The interaction of positive and negative sensory ...

J Comput Neurosci DOI 10.1007/s10827-009-0140-z

The interaction of positive and negative sensory feedback loops in dynamic regulation of a motor pattern Jessica Ausborn & Harald Wolf & Wolfgang Stein

Received: 5 September 2008 / Revised: 30 January 2009 / Accepted: 2 February 2009 # Springer Science + Business Media, LLC 2009

Abstract In many rhythmic behaviors, phasic sensory feedback modifies the motor pattern. This modification is assumed to depend on feedback sign (positive vs. negative). While on a phenomenological level feedback sign is well defined, many sensory pathways also process antagonistic, and possibly contradictory, sensory information. We here model the locust flight pattern generator and proprioceptive feedback provided by the tegula wing receptor to test the functional significance of sensory pathways processing antagonistic information. We demonstrate that the tegula provides delayed positive feedback via interneuron 301, while all other pathways provide negative feedback. Contradictory to previous assumptions, the increase of wing beat frequency when the tegula is activated during flight is due to the positive feedback. By use of an abstract model we reveal that the regulation of motor pattern frequency by sensory feedback critically depends on the interaction of positive and negative feedback, and thus on the weighting of antagonistic pathways. Keywords Motor control . Central pattern generation . Sensorimotor . Proprioceptor . Locust flight Action Editor: Eberhard Fetz Electronic supplementary material The online version of this article (doi:10.1007/s10827-009-0140-z) contains supplementary material, which is available to authorized users. H. Wolf : W. Stein (*) Institute of Neurobiology, Ulm University, Ulm 89069, Germany e-mail: [email protected] Present address: J. Ausborn Department of Neuroscience, Karolinska Institute, Stockholm 17177, Sweden

1 Introduction In many rhythmic motor systems, substantial parts of pattern characteristics are produced by phasic sensory feedback, which is therefore regarded as an integral part of the rhythm generating machinery (e.g. Pearson 2004), although the basic motor pattern can still be expressed after removing all sensory input. Sensory feedback can affect many aspects of a motor pattern, such as pattern frequency and internal structure, phase transitions, and amplitude. The interaction of afferent input and (central) pattern generator provides great versatility, but also requires flexibility in sensory signal processing. This may be one of the reasons why in many systems synaptic connectivity of sensory pathways is complex. Sometimes connectivity even appears contradictory to the function of the sense organ and the sign of feedback provided. For example, the femoral chordotonal organ in the insect leg provides negative feedback, that is, it inhibits motor neurons whose action brings about respective sensory discharges. Yet, studies of the circuitry demonstrate that several of the sensory processing pathways antagonize this negative feedback (“parliamentary principle”; Bässler 1993). In fact, in systems where the cellular basis of sensory actions is well known, one almost inevitably encounters pathways that process information antagonistically (Bosco and Poppele 2001; Burrows 1987; Combes et al. 1999; Lachnit et al. 2004; Lockery and Kristan 1990; Nagayama and Hisada 1987; Schmitz and Stein 2000). The functional significance of these antagonistic pathways is not well understood, in particular, because the effects of sensory feedback are often studied without knowledge of the cellular network basis, or with computer models that disregard antagonistic processing. It is assumed that antagonistic pathways allow greater flexibility of the system and enable state-dependent modulation of the motor output (Bässler 1993; Stein et al. 2008).

J Comput Neurosci

We study the effects of antagonistic pathways in the well characterized sensorimotor system of locust flight. In this system, the tegula proprioceptor is activated by the downstroke of the wing and provides negative feedback, resetting the rhythm via excitation of elevator motor neurons and concomitant inhibition of depressors (Wolf and Pearson 1988). The strength of tegula feedback determines the frequency of the rhythm, with increasing feedback strength initially raising wing beat frequency up to a maximum, and further increases causing an exponential decrease in rhythm frequency (Ausborn et al. 2007). While we were able to show that this decrease is a general feature of negative feedback loops with resetting properties, the reason for the initial frequency increase remains unknown. The fact, that wing beat frequencies are typically higher with tegula feedback present than in the isolated pattern generator is attributed to the reset capability of tegula feedback and the resulting advanced start of wing elevation (Büschges and Pearson 1991; Wolf and Pearson 1988). We here use a cellular model of tegula feedback and flight central pattern generator (cpg) to show that increased wing beat frequency is instead mainly due to a hitherto not examined positive feedback configuration of tegula pathways. This positive feedback supports a continuous rise of rhythm frequency towards higher feedback strengths. It is then the balance of positive and negative feedback pathways that determines the characteristic bell-shape of the feedback–frequency relationship observed in the animal. We thus show that the weighting of different feedback signs is used in a sensorimotor circuit to regulate the dynamics of the motor pattern.

