cyt mett 9 Springer-Verlag 1992

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1 Bil. Cybern. 67, (1992) Bk lg cyt mett 9 Springer-Verlag 1992 Cactivatin f leg reflexes in the stick insect H. Cruse t, K. Dautenhahn +, and H. Schreiner 2 t Universit/it Bielefeld, Fakult/it fiir Bilgie, Pstfach , W-4800 Bielefeld 1, Federal Republic f Germany 2 Universit/it Kaiserslautern, Fachbereich Bilgie, W-6750 Kaiserslautern, Federal Republic f Germany Received January 15, 1992/Accepted in revised frm March 4, 1992 Abstract. Each leg f a standing stick insect acts as a height cntrller. The leg cntains several jints. Mst f these jints are knwn t be cntrlled by feedback lps which are the basis f resistance reflexes (review B/issler 1983). This leads t the questin f whether the resistance reflex f the whle leg can be understd as a simple, vectrial sum f the individual reflexes prvided by the different jints, r whether additinal prperties emerge by simultaneus stimulatin f several jints. Frce measurements were perfrmed while passively mving the middle leg tarsus f a fixed stick insect (Carausius mrsus) stepwise t different psitins. Frm the dynamic and static frces the trques develped by each jint were calculated. They were cmpared with the trques develped when nly a single jint was mved by the same amunt. The cmparisn shws that fr a large range f psitins there are n differences between bth situatins. Differences ccur in tw cases. First, the muscle system cntrlling the cxa-trchanter jint seems t be mre strngly excited when the entire leg is mved than when nly the ne jint is mved. This change increases the linearity f the whle system fr small deviatins frm the zer psitin. Secnd, the trque develped by the extensr tibiae system fr negative steps (crrespnding t increased bdy height), and the levatr f cxa and trchanter fr psitive steps, decreases rather than increases when the whle leg is mved t extreme psitins. This cntributes t a decrease in the slpe f the frce-height characteristic and thus t a mre nn-linear behaviur f the whle system fr the extreme psitins. t is well knwn that the amplificatin factrs f resistance reflexes in the leg shw a large variatin (B/issler 1972a; Kittmann 1991). Our results indicate that any change f the amplificatin factr influences the reflexes in all leg jints in the same way. Crrespndence t: H. Cruse ntrductin The individual jints f a stick insect leg are cntrlled by negative feedback lps (femur-tibia jint: B/issler 1965, cxa-trchanter jint: Wendler 1972; Schmitz 1985; 1986a, b, thracic-cxal jint: Graham and Wendler 1981; Schmitz 1985; fr a review see B/issler 1983). These cntrllers are sensitive t velcity and psitin and can, therefre, in technical terms be called P-D-cntrllers. These feedback lps cause the resistance reflexes bserved when the leg jints are passively mved. n ther experiments, where nt just an individual jint, but the whle leg is passively mved, r where the height cntrl f the whle animal is investigated, the whle leg acts like a feedback cntrller with P-D prperties (Wendler 1964, Cruse Riemenschneider and Stammer 1989, Kemmerling and Varju 1981, 1982, and in the walking animal: B/issler 1977, Cruse 1976a). The questin arises as t whether these prperties f the whle leg are merely the sum f the prperties f the individual jints f the leg, r whether the mvement f the whle leg invlves additinal mechanisms. n rder t answer this questin, experiments were perfrmed in which the resistance reflexes f the three leg jints were investigated separately and cmpared with thse when the entire leg is mved. Fr cmparisn, the trques develped by the single jints in the latter cases have t be calculated frm the ttal frce measured at the leg tip. Material and methds Adult female stick insects Carausius mrsus were used in these experiments. The experiments were perfrmed at the University f Kaiserslautern and at the University f Bielefeld. n Kaiserslautern the animals were fixed drsally t a hlder by means f dental wax. The lngitudinal axis f the bdy was hrizntally riented. The tarsi f the middle and hind legs were placed n balsa beams. One beam was fixed t a frce transducer which culd measure the frce in either ne r tw

