All experiments were performed on wild-caught adult male crabs (Cancer borealis) purchased from local seafood suppliers in Newark, NJ. Prior to experiments, animals were kept in artificial sea water tanks at 13 C. Before dissection, crabs were anesthetized by placing them on ice for 30 min. The STNS was dissected out following standard protocols (Blitz et al., 2004; Tohidi and Nadim, 2009), placed in a Petri dish coated with clear silicone elastomer (Sylgard 184; Dow Corning) and superfused with C. borealis saline, containing (in mM) 11 KCl, 440 NaCl, 13 CaCl₂, 26 MgCl₂, 11.2 Trizma base, and 5.1 maleic acid (pH = 7.4–7.5). A petroleum jelly well was built around the STG for constant superfusion of chilled (10–12°C) saline during the experiment.

PD neurons were identified by their characteristic intracellular waveforms and by matching their activities to the spikes on the corresponding motor nerves. Extracellular activities of motor nerves were recorded with a differential AC amplifier (Model 1700; A-M Systems), using stainless-steel pin wire electrodes placed inside and outside of small petroleum jelly wells built around the nerves. Intracellular recordings, current clamp and voltage clamp experiments were done with Axoclamp 900 A amplifiers (Molecular Devices). The STG was desheathed and the neuron cell bodies were impaled with sharp glass electrodes, prepared with a Flaming-Brown P-97 Puller (Sutter Instruments) and filled with 0.6 M K₂SO₄ + 20 mM KCl solution (15–30 MΩ electrode resistance). All electrophysiological data were digitized at 5–10 KHz with a Digidata 1440 A data acquisition board (Molecular Devices).

We measured the membrane potential and electrical coupling resonance in pairs of PD neurons, in both current clamp experiments and voltage clamp experiments, with dual two-electrode recordings. In all experiments, we recorded the voltage in both the pre- and the postjunctional neurons (V _pre and V _post ) and the current injected into them (I _pre and I _post ). In current clamp experiments, a ZAP (Impedance Amplitude Profile) current was injected into the prejunctional neuron and produced oscillation in both V _pre and V _post . The ZAP function was given by I Z A P = I max cos 2 π f t f t = f lo L e L t − 1 L = 1 t max log f hi f lo where f(t) swept a range of frequencies as a function of time, t, from f _lo = 0.1 Hz to f _hi = 4 Hz. I _max = 3 nA and produced a V _pre roughly ranging from −60 mV to −30 mV. t _max is the total duration of the ZAP waveform which, in most trials was at least 100 s. Additionally, to avoid transients, we always started the ZAP function with 2 pre-cycles of a sinusoidal current applied at the lowest frequency (f _lo = 0.1 Hz) that smoothly transitioned into the ZAP waveform. When measuring in voltage clamp, the same ZAP function was applied to the prejunctional voltage V _pre to force it to alternate between −60 and −30 mV, while the postjunctional neuron was held at a constant voltage of V _post = −60 mV. The prejunctional impedance (Z _pre ), the postjunctional impedance (Z _post ), the coupling coefficient (CC) and the coupling conductance (G _c ) were calculated as shown in Table 1.

All factors measured as a function of frequency, in current or voltage clamp, were fit with a sixth-degree polynomial in MATLAB (The MathWorks Inc.) and the resonance frequency and amplitude were estimated as the peak amplitude of the fit curve and the frequency at which the maximum amplitude was achieved.

All experimental measurements involving electrical coupling were done in the presence of 100 nM tetrodotoxin citrate (TTX; Biotium) saline to block action potentials as well as the descending neuromodulatory inputs, and 5 µM picrotoxin (PTX; Sigma) to block chemical synapses within the STG, all of which are inhibitory.

All experimental data analysis was done using scripts written in MATLAB, and statistical comparisons were done in SigmaPlot 12 (SyStat Software Inc.). Critical significance level was set to α = 0.05. Unless otherwise indicated, all error bars in the figures represent standard error of the mean.

We made biophysical models of coupled resonant neurons of Figures 4A, 5, using single compartment neurons having the Hodgkin-Huxley type currents given in Table 2. The model structure and parameters for the model neurons were implemented from the PD neuron resonance properties as previously described (Fox et al., 2017). Simulations were performed in NEURON 8.0 through the Python 3.8 interface. Analyses were conducted through custom Python scripts using scipy 1.5 and numpy 1.19 packages. All simulations for this study are available on https://github.com/fnadim/ECouplingResonance.

