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Jean-Marc Goaillard, Inserm U641 “Neurobiologie des canaux ioniques”, Faculté de médecine-secteur nord, Université de la Méditerranée, CS80011, Boulevard Pierre Dramard, 13344 MARSEILLE Cedex 15, rf.demvinu@dralliaog
Adam L. Taylor, Volen Center, Rm 306, Brandeis University, MS 013, Waltham MA 02454, ude.siednarb@rolyatla
Stefan R. Pulver, Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, United Kingdom, ku.ca.mac@355ps
Eve Marder, Volen Center, Rm 314, Brandeis University, MS 013, Waltham MA 02454, ude.siednarb@redram
Many neurons display post-inhibitory rebound (PIR), in which neurons display enhanced excitability following inhibition. PIR can strongly influence the timing of spikes on rebound from an inhibitory input. We studied PIR in the Lateral Pyloric (LP) neuron, part of the stomatogastric ganglion of the crab Cancer borealis. The LP neuron is part of the pyloric network, a central pattern generator that normally oscillates with a period of ~ 1 s. We used the dynamic clamp to create artificial rhythmic synaptic inputs of various periods and duty cycles in the LP neuron. Surprisingly, we found that the strength of PIR increased slowly over multiple cycles of synaptic input. Moreover, this increased excitability persisted for 10–20 s after the rhythmic inhibition was removed. These effects are considerably slower than the rhythmic activity typically observed in LP. Thus this slow postinhibitory rebound allows the neuron to adjust its level of excitability to the average level of inhibition over many cycles, and is another example of an intrinsic “short-term memory” mechanism.
Post-inhibitory rebound (PIR) is a common phenomenon that contributes to the firing patterns of neurons (Getting, 1989). It has long been understood that rebound firing after inhibition can provide important timing signals in motor systems (Selverston and Moulins, 1985), and is also important for the generation of oscillations in other brain systems (Llinas, 1988). In most cases, PIR elevates the spike rate compared to that observed before the inhibitory input (Perkel and Mulloney, 1974; Winograd et al., 2008). In other cases, although there may not be an enhancement of the firing rate, the latency of the first spike after inhibition is decreased, which can be functionally important. Generally, the properties of PIR depend upon several of the neuron’s intrinsic membrane currents (Hartline and Gassie, 1979; Harris-Warrick et al., 1995a; Harris-Warrick et al., 1995b).
In most experiments, PIR is evoked by a single hyperpolarizing input. Measured this way, PIR typically peaks tens or hundreds of milliseconds after inhibition (Harris-Warrick et al., 1995a; Harris-Warrick et al., 1995b; Bertrand and Cazalets, 1998; Angstadt et al., 2005). Previous studies have shown that the latency to firing after inhibition depends on both the amplitude and duration of the hyperpolarization, and this was used to suggest that rebound firing latency could be a sensitive pattern detector, as long as the time constants of the effects were relatively rapid in comparison to the duration and frequency of the signal to be detected (Hooper, 1998).
In contrast, in this study we measure PIR in response to long trains of rhythmic inhibition. We do this in the Lateral Pyloric (LP) neuron of the stomatogastric ganglion of the crab, Cancer borealis. We find that PIR builds up over many cycles of rhythmic inhibition, and that enhanced excitability is extremely long-lasting after rhythmic inhibition ends.
Spike frequency adaptation (SFA) has been extensively documented in numerous sensory systems, and it occurs on both short and long time scales (Nelken, 2004; Gardner et al., 2005; Hoger and French, 2005; Gabbiani and Krapp, 2006). Just as there is a slow form of SFA, the phenomenon documented here is a slow form of PIR. Similar slow and long-lasting increases in intrinsic excitability have been previously seen in response to rhythmic depolarizations (Storm, 1988; Marder et al., 1996; Turrigiano et al., 1996). In principle, post-inhibitory rebound that develops and decays over many seconds will serve as a “memory mechanism”, allowing a neuron to keep track of the history of inhibitory inputs over a significant period of time.