2 370 thrax ' femur tib~ Fig. 1. Definitin f the jint angles in the vertical plane. This is the plane f leg mvement used in the experimental series tw and three perpendicular spatial directins. By means f micrmanipulatrs the frce transducer culd be mved t different psitins. n this way the leg was first mved t the "zer psitin". Fr the middle leg, the results f which are described here, the zer psitin is defined in the fllwing way (see Fig. 1): the femur is held hrizntally, i.e., perpendicular t the vertical bdy axis, and perpendicular t the lng axis f the bdy. The tibia psitin is parallel t the vertical bdy axis. The angle between femur and tibia thus amunts t 90 deg. in the zer psitin. Starting frm this psitin, the tarsus culd be mved by hand using the micrmanipulatr t ther psitins. n the Kaiserslautern experiments, the tarsus was mved vertically upwards by either 3, 6, r 9 mm (psitive steps) r dwnwards (negative steps) by - 2, - 4, r - 6 mm. The mvement was carried ut with a velcity f abut 10 mm/s. After this step the tarsus was held in the new psitin fr 4 min. The tarsus was then mved back t the zer psitin. The frces prduced during this step and the psitin f the frce transducer were recrded n a pen recrder (Recmed, Hellige). The latter als served as a cntrl fr the velcity f the mvement. Fr each step we evaluated the dynamic frce value (the difference between the frce exerted befre the step and that exerted directly after the step mvement was finished) and the static frce (the difference between the frce befre the step and the frce 4 min later, i.e., directly befre the tarsus was mved back t the zer psitin). n this paper nly the dynamic frce values are used fr further evaluatin. After 4 min at the zer psitin the next step was perfrmed. The results btained in Kaiserslautern are shwn in Fig. 6 and indicated by pen circles. All ther experiments were perfrmed in Bielefeld. They differed in that the animal was fixed t a hard rubber fam (Veneret) hlder, and all the legs except the left middle leg were fixed t the hlder. The lng axis f the bdy was riented vertically, i.e. parallel t the directin f gravity. The step amplitudes were +/-1, +/-3, and +/ -5 mm in these experiments. The tarsus was fixed t the frce transducer by means f sticky wax. Cntrl experiments shwed n significant differences when the tarsus was nt fixed by the wax but grasped the balsa beam actively. n rder t measure the frces prduced when a single jint is mved individually, the frce transducer was munted n a device such that it culd be mved arund a circle. The center f the circle was riented belw the axis f rtatin f the jint t be investigated. As the thracic-cxal jint is a ball and scket jint, its mvement was split int tw perpendicular directins, the mvement in the vertical plane (in bdy crdinates) with the axis f rtatin parallel t the lng axis f the bdy (drsal-ventral mvement), and the mvement in the hrizntal plane (rstral-caudal mvement). n the latter case the axis f rtatin was parallel t the drs-ventral bdy axis. When measuring the reflex f the femur-tibia jint, the femur was fixed t the hlder and the tibia was fixed t the frce transducer. When measuring the cxa-trchanter jint, the thracic-cxal jint had t be fixed t the bdy by means f dental wax t avid additinal.mvement f this jint. Then the femur was fixed t the frce transducer. As the cxa is t shrt t fix it t a frce transducer, the thracic-cxal jint had t be mved by attaching the frce transducer t the femur. T measure the reflex reactin in the vertical plane, the cxatrchanter jint, which perates in the same plane, was fixed by means f dental wax, and the frce transducer was attached t the femur. A reactin t mvements in the hrizntal plane f the thracic-cxal jint was nly btained by mving the whle leg. n this experiment (first series mentined belw), the lng axis f the bdy was als riented hrizntally, and the frce transducer was munted such that it culd be mved in a hrizntal circle. The centre f this circle was arranged exactly belw the