INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Electrotonic coupling as an intercellular communication pathway is common among neurons in early stages of development but declines during the maturation of brain circuits (Connors et al. 1983; Peinado et al. 1993). One of the exceptions to this general scheme is the inferior olivary (IO) nucleus, the source of cerebellar climbing fibers. The morphological correlate of the electrotonic coupling, gap junctions, are absent in the IO nucleus at birth and develop concurrently with the maturation of the cerebellar cortex (Bourrat and Sotelo 1983). Moreover, in contrast to other electrotonically coupled networks, for example inhibitory interneurons in the cerebral cortex, gap junctions in the IO nucleus constitute the only pathway of communication between olivary neurons (Galarreta and Hestrin 1999; Gibson et al.1999). Chemical synaptic interactions are absent. While the importance of the electrotonic coupling among olivary neurons is commonly accepted, its efficiency and spatial distribution remain unclear.

Gap junctions in the IO nucleus are found in special structures, located mostly in glomeruli at the distal dendrites of olivary cells (De Zeeuw et al. 1990a,b; Sotelo et al. 1974). One glomerulus contains a core of five to six dendritic and axonal spiny appendages, derived from different olivary neurons, coupled by gap junctions, and surrounded by both excitatory and inhibitory synaptic terminals of extrinsic origin (De Zeeuw et al. 1990a). A gap junctional protein, connexin 36, was identified in the IO nucleus (Condorelli et al. 1998). Functional properties of this protein were studied in two cell lines, N2A-neuroblastoma and PC-12 cells, transfected with connexin 36 DNA (Srinivas et al. 1999). In both of these systems, connexin 36 gap junctions showed no significant voltage sensitivity and an exceptionally small single channel conductance of 10-15 pS.

Electrotonic coupling in the IO nucleus is assumed to play a crucial role in synchronizing climbing fiber input into the cerebellar cortex. Furthermore, electrotonic coupling is essential for the generation of the subthreshold membrane potential oscillations (Lampl and Yarom 1997; Manor et al. 1997) thought to underlie the rhythmicity of complex spike activity (Llinas and Welsh 1997). Several attempts have been made to model the oscillatory behavior of the olivary network (Loewenstein et al. 2001; Makarenko and Llinas 1998; Manor et al. 1997; Schweighofer et al. 1999). In all of these models the spatio-temporal structure of the oscillatory behavior is sensitive to specific parameters, such as number of coupled cells, coupling strength, or voltage dependence of the connectivity.

Here we present a systematic study of electrotonic coupling in 138 pairs of olivary neurons, using both electrophysiological and morphological methods in brain slice preparations of the IO nucleus. Electrotonic coupling was observed in 50% of the cell pairs, while most of the pairs were weakly coupled. The coupling was voltage-independent but showed a certain degree of asymmetry. Neurobiotin injection into an olivary neuron produced indirect labeling of nearby neurons in 52% of staining experiments. We estimated that each olivary neuron is directly coupled to about 50 neurons, forming two independent networks of cells with distinct morphology.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Slice preparation

300-µm slices were prepared from the brain stem of 9- to 31-day-old Sprague Dawley rats. Animals were anesthetized intraperitoneally with 60 mg/kg pentobarbital sodium and perfused through the heart with 100 ml of cold (01°C) physiological solution containing the following (in mM): 124 NaCl, 5 KCl, 1.3 MgSO₄, 1.2 KH₂PO₄, 26 NaHCO₃, 10 glucose, and 2.4 CaCl₂. Following decapitation, the brain stem was quickly removed and sliced (LTD 752 M vibroslice; Campden Instruments) in cold sucrose solution containing the following (in mM): 124 sucrose, 5 KCl, 1.3 MgSO₄, 1.2 KH₂PO₄, 26 NaHCO₃, 10 glucose, and 2.4 CaCl₂. The slices were transferred to the sucrose solution at room temperature and incubated for 60 min. The sucrose solution was slowly replaced by physiological solution. Sections were kept at room temperature in the physiological solution until they were transferred into the recording chamber. Using the sucrose solution was found to be critical for increasing the viability of IO neurons.

Recordings

The recording chamber, mounted on an upright microscope stage (Zeiss Axioskop), maintained a constant temperature of 35°C using a temperature control unit and was continuously perfused with physiological solution. Whole cell patch recordings were performed under visual control using infrared differential interference contrast optics (DIC). Recordings were made throughout the IO nucleus from visually identified neurons whose cell bodies were located below the surface of the slice. The pipettes were filled with intracellular solution containing the following (in mM): 4 NaCl, 10³ CaCl₂, 140 K-gluconate, 10² EGTA, 4 Mg-ATP, and 10 Hepes (pH 7.2). In a few experiments, 5 mM EGTA and 0.5 mM CaCl₂ were added to the intracellular solution to prolong the high-threshold Ca²⁺ spike. Neurobiotin (Sigma) was often added to the intracellular solution in a concentration of 0.5% for intracellular staining. The patch pipettes were pulled on a Narishige pp-83 puller and had a DC resistance of 10-15 M. The seal between the electrode tip and the cell membrane was higher than 1 G. Cell capacitance was not compensated, and removing the fast component of the voltage response to a step current injection compensated for the serial resistance. Recordings were made from cell pairs using Axoclamp 2B amplifiers (Axon Instruments) in current clamp mode. A separate amplifier was used for each cell to avoid the possibility of electronic crosstalk within the amplifier. Electrical signals were stored on videocassettes (Neurocorder DR-484) for off-line analysis using the LabVIEW data acquisition and programming system (National Instruments).

