Biol. Cybern. 88, 79–90 (2003) DOI 10.1007/s00422-002-0340-3 Ó Springer-Verlag 2003

From swimming to walking: a single basic network for two different behaviors Tiaza Bem1 , Jean-Marie Cabelguen2 , O¨rian Ekeberg3 , Sten Grillner4 1

Department of Bionics, Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, 4 Trojdena, 02-109 Warsaw, Poland 2 Laboratoire de Neurobiologie des Re´seaux, Universite´ Bordeaux I and CNRS, UMR 5816, 33405 Talence and Inserm EPI 9914, Physiopathologie des Re´seaux Neuronaux Me´dullaires, Institut F. Magendie, 33077 Bordeaux Cedex, France 3 Department of Numerical Analysis and Computer Science, Royal Institute of Technology, 10044 Stockholm, Sweden 4 Nobel Institute for Neurophysiology, Karolinska Institute, 17177 Stockholm, Sweden Received: 12 October 2001 / Accepted in revised form: 16 May 2002

Abstract. In this paper we consider the hypothesis that the spinal locomotor network controlling trunk movements has remained essentially unchanged during the evolutionary transition from aquatic to terrestrial locomotion. The wider repertoire of axial motor patterns expressed by amphibians would then be explained by the influence from separate limb pattern generators, added during this evolution. This study is based on EMG data recorded in vivo from epaxial musculature in the newt Pleurodeles waltl during unrestrained swimming and walking, and on a simplified model of the lamprey spinal pattern generator for swimming. Using computer simulations, we have examined the output generated by the lamprey model network for different input drives. Two distinct inputs were identified which reproduced the main features of the swimming and walking motor patterns in the newt. The swimming pattern is generated when the network receives tonic excitation with local intensity gradients near the neck and girdle regions. To produce the walking pattern, the network must receive (in addition to a tonic excitation at the girdles) a phasic drive which is out of phase in the neck and tail regions in relation to the middle part of the body. To fit the symmetry of the walking pattern, however, the intersegmental connectivity of the network had to be modified by reversing the direction of the crossed inhibitory pathways in the rostral part of the spinal cord. This study suggests that the input drive required for the generation of the distinct walking pattern could, at least partly, be attributed to mechanosensory feedback received by the network directly from the intraspinal stretch-receptor system. Indeed, the input drive required resembles the pattern of activity of stretch receptors sensing the lateral bending of the trunk, as expressed during walking in urodeles. Moreover, our results indicate that a nonuniform distribution of these stretch receptors along the trunk can explain the discontinuities exhibited in the swimming pattern of the newt. Thus, separate limb pattern generators can influence the Correspondence to: T. Bem (e-mail: [email protected])

original network controlling axial movements not only through a direct coupling at the central level but also via a mechanical coupling between trunk and limbs, which in turn influences the sensory signals sent back to the network. Taken together, our findings support the hypothesis of a phylogenetic conservatism of the spinal locomotor networks generating axial motor patterns from agnathans to amphibians.

1 Introduction 1.1 Aquatic and terrestrial locomotion The phylogenetic transition from aquatic to terrestrial locomotion in vertebrates can be regarded as an evolutionary milestone. Still, much of the central nervous system dealing with locomotion is highly developed already in water-living vertebrates. What changes have actually occurred in the neural control of axial movements during this transition? Are the neural networks underlying swimming behavior conserved during evolution or do they become totally reorganized with the appearance of limbs? To address such questions, it is reasonable to look for data from animals with their evolutionary roots in the middle of this transition. Urodele amphibians, which are commonly accepted as the closest sister group of primitive tetrapodes (Bolt 1969, 1977; see also Ashley-Ross 1994), exhibit both swimming and terrestrial walking in adulthood, and are therefore attractive models for this kind of study. In contrast to the extended knowledge of spinal circuits generating motor patterns during swimming in the lamprey (Grillner et al. 1995) or the Xenopus embryo (Roberts et al. 1997), little is known about the spinal networks controlling locomotor behaviors of urodeles (however, see Cheng et al. 1998). Recently, a distributed rhythm-generation capacity, similar to that reported in lamprey (Cohen and Walle´n 1980), has been demonstrated in the isolated spinal cord of the newt Pleurodeles

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waltl (Delvolve´ et al. 1999). On the other hand, EMG data indicate that both swimming and walking patterns of epaxial muscle activity in the newt are different from the swimming pattern in lamprey (Delvolve´ et al. 1997). Whereas the latter consists of a single wave of activity propagating continuously down the body (Grillner et al. 1993), the swimming pattern in the newt is characterized by two discontinuities in the rostrocaudal propagation of activity, occurring near the limb girdles. During walking, the girdle regions exhibit two distinct bursts of activity per step cycle, whereas other parts of the trunk express a single burst. Thus both motor patterns in the newt seem to be influenced by the presence of limbs. We therefore hypothesized that the differences between the axial motor patterns expressed in the lamprey and the newt may be due to the presence of new central pattern generators (CPGs) which have appeared during evolution to control the limbs, rather than to a developmental reorganization of the swimming-generating network itself. Thus, both axial motor patterns would be generated by the same, essentially lamprey-like network that receives different input drives from the limb CPGs, depending on the locomotor mode (Delvolve´ et al. 1997). This hypothesis was recently explored by showing that a connectionist model of a CPG developed from the lamprey locomotor network can produce two typical gaits of the salamander (Ijspeert 2001). That study focused mainly on generation of proper movements by a biomechanical model of the animal and not on patterns of activity produced by the network. In the present study we test whether a model of the lamprey spinal CPG for swimming (Ekeberg 1993) can generate the correct activity patterns, corresponding to those observed during both aquatic and terrestrial locomotion in the newt. We show here that the model network indeed has the capacity to generate both swimming and walking axial motor patterns, if influenced by two distinct input drives. However, to reproduce the walking pattern the intersegmental connectivity of the model network had to be modified. Part of this work has been reported earlier in abstract form (Bem et al. 1997). 1.2 Axial locomotor patterns in the newt The adult newt locomotes spontaneously by both swimming and overground walking. The movements of the trunk and the underlying patterns of activity of epaxial musculature are quite different for these two modes of locomotion. During walking the body expresses lateral bending movements, which have the form of a standing wave in which the bending of the middle trunk is out of phase with those of the neck and tail (Frolich and Biewener 1992; Ross 1964). The underlying pattern of the epaxial muscle activity expressed on one side of the body is shown in Fig. 1A. It contains weak muscle activity and a principal, robust activity. The latter is organized in the following way: the mid-body (M) express a single burst per cycle, out