The ball-and-stick model neurons were built using a point neuron, modeled as a sphere of diameter 100 μm, coupled to a single neurite of length 1,000 μm, divided into 101 compartments. Two forms of the neurite were used, as described in the Results. One was a standard cylinder of diameter 10 µm. The other was a tapered cylinder with diameter tapering (proximally-to-distally) linearly from 20 to 0.5 µm. The parameters used to build the model were R_m = 10000 Ωcm², R_a = 100 Ωcm, Cm = 1 μF/cm². For adding resonance, all compartments were modeled according to the parameters given in Table 2. Simulations were preformed in NEURON as described above.

The model consisted of two neurons coupled with symmetric electrical coupling. Each neuron was built as a two-compartment biophysical model, consisting of a soma/neurite (SN) and an axon (A) compartment. The soma/neurite compartment included a leak and a low-threshold (T-type) inactivating calcium current, which effectively made it a calcium spike oscillator (Torben-Nielsen et al., 2012). The axon compartment included Hodgkin-Huxley type leak, fast sodium and delayed rectifier potassium currents, which allowed it to spike but only when the input from the soma/neurite compartment produced a calcium spike. The combination produced a bursting neuron. The neuron obeyed the following standard Hodgkin-Huxley type current balance equations: C S N d V S N d t = I L − S N + I C a + I a x i a l + I c C A d V S N d t = I L − A + I N a + I K − I a x i a l where C _x and I L − x = g L − x V − E L − x denote the membrane capacitance and leak current of the compartments (x = SN or A), I a x i a l = g a x i a l V S N − V A is the axial current between the two compartments. The electrical coupling current is I c = G c V S N − V S N 2 , where V _SN2 is the voltage of the other neuron’s SN compartment and G _c is the coupling conductance, which may be frequency-dependent (see below). The ionic currents are given as I i o n = g ¯ i o n m i o n p h i o n q V − E i o n where ion = Ca, Na or K, g ¯ i o n is the maximal conductance, and m _ion and h _ion denote the activation and inactivation gating variables governed by d x d t = 1 τ x x ∞ V − x

(x = m _ion or h _ion ). The activation and inactivation powers, p and q, are non-zero integers. The model equations and parameters are provided in Table 3. The parameters of the two neurons were chosen so that, in isolation, their bursting frequencies differed by about 10%.

The G _c frequency dependence was modeled to show resonance at f = 0.75 Hz according to the following equation: G c = 2.625 G ¯ c e − 0.1 f − e − 5 f where 2.625 is a scaling factor so that G c = G ¯ c at the resonance frequency.

Simulations were done in C, using a 4th order Runge-Kutta numerical integrator. The two cells always started with identical initial conditions and each run was 25 s. A 15 s window, ending 1 s before the simulation end (to remove filtering artifacts), was used for measurements of synchrony. The two voltage waveforms were sampled at 1 KHz The Slow waveform was obtained by low-pass filtering the waveforms with a moving average window of length 81 ms. The Fast waveform was obtained as the difference between the Full waveform and the Slow waveform. The level of synchrony was measured as, R ², the square of the correlation coefficient between the (Full, Slow or Fast) waveforms of the two cells in this time window. All analysis was done in MATLAB.

The two PD neurons are very similar in their ionic current expression and anatomical structure and therefore considered to be functionally equivalent, if not identical (Marder and Eisen, 1984; Bucher et al., 2005; Schulz et al., 2006). During normal pyloric activity, these two neurons exhibit synchronous slow-wave oscillations that support their bursting activity (Figure 1A). This synchronous activity arises primarily from their electrical coupling to one another and to the pyloric pacemaker, the anterior burster (AB) neuron (Marder and Eisen, 1984). The electrical coupling strength between the two PD neurons can be determined in the classical way as the coupling coefficient (CC), measured as the ratio of the voltage change of the postjunctional neuron to that of the prejunctional neuron (Figure 1B): C C = Δ V p o s t Δ V p r e .

A more direct measure of the strength of coupling, which does not depend on the input resistance of the postjunctional neuron can be obtained by voltage clamping both neurons, stepping the voltages of the (arbitrarily-designated) prejunctional neuron and measuring the current flow to the postjunctional cell. The coupling conductance (G _c ) can be measured as (Figure 1C): G c = Δ I p o s t Δ V p r e .

