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* Departamento de Biofísica, Instituto de Fisiología Celular, and
FENOMEC (IIMAS), UNAM, 04510 D.F., México
Correspondence: Address reprint requests to Dr. Francisco F. De-Miguel, Dept. de Biofísica, Instituto de Fisiología Celular, UNAM, Apartado Postal 70-253, 04510 D.F., México. Tel.: 525-622-5622; Fax: 525-622-5607; E-mail: ffernand{at}ifisiol.unam.mx.
| ABSTRACT |
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| INTRODUCTION |
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We analyzed these possibilities in pairs of electrically coupled Retzius neurons of the Mexican leech Haementeria officinalis. Each of the 21 segmental ganglia of this species contains nearly 325 neurons distributed in a stereotyped manner (E. Izquierdo, and F. F. De-Miguel, unpublished). Retzius neurons are the largest in each ganglion and release serotonin from presynaptic endings (Henderson, 1983
) and from the soma (Trueta et al., 2003
), by which they modulate swimming (Willard, 1981
; Nusbaum and Kristan, 1986
), local bending (Kristan, 1982
; Lockery and Kristan, 1990
), and learning (Burrel et al., 2001
). The pair of Retzius neurons in each segmental ganglion is coupled by a nonrectifying electrical synapse (Hagiwara and Morita, 1962
; Eckert, 1963
), which is presumably formed between neurites arising from the primary axon (Lent, 1973
; Mason and Leake, 1978
; De-Miguel et al., 2001
). In addition, both Retzius neurons receive a common chemical synaptic input (Hagiwara and Morita, 1962
) which produces EPSPs that spread to the other neuron through the electrical synapse (De-Miguel et al., 2001
).
To explore how electrical coupling affects the integration of EPSPs, we measured morphological and biophysical parameters of Retzius neurons to design a mathematical model that reproduced their electrical responses. The model was combined with experimental evidence to calculate the location of the presynaptic chemical inputs onto the neurites, the space constant of the neurites, and the coupling resistance value. We also made quantitative simulations as to how chemically induced synaptic currents produced by such inputs are distributed in both coupled neurites. As our main finding we show that the leak of synaptic currents from one neuron to another may determine the amplitude of the EPSPs in the driving neurite.
| MATERIALS AND METHODS |
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Electrophysiological techniques
Intracellular recordings were made with borosilicate glass microelectrodes (FHC, Bowdoinham, ME) and were filled with 3 M KCl. Their tip resistances ranged from18 to 25 M
. The microelectrodes were coupled to preamplifiers (Almost Perfect Electronics, Basel, Switzerland), and recordings were filtered by a custom-designed Bessel filter with a cutoff frequency of 400 Hz. Data were acquired by an analog-to-digital board Digidata 1200 (Axon Instruments, Foster City, CA) using Axoscope 8.0 or Pclamp 8.0 and stored in a PC for further analysis.
For current injection, we used an independent microelectrode. This was preferred over single-electrode current clamp in switch-mode because of the need to inject large amounts of current. A constraint of this method was the possible somatic "shunt" produced by each microelectrode. However, after five minutes of recording, the membrane sealed around the electrode tip, allowing accurate estimates of the membrane properties (Fig. 4). Artificial synaptic potentials similar to natural EPSPs were produced by injecting 300500 µs depolarizing current pulses into one of the neurons. The amount of current was adjusted to produce voltage amplitudes of 12 mV. The membrane time constant defined the decay phase of the artificial EPSP (Fig. 6).
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Morphology
The morphology of Retzius neurons was studied by double staining of pairs of neurons. We injected lucifer yellow (LY) into one neuron and Texas Red (TR) or horseradish peroxidase (HRP) (LY, TR, and HRP, Sigma, St. Louis, MO) into the other neuron. None of these dyes cross through the electrical synapse (Muller and McMahan, 1976
; Stewart, 1978
; De-Miguel et al., 2001
). HRP injections were made following the procedure of Muller and McMahan (1976)
. The rest of the procedure was performed as described by Macagno et al. (1981)
. Pairs of fluorescent neurons were imaged in serial z series taken at 1.0 µm intervals under calibrated confocal optics (Bio-Rad, Hemel Hempstead, UK) using fluorescein and rhodamine emission wavelengths and a Nikon X40 oil immersion objective.