Fig. 1A,B. Patterns of activity of epaxial musculature during locomotion in the newt. A EMG activity on one side of the trunk (see body shape) during the walking cycle (0; T ). Principal activity (black areas) is organized in two patterns. The single-burst pattern consists of one burst per cycle, exhibited in the middle (M ) versus neck (N ) and tail (TL) regions of the trunk, whereas the double-burst pattern contains two bursts per cycle (see stars), expressed around the shoulder girdle (SG) and pelvic girdle (PG ). Also shown is the weak activity (dashed areas) occurring in N and TL regions. B Onsets of EMG activity on one side of the trunk (solid line) during the swimming cycle (0; T ). Notice the two discontinuities (indicated by arrows) in the propagation of activity in the newt compared to the continuously propagating activity in the lamprey (dashed line). In A and B longitudinal sites are expressed as a fraction of snout-vent length (SVL). Adapted from Delvolve´ et al. 1997

of phase with similar bursts in the neck (N) and tail (TL) regions, whereas the shoulder and the pelvic girdles (SG and PG) exhibit two distinct bursts per cycle (Fig. 1A). These bursts are expressed almost synchronously in SG and PG, and occur in phase with the M burst in the first half of the cycle, and in phase with the N and TL burst in the second half of the cycle. Thus, the walking motor pattern contains two rhythmic outputs: (i) the single-burst pattern expressed outside the girdles and (ii) the double-burst pattern exhibited within the girdle regions. When swimming, the newt uses undulatory movements where the bendings of the trunk form a traveling wave moving from the neck towards the tail. The limbs are extended and held against the trunk (see the body shape shown in Fig. 1B). Figure 1B shows the onset of EMG activity along one side of the body during one swimming cycle. The wave of activity traveling down the body has two discontinuities in the girdle regions. This constitutes a significant difference compared to the lamprey, which expresses a continuously propagating wave.

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2 Materials and methods A simplified nonspiking model of the segmental locomotor network has been used in which inter- and intrasegmental connections were based on data from the lamprey (Ekeberg 1993). This model was constructed as a chain of coupled oscillatory segmental networks (Fig. 2). At the level of a single segment, the network is composed of two reciprocally inhibiting half-segment oscillators, each containing excitatory interneurons (EINs), inhibitory caudally projecting contralateral interneurons (CCINs), inhibitory lateral interneurons (LINs), and motoneurons (MNs). When tonically excited, this network generates rhythmic alternating activity. EINs maintain activity ipsilaterally by exciting all cells within a half-segment oscillator from which MNs provide the output to the muscles, whereas CCINs suppress contralateral activity. During such prolonged activity, the hyperpolarizing effect of calcium-dependent potassium channels becomes significant in both EINs and CCINs (Hellgren et al. 1992). This, in combination with inhibition from LINs, terminates the ipsilateral activity and allows the contralateral half-segment to become active. Intersegmental connectivity between these local networks is provided primarily by EINs which supply rhythmic excitation to nearby segments symmetrically in both the caudal and rostral direction, and by CCINs which only send their axons caudally (see the dashed vertical lines in Fig. 2). Simulations of walking were performed using the isolated network model, on which the effect of different

Fig. 2. Network diagram. The segmental network consists of two mutually inhibiting half-segment oscillators. Each oscillator contains excitatory interneurons (EINs, E ), inhibitory caudal contralateral interneurons (CCINs, C ), inhibitory lateral interneuron (LINs, L), and motoneurons (M ). Stretch-sensitive receptors (triangles) excite ipsilateral and inhibit contralateral oscillators. Connections between segmental networks (dashed vertical lines) are provided by EINs and LINs which send axons ipsilaterally in both directions and by crossed descending projections from CCINs. Notice the asymmetry of intersegmental connectivity. Excitatory synapses are indicated by white circles and inhibitory synapses by black circles. Adapted from Ekeberg (1993)

