Positive feedback loops sustain repeating bursts in neuronal circuits
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- Friesen, W.O., Mullins, O.J., Xiao, R. et al. J Biol Phys (2011) 37: 317. doi:10.1007/s10867-010-9210-8
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Voluntary movements in animals are often episodic, with abrupt onset and termination. Elevated neuronal excitation is required to drive the neuronal circuits underlying such movements; however, the mechanisms that sustain this increased excitation are largely unknown. In the medicinal leech, an identified cascade of excitation has been traced from mechanosensory neurons to the swim oscillator circuit. Although this cascade explains the initiation of excitatory drive (and hence swim initiation), it cannot account for the prolonged excitation (10–100 s) that underlies swim episodes. We present results of physiological and theoretical investigations into the mechanisms that maintain swimming activity in the leech. Although intrasegmental mechanisms can prolong stimulus-evoked excitation for more than one second, maintained excitation and sustained swimming activity requires chains of several ganglia. Experimental and modeling studies suggest that mutually excitatory intersegmental interactions can drive bouts of swimming activity in leeches. Our model neuronal circuits, which incorporated mutually excitatory neurons whose activity was limited by impulse adaptation, also replicated the following major experimental findings: (1) swimming can be initiated and terminated by a single neuron, (2) swim duration decreases with experimental reduction in nerve cord length, and (3) swim duration decreases as the interval between swim episodes is reduced.
KeywordsNeuronal circuitsLeechReciprocal excitationMutual excitationEpisodic behavior
Bursts per episode
Dorsal posterior (nerve)
Central nervous system
Central pattern generator
Recurrent cyclic inhibition
Our aim is to identify mechanisms that sustain an episode of animal locomotion following a brief sensory stimulus, a topic that has intrigued neurobiologists for many decades. An early success in this area was the identification of crayfish command neurons, whose stimulation activates and sustains the rhythmic movements of swimmerets . Nevertheless, the neuronal interactions that maintain crayfish command cell activity, despite much progress on the oscillator system , remain unknown. In fact, much has been learned from the seminal experiments of Wilson on locust flight  and more recent research on fictive swimming in many other species [4–12], and the investigation of rhythmic oscillations in the spinal cords of neonatal rodents . Nevertheless, little has been learned about the neuronal mechanisms that maintain excitatory activity in any preparation [6, 14, 15]. Electronic circuits are easily constructed to achieve sustained excitation, but what are the neuronal properties and neuronal circuits that drive episodic behaviors?
Experimental data suggest that both cellular properties, such as plateau potentials, and circuit properties, such as positive feedback, might generate sustained excitation [16, 17]. Swimming activity in the isolated CNS (fictive swimming) in Xenopus [18–24], for example, might be maintained when swimming activity releases ATP, which de-activates a K + current leading to increased neuronal excitation. This positive feedback excitation persists until the ATP is converted to adenosine (ADO). ADO de-activates a Ca2 + current, countermanding and terminating the prolonged excitation. There is a delay in this latter step because the ectonucleotidase that converts ADP to ADO is blocked by feed-forward inhibition from ATP. Experimental and modeling studies demonstrate that the elements required for this mechanism are indeed present in the CNS of Xenopus embryos, although the ATP-releasing neurons are not identified. Maintenance of excitation in lampreys is likely to be driven in large part from plateau potentials that are induced when stimulation of the skin evokes Ca2 + influx that in turn, activates a cation channel in the reticulospinal (RS) command system [25, 26]. Thus cellular processes in RS cells aid in converting brief stimulation into protracted depolarization, and thereby engender sustained excitation in the spinal cord swim circuitry for the duration of the swim episode. In addition, there is positive feedback among neurons in the brain stem and upper spinal cord in Xenopus [27, 28]. These studies suggested that a combination of circuit and cellular properties might be sufficient to generate the sustained excitation that causes bouts of locomotion, but neither positive feedback nor cellular properties are definitively linked to swim maintenance in these animals. Moreover, the proposed mechanisms are not associated with individually identified neurons.