thracic-cxal jint. The tarsus was placed n the frce transducer. The spatial psitins f the leg parts in the different psitins were measured by means f a bincular. The angles were first measured relative t a bdy-fixed crdinate system; later, the jint angles were calculated frm these data. The variatin in the angle values shwn in Figs. 2 and 5 is due t tw causes; first, t errrs ccurring when reading the angle values by means f the bincular and, secnd, t interindividual changes f the angle values because f different limb lengths f the individual animals. Results Three series f experiments were perfrmed. n the first series the tarsus f the middle leg was mved, starting frm the zer psitin, frward and backward alng a circle arund the vertical axis f rtatin f the thracic-cxal jint. n this experiment, the thracic-cxal jint is mainly mved arund its vertical axis f rtatin. Hwever, mvements ccur als arund the hrizntal axis f rtatin in this jint. Figure 2 shws the trques prduced in this jint as a functin f the

3 371 a 70 trque [mn mm] (hrizntal cmpnent) ] -[- 80 -e- t / angle [0] m~0 q - -el --el trque [ran mm] (vertical cmpnent) Fig. 2a, b. Trques develped in the thracic-cxal jint f the middle leg when the tarsus is mved in a circle in a hrizntal plane (mean +/-ED.). a rdinate: trque arund the vertical axis f rtatin, abscissa: angle between lngitudinal bdy axis and the prjectin f the lng axis f the cxa in the hrizntal plane9 Frward mvement f the tarsus increases the value f this angle, b rdinate: trque arund the axis parallel t the lngitudinal bdy axis. Abscissa: angle between vertical bdy axis and the lng axis f the cxa9 Dwnward mvement f the cxa increases this angle (see Fig. 1). Nte that the scale f the abscissa f b is twice that f a 120 E 8 1! ~, 12,0 rl -4~ angle [] change f the jint angles9 These represent the mean values frm 17 animals9 n these experiments the cxatrchanter jint mves less than 2 deg. and the femurtibia jint less than 5 deg. The results shw that the trques prduced arund the vertical axis f rtatin, i.e., thse resisting the frward-backward mvement f the jint (Fig. 2a), are f the same rder f magnitude as thse develped by the cxa-trchanter jint and the femur-tibia jint (see Fig. 5b, c). The trques develped by the thracic-cxal jint arund the hrizntal axis, i.e., thse resisting up-and-dwn mvement (Fig. 2b), are much strnger. This shws that the thracic-cxal jint is quite stiff fr this directin..this result agrees with findings shwn in Fig. 5a (the mean start angle is different in bth series f measurements)9 n a secnd series the tarsus was mved up and dwn alng a line parallel t the vertical bdy axis. n this situatin, the thracic-cxal jint is nly mved arund its hrizntal axis f rtatin, nt arund its vertical axis. Thus the axes f rtatin f all three jints, f the femur-tibia and the cxa-trchanter jint, and the hrizntal axis f the thracic-cxal jint, are perpendicular t the plane f mvement (Fig. 1). This is supprted by the fact that the trque arund the vertical axis, measured in a cntrl experiment using a differently riented frce transducer, was smaller than 15 mnmm and thus was negligible. The trques develped at the tibia-tarsus jint are less than 10 mnmm and will nt be cnsidered here. a -3. > T!,: b ~8-3 C -1! E 0. TTT!~T ~,,,r~li~t'tzll x" *5 * step size [ram] animal n. Fig. 3. Slpe f the resulting frce vectr (see Fig. 4a) with respect t a hrizntal line in a bdy fixed crdinate system fr the six leg psitins (mean +/-S.D.). The directin f the vectr is neglected. Open circles: theretical values which shuld have been btained when n influences ccurred frm ther jints (see text), b slpe f the resulting frce vectr (mean f all six leg psitins) shwn separately fr the 19 animals investigated n 19 animals the tw frce cmpnents in the vertical plane (see Fig. 4a, b) were measured fr each step. Figure 3a shws the directin f the frce vectrs (slpe f the resulting frce vectr in the bdy-fixed crdinate system) varying systematically frm psitive t negative steps. Figure 3b shws the mean slpe f a thrax tibia b -b-~ O x x.e_~ X.3-~-? +R" -1" ' r i frce [mn] (vertical