external inputs was tested. During simulations of swimming the model of the network was connected to a model of the mechanical environment (Ekeberg 1993). The body was represented by ten interconnected links. MN activity was transformed into mechanical forces acting at the joints. These forces together with the counteracting forces from the surrounding water were used in a two-dimensional mechanical model, giving a movement of the body which in turn was fed back to the network through stretch-sensitive receptors which excited the ipsilateral and inhibited contralateral side of the network (triangles in Fig. 2; for a mathematical description of the model see the Appendix). 3 Results 3.1 Simulation of walking Our aim here was to explore if it is possible to make the model of the lamprey CPG for swimming generate a walking-like pattern (as observed in the newt) only by manipulating the input drives. The parameters of the network model used in the simulations are given in the Appendix (see Tables A1 and A2). As a first step we tested the effect of different tonic input drives on the generated output. It is an important feature of the lamprey model CPG that, if influenced by external tonic excitation, it is able to produce traveling waves of activity with a frequency, wavelength, and direction of propagation dependent on the strength of the tonic drive and its distribution along the network (Ekeberg 1993). However, as tested in our simulations, whatever the tonic drive parameters are, the model is unable to simultaneously generate both the single-burst and double-burst patterns, as expressed during walking. We therefore conclude that the network model, if not modified, must receive also a phasic drive to generate a complete walking pattern. Secondly, the lamprey model network, which is a chain of identical segmental networks, was divided into five regions corresponding to the N, M, and TL parts of the trunk in the newt where the single-burst EMG pattern is exhibited and two girdle regions (SG and PG, Fig. 3A). All parts received a tonic excitation with a uniform longitudinal distribution (Fig. 3A, left), applied equally on both sides of the network (Fig. 3A, right). In addition to this tonic background excitation, a phasic drive was now superimposed with excitatory and inhibitory components distributed to parts M, N, and TL of the network (Fig. 3B). In order to make the singleburst pattern of the mid-trunk reciprocal to the neck and tail regions (see Fig. 1A), the network was entrained in the following way: In the first half of the cycle excitation was distributed to part M on one side and inhibition to parts N and TL on the same side. In the second half of the cycle the distribution was reversed (Fig. 3B and C, left). All the time, the opposite side of the network was influenced in the opposite way (Fig. 3C, right). Such a distribution of the phasic inputs in parts N, M, and TL resembles changes of local curvature of the body during

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Fig. 3A–C. Input-drives distribution during simulations of walking. A Tonic excitatory drive (light-shaded area) is uniformly distributed at different network regions (left), with equal intensity on the left (L) and right (R) network sides (right). B Phasic drive intensity changes. The drive contains excitatory (dark-shaded areas) and inhibitory (white areas) components that are sent reciprocally to regions N and TL and to region M during the drive cycle (0; T ). C Input-drives distribution along one side of the network (left) and on the two network sides (right). Network region designations are as in Fig. 2A

the walking gait. The intensity of phasic drives that were sent to these network regions at a given longitudinal site was therefore calculated as an output from stretch receptors, corresponding to the lateral bending of the body in a form of a standing wave (see Eq. A9 in the Appendix). This drive was then sent as an excitatory input to CCINs, EINs, LINs, and MNs on the stretched side of the network, whereas corresponding network elements on the opposite side received inhibitory input of the same intensity. As long as excitation and inhibition was distributed among the regions N, M, or TL according to the scheme shown in Fig. 3, the network model was relatively insensitive to the distribution of input-drive intensity within the regions. For example, similar results were obtained for a distribution of drive intensity in the form of the standing wave, as described above, and for a constant value of an input drive within a given region of the network. The generated pattern of activity is shown in Fig. 4A (see black areas, middle). As illustrated, a single burst of

activity per cycle is expressed in part M, out-of-phase with bursts in parts N and TL and thereby the singleburst EMG pattern is reproduced (see Fig. 1A). In addition, the girdle regions SG and PG, which receive only tonic excitation, express – for a certain level of tonic input – two distinct bursts of activity in each cycle of the phasic drive (see Fig. 4A, stars). (The size of the girdle regions is not critical; it can be varied down to two segments, below which the double burst is not longer produced.) However, this pattern is different from the double-burst EMG pattern exhibited in the girdles of the newt: in the newt the bursts are synchronous whereas bursts generated by the network model are asynchronous (cf. stars in Figs. 1A and 4A). This asynchrony is due to the rostrocaudal asymmetry of intersegmental connectivity caused by exclusively descending projections from CCINs (see thick dashed lines in Fig. 4A, left). Indeed, as illustrated in Fig. 4A (right), during both halves of the cycle the inhibition was distributed through these intersegmental connections to the contralateral side in regions SG and PG (see descending pathways from regions N and M, respectively). This in turn resulted in a reciprocal activation of the girdle regions situated on the same side of the network (middle). Thus, the rostrocaudal asymmetry of the intersegmental connectivity was imprinted on the pattern generated and therefore the network was unable to reproduce the symmetry characteristic for the EMG pattern; i.e., a rostrocaudal mirror symmetry with respect to the middle trunk level. Indeed, when such a symmetry was introduced in the network model by reversing the projection of the inhibitory pathways in its rostral part (Fig. 4B, left), this resulted in the same symmetry in the generated pattern (Fig. 4B, middle). Now bursts generated in SG and PG became synchronous (see Fig. 4B, stars), since the inhibition was distributed simultaneously to the same sides of SG and PG from region M (Fig. 4B, right), and the simulated pattern thereby fitted the EMG pattern better (see Fig. 1A). This walking-like pattern was maintained also if the tonic drive to the nongirdle regions was reduced to subthreshold levels (0.03–0.10, arbitrary units). Such subthreshold excitation did not lead to the generation of rhythmicity by the network itself. However, when the network was entrained by the phasic input drives, this facilitated production of bursts of activity, which were more robust and pronounced than without application of this subthreshold tonic drive (data not shown). In this case, suprathreshold tonic excitation was given exclusively to the girdle regions of the model network, where it maintained the generation of rhythmic activity. The reverse distribution of input drives, i.e., an application of a phasic input to the girdle regions and a suprathreshold tonic drive to the rest of the network, did not result in the generation of a walking-like pattern neither by the original nor by the modified model of the swimming CPG (not shown). The walking pattern, as described above, could be produced with different frequencies without major changes of phase relationships. The range of frequencies that was possible to obtain was determined by the