2 Materials and methods 2.1 cpg model The neurons of the locust flight pattern generator were modeled with the simulation environment MadSim (Ausborn et al. 2007; Stein and Ausborn 2004; Straub et al. 2004; MadSim is freely available at http://www.neurobio.de/mad sim). Neurons possessed passive properties according to Ekeberg et al. (1991). Active membrane properties were implemented according to modified Hodgkin–Huxley equations (Ekeberg et al. 1991; Hodgkin and Huxley 1952). Parameters for passive and active neuron properties are given in the supplemental. Each ionic current Ij is represented by

1 may be assigned to a and b, while the exponents p and q may take integer values. The activation a and the inactivation b of each current are described by da ¼ a a ð 1 aÞ b a a dt where αa is the rate by which the gates switch from a closed to an open state and βa is the rate for the reverse process. αa is voltage-dependent and of the form aa ¼

A ðVm V0 Þ 0Þ 1 e ðVm V s

where V0 is the half-maximum potential, A is the rate constant and s is the step width of the curve. βa follows the same equation, except for β of the inactivation gate of the fast sodium channel (βh), which is of the form bh ¼

A 0Þ 1 þ e ðVm V s

The network structure (Fig. 1(a)) and parameters were identical to those of the model used in Ausborn et al. (2007). Since MadSim does not have a representation of an axon, a conduction delay was implemented to represent the time for the release and diffusion of transmitter together with the time that the action potential needs to travel from the soma to the synapse. Values for the conduction delay are given in the supplemental. Neurons were modeled according to Stein et al. (2008) as a soma with three additional unbranched dendritic compartments. Synaptic parameters (i.e. time course and conduction delay) in the model were adjusted by matching recorded and simulated postsynaptic potentials (PSPs). The synaptic current (Isyn) of a single synapse is given by the product of the driving force and the synaptic conductance. Isyn ¼ Eion Vpost Gsyn where the driving force is the difference between the reversal potential Eion of the synaptic current and the postsynaptic membrane potential Vpost. Synaptic conductance Gsyn depended on the opening factor Osyn and on the maximum conductance Gmax: Gsyn ¼ Gmax Osyn

I j ¼ V m E j G j ap bq

Between the minimum membrane potential for transmitter release (VT) and the membrane potential at which the transmitter release saturates (VS) Osyn linearly depended on the membrane potential of the presynaptic neuron Vpre.

where Vm represents the membrane potential, Ej the reversal potential of current j , Gj the maximum conductance, a the activation and b the inactivation of Ij. Values between 0 and

Vpre VT Osyn Vpre ¼ min 1; max O; VS VT

J Comput Neurosci

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Fig. 1 Models of locust flight cpg and tegula feedback. (a) Synaptic connectivity of model flight cpg network using Hodgkin–Huxley model neurons. EL elevator unit, DEP depressor unit, D synaptic connection with delay (corresponding to polysynaptic pathway), numbers indicate interneuron identity. (b) Synaptic connections of the tegula with flight interneurons and motor neurons. Neurons without annotation represent unidentified interneurons, or identified cpg interneurons with inhibitory synaptic contacts to other cpg interneurons. (c) The latency between motor neuron discharge and onset of tegula activity (la), and the duration of tegula activity (d) are functions of cycle period (cp). They were calculated in a closed-loop model according to the equations given. The latency included the time required for activation and contraction of the muscles, for wing movement, and for the activation of the tegula afferents. (d) Schematic representation of simplified model. The charge A of an RC-circuit represents the excitation level of the depressor motor neurons. τ, time constant of RC-circuit. I, tonic charge applied throughout the simulation. Onset and duration of the feedback current were calculated according to the equations indicated (see also

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(c)). Either positive feedback was provided via a long latency loop that enhanced the charge of the RC-circuit, or negative feedback was implemented via a short latency pathway that reduced the charge. In some experiments, both feedback signs were applied simultaneously (details see text). Plus sign excitation; minus sign inhibition. (e) Schematic illustration of how oscillations were achieved in the simplified model with negative feedback configuration. The RC-circuit was continuously charged with tonic positive current. Once threshold was reached the latency (la) and duration (d) of tegula activity were calculated (indicated by heavy arrows). After a synaptic latency (sl) of 7 ms (short latency in (d)), the tegula exerted its inhibitory action on the RC-circuit (grey boxes). (f) Schematic illustration of how oscillations were achieved in the simplified model with positive feedback configuration. Once the threshold of the continuously charged RCcircuit was reached, the latency (la) and duration (d) of tegula activity were calculated (indicated by heavy arrows). After a synaptic latency (sl) of 37 ms (long latency in (d)), the tegula exerted an excitatory action on the RC-circuit (grey boxes)

J Comput Neurosci

The time course of the postsynaptic potential thus depended on the duration of the presynaptic action potential, the time constant of the postsynaptic membrane and the position of the synapse on the postsynaptic neuron (soma or dendrite 1–3, stated in the supplemental). Synaptic strength cannot be deduced from experimental findings since almost all flight-interneurons and motor neurons exist in more than one copy and only one of them can be recorded electrophysiologically at a time. We thus handtuned the model to match the activity-patterns of all model and biological interneurons and tested the validity of our model by perturbations through current injection (Ausborn et al. 2007). Tegula synaptic strengths were hand-tuned to cause a type 0 reset of the flight pattern with a phase response curve similar to the biological situation (Ausborn et al. 2007). Synaptic parameters are given in the supplemental. 2.2 Tegula model The tegulae were modeled as a single afferent neuron with multiple output connections to flight interneurons and motor neurons (Fig. 1(b)), according to Ausborn et al. (2007). The tegula afferents project to nearly all identified flight interneurons (Wolf 1993; Wolf and Pearson 1989). The functions for tegula activation and the duration of tegula activity were derived from experimental data provided by Fischer et al. (2002) and Hedwig and Becher (1998): The onset of tegula activity depends on the timing of the depressor motor neuron discharge and is a linear function of cycle period (Fig. 1(c); Ausborn et al. 2007).