In the medicinal leech, an identified cascade of excitation that initiates fictive swimming has been traced from mechanosensory neurons to the swim oscillator circuit [29–33]. Tactile stimulation of the body wall or depolarization of individual mechanosensory neurons activates swim-control neurons in the subesophageal ganglion, which include trigger neurons (Tr1 and Tr2) , the swim exciter neuron SE1 , and the R3b1 neuron . Excitatory synapses connect Tr1 to swim-gating neurons cells 204/205 located in the posterior midbody ganglia (M9–M16) [36, 37]. Depolarization of a single cell 204 by intracellular current injection is sufficient to drive fictive swimming; such episodes usually end with, but may continue beyond, the evoking cell 204 stimulus [36, 38]. Cells 204 provide excitatory drive to a set of segmentally repeated swim oscillator interneurons (INs; cells 28, 115 and 208) via excitatory synapses . Similarly, cell SE1 also directly excites swim-gating cells, oscillator cells, and swim-related MNs . Because the swim-gating neurons (and SE1 cells) project to most, if not all, segmental ganglia, they provide massive excitation to activate the swim circuitry.
Although the cascade of identified synaptic connections accounts for the initiation of swimming activity, mechanisms that maintain swimming are less clear. The synaptic interactions within the swim-initiating cascade have decay time constants of about 20 ms, and cannot account for the sustained depolarization observed in the swim-gating neurons, Retzius (Rz) cells and swim oscillator neurons. What mechanisms give rise to this sustained output? We propose that a set of intersegmental interneurons with extensive, mutually excitatory intersegmental interactions could provide the sustained drive to maintain swimming activity. Experimental data presented here show that (1) brief stimulation initiates prolonged bursting, (2) maintained bursting activity requires multiple ganglia, (3) mutually excitatory synaptic interactions exhibit long latencies and (4) there are intersegmental positive feedback circuits. To determine whether these mechanisms could give rise to fictive swimming, we constructed a model comprising realistic three-compartment neurons that includes the neuronal interactions in the swim-initiating cascade together with a set of mutually excitatory intersegmental neurons. The impulse frequency of the excitatory neurons is limited by impulse adaptation. We show that (1) this model generates prolonged excitation that drives neuronal bursting, (2) that swim duration depends on cellular properties (impulse adaptation), (3) repeated stimulation initiates and then may terminate excitation, (4) swim duration increases with the length of the ganglion chain and (5) swim duration depends on the interval between swim episodes.
2 Materials and methods
2.1 Physiological experiments
Experiments were carried out on adult medicinal leeches, Hirudoverbana, obtained from Leeches USA (Westbury, NY) and Niagara Leeches (Cheyenne, WY). Leeches were maintained in aquaria in a light-and-temperature-controlled room. Prior to dissection, leeches were anesthetized with cold (4°C) saline with composition 115 mM NaCl, 4 mM KCl, 1.8 mM CaCl2, 2 mM MgCl2, 10 mM Hepes buffer, pH 7.4 . Preparations were superfused with saline during the experiments, which for some experiments contained 50 μM serotonin. Preparations were pinned in glass-bottomed dishes to visualize neurons for intracellular recording. Ganglia were desheathed for experiments requiring intracellular recording. General techniques for dissection and recording are described in previous publications [40, 41].
2.1.1 Leech anatomy and nomenclature
The leech CNS comprises a head ganglion (H), a chain of 21 midbody ganglia—M1 through M21—and a tail ganglion (T). Two lateral intersegmental connectives convey the axons of (1) the oscillator interneurons (INs) and (2) cephalic neurons that control swim expression. A median tract (Faivre’s nerve) conveys the axons of swim-gating neurons, cells 204 and cell 205.
2.1.2 Preparations and electrophysiology
Intracellular recordings of membrane potentials from individually identifiable neurons were obtained via sharp electrodes (resistance about 40 MΩ) using an Axoclamp-2A amplifier (Axon Instruments, Sunnyvale, CA) in bridge mode. Electrical signals were amplified, digitized and stored using a Powerlab instrument and Chart software (AD Instruments, Colorado Springs, CO). Records were archived on CD-ROM discs. To initiate swimming, we usually stimulated a caudal DP nerve with a brief (about 1 s) train of 1–5 V, 5 ms pulses at 25 Hz, or by injected depolarizing current into a neuronal soma.