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Fig. 4A,B. Walking patterns generated by the original (A) and the modified (B) lamprey network model. A In the original model the crossed inhibitory pathways are descending (thick dashed lines) (left). The output pattern (black areas) generated on one side of the network is shown together with input drives (indicated as in Fig. 3C) (middle). The asynchronous activity (stars, middle) expressed at the girdle regions SG and PG is caused by inhibition (black circles) sent contralaterally to the girdles from regions N and M through crossed descending pathways (right). B If the crossed inhibitory pathways are reversed in the rostral part of the network (left), the activity generated at the girdles becomes synchronous (stars, middle), due to ipsilateral inhibitory drives sent to girdle regions (see projection from region M)

(right). Notice that a similar coordination can be obtained if SG receives excitation from region N instead of inhibition from region M (right). Network regions are indicated as in Fig. 2A. Phasic excitatory and inhibitory drives at a given longitudinal site were calculated as outputs from stretch receptors during a standing-wave-like displacement of the body (frequency of 1.8 Hz), with maximal lateral bending equal to 10% of the body length occurring at segments 1, 50, and 100. Tonic input excitation set to 0.29 (arbitrary units), other network parameters are given in Tables A1 and A2 in the Appendix. In B, the extent of CCINs axons projecting to EINs and to CCINs are ten segments rostrally and one segment caudally in the rostral half of the network. Other parameters as in A

network sensitivity to the tonic drive, which could evoke the double-burst oscillations of the frequency of
2–4 Hz in the girdle regions of the network (corresponding to the tonic drive of 0.13–0.4). Thus the walking pattern could be generated with the frequency of
1–2 Hz, which was the frequency of the forcing input drives producing the single-burst pattern.

pattern. This connectivity now facilitated waves travelling rostrally in the rostral part of the body, whereas the caudal part – as in the lamprey – favored downward waves. From both modeling studies and in vitro experiments, it is known that the propagation of activity along the spinal cord in the lamprey can be reversed by manipulating the excitatory gradients (Ekeberg 1993; Grillner et al. 1993). Similarly, as shown in Fig. 5A, an additional excitatory drive sent to the uppermost 40 % of the network (see dark-shaded area in Fig. 5A, right) resulted in a wave traveling continuously downward, as in the lamprey (black areas in Fig. 5A, left). Furthermore, when in addition to the rostral part, extra excitation was applied at two different sites of the network situated more caudally (Fig. 5B, right), each now produced a discontinuity in the propagation of activity, corresponding to a reversed order of segmental activation (see arrows in Fig. 5B, left), similar to that present in the newt EMG pattern (cf. Fig. 1B). In the regions indicated by arrows in Fig. 5B, caudal segments were activated before rostral segments because segmental oscillators with a higher level of input excitation became ‘‘leading oscillators’’ (Grillner et al. 1993) and were driving, with a lag, neighboring oscillators in both the rostral and caudal directions. Thus, a reversed order of activation is produced rostrally to sites of increased

3.2 Simulation of swimming As the body movements of the newt during swimming are similar to those of the lamprey, the mechanical model of the lamprey body (Ekeberg 1993) was included in these simulations (for the parameters see Table A3). Sensory feedback was thus given to the network through the stretch-sensitive receptors (see Table A2). We then investigated what kind of input drive the model network required in order to generate a motor pattern similar to that of a swimming newt. In contrast to the original lamprey model, the modified network was unable to generate a swimming behavior only with tonic excitation uniformly distributed along the network. This was due to the reversed inhibitory connections, which had been introduced in the rostral part of the network to generate the walking

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network through stretch-sensitive receptors now resulted in two local gradients, which in turn gave, as above, two discontinuities in the wave of activity traveling down the body (Fig. 5C, left). In accordance with the ‘‘leadingoscillator’’ theory, a reverse order of activation was generated caudally to the sites where the feedback was lacking (Fig. 5C, left). Our results for both swimming and walking are summarized in Fig. 6. To generate both these patterns the lamprey model CPG for swimming had to be modified in terms of intersegmental connectivity by reversing the dominant direction of the crossed inhibitory pathways in its rostral part (see middle panels in Fig. 6). The input drives also had to be changed compared to the lamprey model (see right panels in Fig. 6). Whereas the lamprey CPG, in order to generate swimming behavior, needs a tonic excitation uniformly distributed along the network or a higher intensity at the most-rostral segments (Fig. 6A, right), the modified network must receive excitation with three intensity peeks, located at the neck and around the two girdles (Fig. 6B, right). For the generation of walking, both tonic and phasic input drives are required, with a distribution which is also related to the location of the girdles. Whereas the tonic drive must be applied at least at the girdle regions, where it is necessary for a generation of rhythmicity, the phasic drive entrains the network regions outside the girdles (Fig. 6C, right).

4 Discussion

Fig. 5A–C. Swimming patterns generated by the modified network model. A The wave of activity traveling continuously downward (black areas) (left) is produced when the most rostral 40% of the network receives extra excitation (dark-shaded area) (right). B Extra excitation at two other sites (right) results in two discontinuities in the wave propagation (left). C Two discontinuities are also produced (left) when sensory input is removed from two sites of the network (whitehatched areas) (right). Notice that the reverse order of activation is generated rostrally to segments of increased excitation (B) and caudally to segments which do not receive sensory input (C). Network parameters as in Fig. 4B. Excitation levels: 0.15 and 0.35 in A and B, 0.18 and 0.38 in C

excitation (Fig. 5B, left). Such a pattern could be generated with the frequency of
2–3 Hz. This corresponded to the level of basic network excitation of 0.15– 0.2 and to the extra excitation (sent to the network regions N, SG, and PG) of 0.35–0.4. Higher levels of basic and/or extra excitation led to higher frequencies of segmental oscillations, but they resulted in patterns of activity different from a travelling wave with two discontinuities. Alternatively, similar discontinuities to the described above could be obtained by removing the sensory feedback from two sites of the network (white-hatched areas in Fig. 5C, right). The excitation received by the

