DYNAMIC PROPERTIES
OF THE INSECT COMPOUND
EYE
PIERRE CARRICABURU and PAUL DUHAZ~ Department
of Physiology. Faculty of Medicine. 45 rue des Saints-Peres. F-75270 Paris. Cedex 06. France (Receioed 25 January
1978)
Abstract-l. The ERG’s of five species of Insects were studied. the stimulus being a white flux modulated in sinusoidal function of time. 2. The amplitudes. phase shifts and Fourier coefficients of distortion were measured and Bode’s diagrams were plotted. 3. Carbaryl intoxication resulted in an important decrease of the flicker fusion frequencies. a decrease of the phase shifts at high frequencies. and a decrease of the coefficients of distortion. 4. A model of the electrical response is propounded, consisting in three linked servo-systems. The order of the system depends on the species, and carbaryl intoxication results in a decrease of that order.
INTRODUCTION
Since the first work by Autrum (1948a. b). on the flicker fusion frequency of insects, several workers have studied the dynamic properties of compound eyes of crustaceans and insects: Agee, 1971; Autrum, 1952; Autrum and Stoecker. 1950. 1952; Benguerrah and Carricaburu, 1976; Blest and Collett. 1965b; Campan, Gallo and Queinnec, 1965; Carricaburu and Fouchard. 1969; Fouchard and Carricaburu, 1972a. b; Gemperlein and Smola 1972a. b; Hamdorf, Beckh and Lowe, 1969; Ruck and Jahn, 1954; Wu and Wang. 1977. The flicker fusion frequencies were found to be severely affected by organo-phosphorous intoxication. as much in insects (Carricaburu, 1972a. b) as in mammals (Carricaburu and Lacroix, 1973). In the present article we consider the insect compound eye as a servo-system, and we study its frequency transfer function, firstly in undamaged animals, then in animals intoxicated by carbaryl, a carbamate insecticide.
transistor. and the other from the eye. Eleven frequencies were used. almost in geometrical progression from 0.7 to I75 Hz. After processing the films were studied with a photographic enlarger. For each frequency, the amplitude of the eye’s response and its phase shift with respect to the stimulus were measured. The ERG’s were found roughly sinusoidal only at high frequencies. At low frequencies. for the amplitudes of the responses, we took the total amplitudes between peaks, and for the phase-shifts. the gaps between the lowest points.of the phototransistor’s signals (extinction of the stimulus) and the lowest (most positive) points of the eye’s response (Fig. I). The amplitudes (in millivolts) at a given frequency obviously depend on the species. As we were only interested in the variations of the amplitudes according to the frequencies, we ran the experimental data through the following mathematical transformations. Calling A, the amplitude (in mV) of the eye’s response at frequency 0.7 Hz. and A, the amplitude at frequency n Hz, we computed: M = 20 log &/A@ where M is the modulus of the frequency transfer function
TECHNIQUE
(FTF) expressed in decibels.
AND IMIXHODS
The animals were placed on holders specially made for
each species. The ERG’s were recorded through stainless steel electrodes attached to the eyes by means of a micromanipulator. The indifferent electrode was a stainless steel plate on which the animals lay. The signals were amplified by a direct current amplifier made by us, displayed on the screen of a cathode ray oscilloscope. and photographed. The stimulus was a white flux modulated in a sinusoidal function over time. It was very simply provided by a quartz iodine bulb whose real image was projected by an elliptical mirror on one extremity of a light guide. Between the bulb and the light guide were placed filters stopping ultraviolet and infrared, and two polaroids; the first was given a rotary movement of variable speed by an electric motor: the second was fixed. Near the input of the tight guide was placed a phototransistor which delivered a sinusoidal electric signal in phase with the stimulus. On the screen of the cathode ray tube, two curves were displayed. one above the other: one from the photo-
The phase shifts. which were functions of frequencies. were expressed in degrees. Figure I shows the way we computed the phase shifts. Curve P is the response of the
Fig 1. Responses of the phototransistor (curve P) and of the eye (curve E) Locusta migratoria. f = IO Hz.
1497
PIERRE CARRICABLRL
1198 phototransistor. with of the eye. obviously
and PALL
period T Curbe E is the response with the same period iY We deter-
classical formulae. Actually. period r was dlbided mtti :x intervals. and we measured the ordinates of the cur\-’ for each of those 18 points. The 18 figures *ere then introduced into a Tektronix model 32 computer. which corn-
mined the positions of the lowest points of E. namely R. R’ and so on. We measured SR = d. the time lag of the response. The phase shifts were computed by:
puted the coefficients. It should be noticed that the computer computed the coefficients with unnecessary accurac) In fact. the accuracy was limited on one hand by the width of the cathode ray spot. and on the other hand by the noise of the animal. In reality. the e)e’s response IO a strictly sinusoidal stimulus is not strict!> periodic in the mathematical sense. but rather pseudo-periodic (Fig. 2). We computed Fourier coefficients for different frequencies. As the figures are not very explicit. we preferred lo gi\e distortion coefficients. defined III the following manner:
cp=?#dsT expressed in degrees. Finally. we drew Bode’s diagrams (Figs 3-7) by plotting on the abscissae the logarithms of frequencies. and on the ordinates the moduli M in the upper part of the drawing. and the phase-shifts I$ at the lower part. Another mathematical study was the decomposition of the ERG’s in Fourier series. If the stimulus has the form B = BO (I + sin w r) then
the eye’s response V=
+ E, Coefficients
Srcontl-order
V, + .-l, sinwr + B,cosc~r + AzsinZwr A,sin3w;-t B,cos3&r + ..... B,.
tlisrorrion:
has the form
coi2wr + A,.