Cell labeling

Neurobiotin (0.5%, Sigma) was injected intracellularly using 250-ms, 500-pA depolarizing pulses delivered at 3.3 Hz for 3 min. Following 1 h of incubation at room temperature, the slice was fixed overnight at 4°C in 2% paraformaldehyde, 0.2% picric acid, and 0.1% glutaraldehyde in 0.1 M phosphate buffer. After washing several times with phosphate buffer, slices were treated with sodium borohydride 0.5% to prevent nonspecific staining and washed again and treated with methanol (10%) and H₂O₂ (3%) to block endogenous peroxidases. The slices were incubated for 3 h in buffer containing 0.5% triton and biotinylated horseradish peroxidase conjugated to avidin (ABC-kit, Vector Labs), washed, and developed under visual control using DAB as chromogen. Sections were routinely counterstained with Cresyl Violet.

To exclude the possibility of nonspecific staining due to extracellular spillover of neurobiotin in control experiments, we advanced the electrode into the slice holding positive pressure as for patch recording and held it in the vicinity of an inferior olivary cell cluster for about 5 min. The sections (n = 9) were processed for neurobiotin as usual (see the previous paragraph). This procedure never led to any cell staining. Larger extracellular injections, using higher positive pressure than for patch recording, sometimes led to staining of blood vessels and to the appearance of swollen (3-4 times normal diameter) cell bodies of olivary neurons with label, but there were no observable labeled dendrites. Normal olivary neurons were not labeled in these experiments (not shown).

Analysis

To compare the strength of electrotonic coupling between different pairs of IO neurons, we calculated the coupling coefficient (CC) from the voltage responses of pre- and postjunctional cells to prolonged (150-250 ms), negative current pulses of various intensities. CC is defined as the ratio between voltage responses of the post- and the prejunctional cell. Although IO neurons have complicated dendritic morphologies, we can model the coupling between two neurons as two isopotential cells with input resistances R₁ and R₂, coupled by a resistance R_c (Fig. 1) as an approximation. Then, the CC from cell 1 to cell 2 (CC₁) is equal to

(1)

where V₂ and V₁ are voltage responses of cell 2 and cell 1, respectively. R_c represents the resistance of the coupling, that is, the resistance of the dendritic path connecting the cells + the resistance of the junction itself. R₁ is the input resistance of cell 1 when coupled to other neurons except cell 2. Accordingly, R₂ is the input resistance of cell 2 when coupled to other neurons except cell 1. The membrane capacitance (C₁ and C₂, Fig. 1) affects the value of the postjunctional voltage during transient events such as an action potential, but not at steady state. Therefore it is not included in the calculation of the CC.

View larger version (13K): [in this window] [in a new window]   Fig. 1. A model of 2 electrotonically coupled cells. R1 and C1 represent membrane resistance and capacitance of cell 1. Similarly, R2 and C2 represent membrane resistance and capacitance of cell 2. Rc signifies a coupling resistance that connects 2 cells and includes both dendritic and gap junctional components. Current was injected either into cell 1 (I1) or cell 2 (I2).

Similarly, the CC from cell 2 to cell 1 (CC₂) is equal to

(2)

It should be noted that R_c1 in Eq. 1 might differ from R_c2 in Eq. 2 if the coupling is not symmetrical.

As follows from this simple model, either differences in the postjunctional input resistance or a nonsymmetrical R_c may cause differences between CC₁ and CC₂. To calculate R_c, one must assume that it is substantially higher than the input resistance of each one of the cells (R₁ and R₂). Then, R₁ and R₂ can be calculated from the slope of a linear portion of the I-V curve, and R_c is readily calculated from Eqs. 1 and 2. Since the input resistance of these cells is in the order of hundreds of M, this simplification is invalid, and therefore, we formulized an equation for calculating R_c using the following four parameters measured experimentally: V₁/I₁, V₂/I₂, CC₁, and CC₂.

Considering the circuit of two point neurons with input resistance R₁ and R₂, coupled by a resistance R_c, we have equations

(3)

and

(4)

Solving Eqs. 1-4 results in

These two equations were used to evaluate the strength and symmetry of the coupling.

As was mentioned above, R_c in our model corresponds not only to the resistance of the junction itself, but includes also the resistance of the entire path from the pre- to the postjunctional cell body. To estimate the corresponding morphological length of the dendritic path, we built a simple compartmental model of two coupled cells using Neuron (Hines and Carnevale 1997). In the model, each cell had a round cell body and one 500-µm long dendrite with specific membrane resistance of 20,000 cm², creating a total dendritic path of 1 mm. The cell input resistance was set to 105 M, within the range obtained experimentally, by selecting an appropriate cell diameter. The R_c of this model was calculated by simulating current injection into the cell body and measuring voltage responses in both cells (using the equations described above). R_c of about 20 G was obtained when the axial resistance of the dendritic path was set to 7.6 G, including 2.5 G for the junctional resistance. This axial resistance was reached using specific cytoplasmic resistance of 200  · cm (Manor 1995), and an average dendritic diameter of 0.7 µm approximated from our preparations stained with neurobiotin. It is important to note that this rough approximation overestimates the actual length of the dendritic path, since it does not take into account an extra leak caused by dendritic bifurcation along the path.

Morphometry

All measurements were done on Zeiss Universal microscope with stepping stage using Neurolucida software (MicroBrightfield). The cells were counted in 50 × 50 × 25 µm volume by superimposing a 50 × 50 µm counting frame on Cresyl Violet-stained slices and counting a number of "top" cell surfaces that came into focus in sequential optical sections through the volume spaced at 1 µm (Coggeshall 1992). Ten measurements were made in three different sections. Since initial 300-µm thick slices shrank to about 100 µm during dehydration, the measured cell density (IO cells per unit volume) was divided by three.