2.1.3 Sucrose knife technique
The methods described here are commonly employed in our lab. We have, however, refined one previously described technique, the sucrose gap here labeled the “sucrose knife,” to reversibly block impulse traffic more quickly in the ventral nerve cord . Briefly, we made a notch in a plastic tube (1 mm i.d.) placed at right angles to the ventral nerve cord. Either normal saline or isotonic sucrose with fast green dye (to detect undesirable turbulence) was passed through the tube to generate a laminar stream locally across the nerve cord at one or two selected sites (Fig. 1a, b). Axon impulses in the nerve cord are quickly (within about 3 s) and reversibly blocked when the isotonic sucrose flows across the nerve cord. For some experiments, we used two sucrose knives to functionally isolate a single ganglion; in others, we physically isolated ganglia by cutting the intersegmental connectives on either side (Fig. 1c).
2.1.4 Procedure for determining the effects of chain length on swim duration
We determined the effect of preparation length on the duration of swimming episodes in a series of experiments on the isolated nerve cord. First, we established the duration of swimming in a full-length M2-T control preparation (n = 4 repetitions separated by 60 s). We then severed the connectives between M2 and M3 to shorten the preparation to M3-T. The duration of swim episodes were then measured with another four swim-initiating DP nerve stimuli. These procedures were then repeated until the preparation was reduced to M7-T in four leeches. In an additional three preparations, we first determined the control episode duration in the M2-T cord, and then the swim duration in partial nerve cords, sequentially reduced from M8-T to M12-T. Finally, we performed some experiments in which a series of intermediate lengths of the nerve cord were examined for swim duration. The metric for swim length in these experiments was the number of bursts per swim episode (BPE). Because of the inter-preparation variability in swim duration, we normalized all values to that of the control, M2-T, condition. Preparations shorter than M12-T normally do not exhibit fictive swimming . We analyzed our physiological data with Chart software. Cycle period was computed with our custom rhythm analysis system . Results are reported as means and standard error.
For examining changes in chain length during ongoing swim episodes, we used standard M2-T preparations with a sucrose knife placed between M17–M18. DP nerve recordings were taken on either side of the knife to ensure its effectiveness, and swimming was initiated by stimulation of a nerve on the rostral side of the knife. Swimming was initiated with the knife either “off” (caudal ganglia connected) or “on” (caudal ganglia disconnected). Then the knife was either left continuously “off” or “on” for the duration of the swim (the “static” condition), or the knife was switched “on” (connected, then disconnected) or “off” (disconnected, then connected), respectively, after the 4th–6th DP nerve burst of swim episodes (the “dynamic” condition). Swim duration in all four conditions was scored by counting the BPE.
2.2 Modeling methods
2.2.1 Model neurons
2.2.2 Model overview
− 40.0 mV
− 39.5 mV
− 40 mV
Impulse travel time/segment
Swim-gating neuron 205 has very weak excitatory synapses with model RE neurons in segments M2 through M8 and helps maintain excitation through reciprocal excitation. Likewise, cells 204 have very weak excitatory synapses with RE neurons in each segment except their own, and weak excitatory synapses with all RCI neurons, except in those in their own segment (Table 1).
2.2.3 Model parameters
Model synaptic parameters
Presynaptic cell (location)
Postsynaptic cell (location)
Time constant (ms)
Fictive swimming in leech preparations is episodic. Whether it is evoked by sensory stimulation, activation of a trigger neuron or arises spontaneously, swimming activity ceases abruptly after a few or many cycles. The number of bursts in an episode typically averages around 15, but can be under ten or well over 30. We ensured that activity in the positive feedback circuits is self-limiting by endowing RE neurons with impulse adaptation, defined as a reduction in impulse frequency in the face of constant excitatory input. We implemented the impulse adaptation property in the model as follows: after each impulse we incremented an “adaptation” parameter by some fixed amount denoted as the “adaptation amplitude.” Impulse threshold was then set to decay with a time constant set by another parameter (Table 2). With the incorporation of impulse adaptation, run-away excitation, which might be expected from positive feedback loops, does not occur.
The resting membrane potential of all simulated neurons was set below impulse threshold; hence, all model neurons are silent unless driven by excitatory input (Table 2). A small random signal (maximum value ±0.1 mV) was added to the neurite potential during each simulation cycle to simulate random fluctuations in neuron resting potential and to avoid metastable states arising from numerical computation. Travel time for all model impulses passing between simulated ganglia was set to 15 ms per segment. This value is derived from published data on the intersegmental travel times in leech oscillator interneurons of medium-sized (1–3 g) animals [39, 50, 51].