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Similarly, Fischer et al. (2002) showed that the duration of the tegula burst is related to cycle period (Fig. 1(c)). Both functions thus included the time needed for depressor muscle activation, muscle contraction, wing movement, and tegula activation. 2.3 Phase–response curves To compare the effects of depolarizing current pulses injected into interneuron 301 in the model and in the animal (Robertson and Pearson 1985), we determined phase–response curves. Phase–response curves plot the change in oscillator period against the phase of the stimulus presentation which elicited the change in the rhythm (Prinz et al. 2003; Wolf and Pearson 1988). In the model, current injections of 0.5 nA (duration 30 ms) were given at various phases of the cycle, with a step width of 0.05. Phase zero was assigned to the first spike in each depressor burst. Stimulus phase was defined as t/P, with t being the latency of the stimulus onset after the start of the preceding depressor burst, and P being the period of the freerunning rhythm. The period change ΔP caused by the current injection was defined as the time difference between (1) the start of the first depressor burst after perturbation and (2) the time at which this burst would have started without perturbation. Thus, if the first depressor burst occurred earlier than in the unperturbed rhythm, ΔP is negative. If the first depressor burst was delayed, ΔP assumes a positive value. In Fig. 3 we plotted the normalized period change (ΔP/P) against the stimulus phase (t/P).

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Fig. 2 Interneuron 301 relays delayed positive feedback to the depressor motor neurons. (a) Schematic representation of polysynaptic pathways from interneuron 301 to the flight motor neurons. All output connection of 301 either lead to a delayed inhibition of the elevator motor neurons or to a delayed excitation of the depressor motor neurons. (b) Interneuron 301 is the only pathway in the flight motor

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network that receives excitation from the tegula and provides (delayed) excitation to the depressor motor neurons. The tegula to 301 pathway thus represents a positive feedback loop. In contrast, all other interneurons lead to an inhibition of the depressor motor neurons when the tegula is active (negative feedback)

J Comput Neurosci

2.4 Simplified model To test the effects of negative and delayed positive feedback on motor pattern frequency we implemented two simplified models of tegula feedback (Fig 1(d)). The central part of the flight system was represented by a series RC (resistor–capacitor) circuit with a time constant of charge of 5 ms. For the negative feedback configuration a constant positive current (I) was applied to charge the RC-circuit. In all other feedback configurations, no tonic current was applied (I=0). The charging level of the RC-circuit (A) corresponded to the excitation level of the depressor motor neurons. This allowed us to investigate the impact of both tegula feedback configurations in a setting that was independent of the influence of a central pattern generator with complex dynamics. Negative and positive feedbacks were implemented using the tegula activation functions (Fig. 1(d)). Once activated, the tegula feedback introduced either short-latency (synaptic latency (sl)=7 ms) negative or delayed (sl=37 ms) positive input current into the RCcircuit. Latencies were estimated using experimental data (Harald Wolf; unpublished data). Stable oscillations were produced by both feedback configurations. The initial cycle period to calculate the first tegula activity was set to 100 ms in all configurations. Negative feedback (Fig. 1(e)): The applied tonic positive current increased the charge of the RC-circuit. Once activated, the negative feedback introduced a negative input current to the RC-circuit that exceeded the tonic positive current and caused a drop in the charge. The feedback was switched off after the calculated duration, and the charge of the RC-circuit increased again due to the tonic current input. When the threshold level was reached, a new cycle started. Positive feedback (Fig. 1(f)): Here, no tonic current was applied (I=

0) and the charge of the RC-circuit did not increase spontaneously. Activation of the positive feedback, however, introduced a positive input current to the RC-circuit. The subsequent tegula activation was then triggered when the defined threshold was exceeded, but with a delay of 37 ms. Since the current tegula activity (as calculated by the activation functions; Fig. 1(d)) was shorter than the delay after which the subsequent feedback started, the charge dropped in between two subsequent tegula activities and oscillations were achieved. The very first tegula activity was elicited manually. The feedback strength of the tegula unit, that is, the amount of current applied to the RC-circuit, was varied as indicated in Figs. 5 and 6. We either applied negative or delayed positive feedback separately, or both feedback types were applied simultaneously. In the latter case, no tonic current was applied (I=0). The continuous charge (by the positive feedback) and discharge (by negative feedback) of the RC-circuit resulted in stable oscillations.