The PD neurons are bursting oscillators and, additionally, these neurons show membrane potential resonance at a frequency correlated with their burst frequency (Tohidi and Nadim, 2009; Tseng and Nadim, 2010; Fox et al., 2017). We were interested in knowing whether the coupling strength between the two PD neurons (the PD-PD coupling) depends on, or is influenced by, their oscillation frequency and, if so, if the coupling also shows resonance. In the context of this manuscript, resonance is defined as a neuronal property that produces a maximum response to oscillatory input at a non-zero frequency. To compare any frequency dependence of the electrical coupling and that of the individual neurons, it was necessary to measure these two factors simultaneously. To do so, we arbitrarily designated the two PD neuron as pre- and postjunctional, injected a sweeping-frequency sinusoidal (ZAP) current into the prejunctional PD neuron and measured the voltage responses in both pre-and postjunctional PDs (Figure 2A). We then switched the pre and post designations and repeated the protocol. In the trials shown here, the ZAP function frequency is swept from 0.1 to 4 Hz, a range that covers the natural burst frequency of PD neurons which is typically between 0.5 and 2.5 Hz. In several trials we also changed the direction of the frequency sweep to go from high to low frequency. There was no difference in our measurements when the direction of the sweeping frequency of the ZAP current was reversed.

In 19 out of 28 measurements, both the prejunctional membrane impedance (Z _pre ; Table 1) and the coupling coefficient (CC) showed clear resonance (Figure 2B). Note that the peak values shown in the figure do not exactly match the peak of the mean profile (solid line) since the peak of the average of multiple non-linear curves is determined by the overall shapes of the individual curves, not just by their peaks. In response to the ZAP current, however, Z _pre and CC showed distinct frequency profiles (Figure 2B): CC had a lower resonance frequency (0.70 ± 0.20 Hz) than Z _pre (0.97 ± 0.36 Hz) and the normalized peak amplitude of CC was larger than that of Z _pre . Additionally, the resonance frequency of CC was correlated with the resonance frequency of both the prejunctional and postjunctional impedance (Z _pre and Z _post , Figure 2C), while its maximum amplitude was only correlated with that of Z _post (Figure 2D).

Membrane potential resonance can be measured using both current clamp and voltage clamp methods, each providing its own advantage. Current clamp measurements allow the membrane potential to change freely and therefore, voltage-dependent ionic currents can also influence the membrane potential. This method allows one to observe neuronal responses in a manner closer to their natural biological activity and, in general, current clamp measurements provide a more realistic value of the impedance amplitude (Rotstein and Nadim, 2019). However, because the electrical coupling coefficient is influenced by the input resistance of the postjunctional neuron, it is not a direct measure of the strength of electrical coupling (Bennett, 1966; Mann-Metzer and Yarom, 1999). A direct estimate of the electrical coupling conductance, G _c , requires measuring the current flowing between the two coupled neurons (Table 1) and, to obtain an accurate measurement of the ionic current, the membrane potentials must be constrained using the voltage clamp method, as we showed in Figure 1C.

To directly measure whether the coupling conductance G _c is influenced by frequency, we voltage clamped both PD neurons at a holding potential of −60 mV. We then applied a ZAP function voltage waveform (ranging from −60 to −30 mV) to the prejunctional neuron, while holding the postjunctional neuron at a steady voltage of −60 mV (Figure 3Ai). This allowed us to simultaneously measure the currents flowing in the pre- and postjunctional neurons (I _pre and I _post ) in response to the change in the frequency of V _pre . As seen in the example in the figure, I _pre showed a clear minimum in response to the voltage ZAP, indicating a minimum in the neuronal admittance (the reciprocal of impedance) value. This simply reflects the membrane potential resonance in the prejunctional PD neuron as measured in voltage clamp (Tseng and Nadim, 2010) (Figure 3Aii, top panel). Interestingly, in response to the prejunctional ZAP function, the postjunctional current, I _post , did not remain constant in amplitude but had a clear maximum amplitude at a non-zero frequency. Therefore, the PD-PD coupling conductance, G _c , also showed a peak at this frequency (Figure 3Aii, bottom panel).

