a 20-µs pulse at E2; the positions of E1 and E2 are indicated by the vertical dotted lines, and the horizontal broken line is zero potential. B: time course of the membrane potential at E2 when there is current injection at E1 only. C: time course of the membrane potential at E2 when there is current injection at E2 only. D: time course of the membrane potential at E2 when there is asynchronous current injection at both electrodes. In each case, results are given for the 4 cable lengths in A.

Qualitative comparisons between the cable model of propagating electrotonus in terminal branches and experiments

A comparison was made between the extent to which quantal release at a test electrode is depressed by simultaneous injection of current at a conditioning electrode at different distances away on different sized terminal branches and the results of the cable analysis. Figure 9 shows the results for 24 different experiments on terminal branches ranging in length from 120 to 200 µm. Shown is the extent of the depression produced at one electrode in response to stimulation at the other for distances between the electrodes of between 40 and 130 µm for these branches and the theoretical predictions of the extent to which the depolarization at the test electrode is decreased by the injection of current at the conditioning electrode.



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Fig. 9. Comparison between experimental results and theoretical predictions for the effects of a conditioning impulse at one site (electrode E1) on quantal release by a test impulse at another site (electrode E2) for different distances between the electrodes. The electrodes were placed symmetrically on the terminal branches and synchronous pulses of 200 µs duration were applied at each electrode. The continuous lines are solutions of the cable model for the peak amplitude of the membrane potential at E2, normalized by dividing by the amplitude of the membrane potential at the same electrode position when only E2 injects current. Results are given for 3 branch lengths, as indicated. The points give the experimental results for the ratio of quantal release at E2 when there is simultaneous injection of current at E1 and the quantal release due to E2 current injection alone.

The predictions of the cable model were also compared with the experimental observations on the different extents to which quantal secretion due to current injection at the test electrode was depressed by current injection at the conditioning electrode at different preceding intervals. Figure 10 shows such a comparison for an electrode separation of 70 µm. There is good agreement between the theoretical predictions and the observations, with very little depression in the quantal release at the test electrode occurring for intervals greater than ~0.25 ms.



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Fig. 10. Comparison between experimental results and theoretical predictions for the effects of a conditioning impulse at one site (electrode E1) on quantal release by a test impulse at another site (electrode E2) for different delays between the pulses. Asynchronous pulses of 200 µs duration and magnitude 15 nA were applied at E1 and E2. The continuous line is the solution of the cable model for the peak amplitude of the membrane potential at E2, normalized by dividing by the amplitude of the membrane potential when only E2 injects current. The branch length was 160 µm, and the electrodes were symmetrically placed with a separation of 72 µm. The points give the experimental results for the quantal release at E2 when there is injection of current at E1 after the time interval indicated on the abscissa; these results are normalized to the quantal release when E2 alone injects current.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The use of quantal release at a site on a branch as a measure of the size of the electrotonus at that site under different conditions that lead to changes in the electrotonus is at most qualitative. There is a nonlinear relationship between the depolarization due to external current injection at a site and the resultant quantal release, at least in the range of quantal releases most commonly observed in this work (namely, 0.1-0.5) (see Katz and Miledi 1967). Another problem involves the extent to which the varying resistance between the tip of the external electrode and the underlying Schwann cell sheath will alter the amount of current reaching the terminal branch. The consequence is that there is poor control over the size of the currents injected by two electrodes on a branch. This is supported by the observation that reversing the test/conditioning sequence between the electrodes gave rise, in general, to different extents of depression of quantal release at the test electrode. Some comment should also be made about the size of the microelectrodes used to inject current and record the quantal release. These were typically of ~12 µm diam and so cannot be treated as a point source as has been done in the theory. [However, an investigation of the effect of a distributed step current input into an infinite cable indicates that the hyperpolarization effect resulting from an extended electrode is considerably enhanced over that found for a point source (see Bennett et al. 1999, Fig. 7).] The use of such electrodes is akin to those used by Katz and Miledi (1967) (~4 µm) and by Dudel et al. (1993) (~10 µm). These electrodes are generally used under a slight negative pressure and so tend to form a loose-patch seal. The effect of this is to increase the resistance between the inside of the electrode and the extracellular solution, therefore increasing the current that crosses the membrane (Katz and Miledi 1967). This has not been allowed for in the cable analysis.

The effect of the Schwann cell sheath is to greatly increase the resistance to both longitudinal and transverse current flow around the nerve terminal branch in comparison to that that would be the case if the terminal was considered to be simply in a volume conductor. Thus the ratio of the external to internal longitudinal resistance of the terminal branch is ~1 as is the ratio of the membrane resistance to external transverse resistance to earth. This would arise because of the very close proximity of the Schwann cell to the terminal branch as well as to the tortuous path the current must take through the interstices of the Schwann cell sheath to reach the volume conductor provided by the bathing solution. The problem of calculating the voltage drop across the sheath or epineurium around nerves and nerve trunks when determining the results of injection of current from external electrodes is an old one, and early calculations show that the drop is substantial (Rashbass and Rushton 1949), as the present investigation also suggests.