The dendritic length was measured by tracing individual dendrites of neurobiotin-stained neurons.

Measurements are expressed as mean ± SD.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Simultaneous double whole cell patch recordings were performed from 138 pairs of IO neurons at separation distances from 0 (adjacent cells) to 92 µm. Separation distance was the minimal distance measured from the cell membrane of one cell body to that of the other cell body. In most of the experiments, one or both of the recorded cells were injected with neurobiotin through the patch pipette. Since filling with neurobiotin was reported to not significantly change membrane properties of the injected cells (Xi and Xu 1996), same neurons were used for electrophysiological measurements. An additional 35 neurons were recorded individually (not as members of a pair), filled with neurobiotin, and used for morphological analysis.

Prevalence of electrotonic coupling and the number of coupled cells

Electrotonic coupling was measured by injecting hyperpolarizing current pulses (150-250 ms) of various intensities into one of the recorded cells and measuring voltage responses in both cells at the end of the pulse. An example is shown in Fig. 2A. Current pulses (bottom) were injected into cell 1 in the left column and cell 2 in the right column, and voltage responses to each current step were averaged (n = 25). Both cells showed a clear response to the injected current. The response in the prejunctional cell was always faster and an order of magnitude larger than the postjunctional cell. In this case, a coupling coefficient of 0.081 was calculated on current injection into cell 1 (CC₁) and 0.057 on current injection into cell 2 (CC₂). Accordingly, the coupling resistance (R_c, see METHODS) was 1.1 G and 1.4 G for R_c1 and R_c2 respectively.

View larger version (22K): [in this window] [in a new window]   Fig. 2. Double patch recording of pairs of electrotonically coupled neurons. A: 200-ms negative current pulses of various amplitudes (bottom trace) were injected into cell 1 (left) and cell 2 (right). Averaged voltage responses (n = 25) are shown for both conditions. The postjunctional response (cell 2 on left and cell 1 on right) had a smaller amplitude and slower rise time than the prejunctional response. Note that pre- and postjunctional responses are plotted at different scales. B: probability of coupling between pairs of neurons as a function of distance between the cells. C: distribution of coupling coefficient (CC) in 20 pairs of electrotonically coupled neurons. Both CC1 and CC2 are plotted in the same graph. D: coupling coefficient (CC) as a function of distance between the cells, measured in 20 coupled pairs. Each pair is denoted by a different symbol. Each symbol appears twice in the figure, indicating coupling during current injection into cell 1 (CC1) and into cell 2 (CC2). Strongly coupled pairs show clear divergence of CC1 and CC2 values, indicating a directional preference of the coupling. E: distribution of coupling resistance (Rc) in 17 cell pairs. Both Rc1 and Rc2 are plotted.

The presence of electrotonic coupling was tested in 100 pairs. A pair was defined as coupled if voltage deflection of more than 0.02 mV in the postjunctional cell could be observed after averaging 15 responses to a negative 100-pA current pulse in the prejunctional cell. According to this criterion, 50% of the pairs (n = 50) were electrotonically coupled. Figure 2B shows the chance of finding coupled pairs as function of the distance between the cells. Within 10 µm, 80% of the pairs showed coupling, whereas at distances larger than 40 µm, the occurrence of coupling dropped to 33%. Although only eight cell pairs were recorded at distances larger than 70 µm, none of them showed coupling.

To estimate the number of olivary neurons coupled directly to any one neuron we counted cell body density in a volume of 50 × 50 × 25 µm using Cresyl Violet-stained sections (Fig. 3, see METHODS). Three populations of cells could be readily distinguished in Cresyl Violet-stained sections. The first population consisted of large, round cells with a diameter 10-18 µm (Fig. 3A, asterisks). The second population consisted of small round cells with a diameter <5 µm (Fig. 3A, arrow). The third population consisted of very thin elongated cells (Fig. 3A, arrowhead). The same three populations were observed in live slices using DIC optics. Recordings showed that only large cells (the first population) were neurons, while the small ones, either round or elongated, were glia. Therefore only the large cells were counted. A density of 3 ± 2 cells in a 50 × 50 × 25 µm-cube was measured (5 × 10⁴ cells/mm³). We used this value to calculate the number of neurons coupled to one neuron as follows (Fig. 3B). Spherical coordinates were established with one cell at the origin. We calculated the number of cells coupled to this cell based on the data shown in Fig. 2B. For example, a spherical volume with a radius of 25 µm contained a total of about three cells; Fig. 3B () shows a total number of cells in each one of the shells. Since the chance of coupling at a separation distance of 25 µm (10-µm distance + 2 cell radii) was 80%, we estimated that the cell at the origin was coupled to about 2.5 other cells. Extending this calculation to the remaining shells in Fig. 3B, we conclude that one olivary cell is coupled to about 50 (n = 49) other cells at distances 100 µm. Figure 3B () shows the number of cells coupled to the cell at the origin in each one of the shells. Since no coupled pairs were observed at separation distances larger than 70 µm, the largest shell in Fig. 3B has an 85-µm radius (70-µm distance + 2 cell radii).

View larger version (62K): [in this window] [in a new window]   Fig. 3. A: Cresyl Violet-stained olivary section. Only large cell bodies, which represent neurons, were counted. In-focus neurons are denoted by asterisks. An arrow and an arrowhead mark 2 in-focus glial cells, round and elongated, respectively. Scale bar, 20 µm. B: 2-dimensional projection of a sphere with a radius of 85 µm, binned into 7 sphere-inside-sphere volumes. In each one of the volumes, the number of cells was calculated (). A number of cells in each volume coupled to a cell in the middle were calculated according to Fig. 2B ().