Unlike the measurements with the step protocol, in which the directionality of the electrical coupling had little influence, we found that the two directions of the coupling often produced slightly different results. Therefore, in this part of the study, we treated the PD1 to PD2 and the PD2 to PD1 in each preparation independently. In 20 of the 28 measured cases, G _c showed resonance. Figure 3Bi shows the averaged resonance profile of these 20 electrical connections.

Because Z _pre and G _c have different units, their amplitudes cannot be directly compared. Yet it is useful to examine how much larger each of these factors is at its peak compared to its baseline. In fact, membrane potential resonance power is often measured as a ratio of the peak impedance Z _max to the impedance at zero frequency (i.e., the input resistance). We used the values of Z _pre and G _c at the lowest frequency (0.1 Hz) as a proxy for the zero-frequency values and normalized these curves to this value for each experiment (Figure 3Bii). A paired comparison between G _c and the impedance profile (Z _pre ; see Table 1) of the prejunctional neuron showed no difference in their relative amplitudes. However, G _c had a significantly lower resonance frequency (0.80 ± 0.26 Hz) than Z _pre (1.27 ± 0.23 Hz). Also, note that the resonance frequencies for Z _pre were different between current clamp and voltage clamp experiments, because, as described above, Z _pre measured in current clamp is influenced by non-linear actions of voltage-gated ionic currents. Finally, unlike with the coupling coefficient CC, we did not observe any correlation between Z _pre or Z _post and G _c either in frequency (Figure 3C) or in amplitude (Figure 3D). This is consistent with the hypothesis that G _c reflects the properties of the electrical coupling and not those of the coupled neurons.

Frequency dependence of electrical coupling may emerge from the properties of the coupled neurons, may be a property of the junctional coupling itself, or arise from the interaction of the two. To demonstrate how resonance of the coupling coefficient CC could arise from the membrane potential resonance properties of the coupled neurons, we coupled two biophysical models that capture the resonance properties of the isolated PD neuron (Fox et al., 2017) with a constant electrical coupling coefficient (parameters for the model given in Table 2). We injected a ZAP current into one neuron and measured the voltage responses of both neurons (Figure 4Ai). Current injection to PD model neuron 1 resulted in membrane potential resonance, mainly due to the intrinsic properties of this neuron, and current flow through the electrical coupling to PD model neuron 2 produces membrane potential resonance in the second neuron. In this simulation, the two PD model neurons were identical and therefore, when isolated, had identical impedance profiles (Z ₁ = Z ₂ in Figure 4Aii). Coupling only slightly changed the impedance profile of either neuron compared to its profile when isolated (Z _pre compared to Z ₁; Z _post compared to Z _2; see Table 1 for notations). In this simulation, the CC vs. frequency curve also showed resonance, with a resonance peak frequency at a value close to, but different from, that of the coupled neurons. This gave rise to the question what factors determine the resonance frequency of CC.

To address this question, we switched to linear resonator neurons in which the impedance profile can be mathematically calculated (Richardson et al., 2003; Rotstein and Nadim, 2014). The full analysis is provided in Supplementary Appendix SA1. In the linear system of two coupled resonator neurons, the value of the coupled impedance profiles, as a function of the respective uncoupled profiles is given by Z p r e = Z 2 − 1 + G c Z 1 − 1 + G c Z 2 − 1 + G c − G c 2 Z p o s t = G c Z 1 − 1 + G c Z 2 − 1 + G c − G c 2 . (Supplementary Equation SA1.8 of the Appendix with notations of Table 1) and the value of CC reduces to the ratio of the amplitudes of the two impedance profiles. C C = Z p o s t Z p r e = G c Z 2 − 1 + G c . (1.1)

Here, Z ₂ is the complex impedance profile of the postjunctional neuron when isolated (Z ₂ is the amplitude of the complex Z ₂, i.e., Z ₂ = ||Z ₂||). Note that for linear resonator neurons, CC only depends on the impedance of the (isolated) postjunctional neuron and not on that of the prejunctional neuron. Although this result does not generally hold for non-linear (e.g., biological) resonators, it still provides a very good approximation in most cases, in addition to a clearer conceptual understanding of the phenomenon.