Adult Cancer borealis crabs were obtained from Yankee Lobster (Boston MA) and maintained in artificial seawater until used. Crabs were cold-anesthetized for 30 min before dissection. The complete stomatogastric nervous system (STNS), consisting of the paired CoGs, the OG, the STG, and several motor nerves was dissected out of the animal and pinned out in an elastomer-coated dish containing chilled (9–13 °C) saline. The physiological saline solution consisted of the following (in mM): NaCl, 440; KCl, 11; CaCl2, 13; MgCl2, 26; Trizma base, 11; and maleic acid, 5, pH 7.45.
The STG was desheathed, and vaseline wells were placed on motor nerves. Stainless steel pin electrodes were placed in the wells for extracellular recordings. Signals were amplified and filtered using a differential AC amplifier (A-M Systems, Carlsborg WA). Intracellular recordings from somata were made using 20–40 MΩ glass microelectrodes filled with 0.6 M K2SO4 + 20 mM KCl, using an Axoclamp 2A amplifier (Axon Instruments, Foster City CA). The LP neuron was impaled with two electrodes, one for measuring voltage and one for passing current. During recordings, the preparations were continuously superfused with chilled saline (9–13 °C). For dynamic- and voltage-clamp experiments, the LP neuron was isolated from inputs by building a vaseline well around the desheathed stomatogastric nerve (stn) with 1 μM TTX in the well to block modulatory inputs, adding 10 μM picrotoxin (PTX) to the bath to block glutamatergic synaptic inputs (Marder and Eisen, 1984), and hyperpolarizing the two Pyloric Dilator (PD) neurons to remove cholinergic inputs. Currents measured in voltage clamp were low-pass filtered using a 4-pole RC filter (Krohn-Hite 3323) with a nominal 300 Hz cutoff prior to digitization.
Data were acquired with a Digidata 1200 data acquisition board (Axon Instruments) and subsequently analyzed in Spike2 (Cambridge Electronic Design, Cambridge UK). Data were analyzed with SigmaStat (Systat Software, Point Richmond, CA). In most cases, we used one-way repeated measures (RM) ANOVA with post-hoc Holm-Sidak tests to establish statistical significance between the measurements of spike rate, delay, and the time constants of their changes. These data passed tests for normality and equal variance. In the case of Figure 4A, the data failed a Levene Median test for equal variance, so we used Friedman’s RM ANOVA on ranks followed by Tukey multiple-comparison tests. Additionally, we had data for the DC hyperpolarization group only in a subset of n=5 preparations, so we performed an RM ANOVA on ranks comparing just the other three groups, with n=10, and then performed a separate RM ANOVA on ranks with the n=5 subset. For the data of Figure 2EF, we were compelled to use conventional (not repeated-measures) ANOVAs, because the sparsity of data did not allow for within-subjects comparisons. All measurements reported in the text are given as mean ± SEM.
The dynamic clamp (Sharp et al., 1993) was used to inject artificial synaptic inputs into the isolated LP cell using the Real-Time Linux Dynamic Clamp (Pinto et al., 2001) running on a 600 MHz Dell Pentium III computer at a sampling rate of 1 kHz. The artificial synapse delivered a current of the form
where I is the current, the maximal conductance of the synapse, m the fractional activation of the synapse, V the membrane potential of LP, and E the reversal potential of the synapse. The variable m was a low-pass filtered version of a square wave with a set period and duty cycle. It satisfied the equation
where m∞ (t) was the square wave (with value either zero or one), and τ was the time constant of the low-pass filter. In the text, the duty cycle given is the fraction of the cycle for which the inhibitory synapse is on, and so is called the duty cycle of inhibition (DCI). For all experiments reported here, E was set to −90 mV, and τ was either 50 ms or 0 ms. In the latter case, there is no low-pass filtering and m = m∞ (t). Because changing the time constant did not significantly affect the delay and spike frequency of the LP neuron (data not shown), experiments with different τ’s are pooled in the results. If necessary, the LP neuron was tonically depolarized so that it rebounded to a membrane potential of between −40 mV and −50 mV when not inhibited. The maximal conductance () was then adjusted such that the most hyperpolarized voltage reached was between −70 mV and −80 mV. To achieve this, the maximal conductance was typically set in the 150–250 nS range.