cmpnent) frce [ran] lb 2"0 3"0 ~' (hrizntal _1 ~ cmpnent) -3-Tcl -ct- 0 Fig. 4a, b. Mean values f the dynamic frce values btained when the tarsus is mved in vertical directin, a The leg in zer psitin (0) and when mved by 5mm up (+5) r dwn (-5). Resulting dynamic frces in a bdy fixed crdinate system fr all six tarsus psitins investigated (+ l, + 3, +5,- 1,-3,- 5). Fr scale see b. b Hrizntal and vertical frce cmpnent after nrmalizatin (clsed circles). The number indicates the step size in mm. Frce cmpnents directed t the bdy and upwards are psitive. Abscissa: hrizntal frce cmpnent, rdinate: vertical frce cmpnent. The abslute results f three extreme individuals are indicated by separate symbls. Thse f the animal with the smallest frce values (n. 1, Fig. 3b) are marked by (+); tw symbls (E3, x ) are used fr the tw individuals with the highest frce values. One f these ( stands fr the untypical animal n. 19 (Fig. 3b). The meaning f the pen circles is explained in the Discussin x 0

4 B 372 the abslute directin f the frce vectrs f each animal. The 19 animals are rdered n the abscissa accrding t their mean slpe9 (Later experiments, where the same animals were measured n eight cnsecutive days, shwed that the variatin f the mean values shwn in Fig. 3b is nt due t variatin between individuals, as similar variatins are fund fr different experimental sessins with the same animal9 As is knwn frm earlier investigatins (B~issler 1972a; Kittmann 1991), the amplificatin factr f the femur-tibia jint reflex depends n the inner state f the animal and can vary by a large amunt (B/issler fund the frces t vary by a factr between 1 and 20). Variatin in the amplificatin factr was als bserved in ur experiments when measuring the frces by mving the whle leg. Since, with ne exceptin (animal n. 19, Fig. 3b), the frce vectrs f all animals shw abut the same slpe (which means that changes in the amplificatin factr influence all reflex systems in abut the same way), a nrmalizatin f the values f the different animals was perfrmed as fllws9 The frces prduced in the negative steps shwed a nearly linear increase with step size, in cntrast t the frces f psitive steps9 Therefre, as a measure fr the different amplificatin factrs, the mean value f bth cmpnents f the three negative step frces was calculated fr each animal9 These values varied between 4.2 mn and 33 mn (i.e., by a rati f abut 1 : 8). These values were used t nrmalize all frce values f this animal t the cmmn mean. After nrmalizatin the frce-step characteristics f all animals fall within a small range (Fig. 4b). T shw the effect f this nrmalizatin, the figure als cntains the data f three extreme individuals9 Fr 11 f these 19 animals the change f the leg gemetry during the steps was measured. Frm the data fr each step a mean leg psitin and a mean value giving the angle changes fr each step was calculated. On the basis f the mean frces f these 11 animals, the trques which were develped by the individual jints fr each step, were determined by means f a graphical cnstructin (see Cruse 1976b). The results are given in Fig. 5 fr all three jints9 The slpe in the frce angle characteristic is much higher fr the thracic-cxal jint cmpared t that f the ther jints. n a third series f experiments the trques were measured when the jints were mved individually ("single jint mvement")9 This was dne fr the femur-tibia jint with 11, fr the cxa-trchanter jint with 6, and fr the thracic-cxal jint with 5 animals. The latter 5 and 6 animals are the same as the 11 animals used in the investigatin f the femur-tibia jint9 This was dne t enable us t cmpare different jints f the same animal, and thus t minimize the changes f the amplificatin factrs9 Hwever, it turned ut that due t the unavidable manipulatins f the animal when changing the experimental device, the amplificatin factrs varied cnsiderably. Thus, the values f each animal had t be nrmalized individually. This was dne as described abve (Fig. 4a), fr the frces measured during mvement f the entire leg but nw using the trque values. As trques and frces are directly related, the amplificatin