The coupled linear resonators provide insight into how electrical coupling influences the resonance properties of the neurons as well as that of CC. For instance, the simulation of two electrically coupled linear resonators (as described in Supplementary Appendix SA1) and injected with a ZAP current shows distinct peak amplitudes in the pre- and post-junctional neuron’s membrane potentials (Figure 4Bi). In fact, coupling two linear resonators with the same maximal amplitude, but distinct resonance frequencies, shifted the resonance frequencies of both neurons toward values in between those of the isolated neurons (Figure 4Bii; compare peak frequencies of Z _pre and Z _post with Z ₁ and Z ₂). The resonance frequency Z _post fell between Z _pre and Z ₂. The postjunctional impedance profile (Z _post : which is V _post /I _pre in Figure 4Ai; see Table 1 for definition) always had a lower amplitude than the prejunctional profile (compare Z _pre and Z _post in Figure 4Bii). In Figure 4Bii, we also show the frequency-dependent profile of CC for comparison (note the different scales). Here, the resonance frequency of CC was close to that of Z ₂.

Interestingly, however, the resonance frequency of CC was not constrained to fall between the resonance frequencies of Z ₁ and Z ₂. This can be readily observed using the linear resonator models when current was injected in the cell with lower resonance frequency (cell 1 in Figure 4Bii) and the electrical coupling conductance was increased. When the electrical coupling conductance was small, the resonance frequency of CC was close to that of Z ₂, but when G _c was increased, this frequency also increased monotonically (Figure 4Biii bottom panel). Not surprisingly, increasing the strength of coupling also caused the resonance frequencies (Figure 4Biii bottom panel) and maximum pre- and postjunctional impedance values (Figure 4Biii top panel) to converge to the same value. These predictions of the analytical linear models can be confirmed by simulating a biophysical model of two coupled resonator neurons. Figure 4Ci shows such a simulation, which is based on the same neurons as in panel Ai, except that the prejunctional neuron’s parameters have been changed to allow for a lower resonance frequency while keeping the same resonance amplitude. The findings for Z _pre , Z _post and CC (Figure 4Cii) are qualitatively similar to those of the linear model, as is the dependence of the resonance frequencies and peak resonance values of these attributes as a function of G _c (Figure 4Ciii). The only small difference between the biophysical and linear models arises at very small G _c values, where, in the biophysical model (Figure 4Ciii), Z _post and CC show a non-monotonic dependence on G _c .

One can also use the coupled linear resonators to predict how a frequency-dependent G _c influences the measured coupling coefficient. To make this comparison, we scaled G _c as a function of frequency in a manner similar to what we had measured in the biological system (Figure 3Bii and left panel of Figure 4D). A comparison of the resulting CC and the CC obtained with a constant G _c value across frequencies showed that the resonance frequency of G _c can clearly amplify the amplitude of CC, by bringing the Z _pre and Z _post curves closer to each other in this range (Figure 4D right panel).

When both neurons are voltage-clamped, the prejunctional neuron with a fixed-amplitude sinusoidal waveform and the postjunctional neuron at a constant holding voltage (Figure 5Ai), the amplitude of the ionic current change recorded in the postjunctional neuron (I _post , which is also the coupling current I _c ) is proportional to the coupling conductance G _c and independent of any resonant properties of either neuron. This follows from the fact that I p o s t = I c = G c V p r e − V p o s t where V _pre and V _post are controlled by voltage clamp and G _c is constant. Although this is an obvious result, it is informative. We demonstrated this in the simulation shown in Figure 5Aii, where the prejunctional model neuron was voltage-clamped with a ZAP function (range −60 to −45 mV) and the prejunctional neuron was held at a steady voltage of −60 mV (parameters for the model given in Table 2). The current (I _pre ) in the prejunctional neuron showed a minimum, while the current flowing to the postjunctional neuron (I _post ) did not change with the frequency of the ZAP function (Figure 5Aiii). This is also clear from our calculations for the coupled linear resonators in voltage clamp as shown in Supplementary Appendix SA1 (Supplementary Equation SA1.11).

However, when these two neurons are part of a circuit of electrically coupled neurons, even when both neurons are voltage-clamped, the measurement of I _post may not have a constant amplitude at all input frequencies due to circuit connectivity. For example, if both neurons are electrically coupled to a third neuron whose voltage can vary freely, indirect current flow through the third neuron may affect the amplitude of I _post . Indeed, in the pyloric circuit, the two biological PD neurons are electrically coupled to the anterior burster (AB) neuron (Marder and Eisen, 1984) and, in our experiments described above, we did not control or monitor the activity of the AB neuron. It is therefore possible that the apparent resonance we observed in our experimental measurement of I _post (Figure 3Ai) was due to the uncontrolled changes in the voltage of the AB neuron. To test this possibility, we coupled the model neurons of Figure 5Ai to a third neuron with the same resonance properties and ran the same voltage clamp protocol (parameters given in Table 2). Indeed, we observed that even though the pre- and postjunctional neurons were voltage-clamped, the voltage of the third coupled neuron (marked 3 in Figures 5Bi,5Bii) showed a peak at an intermediate frequency. Thus, the resonance of neuron 3 resulted in an apparent resonance in our measured I _post , because in this case I p o s t = G c V p o s t − V p r e + G c V p o s t − V 3 .