During an ongoing pyloric rhythm, the LP neuron receives rhythmic synaptic inhibition during each cycle. Therefore, we examined the LP neuron’s response to an artificial synaptic input designed to mimic the kind of rhythmic inhibitory drive it receives in the pyloric network (Fig. 1A). LP generally spiked on release from inhibition during each cycle. The spike rate during rebound slowly increased over the course of this input (Fig. 1B), while the delay-to-first-spike slowly decreased (Fig. 1C). We call this phenomenon slow PIR because it involves a buildup of excitability over the course of many inhibitory pulses.
We observed slow PIR over a range of input periods and duty cycles. The data shown in Figure 1ABC were for a period of 0.93 s and a duty cycle of inhibition (DCI, the fraction of the cycle in which inhibition is applied) of 40%. An example trace with a DCI of 20% is shown in Figure 1D, and one with a period of 1.35 s is shown in Figure 1E. Both exhibit clear slow PIR, reflected both in the spike rate and the delay-to-first-spike.
We quantified a number of properties of the slow PIR observed in the LP neuron, for a range of periods and DCIs. We used periods of 0.5 s, 0.93 s, and 1.35 s. The mean period of the pyloric rhythm in Cancer borealis is approximately 0.93 s, and 0.5 s and 1.35 s are approximately two SDs below and above the mean, respectively (Goaillard et al., 2009). The LP neuron is strongly inhibited by the pyloric rhythm pacemaker neurons for approximately 40% of a pyloric cycle (Goaillard et al., 2009), so the DCIs chosen were centered on this value.
The observed slow increase in spike rate was a robust effect, seen across all preparations examined (Fig. 2AB). This was measured by comparing the mean spike rate in the bursts from two cycles: 1) the first cycle in which the LP neuron fired two or more spikes, and 2) the final cycle. The data shown are only for DCIs of 20% and 40% because duty cycles of 60% often caused fewer than two spikes to be fired over much of the stimulus duration. Varying the input period had a significant effect on the percent increase in spike rate (Fig. 2B). The data are shown only for periods of 0.93 s and 1.35 s because a period of 0.5 s often caused fewer than two spikes to be fired over much of the stimulus duration (as for DCI=60%).
The observed decrease in delay-to-first-spike was also a robust effect, seen across a variety of DCIs (Fig. 2C) and periods (Fig. 2D). The time constant of the increase in spike frequency was difficult to estimate reliably, but was generally longer than 5 s (Fig. 2EF). Because of the difficulties in estimating this time constant, we were able to determine it for multiple DCIs or multiple periods only in a small number of animals. Therefore we pooled data from preparations in which we were only able to estimate this time constant in a subset of conditions (note different n’s for different conditions in Fig. 2EF). No significant differences in the spike rate time constant were observed between conditions. The time constant of the decrease in delay-to-first-spike was always several seconds, and increased as DCI increased (Fig. 2G). In contrast, the time constant showed no significant changes as period was varied (Fig. 2H).
The LP neuron showed a long-lasting period of enhanced firing after artificial rhythmic synaptic input was terminated (Fig. 3A). Typically, the tonic spike rate peaked within a few seconds of stimulus offset and then slowly recovered to steady-state in 20 to 30 seconds (Fig. 3A, bottom). A similarly slow recovery occurred in response to long hyperpolarizing DC current injection of equal total duration; therefore, this phenomenon was not a consequence of rhythmic stimulation (Fig. 3B). The response to long DC hyperpolarization also emphasizes that slow PIR is PIR in the fullest sense of the term, but occurring on a long time scale.