Coupling strength, symmetry, and voltage dependence

We calculated the CC in 20 coupled pairs, where stable and long duration recording conditions were obtained. As shown in Fig. 2C, the CC varied between 0.002 and 0.17, with most of the pairs being weakly coupled. In more than 75% of the pairs the CC was <0.05. In Fig. 2D, CC₁ and CC₂ for each of the 20 pairs are plotted as a function of distance between the cells in a pair. Each cell pair is denoted by a different symbol and each symbol appears in the figure twice, indicating CC₁ and CC₂. There was a tendency for the CC to decrease as the distance between the cells increased. The two most strongly coupled cell pairs were found within a distance of 10 µm (upward triangles), although some adjacent cells had no coupling.

In most of the pairs, a clear difference between CC₁ and CC₂ was evident. Pairs that show similar CC₁ and CC₂ ( < 16%, n = 6), displayed a low CC (e.g., filled circles and bold crosses). It is possible, therefore, that in these cases measurement errors prevented the detection of the difference between CC₁ and CC₂. The difference between CC₁ and CC₂ (27 ± 16%, n = 20) signifies an apparent asymmetry of the coupling. According to Eqs. 1 and 2 (see METHODS), asymmetric coupling between neurons might result either from differences in the input resistance of the two cells, from a rectifying coupling conductance, or both. Supporting the first possibility, there was a difference in input resistance of cells in a pair of 24 ± 16% (n = 84). However, there was no correlation between the direction of the asymmetry and the direction of the lowest input resistance. Moreover, when calculating R_c1 and R_c2 in 17 cell pairs (Fig. 2E), we found an asymmetry of 24 ± 12%. R_c varied between 0.7 to 19.8 G, with 68% of the values falling between 0.7 to 8 G. Therefore asymmetry in the R_c was not reduced compared with the asymmetry in the CC, indicating that the differences between CC₁ and CC₂ can only be partially attributed to differences in the input resistance.

Since the rectifying capability of the coupling may play a pivotal role in the behavior of the olivary network (Schweighofer et al. 1999), we studied this question in detail in three pairs where the coupling was exceptionally strong. In Fig. 4A, current pulses (bottom) were injected into cell 1 in the left column and cell 2 in the right column, and voltage responses in both cells were measured at the end of the pulse. Voltage responses in prejunctional and postjunctional cells are plotted against current pulse amplitude in Fig. 4, B and C, respectively. As previously described, the current-voltage relationship of olivary neurons displays pronounced outward and inward rectifications (Yarom and Llinas 1987). Therefore, to calculate the R_c, we used the initial four data points. In this example the input resistance was 162 M and 164 M for cell 1 and cell 2, respectively. The transfer resistance (the voltage in the postjunctional cell as a function of the current in the prejunctional cell, Fig. 4C) in one direction () was higher than the transfer resistance in the other direction (). Such asymmetry of the transfer resistance cannot occur in a linear system. Since the postjunctional response reflects the voltage rectification of the prejunctional response, the transfer resistance shows similar nonlinearity. As a result, the postjunctional voltage was linearly related to the prejunctional voltage (Fig. 4D). The slope of this linear curve expresses the CC. In the example shown in the figure, CC₁ () was 29% higher than CC₂ (; 0.17 and 0.12, respectively). In this particular example, the asymmetry in CC cannot be attributed to the difference in input resistance since both cells showed a similar voltage-current relationship (Fig. 4B). Furthermore, calculating R_c did not reduce the asymmetry. R_c1 and R_c2 in this example were 681 M and 863 M, respectively.

View larger version (25K): [in this window] [in a new window]   Fig. 4. A: asymmetry in coupling of olivary neurons. Conventions as in Fig. 2A. Each trace was averaged 30 times. This pair is denoted in Fig. 2D by upward filled triangles. B: current-voltage relationship of cell 1 () and cell 2 () shows similar rectification at hyperpolarizing potentials. Both cells had similar input resistance. C: postjunctional voltage as a function of prejunctional current (transfer resistance). Transfer resistance on stimulation of cell 1 () and cell 2 () showed rectification reflecting the prejunctional current-voltage relationship (B). D: postjunctional voltage response as a function of prejunctional voltage. Note the linear relationship. Either cell 1 () or cell 2 () was stimulated.

The linear relationship of the voltages across the junction (Fig. 4D) indicates a constant CC. In other words, the coupling was voltage-independent in the range of voltages negative to the resting potential. To examine the effect of positive voltages on the coupling strength, we depolarized the membrane potential by DC current injection in three cell pairs. The results showed that depolarization of either pre- or postjunctional cells decreased the CC.

As shown in Fig. 5, depolarization of either cell 2 (left column) or cell 1 (right column) decreased the CC by about 50% (compare the second and third families of traces). In addition, due to membrane rectification, depolarization of a cell decreased its input resistance. Therefore according to Eq. 1, the decrease in the CC is expected when a depolarized cell is a postjunctional one. Quantitative analysis revealed that when cell 2 was depolarized, CC₁ decreased from 0.15 (Fig. 5C1, ) to 0.08 (Fig. 5C1, ), whereas when cell 1 was depolarized, CC₂ decreased from 0.16 (Fig. 5C2, ) to 0.09 (Fig. 5C2, ). However, depolarization of the prejunctional cell also decreased the CC albeit to a smaller extent. In the example shown in the figure, depolarization of cell 2 decreased CC₂ to 0.10 (Fig. 5C1, ), whereas depolarization of cell 1 decreased CC₁ to 0.12 (Fig. 5C2, ). It should be emphasized that a linear relationship between the pre- and the postjunctional voltages was always observed (Fig. 5C). Similar results were obtained in other two cell pairs.