3 Results In many rhythmic motor systems, phasic sensory feedback is regarded as an integral part of the rhythm generating machinery (e.g. Pearson 2004). This also applies to the tegula, a wing proprioceptor, which resets the flight rhythm by initiating a new wing upstroke (Wolf 1993). The strength of its feedback determines wing beat frequency (Ausborn et al. 2007). The tegula afferents excite the elevator motor neurons either directly, by excitation of excitatory premotor neurons, or by inhibition of inhibitory premotor neurons. At the same time, the depressor motor neurons are inhibited by the tegula via

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Fig. 3 Activity pattern and reset effects of interneuron 301 in the Hodgkin–Huxley model. (a) Phases of cpg interneuron (open bars) and motor neuron (black bars) activities in the model oscillator. Grey bar interneuron 301, which was active at the interface between wing elevation and depression. Numbers indicate interneuron identity;

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average firing frequencies during a burst are given. (b) Phase– response curves of the biological flight cpg (grey; adapted from Robertson and Pearson 1985) and the model cpg (black) during stimulation of interneuron 301. ΔP/P, phase–response (see Section 2)

J Comput Neurosci

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Fig. 4 Interneuron 301 is sufficient and necessary to mediate the frequency increase of the flight cpg elicited by tegula feedback. (a) The change of cycle frequency, in comparison to the isolated model network, is given for models where the tegula selectively affected a single interneuronal pathway or only one of the motor neurons. The interneuron 301 pathway alone was sufficient to elicit a cycle frequency that matched that of the complete model (dashed line), which included tegula synapses on all cpg interneurons. None of the other interneuronal pathways caused a considerable change in cycle

frequency. (b) (i) Motor output and tegula activity of the model cpg which included all tegula synapses. (ii) Same for a model in which only the synapse from the tegula to interneuron 301 was present. Arrows indicate missing elevator motoneuron discharge. (c) Activity of motor neurons and tegula when the synapses from tegula to both interneuron 301 and elevator motoneuron were present. (d) When the synapse from tegula to interneuron 301 was removed, but all other synapses were active, cpg cycle frequency was low and corresponded to that of the deafferented network (see text for details)

excitation of inhibitory or inhibition of excitatory premotor neurons (Fig. 1(b)). Since the tegula is activated by the wing downstroke, which in turn is elicited by depressor activity, tegula feedback represents a negative feedback loop.

3.1 Interneuron 301 relays delayed positive feedback from the tegula

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J Comput Neurosci

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Fig. 6 The balance of opposing feedback signs determines the dynamics of motor patterning. (a) Cycle frequencies in the simplified model are plotted against feedback strength. Latency and duration of the feedback depended on cycle period (according to the tegula activation functions given in Fig. 1(d)). Only positive feedback was provided. Cycle frequency increased with higher tegula feedback strength. (b) When only negative feedback was implemented, cycle frequencies decreased when tegula feedback strength was increased. (c) When both, positive and negative feedback were combined, strengthening tegula feedback resulted in a continuous increase of

cycle frequencies. (d) Each strength used for positive feedback was raised to the power of 2.5 to determine the strength of the negative feedback. With this balance of feedback types, cycle frequency increased at low feedback strengths, reached a maximum value and decreased again at high stimulus strengths. Outlined dots positive feedback only; outlined diamonds negative feedback only; black triangles negative and positive feedback combined. Lowest feedback strength applied was 1 for all feedback conditions. Without feedback (feedback strength=0) no oscillations were present

opposes the wing upstroke instead of supporting it: Interneuron 301 receives an excitatory synapse from the tegula (Büschges et al. 1992) but relays this excitation to the depressor motor neurons (Robertson and Pearson 1985). In addition it differs from the remaining interneurons because it is the only neuron of the core central pattern generator which receives direct synaptic input from the tegula, but is not directly presynaptic to elevator or depressor motor neurons (see Fig. 1(a), (b)). Rather, 301 polysynaptically affects both motor neuron types and leads to a delayed increase of depressor motor neuron activity and a concomitant decrease of elevator motor neuron activity (Fig. 2). For example, it polysynaptically excites the depressor motor neurons via interneurons 503 and 201. The tegula influence mediated by interneuron 301 thus represents a positive feedback loop which opposes the feedback sign of all other interneuronal pathways (Fig. 2(b)). Due to its polysynaptic transmission pathway, the 301-mediated positive feedback is delayed with respect to the negative feedback provided by the other interneur-

ons. Despite our detailed knowledge regarding the synaptic connectivity pattern of the tegula afferents, it is unclear if and how this positive feedback pathway alters or contributes to the apparent tegula function during flight, namely, to activate a new flight cycle by resetting the pattern (Wolf 1993). In general, the functional relevance of parallel and contradictory feedback pathways is still unknown. We thus aimed at characterizing the functional relevance of such antagonistic pathways in the locust flight system. A selective investigation of the tegula-to-301 connection in a biological preparation is difficult since interneuron 301 exists as a bilateral pair of neurons, with one copy in each mesothoracic hemiganglion, the pair acting as one unit (Robertson and Reye 1988). A simultaneous manipulation of both neurons would be necessary to selectively change this tegula feedback pathway. We thus used a model of the flight central pattern generator with tegula feedback (Ausborn et al. 2007) to examine the effects of negative and positive feedback on the flight system. The details of the model are given in Section 2 (identical to those used in