The peak offset firing rate was sensitive to the DCI of the synaptic input (i.e. ‘down time’; Fig. 4A), but was not affected by the period of the rhythmic drive (Fig. 4B). (Fig. 4A is consistent with Fig. 2A because the former shows absolute spike rate vs. DCI, and the later shows the change in spike rate vs. DCI.) Consistent with this, the offset firing rate after 18.6 s (= 20 cycles × 0.93 s/cycle) of constant hyperpolarization peaked at a significantly higher frequency than that of the rebound spiking after rhythmic trains (Fig. 4A, black bar). This makes sense, since constant hyperpolarization is analogous to a DCI of 100%. The steady-state spike rate during rhythmic inhibition predicted the peak offset spike rate (Fig. 4C), even across different combinations of period and DCI. Thus the higher the steady-state spike rate during rhythmic inhibition, the higher the spike rate after rhythmic inhibition ceased.
Period and DCI also affected the steady-state delay to firing. There was a significant effect of DCI on steady-state delay with period held constant at 0.93 s (P<0.001, n=9, one-way RM ANOVA, data not shown), and a significant effect of period on steady-state delay with DCI held constant at 40% (P<0.001, n=6, one-way RM ANOVA, data not shown). This indicates that steady-state delay depends on period, unlike the spike rate at offset.
To determine whether slow PIR was associated with a large change in conductance, we measured the LP neuron’s input resistance over the course of many inhibitory pulses by examining the current injected at the end of each inhibitory pulse and the resulting voltage deflection. We found no significant difference in input resistance between the first and last cycles of inhibition (mean difference was −4.8±3.4%, P=0.11, n=10, paired t test, data not shown). Consistent with this, we found that blockade of Ih with 5 mM Cs+ (Golowasch and Marder, 1992) did not reliably modify slow PIR (n=3, data not shown).
To determine whether slow PIR might be associated with a change in spike threshold, we measured the threshold of the first spike after each inhibitory pulse, and compared these thresholds between the first and last cycles. There was a small but significant decrease in spike threshold (mean difference was −0.9±0.4 mV, P<0.05, n=10, paired t test, data not shown). The extent to which slow PIR is attributable to this rather small change is unclear.
Voltage-clamp experiments reveal a slowly-decaying 100–400 pA net inward current evoked after a 20 s step from −45 mV to −75 mV (n=6, data not shown). The magnitude and time course of this current are consistent with the rebound depolarizations observed following DC hyperpolarization in current clamp (Fig. 3B).
Postinhibitory rebound (PIR) has long been recognized as an important mechanism of central pattern generation in motor systems (Perkel and Mulloney, 1974; Getting, 1989) and in the generation of oscillations in other brain circuits (Llinas, 1988). But PIR is usually thought of as operating in response to a single inhibitory input, or during a single cycle of an oscillation. Here we describe a form of PIR operating on longer time scales. In the case of the LP neuron, this slow PIR allows the cell to adjust its excitability to the average level of inhibition over approximately ten cycles. Thus it constitutes a form of short-term cellular memory (Storm, 1988; Marom and Abbott, 1994; Marder et al., 1996; Turrigiano et al., 1996; Egorov et al., 2002; Pulver and Griffith, 2010).
Consistent with this description, the spike rate of the LP neuron at steady-state (and at offset) varied as a function of the duty cycle of inhibition (DCI), but was independent of period (Fig. 4AB). This is expected of a process that depends upon the activity level averaged over a duration substantially longer than a single period.