The quantitative analysis of the neurite length and diameter, and of the number of sites of contact of pairs of neurons was made from deconvolved (X-Cosm free software; http://ibc.wustl.edu/bcl/xcosm/xcosm.html; Biomedical Computer Laboratory,Washington University, St. Louis, MO) confocal z series, taken using a Nikon X100 oil immersion objective (NA 1.25). Calibration of confocal images and the choice of the number of iterations of the deconvolution process were made using yellow-green or red-fluorescent carboxylate-modified microspheres of 2.0 and 0.5 µm diameter (FluoSpheres, Molecular Probes, Eugene, OR; Fig. 2). Measurements were made manually using Confocal Assistant 4.02 (Bio-Rad) and Metamorph Imaging System 3.6 software (Universal Imaging, West Chester, PA).
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Electron microscopy
Cultured neurons were washed with 0.08 M cacodylate buffer (Sigma) and fixed for 10 min with 0.6% glutaraldehyde (Sigma) and 0.4% paraformaldehyde in 0.08 M cacodylate buffer, pH 7.4. Postfixation was made with 1% osmium tetroxide (Fluka, St. Louis, MO) in cacodylate buffer. Thin sections were counterstained with uranyl acetate for 10 min and with lead citrate for 2.5 min. Observations were made in a Jeol 1010 electron microscope (Jeol USA, Peabody, MA). Measurements of the membrane perimeter were made from digitized images using Metamorph Imaging System 3.6 software (Universal Imaging).
Modeling
A model of electrically coupled Retzius neurons was designed using linear cable theory applied to circuits representing the somata linked with neurites. A detailed description of the model and the mathematics used for this design are in Appendix 1 of the Supplementary Material. The strategy for designing the model was based on our own morphological evidence and on the approach of Yang and Chapman (1983)
. We considered the cell soma as a circuit with parallel capacitance and resistance, the neurites as finite cables with electrotonic length L =
/
, and the electrical synapse as a coupling resistance (rc) connecting neurites of both Retzius neurons (Fig. 2). The parameters used in the model are defined in Table 1. Simulations of chemically induced synaptic currents were made assuming that inputs were established onto single electrically coupled neurites. It is also noteworthy that electrically coupled neurites were in parallel (Fig. 3); therefore, when current was injected into the soma of one neuron, all of the neurites displayed the same voltage changes.
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| RESULTS |
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The morphology of 17 pairs of neurons filled with intracellular dyes was similar to those previously described (Lent, 1973
; Mason and Leake, 1978
; De-Miguel et al., 2001
). Both neurons in each ganglion were a mirror image of each other. The 6080 µm soma was connected to a primary axon from which multiple neurites were sent in all directions. Branches of the primary axon traveled out of the ganglion through the connective nerves and through the nerve roots (Fig. 2 A).
In seven pairs of neurons studied by double staining, the contact sites were formed by neurites sent to the central region of the neuropile (Fig. 2; De-Miguel et al., 2001
). The length of this population of neurites was 49.93 ± 5.7 µm (n = 90 neurites). After the deconvolution process to the z series of images, we found that neurites making contact had constant diameters with an average value of 1.08 ± 0.03 µm.
Most of the 45.4 ± 2.6 contact sites were at the tips of the neurites and had the same diameter (Fig. 2 B); thus, for modeling purposes, we considered that the contact sites did not contribute to the capacitance of the circuit. As seen by comparing the responses of the model and neurons shown in Figs. 5 and 6, this was a good approximation. Our measurements were within the linear range of resolution of our optical system, as shown by the calibration with fluorescent beads of 0.5 and 2.0 µm and emission wavelengths in the rhodamine and fluorescein ranges (Fig. 2 C), similar to those of the fluorescent dyes injected into the neurons. Fig. 2 D shows a partial reconstruction of a neurone with the region of neurites making contact surrounded by the red lines. In three neurons, the percentage of neurites without branches making contact with the coupled neuron was 71%, 76%, and 63%, respectively (n = 204 neurites). The rest of the neurites making contact (n = 59; discontinuous lines in Fig. 2 D) had one (91%) or more (9%) branches, all of which had the same diameter as the mother neurites, thus failing to follow the 3/2 power rule for an electrotonically equivalent cable (Rall, 1959
). The distribution of the contact sites in the arborization of a Retzius neuron is shown in Fig. 2 E. Note that most of the contact sites were established by neurites proximal to the soma.