3 Experimental results
3.1.1 Brief stimulation initiates prolonged bursting
The central swim oscillator in the leech nerve cord is driven by a set of segmentally repeated swim-gating neurons [37, 56, 57]. Although their activity is critical for driving the swim oscillator neurons, depolarization of these cells by intracellular current injection is not self-sustaining; that is, there is no evidence for plateau potentials. This suggests that circuit properties underlie gating cell depolarization; we explore here mechanisms that might generate this swim-sustaining excitation.
3.1.2 Maintained bursting activity requires multiple ganglia
Previous experiments on the leeches showed that single isolated or nearly isolated ganglia comprise sufficient components of the central swim oscillator to generate at least rudimentary swim oscillations [44, 56, 58]. These oscillations in isolated leech ganglia are weak, erratic, and not sustained. Perhaps not surprisingly, when we compared isolated ganglia with more extended preparations, we found that the swim maintenance system reflects these differences. The first question we addressed was whether individual, isolated ganglia can generate sustained excitation in response to external inputs in two types of preparations: individually isolated ganglia and single ganglia that were physically connected with the ventral nerve cord, but functionally isolated through the use of dual sucrose knives. The sucrose knife can reversibly disconnect and then reconnect ganglia from the rest of the nerve cord without physical trauma.
We carried out analogous experiments in M2-T preparations, but now implemented two sucrose knives simultaneously to block impulse traffic in the M9–M10 and the M10–M11 intersegmental connectives, (Fig. 5b inset). When normal saline flowed across these connectives impulse traffic was unimpaired. However, with a latency of less than 3 s, initiation of the flow of isotonic sucrose blocked impulse traffic. In these experiments, we stimulated one of the M10 DP nerves to activate the swim circuit and recorded the ensuing swimming activity with three suction electrodes, one placed rostral and one caudal to the sucrose knives, as well as one on a DP(10) nerve. Because recording from swim-gating neurons when using dual sucrose knives is difficult, we monitored intracellular activity in the large Retzius cells (Rz), which are easily penetrated and whose depolarization response to DP nerve stimulation is similar to that of cell 204 (n = 7 Rz neurons). We found that, in the control M2-T condition (Fig. 5b1), stimulation of the DP nerve depolarized the Rz cell throughout the swim episode. In contrast, the acutely isolated M10 ganglion (Fig. 5b2) did not exhibit fictive swimming, and intracellular depolarization in the Rz cell was not sustained, but rather decayed with a time constant of about 2 s (Fig. 5b2). Reconnection of M10 by saline flow in the sucrose knives restored the control response (Fig. 5b3). Similar depolarization profiles were observed in one successful cell 204 penetration (not shown). Results from these experiments indicate that intrasegmental interactions cannot sustain excitation.
Interactions that might account for the differences in the activities of isolated and extended nerve cords are shown in the insets of Fig. 5a. In isolated ganglia (upper inset), input from DP nerve stimulation transiently depolarizes segmental cells. In full-length preparations, interganglionic excitatory interactions may prolong this activity because of positive feedback connections (lower inset). We next present experimental data that suggest the existence of such intersegmental positive feedback circuits.
3.1.3 Excitatory synaptic effects exhibit long latencies
Another striking example of such delayed excitation is illustrated in Fig. 6b, where brief depolarization of cell 204 in M10 evokes a strong depolarization in cell 208 in the same ganglion. The delay is 44 ms, incompatible with a direct connection, which was already ruled out by earlier experiments .
It also seems unlikely that the long latency is the sum of multiple synaptic delays that might occur in a cascade of interactions. In the leech, synaptic delays are about 5 ms ; hence, the 44-ms latency caused by serial synapses would require a chain of at least eight neurons. The long latency of the excitatory responses might arise from another source, impulse travel times. Travel times for impulses conducted between segments for leech oscillator interneurons in medium-sized (1–3 g) animals are about 15 ms [39, 50, 51], although the precise conduction velocity of axons depends on many factors, including temperature and axon diameter. For a chain of 21 ganglia, the impulse travel time from end to end is about 300 ms. The very substantial latencies between swim-initiating stimulation of swim-gating neurons and the abrupt onset of sustained depolarization in these neurons suggest that positive feedback between neurons located at least one, but perhaps many segments apart could be important in swim initiation and maintenance. Multiple searches for direct, intersegmental excitatory synaptic loops have so far failed. We posit the existence of such intersegmental excitatory interactions as the source of the sustained drive that maintains swimming activity. This conjecture is incorporated into the model by a set of intersegmental excitatory neurons, one per segment, with broad, reciprocal interactions.