Hooper (1998) found that both period and duty cycle of a rhythmic inhibitory input affected the steady-state delay to firing in the PY neurons of the pyloric network, but did not examine the effect of these parameters on spike rate. We found that both period and DCI had a significant effect on steady-state delay, but that offset spike rate was independent of period (Fig. 4). Hooper et al. (2009) found some of the same effects reported here, but did not examine changes in spike rate during long trains of inhibitory inputs, or look at the effects of changing DCI while holding period fixed. Thus our results are consistent with previous work, but reveal additional dimensions of the effects of rhythmic inhibition on excitability.
It is not clear what mechanisms underlie slow PIR in the LP neuron. The hyperpolarization-activated inward current (Ih) seemed a likely candidate, because it activates upon hyperpolarization, increases excitability, and has appropriate time constants (Golowasch and Marder, 1992; Pape, 1996; Hille, 2001). But experiments in which we blocked Ih with extracellular Cs+ did not reliably block slow PIR. Furthermore, we did not observe a significant decrease in input resistance over the course of multiple inhibitory pulses, as would be expected if Ih were slowly increasing. Another candidate is the slow deinactivation of the fast Na+ current (Rudy, 1978; Fleidervish et al., 1996), and this might account for the small change in spike threshold we observed. Additionally, there could be a low-threshold Ca2+ current that is strongly deinactivated by hyperpolarization, perhaps supplemented by a calcium-activated nonselective cation (CAN) current (Golowasch and Marder, 1992; Zhang and Harris-Warrick, 1995; Zhang et al., 1995). Yet another candidate is a pump current, which could generate a slow activity-dependent current without changing membrane conductance (Baylor and Nicholls, 1969; Pulver and Griffith, 2010).
Another possibility is that the observed long time constants arise not from the slow kinetics of a single channel, but from an interaction of two or more channels with fast kinetics. For instance, fast inward and outward channels could both be deinactivated by hyperpolarization, in such a way that they nearly cancel each other. This could give rise to an observed time constant much longer than either of the individual time constants. The very long interspike intervals possible in the Connor-Stevens model of the crustacean walking leg axon are an example of this sort of phenomenon (Connor, 1975; Connor et al., 1977; Connor, 1978). This often happens when a nonlinear dynamical system (such as a neuron) has parameters close to those that would yield two equilibrium points (i.e. a constant steady-state), one stable and one unstable. In the language of nonlinear dynamical systems, the absent equilibrium points leave behind a “ghost”, and the state of the system changes slowly in the vicinity of this ghost (Strogatz, 1994).
Winograd et al. (2008) recently described a hyperpolarization-activated increase in excitability in prefrontal cortex that decays with a time constant apparently much longer than 30 s, which was dependent on Ih. Thus these two forms of PIR appear to be distinct.
Slow PIR can be viewed as a cellular short-term memory mechanism, like neuronal multistability or delayed excitation (Storm, 1988; Marder et al., 1996; Egorov et al., 2002; Pulver and Griffith, 2010). Such mechanisms may underlie some forms of working memory, either alone or in concert with reverberatory synaptic mechanisms (Goldman et al., 2003; Loewenstein and Sompolinsky, 2003; Major and Tank, 2004; Major et al., 2008).
Slow PIR can be viewed as the “flip side” of delayed excitation, in which prolonged depolarizing current injection causes slowly increasing excitability (Getting, 1989). Delayed excitation has been proposed as a mechanism for temporal integration of excitatory inputs on a time scale of tens of seconds (Storm, 1988; Marom and Abbott, 1994; Turrigiano et al., 1996). Slow PIR might be an analogous mechanism for inhibitory inputs.
Slow PIR is a form of cellular dynamics that enables a cell to tune its excitability in response to the overall level of recent inhibition received. It is a form of cellular memory that depends not on changes in synaptic strength, but on the intrinsic membrane processes of the neuron itself. Plasticity time scales of 10–20 s may be particularly well-suited to circuit functions in which it is important for the animal to integrate information over a period of time before making a decision.
Support contributed by NIH NS50928 (ALT), NIH MH46742 and the McDonnell Foundation (EM).