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= 50 µm and space constant
. The electrotonic distance of the neurites was defined as the
/
coefficient (Fig. 3). The cables from each neuron were coupled by a resistor (rc). Note that with this configuration, artificial or simulated synaptic potentials produced at one soma would give the same voltage changes along all of the coupled neurites, as they are connected in parallel.
Electrical parameters of the soma
The contribution of the soma to EPSP integration was determined by its impedance, Zsoma = rs/1 + j
(see the Supplementary Material, in which the intrinsic parameters were rs (the soma membrane resistance) and
(the time constant; Table 1; see Supplementary Material). Both parameters were measured from somata that were isolated and kept in culture (Fig. 4 A) where they maintained their resting potential values similar to those of neurons in the ganglion.
A
value of 20.8 ± 3.4 ms (ranging from 18 to 40 ms) was obtained from exponential fits to the steady-state voltage responses at the end of square hyperpolarizing current pulses of 500 ms (Fig. 4 B) in 12 neurons maintained at -60 mV by the injection of negative DC current. The soma shunt produced by the microelectrode was minimal, since the values of
before and 5 min after the insertion of a second electrode were similar (Fig. 4 B), showing that the cell membrane sealed around the electrode. Therefore, we assumed that our estimates gave an accurate approximation to the real value of
. Data from neurons that failed to recover after the second impalement were excluded from our analysis.
The values of the membrane resistance (rs), were obtained from the formula rs =
/(soma surface area) (Cs), where Cs is the specific membrane capacitance (1 µF/cm2). Since the membrane infoldings could have a significant contribution to the surface area, estimates of this parameter were made from electron micrographs (Fig. 4, C and D). The amount of infolding of these neurons was similar to that of neurons in the ganglion (V. H. Hernandez, M. Morales, and F. F. De-Miguel, unpublished). The radius obtained from the real perimeters were used to calculate the total surface area, assuming that the neurons were spherical. In eight neurons, the areas obtained by this method ranged between 1.13 x 10-4 and 3.14 x 10-4 cm2, and were 25% larger than those calculated from images obtained under phase contrast optics. The corresponding values of rs were between 90 and150 M
(Table 1).
Sinusoidal domain responses of neurons and model
To test the accuracy of the model and the values of the parameters estimated above (Table 1), we studied the frequency responses to injection of sine wave currents of six pairs of neurons with steady-state coupling ratios between 0.26 and 0.63. These responses were compared with model simulations (Fig. 5; Eq. 14 of the Supplementary Material). The model predictions compared well with the frequency responses of every pair of neurons and were similar to the responses of a first-order, low-pass filter, demonstrating that the system operated linearly. The best fits of the experimental data with the model predictions in every pair of neurons were obtained when
= 100 µm, that is, twice the individual neurite length (50 µm;
/
ratio of 0.5), but similar to the distance between both somata. This low
/
coefficient guaranteed an efficient EPSP conduction along the neurites.
The rc values calculated ranged from 30 M
when the coupling ratio was 0.72, to 340 M
when the coupling ratio was 0.22. Two extreme conditions of the model (Yang and Chapman, 1983
) failed to fit with our data. If
is infinite, a fair representation of the circuit is with both somata bound directly by rc (Fig. 5 C, left inset). The second condition occurred when the rc value is so low that both somata are coupled by a continuous cable (Fig. 5 C, right inset).
To show the effect of
and rc on the spread of EPSPs along the neurites, the shape and amplitude of artificial EPSPs at both somata were compared with model simulations. Fig. 5 shows an example in which the steady-state coupling ratio was 0.35. The amplitude of the simulated EPSPs was fixed at V1, and the rc values were changed between 15 (below the value estimated for this coupling ratio) and 80 M
(Fig. 6). When the
/
coefficient was fixed at 0.5 and the rc value at 30 M
, the shape of the simulated responses reproduced that of artificial EPSPs. As expected, changing the rc value produced an inversely proportional change in the amplitude of the EPSP at V2 without affecting its kinetics.
Location of presynaptic inputs in the coupled neurites
To estimate the location of presynaptic chemical inputs, we compared the somatic coupling ratio of natural and artificial EPSPs (Fig. 6). Owing to the passive properties of the neurites, a chemical input located right beside the electrical synapse should produce the largest somatic EPSP coupling ratio. This ratio should decrease as the input is more proximal to the soma. For this reason, the coupling ratio of EPSPs produced in the coupled neurites should be larger than that of artificial EPSPs produced at the soma. On the other extreme, the coupling ratio of EPSPs produced in noncoupled neurites should be smaller than that of artificial EPSPs.