3.2 Comparison of modeling results with physiological data
3.2.1 Brief input engenders prolonged excitation that drives bursting behavior
In mid-chain, the initial bursts in RCI circuits resemble those of fully-activated swim episodes, but the initial bursts in the rostral and caudal chain are brief and would not be viewed as fully developed bursts in a physiological preparation. For consistency, we always determined BPE in a swim episode from the RCI(11) trace (Fig. 7). Using the first burst of RCI(11) as a marker for the initiation of swimming, the latency between Tr stimulation and swim onset is 0.33 s. This large latency arises from intersegmental impulse travel times, which are set at 15 ms/segment; synaptic delay in these simulations is less than 1 ms. The swim episode terminates when RE activity drops out (sequentially from rostral to caudal in this episode) and consequently the activity in swim-gating neurons ceases because of the loss of excitatory drive from RE neurons (model swim-gating neurons, as in the leech, do not interact with each other).
3.2.2 Swim duration depends on impulse adaptation parameters
3.2.3 Mechanisms that initiate and terminate excitation by a single input
We selected model parameters for neurons in these simulations to mimic the physiology of identified leech neurons. Similarly, synaptic interactions were modeled on physiological data. The parameters that defined impulse adaptation properties were chosen such that input from a short burst of trigger neuron impulses would generate a swim episode of moderate length, seven or eight bursts. Once selected, this set of parameters was not changed for the additional simulations described below.
Swimming locomotion in leeches is initiated, and can also be terminated, by sensory triggers [38, 60]. During normal leech behavior, such sensory-induced swim termination occurs when the leech encounters some physical barrier. A neuron downstream of sensory neurons, the trigger neuron Tr2, shares this fascinating property, whereby excitation of this neuron can both initiate swimming and terminate an ongoing swim episode . Termination does not occur if the second Tr2 depolarization is timed to occur near the beginning of a swim episode.
Termination of swimming by the swim-initiating Tr input seems paradoxical. One might expect that a second excitatory pulse from Tr would increase swim duration, rather than truncate swims. An advantage of neuronal modeling is that mechanisms that might underlie such puzzling and non-intuitive results can be investigated in detail.
3.2.4 Swim duration is correlated with chain length
We performed analogous experiments on the swim model. In these, we determined swim duration (again BPE) in the M2–M18 control chain and then sequentially reduced chain length. Our reduction procedure was simply to hyperpolarize all model neurons in segments to be removed. This approach simultaneously eliminated all oscillator neurons, RE neurons and gating neurons (if present), one segment at a time; swim initiation was via stimulation of the Tr neuron. Unlike the physiological data, removal of the first four anterior segments had little effect on the duration of excitatory activity in swim-gating neurons or on swim duration (Fig. 11b). Further shortening of the simulated nerve cord, however, led to a nearly linear decrease in the duration of gating cell activation and swim duration. With a swim episode defined as a minimum of two RCI bursts within 2 s, no swimming occurred in model chains with less than six segments; a single burst with increasingly briefer duration occurred in chains comprising five or four segments. These experiments show that maintenance of RE positive feedback requires a minimum of six segments. Considering that the model structure and model parameters were not selected to generate these results, the congruence between the physiological and model data is remarkable. It appears that swim maintenance in the leech is a mass-action phenomenon that can be accounted for by intersegmental mutually excitatory loops.
3.2.5 Re-initiated impulse duration depends on swim interval
We carried out similar experiments on the M2–M18 model chain. Here, we first initiated a swim episode by activating the Tr neurons and then, with variable delay after the end of this episode, initiated a second one (Fig. 12c). The results of the model experiments were similar to those of physiological experiments. At short delays between swim episodes, the duration of the excitation and the BPE of the second episode was less than that of the initial one (Fig. 12d). At greater delays (4–6 s), however, both of these variables were increased. A notable difference between physiological experiments and modeling results is that the time scale is different. Residual effects on swim duration were observable at delays of up to 60 s in nerve cord preparations, but not in the model studies, where swimming was back to control after a delay of 10s. Moreover, an enhancement of swim duration above control levels at intermediate delays (4–6 s in model studies) was not observed in the leech nerve cord.