View larger version (27K): [in this window] [in a new window]   Fig. 5. A: coupling strength was reduced upon depolarization. Current was injected into cell 1 (left) and cell 2 (right). Top traces: prejunctional response. Middle traces: postjunctional response with no DC current injection. Bottom traces: postjunctional response when the postjunctional cell was depolarized by 10 mV. Note reduced response amplitude of the postjunctional cell upon depolarization. B: current-voltage relationship of cell 1 (B1) and cell 2 (B2) at the resting potential () and upon depolarization (). The slope of current-voltage relationship (input resistance) is linear upon the depolarization. The input resistance measured at small current pulse amplitudes (100 pA) is reduced at depolarizing levels compared with the resting potential. C: slope of the postjunctional response as a function of the prejunctional response (CC) decreases upon the depolarization of either the prejunctional cell () or the postjunctional cell (). C1: the postjunctional cell was cell 2. C2: the postjunctional cell was cell 1. The relationship was linear at the resting potential and upon depolarization, indicating constant CC, independent of the voltage. Depolarization of the postjunctional cell reduced CC to a greater extent due to its action on the postjunctional input resistance. This cell pair is denoted in Fig. 2D by upward unfilled triangles.

Coupling during an action potential

Due to membrane capacitance, electrical coupling is much less efficient during transient than steady state events. On the other hand, coupling during action potentials may play an important role in olivary physiology, synchronizing the climbing fiber output to the cerebellar cortex. Therefore we studied action potential induced currents in pairs of coupled cells. Both spontaneous and evoked action potentials elicited a characteristic response in the postjunctional cell. Figure 6A represents spike-triggered average of 12 responses in pre- and postjunctional cells to 20-ms, 200-pA depolarizing pulses. Either cell 1 (Fig. 6A1, c1) or cell 2 (Fig. 6A2, c2) was stimulated.

View larger version (20K): [in this window] [in a new window]   Fig. 6. A: 20-ms, 200-pA depolarizing current pulses injected into cell 1 (A1, c1) or cell 2 (A2, c2) elicited an action potential in the prejunctional cell and a voltage deflection in the postjunctional cell (A1, c2; A2, c1). Each trace represents a spike-triggered average of 12 responses. An action potential, plotted at the same gain as the postjunctional response, is indicated with a dashed line. Note that the postjunctional response to an action potential was followed by an oscillating waveform. A similar waveform is evident in the prejunctional voltage trace, plotted at high gain. The resting potential of the postjunctional cell is denoted by a solid line. B: 2 distinct spontaneous waveforms were recorded in a pair of coupled neurons (B1, asterisk and double asterisk). The peak-to-peak amplitude distribution of these events (histograms, bottom) shows 2 distinct groups in cell 1 (c1, black and white columns). The same 2 groups are somewhat less separated in cell 2 (c2). The black columns in cell 1 were associated with black columns in cell 2. The pair of the recorded cells was electrotonically coupled, as demonstrated by eliciting an action potential in either of the cells by 100-ms depolarizing current pulses (B2). B1, inset: possible connectivity among the 4 cells, the 2 recorded and 2 others, coupled to both of the recorded cells. B2, inset: one of the cells was stimulated through the patch pipette. C: recordings using 5 mM EGTA intracellularly. Both cells developed prolonged action potentials. The postjunctional response to the prejunctional action potential was strong enough to cause firing in the postjunctional cell. As a result, 2 coupled cells developed 0.05 Hz synchronous rhythmic spike activity (C1). C2: another cell pair. Asterisk denotes simultaneous spikes.

The postjunctional responses were always composed of an initial fast depolarizing event followed by 2-3 damped oscillatory cycles (Fig. 6, A1, A2, and B2, bottom traces). Whereas the initial depolarization and the following slow hyperpolarization are likely to represent the well-characterized olivary dendritic action potential (Llinas and Yarom 1981), the additional oscillatory waves probably reflect transient subthreshold network activity. Examination of the voltage waveform in the two cells shows that, as expected, the brief depolarizing phase of the action potential undergoes larger attenuation than the more prolonged afterhyperpolarizing phase. As a result, the positive and negative phases of the postjunctional response are almost equal in amplitude. In an attempt to identify the source for the damped oscillations that followed the initial response, we plotted the prejunctional voltage at the same scale as the postjunctional response(dashed traces in Fig. 6A1,2). The time courses, as well as the amplitude of these oscillatory waves, are similar in both cells, suggesting that the oscillations occur simultaneously in both. However, in the prejunctional cell, the voltage trajectory of the action potential and the associated conductances partially mask these oscillations.

In some cases, whether or not the recorded cells fulfilled our criterion for coupling, we observed spontaneous events that resembled those evoked by prejuctional action potentials that occurred simultaneously in both cells (Fig. 6B1). In this example, two events are shown (asterisk and double asterisk). The distribution of the peak-to-peak amplitudes of these events in cell 1 (Fig. 6B1, bottom, c1) shows two distinct groups. In cell 2 (c2), two peaks are also distinguishable though the groups partially overlap. The events in the left group in the histogram of cell 1 (filled columns) were always associated with the events in the left subgroup in the histogram of cell 2 (filled columns). These observations strongly suggest that the two groups of the spontaneous events were generated by spikes evoked in two distinct neurons electrotonically coupled to both of the recorded cells. Moreover, in this case the two recorded neurons were electrically coupled as well (Fig. 6B2). Thus as shown in the inset, at least four olivary neurons were connected.