In seven pairs of neurons the coupling ratio of artificial EPSPs was smaller than that of natural EPSPs, as expected for inputs located in the coupled neurites. Fig. 7 A superimposes natural and artificial EPSPs from a pair of neurons with a steady-state coupling ratio of 0.56. The amplitudes were normalized for comparison of their kinetics. In this representative pair of neurons, the coupling ratio of 10 averaged artificial EPSPs was 0.28, whereas the average coupling ratio of 30 natural EPSPs was 0.41 ± 0.04.
From the bimodal experimental rise time distribution of EPSPs recorded at the soma of one neuron (Fig. 7 B), we assumed that one input to each neuron was located symmetrically on each side of the electrical synapse. The exact location of both presynaptic chemical inputs was determined by simulating the somatic rise time of EPSPs in terms of the electrotonic distance along the coupled neurites. Since the rise time dependence of the input position comes from the
/
coefficient, its value was adjusted in the model to calculate the input locations which produced EPSPs with somatic rise times of 5.6 and 9.6 ms. The
/
coefficient which gave the best fits was 0.45 ± 0.7, and the distance from the electrical synapse to the chemical inputs was 0.15 ± 0.05
, or 7.5 µm, assuming that
= 50 µm (n = 7 neurons). These results were similar if the rise time distributions of EPSPs were obtained using a physiological (1.8 mM) calcium concentration (Fig. 7 B) or if the presynaptic release probability was reduced by using a solution with 1.0 mM calcium and 2.0 mM magnesium during the recordings (not shown).
Electrical coupling modulates the amplitude of EPSPs
Electrical coupling of the neurites affected two variables that determined the amplitude of EPSPs. One was the distribution of chemically induced synaptic currents in both coupled neurites, and the second was their impedance. The distribution of synaptic currents as a function of the value of rc was calculated by the model (Fig. 8 A). As expected, when rc = 0 M
, both neurites behaved as a continuous cable, and current spread equally well toward both somata. For this reason, the current values at different rc values were normalized to those calculated when rc = 0. The asymmetry of the curves in Fig. 8 A was due to the input location at 0.15
from the electrical synapse.
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, respectively. Since by Ohm's law the amplitude of the EPSPs in the driving neurite was dependent on the product of the impedance and the current, increasing the rc value produced larger EPSPs. Again, the values presented in Fig. 8 C were normalized to those predicted when rc = 0 M
. As can be seen, the EPSP amplitude was 80% larger when the coupling resistance was 340 M
. Fig. 8 C also shows that the EPSP amplitude decayed along the neurites in a Gaussian manner independently on the rc value because of the frequency dependence of EPSP passive spread (Jack et al., 1975Interestingly, our model predicted that the amplitude of EPSPs produced in the coupled neurite by the arrival of synaptic current from the driving neurite was the same at all values of rc (Fig. 8 C). This was because at high rc values, the impedance increase compensated for the reduction of the amount of current leaking through the coupling resistance. Simulations of EPSPs arriving at the somata of both coupled dendrites at different coupling resistance values and placing the inputs at both different distances from the electrical synapse of one neuron are shown in Fig. 9.
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| DISCUSSION |
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coefficient of the coupled neurites allowed synaptic currents produced in either neurite to arrive at the soma of both neurons. In the driving neurite, the EPSP amplitude was dependent on the coupling resistance value. In the coupled neurite, the amplitude of EPSPs produced by synaptic currents arriving from the driving dendrite was constant at all coupling resistance values.
Possible functional significance
Retzius neurons generate action potentials from the summation of EPSPs produced at their coupled neurites (Fig. 1). Therefore, the amplitude modulation of EPSPs in the driving neurite by the electrical synapse could influence the firing frequency of the neurons, because summation of larger EPSPs produced at high rc values would increase the probability of reaching the threshold for action potentials. In the coupled neuron, the constant-amplitude EPSPs arriving from the driving neuron regardless of the coupling resistance value guarantees that each EPSP produced in the coupled neurite may take part in the integration process. In addition, currents produced by action potentials in the primary axon back-propagate to the coupled neuron through the electrical synapse (Fig. 1 D). Therefore, this combination of chemical and electrical synapses with purely passive membrane properties allows several effects on integration.