Our results support the hypothesis that the spinal networks controlling axial movements have been preserved during the evolutionary transition from swimming to walking vertebrates. We show here that the model of the lamprey CPG for swimming, if influenced by specific input drives, can generate two distinct rhythmic outputs, which well match the main features of the swimming and walking axial motor patterns in the newt. To reproduce the walking motor pattern a change of intersegmental connectivity in the model CPG seems necessary (see Sect. 4.1). Some features of the axial motor patterns were not reproduced in the simulations; in particular the weak activity causing co-contraction in the neck and tail regions during walking is not present. This is further discussed in Sect. 4.2 in the perspective of future experiments. The source for the two input drives, dependent on the locomotor mode, remains an open question. An attractive possibility is that limb CPGs are involved. Indeed, both drives are related to the presence of limbs, as indicated by discontinuities in their distribution occurring primarily near both girdles (see Fig. 6). We elaborate on this in Sect. 4.3. Finally, our results should be compared with those of Ijspeert (2001), who studied the evolution of the lamprey CPG for swimming in a biomechanical model of the salamander. Both that study and the present one sup-

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careful comparison of produced outputs with patterns of muscles activity recorded during locomotion in the newt. In addition, our results indicate that at least part of the input drives to the lamprey CPG, which are necessary for generation of swimming and walking patterns of the newt, can be produced by the intraspinal stretch-receptor system (see also Sect. 4.3). However, in our simulations the sensory feedback produced during swimming is generated by the model of the lamprey body, whereas sensory feedback produced during walking is given a priori since we did not construct any biomechanical model of the newt locomotion on the ground. These results should therefore be obtained in the future. On the other hand, a biomechanical model of the body of the salamander (Ijpeert 2001) allows for simulations of movements during both aquatic and terrestrial locomotion, while the network model, developed from the lamprey CPG for swimming, is shown to control both types of gaits. In contrast to our study, Ijpeert (2001) focuses on the parameters of generated movements, which determine fitness functions for developing CPG, without including sensory feedback in the model. The outputs generated by the network are different from biological data of the newt: the swimming pattern does not contain discontinuties whereas the walking pattern lacks double-burst parts. Thus, if these features of the activity patterns are not necessary for generation of proper movements, what are their functions during locomotion of the newt? Or, perhaps they do not have any particular function but simply result from a discontinuities of stretch receptors distribution (see Sect. 3.2) and/or a coupling between limb and trunk generators, as suggested in Sect. 4.3. 4.1 Intersegmental connectivity

Fig. 6A–C. Summary of the results. The lamprey model network (A) can produce both the swimming (B) and walking (C) axial motor patterns observed in the newt if intersegmental connectivity (middle panels) and input drives (right panels) are modified. A Swimming behavior in the lamprey is generated when the network with descending crossed inhibitory connections (thick dashed lines, middle) receives a tonic input drive, uniformly distributed except for the increased intensity at the rostral end (dark-shaded area, right). B The swimming pattern in the newt is produced when the network with modified connectivity (see reverse polarization of inhibition in the rostral part, middle) receives tonic input drive with intensity gradients occurring in the rostral part and around both girdles (right). C The modified network generates the walking pattern when, in addition to the tonic drive of higher intensity at the girdles, it receives a phasic drive outside the girdles (see arrows) (right)

port – using different methods of investigation – the idea of spinal locomotor networks being conserved across a transition from aquatic to terrestrial locomotion. In our work this conclusion is based on the effect of different input drives on the lamprey CPG and on a

In order to reproduce the walking pattern, the asymmetrical distribution of the intersegmental inhibitory connections had to be reversed in the rostral part of the model network (Fig. 4B). This was done basing on the following assumptions: In addition to the locomotor CPG, optokinetic and/or vestibulocollic reflexes can participate in the generation of activity in the neck part of the trunk. However, although the role of locomotor CPG may be limited for the neck activity, the doubleburst pattern in the region of the shoulder girdle cannot be explained by reflexes. Our results indicate that for a proper coordination of this double-burst pattern with the single-burst pattern, the crossed inhibitory pathways ascending to the neck region are necessary. We assumed here that these pathways belong to the CPG controlling trunk movements during both locomotor modes. Therefore we had to reverse intersegmental inhibitory connections in the rostral part of the model CPG for swimming. This modification facilitates a caudorostral propagation of activity in the rostral part of the network and must be counterbalanced by additional rostral excitation during the generation of swimming (Fig. 5A). Interestingly, a majority of in vitro spinal cord preparations of the newt transected rostrally to the hindlimb girdle

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produce a wave of activity traveling caudorostrally when stimulated by a uniform concentration of NMDA in the bath (Delvolve´ et al. 1999). Under these experimental conditions the network connectivity itself must be responsible for this reversed coordination of the generated activity, which adds further support to our modification of the original network model. In the lamprey locomotor circuits longitudinal inhibitory pathways are built of neurons projecting rostrocaudally (CCINs; Buchanan 1982) and a reverse inhibitory projection has, to our knowledge, never been reported. Does this suggest that new inhibitory projections must have been built during evolution from lampreys to urodeles? By evolving artificial controllers of locomotion using genetic algorithms, it has been demonstrated that there are many alternative solutions to the lamprey intersegmental connectivity which all lead to the generation of oscillatory patterns capable of swimming (Ijspeert et al. 1999). Interestingly, in the lamprey spinal cord there exist – besides inhibitory – also excitatory CCINs projecting to similar target cells (Buchanan 1982). These pathways may subserve in the rostral part of the network as a substitute for rostrally projecting inhibitory interneurons, as they can similarly provide a proper coordination during walking (by providing to the girdle SG an excitatory drive from region N instead of an inhibitory drive from region M; see Fig. 4B, right). This further suggests that during the transition from aquatic to terrestrial locomotion, circuits already existing in the lamprey spinal cord but playing a minor role may have been upregulated and used according to new evolutionary needs.