It should be noted that the simulation results presented here are not highly sensitive to the specific choice of parameter values. Because Eqs. 1 and 2 are linear in the potentials, the effect of varying nu Iin, for a constant input current Iin, is simply to rescale these potentials so the choice of value for nu  = <RAD><RCD><IT>r</IT><SUB>m</SUB><IT>r</IT><SUB>i</SUB></RCD></RAD> is not critical for the results presented here. On the other hand, the parameters kappa  = r0/ri and µ = rm/re are involved in a nontrivial way. In the absence of accurate experimental measurements, both these parameters have been taken to be equal to 1. The effect of other choices has been investigated in Bennett et al. (1999). There it was shown that varying kappa  over two orders of magnitude, from kappa  = 0.1 to kappa  = 10, causes quite a large change in the magnitude of the membrane potential but a much smaller change in the ratio of the maximal hyperpolarization to the maximum depolarization, which decreases from 0.47 to 0.22 (see Bennett et al. 1999, Fig. 6A). Similarly, varying µ over the range µ = 0.1 to µ = 10 changes the membrane potential considerably, but the polarization ratio only changes from 0.45 to 0.30 (Bennett et al. 1999, Fig. 6B). These facts, plus the enhancement of the hyperpolarization when a more realistic distributed input is used (Bennett et al. 1998, Fig. 7), suggest that the results from the model are robust under reasonable parameter variation.

Katz and Miledi (1965) first estimated the DC length constant of the motor-nerve terminal at ~250 µm, based on a diameter of 1.5 µm, Rm of 3,000 Omega  cm2 and Ri of 200 Omega  cm; this DC length constant is similar to that in the present work. They also calculated an AC length constant of ~60 µm for the case of an action potential with a characteristic frequency of 1 kHz, Rm of 5,000 Omega  cm2 and a membrane capacitance of 1 µF cm-2 (Katz and Miledi 1968). This then lead to the argument that if the action potential failed to propagate through the last node of Ranvier, then most terminal branches that are substantially longer than 60 µm would fail to be depolarized sufficiently to release transmitter. Using pulses of 200 µs duration gives a characteristic frequency of 5 kHz, which according to the calculation of Katz and Miledi (1968) would give an AC length constant of ~30 µm, not much different to that obtained in the present work.

The question arises as to whether the propagation of the electrotonus along terminal branches is modified by accompanying changes in voltage-dependent channels, as might occur between different regions of a branching and excitable terminal system (Moore et al. 1988). Motor-nerve terminals possess voltage-dependent sodium, calcium, and potassium channels as well as calcium-dependent potassium channels (Angaut-Petit et al. 1989). The spatial distribution of these along single terminal branches at the amphibian endplate is heterogeneous, with sodium channels decreasing in number in the proximo-distal direction along the terminal branches, whereas potassium channels reach a peak density about the center of the branches (Mallart 1984). The sodium channels were always blocked in the present work with tetrodotoxin, and blocking the calcium channels with cadmium did not change the characteristics of the effects of conditioning electrotonus on the quantal release by the test electrotonus, when the calcium block was excluded from the vicinity of the electrodes. It seems then that neither sodium, calcium, nor calcium-activated potassium channels are involved in the changes in quantal secretion observed with these stimulus paradigms.

The question arises as to whether activation of KA channels at the test electrode contributes substantially to the inhibition observed there on a conditioning pulse. Release at the test electrode, due to current injection there, is maximally depressed when there is simultaneous current injection at the conditioning electrode; this depression is much less (or nonexistent) when injection at the two electrodes is separated in time. But any contribution from KA channels would be expected to be greatest when the conditioning current injection precedes the test current injection. It thus seems unlikely that an IKA contributes substantially to the inhibition at the test electrode due to current injection at the conditioning electrode.

The experimental results presented here confirm many of the observations made with a similar technique on nonvisualized terminal branches by Dudel et al. (1993). At short intervals of <1 ms between the pulses given through the two electrodes on a branch, depression of quantal release was always observed at the test electrode as in the present work. The cable analysis shows that this can be explained by the hyperpolarizing effects that the conditioning electrode has on the electrotonus generated at the test electrode, given that the extent of quantal release is dependent on the absolute level of depolarization at the test electrode (Katz and Miledi 1967). These explain both the changes in the extent of depression in quantal release at the test electrode for different distances between this electrode and the conditioning electrode as well as the extent of depression at the test electrode for different test-conditioning intervals at a fixed separation between the two electrodes. Furthermore, as in Dudel et al. (1993), at no time during the thousands of measurements of evoked and spontaneous release made at the test electrode was this release detected at the conditioning electrode, when the latter was not used to inject current. However, one discrepancy between the present observations and those of Dudel et al. (1993) is that the latter observed a facilitation of the test quantal release following 2 ms after the conditioning stimulus. We have not observed any effects on quantal release for intervals between the conditioning/test stimuli greater than ~0.25 ms. The present cable theory does not provide an explanation for such an enhanced release either.

As the conditioning/test electrodes were placed on visualized terminal branches, it was possible to show that even when these were on different branches there was a depression in quantal release at the test electrode. This indicates that the entire terminal branching system at the endplate should be viewed as a branching system in electrotonic continuity. In this case the extensive theory of cable analysis of branching dendritic trees is applicable (see, for example, Rall et al. 1992). However, there does not seem to be any treatment of the problem considered here, namely that of the injection of current from extracellular electrodes at two sites on a short cable in a volume conductor. This analysis is a simplification in that it deals with the case of two electrodes on the same or contiguous branches as if no other branches existed, including the parent axon. At its present stage of development, the theory can at best be used to provide a qualitative explanation of how a conditioning depolarizing current on a motor-nerve terminal gives rise to a depression of quantal release at a test electrode on the terminal.


    FOOTNOTES

Address for reprint requests: M. R. Bennett, Neurobiology Laboratory, Dept. of Physiology, University of Sydney, N.S.W. 2006, Australia.

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 9 March 1998; accepted in final form 3 November 1998.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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




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