A normalized comparison between the impedance profile V _pre and I _post (Figure 5Biii) shows that even when the three neurons are identical in their properties (and therefore have the same isolated resonance frequency), I _post may show resonance at a different frequency, as we had observed in our experimental measurements of Figure 3. Therefore, a potential mechanism for electrical coupling current resonance is through frequency preference inherited from other electrically coupled cells.

Voltage clamp measurements of distal currents are inevitably subject to space clamp errors (To et al., 2022). Considering that gap junctions are most probably located at a distal location to the soma (Otopalik et al., 2019a), it is likely that our voltage-clamp estimate of G _c , or even our measurement of Gc resonance is affected by space clamp errors. To examine the extent of such an error, we used a multi-compartmental ball-and-stick model of the PD neurons to estimate the effect of coupling distance from the somatic recording site on G _c . Two ball-and-stick models were examined (Figure 6 schematics), one with a standard cylindrical neurite of constant diameter (10 µm), the other with a tapering diameter (20–0.5 µm). As described in a recent detailed study (Otopalik et al., 2019b), the tapered model is a better estimate of the structure of STG neurons.

To estimate the effect of coupling position on G _c , the somas of both ball-and-stick model neurons were voltage clamped and a voltage step (from V _hold to V ₁) was applied to one (cell 1), while the other (cell 2) was held at a constant voltage (V _hold ). G _c was then measured as G c = I 2 / V 1 − V h o l d .

When the position of the coupling was changed along the neurite, the estimated G _c attenuated (Figure 6). The extent of attenuation was much less for the tapered neurite compared to the standard one, except at the very tip, where the tapered neurite became very small in diameter. This was consistent with the findings of Otopalik et al. (2019b) in which they estimated attenuation of a chemical synaptic input. However, considering that the two PD neurons have a relatively strong apparent coupling coefficient, we estimate the coupling position to be no further than halfway along the tapered neurite. Additionally, when we added the ionic currents that produce resonance (Table 2) to these neurons, there was little resonance effect measured in G _c (data not shown).

We used computational modeling to understand the potential function of resonance in the electrical coupling conductance in this system. We used a computational model of two electrically coupled bursting neurons and chose the parameters of the two neurons to produce bursting oscillations with different cycle frequencies when uncoupled. We then coupled the two neurons and examined the synchronization of their activity at different electrical conductance strengths (Figure 7A). The level of synchronization was measured as the coefficient of determination (R ²) between the two voltage waveforms (Lane et al., 2016). We measured the synchrony of the full bursting waveforms between the two neurons (full). In addition, we lowpass-filtered the traces to measure the synchrony of only the slow waves (slow), and high pass-filtered to measure the synchrony of only the spiking activity (fast).

To examine the effect of resonance in G _c on the synchrony between the two neurons, we produced a G _c frequency profile similar to that observed experimentally (compare G _c vs. f in Figure 7B with Figure 3Bi). Although the two model neurons had different intrinsic burst frequencies, they always oscillated with the same frequency (i.e., they were phase locked) when coupled. To understand the role of G _c resonance, we changed this burst frequency by modifying the intrinsic properties of the bursting neurons (see Methods). We found that when the two cells oscillated at either low or high frequencies, where the G _c was smaller, the slow wave synchrony between the two neurons was smaller (Figure 7C, Bi, Biii). In contrast, when the network frequency matched the G _c resonance frequency, the level of synchronization was maximal (Figure 7C). In contrast to the slow wave, the fast spiking activity of the two neurons was not noticeably altered by frequency. When G _c was kept constant as a function of frequency, then network frequency did not affect the level of synchrony between the two neurons, either in the slow wave or in the spiking activity. The level of synchrony in this case was determined simply by the value of the electrical coupling conductance G _c .