Other evidence contributes to the understanding of how EPSPs are integrated by these neurons: 45 of the neurites make contact with the coupled neuron, suggesting a similar number of electrical synapses. Since several, if not all, of them may have chemical inputs, the dominance of unitary events in the amplitude distributions of EPSPs (F. F. De-Miguel and E. García-Perez, unpublished) makes it probabilistically very unlikely that double or triple synaptic events are produced at individual neurites. As a consequence of this, the summation of unitary EPSPs arriving from different coupled neurites must occur at the primary axon. An advantage of this design would be a reduction of nonlinear effects produced by temporal summation in the same neurite (Magee, 2000
).
It is remarkable that the cytoarchitecture of the coupled neurites is designed to function as a single unit. For example, the 0.5
/
coefficient of a single coupled neurite is half of those of mammalian or lamprey motoneurons (Christensen and Teubl, 1979
; Gustafsson and Pinter, 1984
; Bras et al., 1987
), lateral geniculate neurons of the cat (Bloomfield et al., 1987
), guinea pig cerebellar Purkinje cells (Rapp et al., 1994
), or electrically coupled photoreceptor cells in the turtle retina (Detwiler and Hodgkin, 1979
). In Retzius neurons this small coefficient allows pairs of coupled neurites to act in series, integrating EPSPs produced by both neurons, regardless on the value of the coupling resistance.
Another aspect of the cytoarchitecture that is relevant from the functional point of view concerns the large areas of the soma and axons as compared with those of the fine neurites. Retzius neurons take advantage of their soma surface to release large amounts of serotonin upon high-frequency trains of impulses (Trueta et al., 2003
). The large membrane area of the soma and primary axon as compared with that of the neurites produces a very low somatodendritic conductance coefficient (
10-2 to 10-1; see the Supplementary Material). This relationship is opposite to that of vertebrate neurons, in which the surface area of the soma is only a fraction of that of the dendrites (Rall, 1959
). The low
value suggests that the specific membrane resistance of the soma and primary axon is larger than that of the neurites and explains why, despite such morphology, it is possible to record from the soma the EPSPs produced in the small neurites. This coefficient also suggests that EPSPs recorded at the soma are attenuated as they arrive at the primary axon.
Possible general significance
An increasing amount of evidence from electrophysiological experiments and from the expression patterns of gap junction proteins indicates that a large proportion of central neurons of vertebrates and invertebrates are electrically coupled (for a review, see Dermietzel and Spray, 1993
). Some of the functions of electrical synapses, such as the mediation of fast behavioral responses and the synchronization of groups of neurons, are common to invertebrates and vertebrates, including mammals (Furshpan and Potter, 1959
; Lin and Faber, 1988
; Christie et al., 1989
; Valiante et al., 1995
; Ishimatsu and Williams, 1996
; Mann-Metzer and Yarom, 1999
; Galarreta and Hestrin, 1999
; Gibson et al., 1999
), and so are their modulatory capabilities (Colombaioni and Brunelli, 1988
; DeVries and Schwartz, 1989
). In addition, the coexistence of chemical and electrical synapses is well-established in the vertebrate nervous systems (Martin and Pilar, 1963
). Therefore, even though electrical coupling in invertebrates is mediated by a different set of proteins (Phelan et al., 1998
), it is likely that EPSP spread through electrical synapses may also be conserved as part of the integrative mechanisms of neurons of higher animals. Therefore, our prediction of an amplitude modulation of synaptic potentials by electrical synapses may be a first approximation to the understanding of a common mechanism of synaptic integration in the nervous system.
| SUPPLEMENTARY MATERIAL |
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| ACKNOWLEDGEMENTS |
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The Computing and Microscopy Units at our Institute provided continuous support during this project. E.G.P. was supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) and Dirección general de estudios de posgrado. M.V.C. and E.G.P. received complementary fellowships from a Human Frontiers Science Program grant (RG-162/98) to F.F.M. Human Frontiers Science Program (RG-162/98), CONACYT (1285-N9204), and Programa de apoyo a proyectos de investigación e inovación tecnológica (IN-207593) grants to F.F.M. gave support to this project.
Submitted on June 26, 2003; accepted for publication August 19, 2003.
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