4.3 Interaction with limb CPGs We have already put forward the hypothesis that the specific input patterns necessary for swimming and walking may originate from interactions with separate limb CPGs. In this section we consider different possibilities for a coupling between such limb CPGs and what we will refer to as the trunk CPG, i.e., the lamprey-like network innervating the epaxial muscles of the trunk. In fact, there are several different plausible alternatives which all achieve the same net result. The first, and perhaps most obvious alternative is that there are direct intraspinal projections from the limb CPGs to the trunk CPG. During walking, these projections would then be the source for the phasic input required by the trunk CPG. Assuming that the limb CPGs are located near the girdles, this would imply long-range connections in order to reach the other parts of the cord (Fig. 7A). The girdle regions would receive tonic excitation from some supraspinal source (indicated by arrows) during both locomotor modes. A second possibility is that the limb and trunk CPGs are not directly connected (Fig. 7B). Still, they will not

4.2 Weak activity A weak activity, as illustrated in Fig. 1A (see dashed areas), was never obtained in our simulation. This activity is expressed during almost half of the walking cycle, contralateraly to the side of the trunk where the main activity occurs (cf. activity in a first and second half of the cycle, Fig. 1A). Such long-lasting coactivation of both sides of the network is, however, not possible when activation of one side produces immediately, or with some synaptic delay, substantial inhibition of the other side. Among spinal locomotor network models there are no examples of such a capability (for a review see McClellan 1996). A putative possibility for such a temporary coactivation of two half-centers is a positive feedback, postulated as a mechanism for sustaining activity in the spinal locomotor circuitry in Xenopus (Roberts and Perrins 1995; Wolf and Roberts 1995). Indeed, in a population of mutually excitatory neurons of different membrane and synaptic properties (which could be EINs in our model network), a positive feedback might subserve in maintaining some level of excitation if only a number of cells receive inhibition from the opposite side of the network, whereas at the same time some cells are excited via ipsilateral excitatory pathways. This possibility should be tested in further experiments.

Fig. 7A–C. Possible types of coupling between the limb (L) and trunk (T ) CPGs. A Limb CPGs are directly coupled to the trunk CPG through widespread intraspinal pathways which convey phasic input during walking. Girdle regions (dark-shaded areas) are excited from elsewhere (dotted arrows). B The generators are not coupled centrally (left) but interact via mechanical coupling between limbs and trunk at the body level (right) from which sensory information is sent back to the networks (vertical arrows) in the form of a phasic signal which entrains the trunk CPG during walking. Girdle regions still receive excitation from elsewhere (dotted arrows). C In addition to a sensory coupling as in B, limb CPGs are coupled to the trunk CPG locally at the girdle level where they then provide a nonphasic excitatory drive

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operate as independent networks since they interact via the sensory feedback. Each of the generators controls the movement of a given part of the body, whereas the sensory feedback provides information about the body as a whole, resulting from the integration of central commands through mechanical coupling. During walking, as in the case of the direct coupling, a tonic excitation necessary for activation of the girdle regions is received from supraspinal levels, while the phasic input is conveyed through intraspinal stretch-sensitive receptors whose existence in urodeles has been strongly suggested (Schroeder and Egar 1990; see also Anadon et al. 1995). Indeed, the lateral bending of the trunk during walking has the form of a standing wave with two nodes situated at the girdles (Frolich and Biewener 1992; Ross 1964), and therefore an input from lateral stretch receptors should have the same temporal structure as the phasic drive applied in our simulations (Fig. 3C). According to our predictions, there should be no phasic input to the girdle regions. In fact, at the nodes of a standing wave the body curvature is minimal so these

regions would escape any stretch-receptor entrainment during walking. Another possibility is that these regions do not even have stretch receptors, which would also explain the discontinuities in the wave propagation during swimming, as indicated by our results (see Fig. 5C). Consequently, it would be interesting to investigate the longitudinal distribution of intraspinal mechanoreceptors in urodeles. So far, we have assumed that the tonic input comes directly from supraspinal sources. Another possibility is that the trunk CPG receives its tonic excitation through a direct, nonphasic coupling with the limb CPGs at the girdle levels (Fig. 7C). We propose here a model of such a coupling, which we call ‘‘orthogonal’’ coupling. The phasic input would still be received from the sensory feedback, or possibly a direct projection, as described above. The model is based on the idea that each limb CPG is constructed as a chain of coupled oscillatory networks which control separate joints (Grillner 1981; see also Cohen 1988 and Cheng et al. 1998). Here we do not intend to develop the entire model of limb CPG. For