J Comput Neurosci

Ausborn et al. 2007). In short, we represented each identified neuron type of the core central pattern generator as well as the elevator and depressor motor neurons by one functional unit based on modified Hodgkin–Huxley equations. The underlying network structure is shown in Fig. 1(a). This model network generated oscillatory activity which accurately resembled the motor pattern of the deafferented (without any sensory feedback) flight system (Fig. 3(a); compare e.g. Wilson 1961). Cycle frequency was 9.7 Hz. Interneuron 301 is one of the few interneurons which reset the flight rhythm when depolarized by current injection (Robertson and Pearson 1985; details in Section 4). Although our model was originally designed to generate just the activity patterns of motor- and interneurons, it reproduced this reset behavior: Short (30 ms) depolarizing (0.5 nA) current stimuli injected into the model interneuron 301 reset the rhythm and started a new flight cycle, independent of stimulus phase. To visualize the response of the model to these current pulses at different phases of the rhythm, we plotted the respective phase–response curve (Fig. 3(b)). Consistent with an excitation of the depressor and a corresponding inhibition of the elevator, the phase–response curve shows that the start of the subsequent depressor burst was advanced when interneuron 301 was activated inbetween depressor bursts (phases 0.1–0.8). By contrast, whenever current pulses were applied immediately before or during the depressor burst (phases 0.9 to 0.1), the excitation of the depressor part of the network provided by interneuron 301 elicited a prolongation of the depressor phase and hence delayed the beginning of the subsequent cycle (stimulus phases of 0.6–0.9 had little effect since the oscillator was about to start a depressor phase anyway). The model phase– response curve matched the phase–response curve of the biological preparation (Fig. 3(b)). Thus, in the biological system as well as in our network model, interneuron 301 plays an important role in flight rhythm generation. 3.2 Delayed positive feedback speeds up the rhythm Interneuron 301 receives direct excitatory input from the tegula. To test whether this tegula synapse alters or contributes to the known tegula effects on the flight motor network, we added tegula feedback to the model by implementing all known synaptic connections from the tegula onto flight cpg neurons (Fig. 1(b)). To achieve functionally relevant closed-loop conditions, the tegula was activated depending on the output of the cpg. The activation of the tegula was calculated by using linear functions (Fig. 1(c)) derived from experimental data. Onset and duration of tegula activity depend on the depressor motor neuron discharge and are linear functions of cycle period (Ausborn et al. 2007; see also Section 2). As a result of this realistic tegula feedback, the elevator motor neuron

unit was prematurely activated in each cycle, thus starting a new cycle (reset). Consequently, the flight rhythm sped up and cycle frequency increased from 9.7 to 17.5 Hz (compare Ausborn et al. 2007). Which tegula synapses account for the increase of cycle frequency when the tegula feedback loop is closed? To test this, we estimated the importance of the different tegula synapses for the motor pattern by first silencing all tegula synapses and then selectively activating each tegula synapse separately, one at a time. We kept the strength of the active synapse identical to that in the original tegula feedback model (Ausborn et al. 2007). We then compared the obtained cycle frequencies to those of the isolated pattern generator. Unexpectedly, only the tegula synapse onto interneuron 301 increased cycle frequency noticeably, while all other synapses had only weak or no effects (Fig. 4(a)). The effects of the synapse between tegula and interneuron 301 were sufficient to elicit cycle frequencies that were almost identical to those obtained in the complete tegula feedback model (dashed line in Fig. 4(a)). Despite their similar frequencies, the motor patterns generated by the network with the complete set of tegula synapses and that with only the synapse from tegula to interneuron 301 present showed distinct differences. While both models produced stable oscillations, the elevator motor neuron was reliably activated only when all tegula synapses were present (Fig. 4(b) (i)). With only the tegula feedback to 301 present, by contrast, elevator activity was missing in about 50% of the cycles (arrows in Fig. 4(b) (ii)). It appears, thus, that tegula feedback increases cycle frequency via interneuron 301 (and the delayed excitation of the depressor part of the network caused by 301), while the elevator premotor neurons do not receive sufficient excitation to reliably activate the elevator unit in this configuration. Adequate activation of the elevator motor neuron could be achieved, however, by implementing the direct excitatory synaptic connection from the tegula to the elevator unit (in addition to the synapse from tegula to interneuron 301). In this configuration, the elevator unit was reliably activated in every flight cycle (Fig. 4(c)), and the rhythm thus exhibited regularly alternating depressor and elevator discharges. This indicates that direct tegula excitation of the elevator motor neuron provided sufficient input for adequate elevator activation, while interneuron 301 determined the timing of the rhythm. In fact, when we reinstated all other tegula synapses, proper activation of the elevator-unit could only be obtained when the synapse onto the elevator unit was also present (data not shown). Our results so far emphasize the importance of 301 for frequency regulation of the flight rhythm by the tegula. To further scrutinize the relevance of the synapse from tegula to interneuron 301, we selectively removed this connection from the network while leaving all other tegula synapses