factr is the same whether it is calculated n the basis f the trque r the frce9 Thus, the nrmalizatin influences the data in the same way as abve9 T this end, the nrmalizatin factr was again taken frm the three trque values btained when we increased the angle values (crre- a thrax- cxa jint 9.s. f trque 200 rn ram] 16 b cxa - trchanter jint trque.200 [mn ram] c femur tibia jint trque. [mn ram] ~ [ angle [1 t~' 6' angle [] ' '~" 1g O-- -/.0 angle [] ~ i_160_120_80 6~ -5' 150' -12(. i -40, z, ] J J Fig. 5a-e. Mean values f the trques develped by the three leg jints between a thrax and cxa, b cxa and trehanter and e femur and tibia, when the jint is mved by a given angle (abscissa) frm the zer psitin by mving the whle leg. Step size and directin is marked fr the extreme cases ( + 5, - 5). Fr definitin f the angles see Fig. 1

5 9 ~ 373 spnding t negative steps). The results can be seen in Fig. 6a, b, c fr the three jints. The nrmalizatin factrs varied between 1 and 7.7 fr the thracic-cxal jint, between 1 and 3.7 fr the cxa-trchanter jint, and between 1 and 68 fr the femur-tibia jint. Finally the rdinates f these three mean characteristics were multiplied by a factr t fit the results shwn in Fig. 5a, b, c. The characteristic f the cxa-trchanter jint (Fig. 6b, crsses) shws a very different slpe fr psitive and negative steps. Therefre, fr the nrmalizatin in this case nly the values f the ther branch, namely that f the psitive steps, were used. Discussin The questin t be answered by this investigatin is whether the resistance reflex which can be measured fr the mvement f the entire leg can be interpreted as the simple (vectrial) sum f the resistance reflexes which are knwn t exist in the individual leg jints. This requires a cmparisn f the trques generated in bth situatins, i.e., a cmparisn f the results shwn in Figs. 5 and 6. A cmparisn f the abslute values is nt pssible because f the large variatin in the amplificatin factrs (B/issler 1972a). The fact that in spite f this variatin the frce values after nrmalizatin fall within a narrw range (Fig. 4b) shw that, fr the whle leg mvement, a change in the amplificatin factr influences all frce values, and thus all trque values, by the same amunt. This indicates that the amplificatin fac- trs f the individual jints d nt vary independently frm each ther. Rather, these factrs seem t change by the same amunt fr all leg jints. Our qualitative impressin is that there is a general trend fr the amplificatin factrs t be higher and t vary less in the whle leg mvements. When cmparing the nrmalized data, n bvius differences can be fund fr mst f the values between the trques f the single jint mvements and thse btained fr the whle leg mvements. Nevertheless, there are tw qualitative differences. n the whle leg mvements, the trques f the cxa-trchanter jint and thracic-cxal jint seem t decrease when the highest angle values are reached (Fig. 5). By cntrast, fr the single jint mvements the trques cntinue t increase fr even higher angle values (Fig. 6a, b). Fr the femur-tibia jint a crrespnding situatin is fund fr the lwer angle values (Fig. 6c). Because f the large S.D. this decrease f the trque at the extreme values is nt significant. Hwever, much the same results were btained in an experiment which was perfrmed several years ag with 16 animals in Kaiserslautern. The result f these experiments are als given in Fig. 6b, c (pen circles). Althugh the decrease f trque values is nt significant, the mean value is significantly smaller (p < 1%) than the value expected if the trque had increased as bserved in the single jint mvements. One culd argue that the decrease f the trques fr the extreme values in Fig. 5 may simply be due t the fact that, when mving the whle leg, the velcity f the angular mvement is nt the same as that f the tarsus, a thrax- cxa jint -500 trque [ran ram] b cxa - trchanter jint -280 trque 9 rn ram] c femur- tibia jint -240 trque 9 [ran mml 160 2O angle [] 120 " lic 9 D1].O " 1gO -100" 9 T O 40 angle [*l + 1~0 1s angle l ~ , -400 / C - ' L L! ~ Fig. 6a-c. Trques develped by the three jints, when the jints between thrax and cxa a, between cxa and trchanter b and between femur and tibia e are mved separately (crsses, mean +/-S.D.). These values are cmpared with the trque values shwn in Fig. 5 (clsed circles) and anther series perfrmed by a similar measurement (pen circles) in which the whle leg is mved9 Nte that the rdinate f a has a different scale than that f b, c and f Fig. 5a, b, c