As with coupling at the steady state, action potential coupling also showed a certain degree of asymmetry. In the example shown in Fig. 6A, we calculated CC₁ (0.019) and CC₂ (0.024) as a ratio between the post- and the prejunctional voltages, measured from the baseline at time of the peak amplitude in the postjunctional response. On the other hand, CC₁ and CC₂, calculated in the same way but at the time of the maximal hyperpolarization in the postjunctional response, were 0.048 in both directions. The asymmetry in the coupling during the depolarizing phase might result in part from the width of the action potentials, since the action potential in cell 2 was slightly wider than in cell 1. The relatively large CC of the depolarizing phase suggests that action potentials propagate actively to the site of the gap junction, and therefore, a smaller attenuation is expected.

Under normal recording conditions we never saw coupling sufficiently strong for a spike in the prejunctional cell to trigger a spike in the postjunctional cell (n = 122 pairs). However, when action potentials were artificially prolonged they elicited postjunctional action potentials. As shown in Fig. 6C, when 5 mM EGTA was added to the pipette solution of both cells (see METHODS) within 10 min of patch recording, IO neurons developed extremely prolonged action potentials (about 250 ms), followed by a prolonged afterhyperpolarization. Under these conditions, two coupled neurons patched simultaneously developed slow (<0.05 Hz) supra-threshold synchronous rhythmic activity (Fig. 6C1). Occasionally one cell failed to generate an action potential and for several cycles the cells oscillated out of phase, as shown in Fig. 6C2.

Dye coupling: an independent measure of electrotonic coupling

Neurobiotin, a tracer molecule able to pass through gap junctions, is commonly used to demonstrate coupling between cells (Mills and Massey 2000). We directly labeled 103 recorded neurons, of which 35 were labeled during single patch recordings and 68 were labeled during double patch recordings where the tracer was added to only one (n = 14) or both (n = 54) recording electrodes.

Directly labeled neurons showed fully stained dendritic tree up to the level of single spines and had dark brown appearance. Out of 103 directly stained IO neurons, 84 neurons showed curly dendrites where the main dendritic shafts extended back toward the cell body ("curly" neurons; Fig. 7, B and D). Another 11 neurons had straight, sparsely bifurcating dendritic shafts ("straight" neurons Fig. 7, A and C). The remaining eight cells were difficult to classify. The classification into two types of neurons is in agreement with previous observations of Golgi impregnations (Scheibel and Scheibel 1955). Since relatively few of the labeled cells had straight morphology, we are not able to report on possible correlation between cell morphology and physiological parameters.

View larger version (129K): [in this window] [in a new window]   Fig. 7. A: 2 straight neurons labeled directly during simultaneous pair recording. No indirectly labeled cells were found. The section was counterstained with Cresyl Violet. Scale bar, 20 µm. B: curly neuron labeled directly through the patch pipette. No indirectly labeled cells were found. The section was counterstained with Cresyl Violet. Scale bar, 20 µm. C: dye injection into 1 straight neuron resulted in indirect labeling of 9 additional neurons, 2 of them are shown in the figure. A darkly stained dendrite belongs to the cell that was labeled directly. The indirectly labeled neurons are "straight," which can be seen from their dendritic morphology. Arrows denote examples of intersections of dendrites of different cells, possible locations of gap junctions. Scale bar, 20 µm. D: dye injected into 1 curly neuron resulted in indirect labeling of an additional 11 neurons. Some of the cells are out of focus in the figure. Indirectly labeled neurons had clearly stained cell bodies (e.g., arrow), but very weakly labeled dendrites. Scale bar, 20 µm.

In 52% of all staining experiments, indirectly labeled neurons were found in the vicinity of the injected neuron(s). In contrast to directly labeled neurons, indirectly stained cells had reduced labeling intensity with a light brown appearance. Neurons that gave rise to indirectly stained neighbors tended to have somewhat lower input resistance than those that did not have dye coupled cells (168 ± 74 M, n = 22 pairs and 225 ± 94 M, n = 12 pairs; P = 0.09). The substantial SD can be explained in part by the nonuniform age of the subject animals (9-31 days old).

The number of indirectly labeled neurons varied from 1 to 11 with an average of 3.8 ± 2.9. The three main subnuclei of the IO complex showed no significant difference in percentage of staining experiments where indirectly labeled cells were found, and they yielded a similar distribution in the number of indirectly labeled neurons (Fig. 8A). The variability in the number of coupled cells is illustrated in Fig. 8A by the large SD in number of indirectly labeled cells. When many indirect labeled cells were found in a given experiment they differed in staining intensity (Fig. 7D). There was no obvious correlation between the staining intensity of the indirectly stained neurons and their distance from the injected neuron. However, all indirectly labeled neurons were found in, or adjacent, to the dendritic field of a directly labeled cell (Fig. 7, C and D).

View larger version (14K): [in this window] [in a new window]   Fig. 8. A: mean ± SD number of indirectly labeled cells per directly labeled cell in experiments in which at least 1 indirectly labeled cell was found. The data distinguish 3 main subnuclei of the IO complex [principal olive (PO), medial accessory olive (MAO), and dorsal accessory olive (DAO)]. B: area of indirectly labeled cell bodies (mean ± SD) observed adjacent to directly stained straight or curly cells.