J Comput Neurosci

intact. Here, cycle frequency was 10.4 Hz and thus almost identical to that of the isolated cpg (9.7 Hz; Fig. 4(d)). Tegula feedback to interneuron 301 was thus not only sufficient, but also necessary to speed up the flight rhythm. 3.3 Dynamics of frequency regulation with delayed positive feedback Recently, we have shown that negative sensory feedback that resets a motor pattern allows a frequency regulation such that stronger feedback causes lower motor pattern frequencies (Ausborn et al. 2007). We demonstrated that this general regulation principle is functionally relevant in the locust flight system. Consistent with this, the frequency of the model pattern changed dependent on the feedback strength provided by the tegula unit. We altered feedback strength by multiplying the value of each tegula synapse with the same factor (ranging from 0 to 10; Fig. 5(a)). Activating the tegula with low feedback strengths increased cycle frequency, compared to the isolated cpg. When we raised the strength of the tegula feedback, cycle frequency reached a maximum and then started to decrease exponentially until it reapproached the value of the isolated cpg. While the decrease of wing beat frequency at high feedback strengths is due to the negative feedback provided by the tegula, the initial increase with low tegula strengths cannot be explained by this type of feedback (Ausborn et al. 2007). Its origin is currently unknown. To test if the initial increase can be attributed to the delayed positive feedback loop via interneuron 301, we removed all tegula synapses in the network model except for the synapse of the tegula to interneuron 301, such that all pathways providing negative feedback were inactive. Fig. 5(b) shows that in this configuration an increase in feedback strength quickly increased cycle frequency. At high tegula feedback strengths wing beat frequency saturated. No decrease in cycle frequency was observed. It is thus conceivable that the delayed positive feedback accounts for the initial increase in cycle frequency in the complete tegula feedback model. At a first glance it seems reasonable to also perform the opposite test, namely, to selectively remove the tegula synapse to interneuron 301 and to leave the remaining synapses intact. Unfortunately, due to the connectivity of the cpg (Figs. 1(a), (b)) this would not result in an isolated negative feedback. Interneuron 301 receives indirect excitation from the tegula via interneurons 504 and 401, and inhibition from interneuron 501 is removed when the tegula is active. Activating the tegula thus always results in a delayed excitation of the depressor part via 301 (and thus in an implicit delayed positive feedback), even when the direct tegula excitation of 301 is missing. A complete removal of interneuron 301 is not a feasible experiment either, since this disables pattern generation in the network.

3.4 The balance of negative and delayed positive feedback determines the dynamics of frequency regulation To separate the effects of negative and positive feedback we thus used a simplified model with regard to the representation of the cpg. In this reduced model, we replaced the central pattern generator by an RC-circuit that received a constant charging current (similar to Ausborn et al. 2007; details see Section 2). The charging level of the RC-circuit represented the excitation of the depressor motor neurons. Replacing the central pattern generator by a non-oscillating passive element allowed us to investigate the impact of tegula feedback independent of the influence of a specific type of oscillator model (Ausborn et al. 2007). Sensory feedback was implemented in the same way as in the Hodgkin–Huxley model, namely, with the linear functions given in Fig. 1(d). Cycle Period was defined as the time between two identical RC-circuit charging levels of consecutive cycles (for example see Fig. 1(e)). For this we arbitrarily, but consistently for all models, chose a level of 0.75. The latency of tegula activation was then calculated in reference to this point in time. In this model, the feedback provided by the tegula could easily be changed in sign. We tested the response of the network to changes of the feedback strength in three situations: (1) The tegula provided delayed positive feedback by contributing to the charge of the RC-circuit when activated. (2) The tegula exerted negative feedback by reducing the charge. (3) We combined negative and delayed positive feedback. 1. When the tegula provided delayed positive feedback, an increase of feedback strength sped up the rhythm, that is, the oscillation frequency increased (Fig. 6(a)). With sufficiently high feedback strengths, the frequency saturated, but it never decreased. 2. When the tegula provided negative feedback, cycle frequency decreased with higher feedback strengths (Fig. 6(b)). While this decrease was similar to the intact flight model, the reduced model was unable to reproduce an important feature of the biological flight system and the Hodgkin–Huxley model of the flight pattern generator, namely, the initial increase in cycle frequency at low tegula feedback strengths (Fig. 5(a); compare also to Ausborn et al (2007). 3. When we combined positive and negative feedback, a synchronous strengthening of both, positive and negative feedback pathways, also resulted in a continuous increase of cycle frequency up to saturation at high feedback strengths (Fig. 6(c)). The obtained curve thus had a shape that was similar to that when only positive feedback was provided. Thus, combining positive and negative feedback resulted in a frequency regulation that did not resemble that of the biological system