6 but depends upn the range f the mvement. As the dynamic part f the reactin depends n the stimulus velcity (B/issler 1972b), this might influence the resulting frce. Hwever, similar results are als fund fr the static frces, i.e., thse frces measured fur minutes after the leg was mved (nt shwn here). Thus, at least the latter results cannt be explained by pssible, small differences in angular velcity. Anther, even mre bvius difference between bth measurements can be bserved fr the trques f the cxa-trchanter jint. When mving this jint individually, the slpe f the characteristic differs cnsiderably fr psitive and negative steps. This difference amunts t a factr f abut 5 (Fig. 6b). This agrees qualitatively with the results f Schmitz ( 1988a, b) wh fund a factr f 3.6. The latter value was btained fr the angles between 145 and 165 deg. and Schmitz fund that this difference increased fr smaller angle values. When the whle leg is mved, n significant difference is fund fr psitive and negative steps in the linear part f the reactin (Fig. 5b). This is als true fr the experiment with hrizntally riented animals (Fig. 6b, circles). n anther investigatin, Schmitz ( 1985, Fig. 3c) measured the frce develpment f the cxa-trchanter jint while mving the whle leg. n this experiment the cxa-trchanter jint was mved stepwise in bth directins, and the frce value was again abut the same in bth cases. When the jints were mved individually, the limb was fixed t the frce transducer. One culd argue that the differences fund in the reflex respnses are due t the fixatin f the limb and thus t a different stimulatin f leg sense rgans, in particular the campanifrm sensillae. Hwever, the qualitative results fr the cxatrchanter jint were the same in the fllwing, additinal experiment (2 animals). Here, as in the experiments where the entire leg is mved, the tarsus, rather than the femur, was fixed t the frce transducer and was mved in a circle arund the cxa-trchanter jint s that the angle f the femur-tibia jint was held cnstant. The shape f the trque angle characteristics measured fr the individual jints (Fig. 6) cannt easily be quantitatively cmpared with ther results frm the literature. Althugh several investigatins exist, a smewhat different methd was used in each case. Schmitz (1986a, b) used the same methd t investigate the cxa-trchanter jint, but measured nly the reactin t +/-10deg. stimuli in different angle ranges. As mentined abve, as far as a cmparisn is pssible, his results agree with urs. Wendler (1972) als investigated the cxa-trchanter jint, but presented nly electrphysilgical recrdings frm the depressr muscle nerve during sinusidal stimulatin. The femurtibia jint has been thrughly investigated, hwever, frce measurements f steps f different sizes are nly published fr negative steps, i.e., stimuli exciting the flexr frce (Strrer and Cruse 1977). Althugh the methd was different - the leg jint was held fixed and the jint mvement was simulated by stimulating the apprpriate receptr, the chrdtnal rgan- the results agree with ur findings. B/issler (1965) used the same stimulatin, but measured the amplitude f the freely mving tibia. He als fund a mntnic increase in the reactin and a smaller respnse f the extensr tibiae muscle cmpared t the flexr system. N data are knwn frm the literature cncerning the vertical mvement f the thracic-cxal jint. Mvements f this jint in the hrizntal plane arund a vertical axis f rtatin have been dne by Schmitz (1985). The jint was mved by 15 deg. in the anterir directin and back t the 90 deg. starting psitin. The amplitude f the frce change was the same in bth directins which agrees with ur results, as can be seen frm the characteristic shwn in Fig. 2, which