3.2.6 Dynamics of swim modulation
We carried out a series of physiological and modeling experiments to explore mechanisms that underlie the sustained excitation that drives swimming activity in nerve cords of the medicinal leech. Earlier experiments had shown that a set of swim-gating neurons, seven cells 204 and a single cell 205, are the immediate source of excitation to the oscillatory circuit that generates the rhythm [37, 56]. Other physiological experiments showed that swimming can be initiated and terminated by an individual trigger neuron [29, 52]. Experiments on leech nerve cords described here showed that (1) the swim-gating neurons and some cells of the oscillator circuit have long latency, mutually excitatory interactions with unidentified intersegmental interneurons, (2) swim duration is a nearly linear function of the length of experimental nerve cords, (3) the duration of swim episodes evoked following any swim episode is a function of the interval between swim termination and initiation of the subsequent episode and (4) that swim duration in the nerve cord is determined not by the length of the cord at initiation, but by continuous interactions among segments. We constructed a computer model that embodies many of the known interactions of the leech swim oscillator circuits. In addition, the model included a set of intersegmental positive feedback loops. Without adjustment of parameters, this model replicated many of the results obtained in the physiological experiments.
4.2 Positive feedback and delayed swim onset
A puzzle about leech swimming is the long latency that often occurs between stimulation and swim onset. Swimming usually begins abruptly, but the latency can exceed 1 s (Figs. 4, 5, and 6). The large latencies, and the lack of sustained excitation in isolated ganglia imply that the sustaining, excitatory interactions are intersegmental. The implication is that there are complex intersegmental processes intervening between the initiation of excitation and the activation of the swim-maintaining system. Our model studies provide a partial explanation for the curious delay as follows. First, the excitatory interactions among the RE cells are intersegmental (one to three segments in the model) with conduction times of 15 ms. Impulses therefore require up to 45 ms to reach their target cells and up to another 45 ms to return to their source. Second, the interactions between RE neurons are relatively weak with a modest decay time constant (20 ms). Therefore, considerable temporal and spatial summation is required to generate high impulse frequencies. Consequently, positive feedback with a gain of at least one requires coactivation of a large fraction of the RE neurons. In our model, very brief trigger neuron activation can bring about this result, but the process may require up to 300 ms. Had we increased the projection distance of the RE neurons with a concomitant reduction in synaptic strength, one could expect the latency to be even greater. Based on these considerations, we suggest that an intersegmental network of widely projecting excitatory interneurons underlies long-latency swim initiation in the leech nerve cord.
4.3 Swim maintenance via positive feedback
Although our model replicates physiological data qualitatively well, there are quantitative differences. Model swim durations were briefer than those of most nerve cord preparations—7 or 8 BPE in the model compared with the 15 or more BPE in the nerve cord. No doubt manipulation of model parameters can generate longer episodes, but we have not explored the effects of such parameter changes on swim termination and other physiological experiments. The model impulse adaptation time constant, 2.1 s, is considerably larger than the adaptation time constant (88 ms) in MNs determined from physiological experiments . It remains to be determined whether the time constant for impulse adaptation in swim-gating neurons is large enough to generated protracted swims. The model predicts the existence of mutually excitatory interneurons widely distributed along the nerve cord, perhaps in every segment. Gating cells 204 and 205 are likely participants in mutual excitation as is the oscillatory interneuron cell 208. Each of these cells can trigger swim episodes; hence, they have access to the swim-maintaining circuits. Each also is continuously excited during fictive swimming; hence, each one is driven by the excitatory circuit. One cell 208 soma occurs in every midbody segment and many (perhaps all) receive excitatory synaptic input from the gating cells 204 and 205  and from the cephalic swim excitor neuron cell SE1 . Nevertheless, cell 208 does not directly feed excitation back onto these neurons; similarly, the gating neurons do not interact directly with each other.