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(compare Ausborn et al. 2007) or that of the Hodgkin– Huxley model (Fig. 5(a)). A comparison of the number of tegula synapses that provide either negative or positive feedback, however, shows that more pathways are involved in the former than in the latter (only the 301 synapse). It is thus likely that negative feedback is much more strongly represented in the system than is positive feedback. We thus weighted the two feedback types differently by enhancing the strength of the negative feedback pathway. First, each strength used for positive feedback was multiplied by a fixed factor (ranging between 2 and 100) to obtain the strength of the negative feedback. This proportional change of feedback strength, however, did not qualitatively change the shape of the curve. Rather, increasing the feedback strength resulted in a continuous increase of cycle frequency (data not shown), very similar to the configuration with positive feedback only. We thus amplified the negative feedback even further and raised each feedback strength to the power of a fixed value (ranging between 1.5 and 3.5). This enhanced negative feedback was immediately obvious in the dynamics of the frequency regulation. Cycle frequency increased quickly at low feedback strengths, but then reached a maximum value at intermediate feedback strengths, after which it started to decrease again. We found that an exponent of 2.5 best matched the data obtained in the Hodgkin–Huxley model (Fig. 6(d)). The weighting of positive and negative feedback pathways thus determined the characteristic shape of the tegula frequency regulation.

4 Discussion In the present report we use a realistic network model of the locust flight pattern generator (see Ausborn et al. 2007) to examine the functional significance of antagonistic sensorimotor pathways. These pathways connect the tegula wing hinge sensor to the flight motor neurons, mostly via interneurons of the central pattern generating circuit. The tegula provides both, fast negative and delayed positive feedback to the central pattern generator. Delayed positive feedback is selectively provided by interneuron 301, while the previously studied negative feedback is mediated by all the other pathways (Pearson and Wolf 1988; Wolf and Pearson 1989). Contrary to previous assumptions (e.g. Ausborn et al. 2007; Wolf and Pearson 1989), the increase in wing beat frequency brought about by tegula activation is due to the delayed positive feedback provided by 301, rather than simply by the advanced discharge of elevators due to the fast negative feedback. In fact, the bell-shaped dependency of pattern frequency on feedback strength results from a superposition of a frequency rise due to

positive feedback and a frequency decline due to negative feedback. At low feedback strengths, the positive feedback dominates and produces the rapid rise in frequency, towards higher feedback strengths negative feedback gains impact and reduces pattern frequency, eventually down to the starting values. 4.1 The functional role of parallel and antagonistic sensory pathways In many systems the feedback provided by sensory organs is defined by their impact on the motor output or behavior, but the connectivity patterns mediating these feedbacks remain enigmatic. At the same time distributed processing has been shown to be present on many different levels of sensory processing (Haberly 2001; Hultborn 2001). The functional relevance of parallel antagonizing pathways and thus, at first glance, contradictory sensory configurations, is however often unknown. Sufficient knowledge of the underlying neuronal network is always essential for such investigations. In a number of systems, where the cellular level of the processing network is accessible, pathways conveying sensory information antagonistically are not uncommon (Bosco and Poppele 2001; Burrows 1987; Combes et al. 1999; Ekeberg 1993; Lachnit et al. 2004; Lockery and Kristan 1990; Nagayama and Hisada 1987; Osborn and Poppele 1992; Schmitz and Stein 2000; Stein et al. 2008). This situation is captured by the term “parliamentary principle” coined by Bässler (1993), which illustrates that several parallel and partly antagonistic pathways impinge on the motor output with different weights. The outcome of this parallel processing depends on the actual (situation- and task-dependent) weights of the different pathways—reminiscent of the votes in a given parliamentary ballot. The functional role of parallel antagonistic processing pathways has mainly been discussed in the context of gain control mechanisms (Borst and Haag 2002; Stein and Sauer 1998) and flexibility of motor control (Stein et al. 2008). For instance, the differential weighting of parallel antagonistic pathways may not only adjust the strength of a given reflex but it may indeed alter its sign from negative feedback— such as a resistance reflex in postural control—to positive feedback—such as an assisting reflex in the swing phase of walking movements (Stein et al. 2008; Schmitz, J., personal communication). Parallel antagonistic pathways thus can form the basis of reflex reversal. Here we demonstrate that the control of pattern frequency is another role for antagonistic pathways. This appears particularly important for behaviors where pattern frequency is of great functional significance. And indeed, the timing and speed of the wing stroke, and thus indirectly of stroke period, are critical for aerodynamic force production in insect flight.