has a symmetrical frm. Electrphysilgical investigatins als exist (Graham and Wendler 1981; Graham 1985), using sinusidal stimulatin, but permit n cmparisn with ur frce measurements. Althugh, the cmparisn between Figs. 5 and 6 permits the fllwing interpretatin: basically, the levatr trchanteris system seems t be mre strngly excited when the whle leg is mved. With this exceptin the results shw that within a given range - frm step t step the behaviur f the whle leg shws n difference t that expected if the jint reflexes wrked independently frm each ther. Hwever, when the leg reaches the extreme psitins f step + 5 r - 5, the reflex amplitudes f the femur-tibia jint r f the tw jints between cxa and trchanter, and between thrax and cxa, respectively, are diminished cmpared t the reflex when these jints are mved separately. Thus, when the whle leg is mved, i.e., in the mre bilgical situatin, sme muscles decrease their frce utput when mved t the extremes. These muscles are the extensr tibiae fr the femur tibia jint, and the levatr trchanteris fr the cxa-trchanter jint. f this had nt been the case, the directin f the frce vectrs wuld have depended less n the step size and directin than shwn in Fig. 3a. The frce directins which wuld have appeared if the muscles had increased their frce as when being mved individually, are shwn as pen circles fr step +5 and -5 in Fig. 3a. The crrespnding changes in the frce vectrs are indicated in Fig. 4b by pen circles. This shws that the amplitude f the frce vectr is smaller when the whle leg is mved. t shuld be mentined that a change f reflex sign, which was reprted in an earlier abstract (Dautenhahn and Cruse 1990), culd nt be supprted by the mre detailed experiments described here. The jint trques may be bilgically less imprtant than the frce utput, in particular the cmpnent acting parallel t the vertical bdy axis. This is the cmpnent that prvides supprt fr the bdy when the animal stands n a hrizntal plane. Althugh the trques may decrease at the extreme psitins measured, this frce value is increased mntnically with step size (Fig. 4a, rdinate, see als Wendler 1964; Cruse et al. 1989). This is als the case fr several ther starting psitins f middle and hind legs with nly minr quantitative differences. The results f these experiments are nt shwn in detail here. They were btained in experiments with the animals riented hrizntally, and with the fllwing starting psitins fr

7 375 the middle leg: tw starting psitins differed frm the zer psitin used here because the tarsus was mved hrizntally either 5 mm away frm, r 5 mm t, the bdy. Tw ther starting psitins were btained by mving the tarsus frm the latter psitin, r frm the zer psitin in a circle arund the vertical axis thrugh the cxa by 30 deg. in the anterir directin. These experiments shw furthermre that the result f Fig. 5 is nt dependent n whether the lng axis f the bdy is riented vertically, i.e., parallel t the directin f gravity, r hrizntally. Thus, cncerning the vertical frce cmpnent, a change f the amplificatin factr in the levatr system increases the linearity f the system in the whle leg mvement, whereas a decrease f the trques at the extreme psitins changes the linear behaviur such that the characteristics shw a kind f saturatin effect at extreme values. The results shw that eliciting a reflex in ne jint can als influence the reactin in anther. Such distributed reflexes were described earlier n the basis f electrphysilgical investigatins. Fr crustaceans, Clarac (1977) and Ayers and Davis (1977, 1978) describe reflexes which excite muscles extrinsic t the passively mved jint. An interesting example was described by Delcmyn (1971) fr the cckrach. He extended the femur-tibia jint and thereby elicited an excitatin f the flexr muscle which was nt measured as such. nstead, he recrded frm the extensr muscle in the cxa which crrespnds t the Depressr trchanteris in the stick insect. Extending nly the tibia als excited the depressr. n ur experiments with negative steps the Flexr tibiae is excited tgether with the Levatr trchanteris because here the cxa-trchanter jint is nt