In all cases where directly labeled cells were straight, all of the indirectly labeled cells were also straight, as could be observed from their dendritic morphology (Fig. 7C; n = 4 experiments). However, when directly labeled cells were curly, only the soma of the indirectly labeled cells was visualized, and the dendrites were either unstained or only weakly stained (Fig. 7D). Thus it was impossible to determine the "type" of the indirectly stained cells based on dendritic tree structure. However, dendrites of curly cells are usually thinner than those of straight cells and by this criterion indirectly stained cells adjacent to curly neurons appeared to belong to the curly type. To test this we used cell size as an additional criterion since the two cell groups have been reported previously to differ considerably in their cell body size (Scheibel and Scheibel 1955). We than measured cell body area of indirectly labeled cells. The cell body area was 99 ± 14 µm² (n = 11, 3 staining experiments) when the injected cell was curly, and 167 ± 25 µm² (n = 9; 3 staining experiments) when the injected cell was straight (P 0.001; Fig. 8B). There was virtually no overlap in cell soma size between the two groups. We conclude that curly cells were dye coupled to other curly cells, and straight cells were coupled to other straight cells. Coupled networks of the two morphological types were not interconnected.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Electrotonic coupling between pairs of simultaneously recorded IO neurons was observed in 50% of the recordings. The coupling coefficient (CC) ranged between 0.002 and 0.17, with most of the pairs being weakly coupled. The coupling was voltage independent in the range of potentials negative to the resting potential (hyperpolarization). Depolarization of either of the cells decreased the coupling strength. Coupling in different pairs displayed different degrees of asymmetry, expressed as a directional preference. The chance of finding a coupled cell pair was 80% in immediately neighboring cells but dropped to about 30% at distances larger than 40 µm. No coupling was observed at distances larger than 70 µm. Dye injection into olivary neurons produced indirect labeling of 1-11 nearby cells in 52% of experiments.

Coupling strength

Gap junctions, the morphological correlate of electrotonic coupling, are found typically between spines of distal olivary dendrites within glomeruli (De Zeeuw et al. 1990a,b). Therefore current spreading from one coupled cell to another must travel through dendrites and dendritic spines before reaching the junction. Accordingly, R_c in our model of two coupled cells (Fig. 1) corresponds not only to the resistance of the junction itself, but includes also the resistance of the entire path from the pre- to the postjunctional cell body. Assuming an average junction of about 100 channels (De Zeeuw et al. 1996) of 10-15 pS each (Srinivas et al. 1999), the junctional resistance is in the range of several gigaohms. R_c calculated in our experiments ranged from 0.7 to 19.8 G. Therefore we conclude that, at least for the upper values of calculated R_c, the majority of the coupling resistance is due to dendritic axial resistance rather than to gap junctions themselves. As was shown in METHODS, taking into account the leakiness of the dendritic membrane, R_c of 20 G corresponds to a maximum of 1 mm of dendritic length assuming unbifurcating dendrites. Since the longest dendrites in our labeled cells were about 400 µm, all cases in which coupling was found can be explained by direct connections between the recorded cells. Junctions located remotely on dendrites presumably account for weak CC. Alternatively, weak coupling could result from measuring indirect connections between relatively strongly coupled cells. For example, CC = 0.01 might be measured between two neurons, both of which are coupled to an intermediate neuron with CC = 0.1. However, if indirect coupling of this sort is common, we should also have encountered many instances of direct coupling, with CC = 0.1, and hence a bimodal distribution of CC. We conclude that it is more likely that the majority of measurements reflected direct, but weak, connections. Moreover, in most cases, we have to assume that there was more than one junction connecting the cells.

To evaluate the strength of the coupling, we used steady state voltage responses to prolonged current pulses. Under these steady state conditions only the membrane resistance determines the amplitude. On the other hand, the capacitance of the postjunctional membrane plays an important role in determining the efficiency of electrotonic coupling during brief events like action potentials. Transmission of action potential currents might have functional importance, potentially synchronizing firing of olivary neurons. Our experiments show that despite the long duration of olivary action potentials (about 20 ms) and the proximity of high-threshold Ca²⁺ channels to the distally located gap junctions, a spike in one IO neuron never elicited firing in the coupled neuron. Consistent with the role of membrane capacitance in determining coupling strength, synchronous firing of coupled olivary neurons was observed after artificial prolongation of the high-threshold Ca²⁺ spike using 5 mM EGTA in the pipette solution (Fig. 6). Nevertheless, synchronization of firing by electrotonic coupling might occur in vivo for the following reasons. First, inferior olivary neurons in vivo might have higher excitability than in slice preparations. Second, the summation of several synchronized postjunctional responses could reach threshold and induce firing. Therefore a common input sufficient to induce action potentials in part of the network might activate the entire network. Third, the pronounced afterhyperpolarization following a spike in olivary neurons (Fig. 6) is well transmitted through gap junctions and might synchronize coupled neurons by triggering a rebound low threshold Ca²⁺ spike. In addition, the coupling might serve to produce subthreshold oscillations and only indirectly synchronize suprathreshold activity (Lampl and Yarom 1993, 1997; Llinas and Yarom 1986; Manor et al. 1997).

Symmetry and voltage-dependence

Measuring the CC on stimulation of cell 1 (CC₁) or cell 2 (CC₂) revealed an average asymmetry of 27%. Calculating R_c did not significantly reduce the coupling asymmetry, indicating that the phenomenon cannot be explained by differences in the input resistance of the coupled cells. This directional preference is illustrated in Fig. 4C by distinct transfer resistance curves on direct stimulation of cell 1 or cell 2. Asymmetric transfer resistance can, theoretically, be the product of nonlinear dendritic membrane properties combined with an asymmetric location of the junction, e.g., dendro-somatic. However, in such a case, the relationship between the pre- and postjunctional voltage would be nonlinear. The observed linear relationship (Fig. 4D) favors the possibility that the coupling resistance itself exhibits a directional preference. Nonetheless, we cannot completely eliminate the possibility that nonhomogeneous distribution of voltage dependent channels along the dendritic path that connects the two neurons will generate an apparent asymmetry. However, in such a scenario, these putative channels should be located in a restricted area remote from the cell body.