Our physiological data strongly suggests intersegmental circuit properties play a large role in sustaining swim excitation and our model data is consistent with this view. The view that mutually excitatory circuits sustain locomotory behavior is gaining traction. They are thought to contribute to swimming in the Xenopus tadpole [27, 61] and are viewed as one source of excitation for burst generation in lamprey swimming [62–64]. We posit that there is at least one additional, mutually excitatory interneuron in many, perhaps all, segmental ganglia that excite the swim-gating cells, and perhaps cell 208. Searching for such neurons seems warranted given the results presented here. We predict that these neurons would be strongly depolarized during swim episodes and would individually be capable of triggering swim episodes, particularly in the presence of bath-applied serotonin.
4.4 Comparison to the lamprey hemicord
Interestingly, results from the lamprey hemicord are remarkably similar to ones found here. Hemicords are generated by a longitudinal cut down the lamprey spinal cord, removing crossed inhibitory inputs. Following electrical stimulation to the hemicord, an episode of bursting is generated by swim CPGs, but at a much higher frequency due to the removal of the crossed inhibitory projections . Like the results in the leech nerve cord presented here, swim episode duration in the lamprey hemicord is reduced when the length of the cord is reduced and when the interval between swim episodes is reduced . Further, like the leech, the duration of the swim episode is independent of the intensity of the initiating stimulus. In these reduced lamprey preparations, the bursting is thought to be sustained by positive feedback among the excitatory interneurons (EIN; ). EINs are shown to excite other EINs, and in one case a mutually excitatory pair was observed . Although it is unclear what role these processes observed in the hemicord play in the intact swim system, it is intriguing that such similar results were observed in the two species.
4.5 Limits of our model
Our model was constructed specifically to determine whether reciprocal excitation, limited by impulse adaptation, can account for our observations regarding initiation, maintenance and termination of fictive swimming in the leech nerve cord. Our model is realistic in that the unit neurons have multiple compartments that simulate soma, neurite and axon dynamics and which mimic the physiology of identified cells. The circuit interactions approach those identified in the leech, but do not include some potentially important elements, such as the SE1  and Rb31  neurons in the subesophageal ganglion, cells 208  in midcord ganglia, and the recently discovered caudal neuron E21 .Cell 208 is broadly excitatory; its properties are combined in our model with those of cell 204 and 205. Trigger neurons are combined into one generic Tr neuron. We have not explored how more detailed modeling of these neurons would alter the output of the simulations. A different parameter set for the model RE neurons would lead to alternative, perhaps even more realistic results. Nevertheless, there is good qualitative and sometimes quantitative agreement between independent experiments on the leech nerve cord and the neuronal model without parameter tuning. The similarity between experiment results and model output suggest that the time is right for more experimentation rather than for a more detailed model.
4.6 Generality of the results
Although the data are not shown, our model generates similar output when the limiting factor for reciprocal excitation is fatigue in synaptic connections between RE neurons. It seems likely that many neuronal configurations that include the two essential elements of our model, positive feedback and self-limitation, could generate many of the features of our simulation. Specific structures incorporated into our model—positive feedback loops, impulse adaptation, and intersegmental circuits—are already indentified in the leech nerve cord. Reciprocal excitation between IN 208 and a swim-initiating neuron, cell 21, one segment away was identified in another leech species , although not in Hirudo (W.O. Friesen, unpublished observations). Such properties are known also in the Xenopus swim system [27, 28]. The challenge is to identify positive feedback loops in other preparations. Given such loops, our modeling study points to the properties to be expected of such circuits.
Activity that is driven by positive feedback is characterized by an abrupt transition from quiescence to full, maintained activity and abrupt termination when inhibitory processes reduce positive feedback below a gain of 1.0. Our modeling experiments show that positive feedback is a feasible means of generating continuous excitation when activated by a brief trigger. Because model experiments replicate results obtained in a series of experiments not used to construct the model, the model achieves a certain validity. Essential features of our model are positive feedback interactions combined with a cellular, negative property in the form of impulse adaptation. The model is readily generalized by incorporating synaptic fatigue in the positive feedback circuit. In fact, any circuit incorporating positive feedback with negative, self-limiting processes could generate triggered bouts of excitation. Although the excitation in leech swim-gating neurons is thought to arise from circuit properties, these processes can also be found at the level of the individual neuron, for example in plateau potentials mediated by calcium-activated inward currents (ICAN). An additional cellular process that can limit positive feedback loops is the calcium-activated potassium current (IKCa). The activity-sustaining neuronal circuits in animals are likely to incorporate several of these mechanisms.
Funding was provided by NSF grant IOB-0615631.