fixed, but als extended. On the basis f the reflex fund in the cckrach ne wuld expect that the excitatin f the Levatr might be smaller than when the cxa-trchanter is mved alne. Hwever, the exact ppsite was fund (Fig. 6b). One pssible interpretatin is that the reflex fund in the cckrach des nt exist in the stick insect. The ther interpretatin is that, in bth cases, the jint reflexes perate tgether in rder t mve the tip f the leg, the tarsus, in a directin ppsite t the impsed mvement. This wuld be a cnsistent explanatin fr bth experiments. Acknwledgements. Part f this wrk was supprted by DFG (Cr 58/8-1). We wuld like t express ur thanks t Prf. Dr. U. B/issler and Prf. Dr. J. Dean fr helpful discussin and A. Baker fr prf reading the English manuscript. References Ayers JL, Davis WJ (1977) Neurnal cntrl f lcmtin in the lbster, Hmarus americanus.. Types f walking leg reflexes. J Cmp Physil 115:29-46 Ayers JL, Davis WJ (1978) Neurnal cntrl f lcmtin in the lbster, Hmarus americanus.. Dynamic rganizatin f walking leg reflexes. J Cmp Physil 123: B/issler U (1965) Prprireceptren am Subcxal-und Femur-Tibia- Gelenk der Stabheuschrecke und ihre Rlle bei der Wahrnehmung der Sehwerkraftrichtung. Kybernetik 2: B/issler U (1972a) Der Regelkreis des Kniesehnenreflexes bei der Stabheuschrecke Carausius mrsus: Reaktinen auf passive Bewegungen der Tibia. Kybernetik 12:8-20 B/issler U (1972b) Der "Kniesehnenreflex" bei Carausius mrsus: Obergangsfunktin und Frequenzgang. Kybernetik 11:32-50 B/issler U (1977) Sensry cntrl f leg mvement in the stick insect Carausius mrsus. Bil Cybern 25:61-72 B/issler U (1983) Neural basis f elementary behavir in stick insects. Springer, Berlin Heidelberg New Yrk Clarac F (1977) Mtr crdinatin in crustacean limbs. n: Hyle G (ed) dentified neurns and behavir f arthrpds. Plenum Press, New Yrk pp Cruse H (1976a) The cntrl f the bdy psitin in the stick insect (Carausius mrsus), when walking ver uneven surfaces. Bil Cybern 24:25-33 Cruse H (1976b) On the functin f the legs in the free walking stick insect Carausius mrsus. J Cmp Physil 112: Cruse H, Riemenschneider D, Stammer W (1989) Cntrl f bdy psitin f a stick insect standing n uneven surfaces. Bil Cybern 61:71-77 Dautenhahn K, Cruse H (1990) Resistance reflexes in the leg f an insect: is the whle mre than the sum f its parts? n: Eisner N, Rth G (eds) Brain- perceptin- cgnitin. Prceed. f the 18th Grttingen Neurbilgy cnference, 55, Thieme, Stuttgart New Yrk Delcmyn F (1971) Cmputer aided analysis f a lcmtr leg reflex in the cckrach. Z Vergl Physil 74: Graham D (1985) nfluence f cxa-thrax jint receptrs n retractr mtr-utput during walking in Carausius mrsus. J Exp Bil 114: Graham D, Wendler G (1981) The reflex behaviur and innervatin f the tergcxal retractr muscles f the stick insect Carausius mrsus. J Cmp Physil 143:81-91 Kemmerling S, Varju D (1981) Regulatin f the bdy-substrate-distance in the stick insect: respnses t sinusidal stimulatin. Bil Cybern 39: Kemmerling S, Varju D (1982) Regulatin f the bdy-substrate-distance in the stick insect: step respnses and mdelling the cntrl system. Bil Cybern 44:59-66 Kittman R (1991) Gain cntrl in the femur-tibia feedback system f the stick insect. J Exp Bil, 157: Schmitz J (1985) Cntrl f the leg jints in the stick insects: differences in the reflex prperties between the standing and the walking states. n: Gewecke M, Wendler G (eds) nsect lcmtin. Parey, Berlin Hamburg 1985 pp Schmitz J (1986a) The depressr trchanteris mtneurnes and their rle in the cx-trchanteral feedback lp in the stick insect Carausius mrsus. Bil Cybern 55:25-34 Schmitz J (1986b) Prperties f the feedback system cntrlling the cxa-trchanter jint in the stick insect Carausius mrsus. Bil Cybern 55:35-42 Strrer J, Cruse H (1977) Systemanalytische Untersuehungen eines aufgeschnittenen Regelkreises am Bein der Stabheuschrecke Carausius mrsus. Kraftmessungen an den Antagnisten Flexr und Extensr Tibiae. Bil Cybern 25: Wendler G (1964) Laufen und Stehen der Stabheuschrecke: Sinnesbrsten in den Beingelenken als Glieder vn Regelkreisen. 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