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This has been demonstrated for locust flight (e.g. Wolf 1993) as well as for dipteran flight (Lehmann 2004). 4.2 The role of interneuron 301 in generating the flight pattern According to our experiments, of all interneurons only interneuron 301 had a prominent effect on wing stroke frequency. Together with interneuron 501, 301 forms the core of the flight pattern generator. In particular, interneuron 301 mediates the switch from elevator to depressor phase. Interneuron 301 is active at the interface between both phases (Fig. 3(a)) and it influences the postsynaptic interneurons 511 and 501 in such a way that the transition from elevator to depressor phase is elicited (Robertson and Pearson 1985). The remaining interneurons had no or only minor effects, some even slowed down rhythm frequency when activated by the tegula (Fig. 4(a)). Is there a role for the other interneurons, many of them mediating fast negative feedback, in addition to their function in building the central pattern generator? There is much more to the locust flight pattern than just wing beat frequency, of course. We focused on this latter aspect in the present study due to the limitations of our model, in particular, the reduction in the number of motoneurons to one elevator and one depressor unit. Important details of the flight motor pattern, such as the relative timing of the different elevator or depressor motoneurons, was beyond the scope of the present experiments, therefore. It is these details of motor neuron activity, however, that determine behaviorally relevant aspects of flight performance, for instance, the wings’ aerodynamic angle of attack (Pfau and Nachtigall 1981) and force production (Wolf 1993). It appears likely that such aspects are also controlled by the central oscillator network, in addition to direct fast connections from sensory receptors to flight motor neurons. Furthermore, phase response curves measured in the complete tegula feedback model (Ausborn et al. 2007) differed considerably from those measured with short depolarizing pulses to interneuron 301 (which corresponds to an activation of the tegula-to-301 synapse; Fig. 3(b)). For phases around 0.35, where the tegula is active during unperturbed flight, both phase response curves predict a similar decrease in cycle period. At other phases, however, the two curves deviate. Thus, during regular flight the system could rely on its tegula-to-301 synapse but under perturbations the synapses to the remaining interneurons are essential to produce the desired effect on the rhythm. The facts that the tegula synapse onto 301 alone could increase wing beat frequency and that in this case the direct connections from the tegula to the elevator motor neurons were required for a regular discharge of the latter (Fig. 4) indicate two important features. First, it demonstrates that

individual interneurons may have significant impact on flight motor activity and that other interneurons may well play a role in controlling other features of the flight motor pattern. Second, the importance of direct fast synaptic contacts from wing sensors to flight motor neurons is highlighted, in agreement with previous physiological experiments (e.g. Ausborn et al. 2007; Wolf and Pearson 1988). In particular, it has previously been shown that the ability of the tegula to advance the wing upstroke is aerodynamically relevant (Wolf 1993). It was always assumed that this advance corresponded to a reset of the cpg at the beginning of the elevator phase. At wing beat frequencies of 20 Hz or more, however, a timely and aerodynamically adequate activation of elevator motor neurons is difficult when it has to be achieved via the reset of a network of neurons (the cpg). Rather, we show here that the tegula resets the pattern generator to the depressor phase and that the activation of the elevator motor neurons is accomplished via direct connections that bypass the cpg. The tegula indeed possesses such direct connections to elevator motor neurons and to premotor interneurons that don’t participate in rhythm generation (e.g. interneurons 710, 566 and 567; Pearson and Wolf 1988; Ramirez and Pearson 1993; Wolf and Pearson 1989). 4.3 Uniqueness of the model, and general implications Building models is essential for gaining insights into the general principles of network function. Yet it is often not possible to derive all necessary model parameters directly from physiological investigations. Model parameters are thus usually adjusted to produce a realistic motor output and the validity of the model is then tested by running physiological standard tests that should yield similar results as in the animal (details in Ausborn et al. 2007). Recent experimental and theoretical data suggest however that functional circuit performance can be obtained from circuits possessing very different cellular properties (Prinz et al. 2004), indicating that not a specific set of parameters is essential for pattern generation. Rather, many combinations of parameters exist which may generate similar outputs. This raises the question of whether different circuit parameters would have given different results for the frequency regulation with combined positive and negative feedback. The influence of sensory feedback loops on pattern generators that produce similar outputs despite different network parameters has not been tested so far. It is, however, reasonable to assume that the response to sensory input can depend on the chosen model parameters. As a result, the sensory feedback may either strongly entrain the oscillator, or it may not. We thus used a simplified model to test the general applicability of frequency regulation by positive and negative feedback

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loops. We replaced the oscillator with a continuously charged passive element and found that the regulation of motor pattern frequency showed the same characteristics as in the more realistic model. It is thus conceivable that the results shown in this study do not depend on the specific parameter set chosen. The actual range of frequencies obtained, however, may well depend on the particular structure of the oscillator. For the flight system of the locust, an assessment of the role of the positive and negative feedback pathways in further detail will be possible only in a correspondingly more detailed model of the flight cpg, allowing, for example, differential control of individual motor neurons and the muscles supplied by them. Of particular interest may be the impact of several sensory signals that occur simultaneously, such as those of the tegula and the wing hinge stretch receptor. A close interaction might be expected since the discharge of the stretch receptor occurs in a time interval close to where the delayed positive feedback of the tegula takes effect (Heukamp 1984; Pearson and Ramirez 1990; Reye and Pearson 1988; Wolf and Pearson 1988). Acknowledgements This research was supported by a scholarship from the “Studienstiftung des Deutschen Volkes” to Jessica Ausborn. The University of Ulm provided infrastructure, primarily regarding the modeling project. Particular thanks go to Wolfgang Mader who was not only an important partner for discussion but maintained and advanced the modeling tools. We thank Stefanie Rukavina for helpful discussions.

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