Fig. 8A–B. Orthogonal coupling between limb and trunk CPGs. A The trunk CPG has a form of a chain of segmental oscillatory networks, repeated caudorostrally (left). At the girdle level two additional segmental networks extend from the chain orthogonally, in the ventral and dorsal directions (middle). These two segmental networks give rise to the two new chains, extending from the left to the right, which constitute limb CPGs (right). B CPGs controlling homolog limbs have the form of two chains of coupled oscillatory networks (flexor, F; extensor, E), similar to the trunk CPG from

which they emerge. During walking, both chains F and E are activated by external inputs (white arrows, left). From both chains the excitation is sent bilaterally to the trunk CPG at the girdle level (black arrows). During swimming, the trunk CPG and chain E are activated by external inputs (white arrows, right). Chain E generates tonic activity due to a block of inhibitory transmission (note the lack of horizontal lines between the oscillators) and provides additional excitation at the girdle level of the trunk CPG (black arrows). Chain F is entrained from the trunk CPG (black arrow)

88

the purpose of this study we consider only circuits controlling the most proximal joints of homologous limbs, i.e., joints acting in both limb and body axes, assuming that these parts of limb CPGs are directly coupled to the trunk CPG (see the square in Fig. 7C). Figure 8a illustrates the idea of ‘‘orthogonal’’ coupling between generators. The trunk CPG is constructed as the lamprey CPG for swimming. It has a form of a chain of segmental oscillatory networks, repeated caudorostrally, each of which is built of two half centers (cf. Fig. 2) (Fig. 8A, left). At the girdle level two additional segmental networks extend from the chain orthogonally, in the ventral and dorsal directions (Fig. 8A, middle). These two segmental networks give rise to the two new chains, extending from the left to the right, which constitute limb CPGs (Fig. 8A, right). Thus, limb CPGs emerge from the trunk CPG by repeating the same structure of segmental network in the new dimensions. As illustrated in Fig. 8B, each chain controls flexor (F) or extensor muscles (E), acting on both sides of the body (see horizontal arrows). During walking (Fig. 8B, left), both chains are activated by external tonic inputs (see white arrows), which maintain a rhythmic alternating activity in the half-segment oscillators (active oscillators, dark-shaded circles; nonactive oscillators, light-shaded circles), whereas the trunk CPG is not necessarily activated. Homologous limbs are alternating, as MNs innervating homologous muscles receive inputs from opposite sides of each chain (see horizontal arrows). On the other hand, basic alternation of ipsilateral antagonist muscles F and E is assured by a sensory feedback or by an interaction between two chains in the other part of the limb CPG (not shown). Thus, the flexor and contralateral extensor oscillators are active simultaneously over the entire walking cycle. Thereby, both sides of the trunk CPG at the girdle region receive continuously an excitatory drive through pathways, which constitute the orthogonal coupling between generators (see black arrows). Kinematic and electrophysiological studies indicate that, during swimming, limbs are held against the body and extensor muscles are tonically active (Delvolve´ et al. 1997; Frolich and Biewener 1992). This is explained in our model, as illustrated in Fig. 8B (right). Tonic inputs are sent to the trunk and extensor chains (white arrows in Fig. 8B). However, only excitatory pathways are activated in the extensor chain, whereas inhibitory transmission is blocked (see lack of horizontal connections between oscillators) which prevents generation of a rhythmic activity. From this chain the excitation is sent to the trunk CPG (black arrows in Fig. 8B), otherwise active during swimming, where it provides an increased excitatory level at the girdle regions. On the other hand, the trunk CPG entrains oscillators controlling most proximal joints in the otherwise nonactive flexor chain (see black arrow in Fig. 8B). This can explain a rhythmic activity expressed during swimming in muscles acting in both limb and body axis, coordinated 1:1 with epaxial muscles activity (Delvolve´ et al. 1997). Thus, such interaction between limb and trunk CPGs, which consists of both orthogonal and sensory coupling,

explains entirely the origin of the two input drives by the presence of limbs. Acknowledgements. We thank Drs. T. Gorska and P. Meyrand for their helpful comments on the manuscript. This study was supported by the Swedish Institute, status grant 18/st from the KBN, and the exchange program of the Polish Academy of Sciences and Centre National de la Recherche Scientifique.

Appendix: Neural and mechanical model of the lamprey swimming (after Ekeberg 1993) A simplified model neuron can be regarded as representative for a population of functionally similar cells (i.e., EINs, CCINs, LINs, or MNs). The inhibitory and excitatory synaptic inputs are added separately and are both subject to a dendritic time delay sD . The excitatory input is then transformed by a function which provides saturation at high levels of excitation. The inhibitory input is substracted from the results. Spike-frequency adaptation is modeled as a delayed negative feedback with a time constant sA . The delayed values of the excitatory synaptic input (nþ Þ, the inhibitory synaptic input (n Þ, and the output (#Þ are calculated from ! d 1 X n_¼ ui wi  nþ dt þ sD i2W þ

d 1 n_ ¼ dt sD

X

! ui wi  n

i2W

d 1 # ¼ ðu  # Þ dt sA

ðA1Þ

where Wþ and W are sets of excitatory and inhibitory synapses, respectively, wi is the strength of synapse i, and ui is the output from the corresponding presynaptic neuron. The output from the model neuron represents the mean firing frequency of the population. It is given by  u ¼ 1  exp½ðh  nþ ÞC  n  l# if positive 0 otherwise ðA2Þ where h is a threshold for activation, C is a gain constant, and l controls the level of adaptation. The Table A1. Neuron parameters for excitatory interneuron (EIN ), contralateral inhibitory interneuron (CCIN ), lateral inhibitory interneuron (LIN ), and motoneuron (MN ): h, firing threshold; C, gain; sD , dendritic time constant; l, adaptation; sA , time constant of adaptation Neuron type

h

C

sD

EIN CCIN LIN MN

0.2 0.5 8.0 0.1

1.8 1.0 0.5 0.3

30 20 50 20

ms ms ms ms

l

sA

0.3 0.3 0 0

400 ms 200 ms

89 Table A2. Synapse parameters. The model neurons are connected within a segment as shown in Fig. 2, and also to a number of rostral (rostral extend ) and caudal (caudal extend ) neighboring segments. Strength denotes the connection weight wi (Eq. A1) divided by the number of segments it connects to. EC, stretch-sensitive edge cells; BS, brainstem input to the network providing tonic excitation; ex, excitatory; in, inhibitory

where i 2 f1; . . . ; 9g, mi is the mass, and Ii is the moment of inertia. The moment of inertia for a link i is estimated from that of an elliptical cylinder:  2  a li ðA5Þ Ii ¼ m i i þ 16 12