An asymmetry of gap junctional resistance has been described in many systems in association with voltage-dependence (Loewenstein 1981; Moreno et al. 1994). The linear relationship between the pre- and postjunctional voltages observed in our experiments (Fig. 3D) suggests that the CC did not depend on voltage in the range of potentials negative to the resting potential. Depolarization of either the pre- or the postjunctional cell by injection of DC current reduced the CC in both directions, but the linear relationship between the pre- and postjunctional voltages remained. On the other hand, prolonged hyperpolarizing pulses injected during DC depolarization had to restore the original membrane voltage, and consequently, the original value of the CC, breaking the linear relationship. Therefore we have to assume that an additional process occurred on depolarization and was responsible for the observed reduction in the CC. The most plausible explanation is an increase in intracellular Ca²⁺, which is known to reduce electrotonic coupling (Loewenstein 1981). Such an increase would reduce the coupling conductance in both directions, while maintaining the original asymmetry.

Asymmetry in the flux of chemical permeants was reported in heterologous junctions, made by expressing two different connexins in adjacent coupled cells (Loewenstein 1981; Zahs and Newman 1997). Such an asymmetry was not demonstrated for inorganic ions. Moreover, different types of connexins are unlikely to be expressed among the IO cells since only connexin 36 has been found in these neurons so far and connexin 36 might represent the only connexin type expressed in neurons (Rash et al. 2000).

Regardless of the mechanism, the asymmetry might provide the olivary system with a unique property. Specifically, it can generate a condition where information within the nucleus flows in a directionally selective way. Interestingly, Fukuda et al. (2001) demonstrated that the synchronous complex spike activity in the cerebellar cortex propagates in the directionally selective way. Furthermore, optical imaging of the subthreshold oscillations in slice preparations demonstrated directional propagation of waves of subthreshold activity (Devor and Yarom 2002).

Size of the coupled network

How big are networks of electrotonically coupled olivary neurons? This question might have important implications for olivo-cerebellar function, determining the extent of synchronous climbing fiber input to populations of Purkinje cells (Welsh et al. 1995). To estimate the extent of connectivity we used two techniques: transfer of neurobiotin through gap junctions and simultaneous double patch recording. The results of neurobiotin labeling showed that one olivary neuron is coupled to 11 other neurons with an average of 3.8. All indirectly labeled cells were found in, or immediately adjacent to the dendritic field of the directly stained neurons, with no correlation between the intensity of dye-coupled neurons and distance to the directly labeled cell soma. Therefore it is likely that only direct connections were detected by this technique. The extent of coupling revealed by neurobiotin underestimates the real value. Indirectly labeled cells were observed only in 52% of staining experiments, implying that about one-half of olivary neurons were not connected to any other cells. On the other hand, double patch recordings showed that the chance of finding a coupled pair in the immediate vicinity of a recorded neuron was 80%. Therefore in agreement with previous reports (Arabshahi et al. 1997), neurobiotin does not always pass through gap junctions.

The second estimation of the extent of coupling is based on simultaneous double patch recordings. From the probability of finding a coupled pair as a function of distance between the cells (Fig. 2B) and from measurements of the cell density, we calculated that one neuron should be connected to about 50 others. It is important to note that this number might underestimate the extent of the direct coupling since somatic recordings may not reveal coupling through remote dendrites.

It is interesting to note that Ruigrok et al. (1990), assuming a mean packing density of 23 neurons per 1.6 · 10⁶ µm³ (Sheibel and Sheibel 1955), calculated that 115 neurons would be positioned within the dense part of the dendritic tree of cat curly olivary neuron. The density calculated in our experiments is about threefold higher. This can be attributed to differences in the species (rat versus cat) or the methods used (Cresyl Violet versus Golgi). If each olivary neuron was coupled to as many as 115 other neurons, a dramatic decrease in input resistance would be expected. However, neurons, which showed dye coupling, differed only marginally in their input resistance from neurons that showed no dye coupling. Therefore not all the neurons whose dendrites intermingle make gap junctional connections between them.

De Zeeuw and collaborators (De Zeeuw et al. 1996) calculated the maximal number of coupled olivary neurons from the expected drop in input resistance due to coupling conductance. Their conclusion was that each olivary neuron is coupled to about 6-13 others, well below 115. This value, which is considerably lower than our estimate, is explained by their use of a lower R_in (30-60 M) and a relatively high CC (0.25).

Cells indirectly labeled following injection of neurobiotin into olivary neurons with "straight" dendrites were all of the same straight type. Injection of olivary neurons with "curly" morphology, on the other hand, indirectly labeled only curly neurons. Therefore the IO nucleus contains two non-interconnected cell populations made up of curly and straight neurons, respectively.

For the first time, in this study we estimate the size of inferior olivary electrotonically coupled network using physiological measurements and demonstrate two independent, overlapping in-space networks of cells with distinct morphology. An asymmetry of the coupling is a newly characterized feature of olivary functional connectivity. Optical imaging of the subthreshold activity in olivary brain slices, reported in the accompanying paper (Devor and Yarom 2002), demonstrates directional organization in the nucleus.