Presynaptic neuron

Postsynaptic neuron

Type

Strength Extend (rostral, caudal)

EIN EIN EIN EIN CCIN CCIN CCIN CCIN LIN EC EC EC EC BS BS BS BS

EIN CCIN LIN MN EIN CCIN LIN MN CCIN CCIN EIN LIN MN EIN CCIN LIN MN

ex ex ex ex in in in in in in in in in ex ex ex ex

0.4 3 13 1 2 2 1 2 1 0.07 0.03 0.01 0.02 2 7 5 5

where mi is the mass, ai is the width, and li is the length of the cylinder. The body is assumed to be 25 cm long, with elliptical cross-sections with a height of 3 cm along the entire body and with the width of the cylinder equal to 2 cm in the rostral 30 segments, decreasing linearly towards the tail. Values of mi and Ii , corresponding to the shape of the body, are given in Table A3. Water forces parallel ðWjj Þ and perpendicular ðW? Þ to the body axis are calculated from

(2, (2, (5, (5, (1, (1, (1, (5, (5, (0, (0, (0, (0,

2) 2) 2) 5) 10) 10) 10) 5) 5) 0) 0) 0) 0)

Wjj ¼ v2jj kjj

xi þ

ðA3Þ

where i 2 f1; . . . ; 9g, li is the length of link i, xi and yi denote the position of midpoint of the link, and ui denotes the angle from the x-axis. Each link i is acted upon by: muscular torques Ti , water forces Wi , and inner forces from neighboring links Fi and Fi1 . Thus the movement can be calculated from

where q is the density of the fluid, A is the area perpendicular to the movements, and C is the drag coefficient given by the shape of the object. Muscles are modeled by including both an elastic and a viscous component. The torque acting at a particular joint is assumed to be a linear function of the MN activity on the two sides (ML and MR Þ: Ti ¼aðML  MR Þ þ bðML þ MR þ cÞðuiþ1  ui Þ d þ d ðu_ iþ1  u_ i Þ dt

mi

ðA4Þ

ðA8Þ

where a is the gain of the muscles, b is the stiffness gain, c is the tonic stiffness, and d is the damping coefficient. Here, the same set of parameters has been used throughout the body: a ¼ 3 N mm, b ¼ 0:1 N mm, c ¼ 10, and d ¼ 30 N mm ms. The activity level of a stretch receptor is roughly proportional to the curvature of the body at the site of the cell. Thus

Table A3. Mechanical properties of the links Link (i)

mi (g)

Ii (g mm)

k? ðNs2 =m2 Þ kjj ðNs2 =m2 Þ

1 2 3 4 5 6 7 8 9 10

4.5 4.5 4.5 4.5 3.8 3.15 2.5 1.8 1.1 0.45

45.0 45.0 45.0 45.0 35.6 27.5 20.4 14.2 18.6 13.4

0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045

2

d xi ¼ Wi;x þ Fi;x  Fi1;x dt2 d2 mi 2 yi ¼ Wi;y þ Fi;y  Fi1;y dt d2 li Ii 2 ui ¼ Ti  Ti1  ðFi1;x þ Fi;x Þ sin ui dt 2 li þ ðFi1;y þ Fi;y Þ cos ui 2

ðA6Þ

where vjj and v? are the parallel and perpendicular components of the velocity, and kjj and k? are the corresponding water resistance coefficients. The latter (see Table A3) are estimated from A W ¼ qv2 C ðA7Þ 2

neuron parameters used in the simulations are given in Table A1. The segmental network shown in Fig. 2 is repeated along the spinal cord. Here 100 segments are included. Synaptic connections from each neuron are distributed to target neurons in nearby segments both caudally and rostrally, using the same synaptic strength as within the segment, as given in Table A2. The mechanical model of the body contains ten links connected by nine joins. The movement of the links are constrained by the joins, forcing them to stay connected, which is expressed mathematically as li liþ1 cos ui ¼ xiþ1  cos uiþ1 2 2 li liþ1 sin uiþ1 yi þ sin ui ¼ yiþ1  2 2

W? ¼ v2? k?

0.03 0.02 0.01 0 0 0 0 0 0 0

90

 f ¼

ðui  uiþ1 Þ li þl2 iþ1 0

when ui > uiþ1 otherwise

ðA9Þ

where f is the output of a stretch-sensitive edge cell. The inner forces are calculated in the following way. The mechanical constrains, as expressed by (A3), can be written in compact form: gðpÞ ¼ 0

ðA10Þ

whereas the motion (A4) can be expressed as d p¼v dt

ðA11Þ

and M

d v ¼ w þ CðpÞf dt

ðA12Þ

where p is a column vector composed of the position coordinates of all the links, v is the corresponding speeds, w is the water forces and muscles torques, M is the mass matrix, C is the transpose of the Jacobian of g ( p), and f is a vector containing unknown inner forces. Thus, (A10)–(A12) lead to a system of linear equations in f: ðCT M1 CÞf ¼ CT

d v  CT M1 w dt

ðA13Þ

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