DI_HAZE
etc. can
be computed
by
Third-order
tlisrorrion:
Fourier’s
0.7
1.7
6.2
Fig. 2. Responses
of Locusta
miyratoria
at different cated
frequencies. animal.
Left:
undamaged
animal.
Right:
intoxi-
1499
Dynamic properties of the insect compound eye If the eye was a linear system. the response to a sinusoidal stimulus would be sinusoidal. and we would have: D, = D, = 0. The less linear the system. the higher the distortion coefficients. Five insect species were studied: Locustcl migraroria and Gryllulus domesticus(Orthoptera). Blahera fusca (Dictyoptera). Sarcophaga argyrostoma (Diptera) and Labiduru riparia (Dermaptera). All these animals had been raised in various laboratories of the University of Paris. For each species. we studied the FTF of undamaged animals, then the FTF of the same animal intoxicated by carbaryl. We showed that this insecticide had an effect on the ERG by the synaptical junctions (Carricaburu. sectionning 1977a. b). In this way we could determine the FTF for the entire eye and for the photoreceptor. It should be observed that we could not study the action of carbaryl in Labidurn riparia because of the very high sensitivity of that species to insecticides. The animals used to die within I min after application of carbaryl. In other animals carbaryl intoxication was processed by pouring a few drops of a l/lOO.OOOacetonic solution onto the head and thorax.
RESULTS
Fig. 3. Bode’s diagram of Locusra Myraroria.
I. Locusta migratoria
Figure 2 shows the responses at different frequencies. on the left for undamaged animals, on the right for intoxicated animals. All the responses of undamaged animals are very far from being sinusoidal. On the other hand. the responses after intoxication are simpler, and have a sinusoidal aspect at frequencies as low as 10 Hz. Table 1 gives the corresponding distortion coefficients. Figure 3 gives Bode’s diagrams, in a continuous line for undamaged animals and in dots for intoxicated animals. In undamaged animals, the modulus of the FTF decreases from 0.7 to 17 Hz, passes through a maximum at 28 Hz, and decreases again. The phase shift is very high, even at the lowest frequencies. It increases regularly up to the flicker fusion frequency (FFF) at about SOHz. The curve shows an inflexion point at 15 Hz. Intoxicated animals have a quite different FTF. The modulus increases from 0.7 Hz to a maximum at 1.6 Hz, and then decreases to the FFF at 27Hz. The phase shift is lower than in undamaged animals. 2. Gryllulus domesticus The shape of the responses is similar to that of Locusta migratoria. It is very different from a sinusoid
in undamaged animals and at low frequencies. Table 2 gives the distortion coefficients. Here again, carbaryl Table 1. Coefficients of distortion
intoxication results in a simplification of the responses, a modification of the FTF with a marked decrease of the FFF. Figure 4’is Bode’s diagram. In undamaged animals the modulus decreases from 0.7 Hz to the FFF at 51 Hz, with a maximum at 15 Hz. It is not exactly a mathematical maximum. but an area situated between two points of inflexion. The phase shift shows a very marked inflexion at about 15 Hz. After intoxication, the modulus shows a maximum at 13 Hz. The phase shift is slightly increased. with a point of inflexion at 18 Hz.
3. Blabera fusca We have previously pointed out that neither organo-phosphorous insecticides (parathion) nor carbamates (carbaryl) seemed to act on the ERG of cockroaches. The ERG in response to an electronic flash suffers no modification after intoxication. Actually, the action of carbaryl is very marked on the FTF. as can be seen in Fig. 5. The modulus of undamaged animals shows two maxima. at 9.5 and 16 Hz. whereas the phase shift increases with a point of inflexion at 13 Hz and a maximum at 16 Hz. After intoxication the modulus shows only one very marked maximum at 6 Hz. The phase shift increases with the frequency. passes through a maximum at 3.5 Hz, through a minimum at 6 Hz, then increases. Here again. the FFF
of Locusta migrutoria Table 2. Coefficients of distortion
D2
D3
F
D2
D3
0.7 1.7 3 6.2 10 15 17 29 54
0.13 0.04 0.02 0.02 0.007 0.0004 0.0025 0.012 0
0.0078 0.002 0.0003 0.0009 OX004 0 0 0 0
D2
0.17 0.10 0.11 0.04 0.03 0.002 0.09 0.09 0.01
0.03 0.005 0.008 0.002 0.001 0.0007 0.009 0.002 0.001
0.17 0.05 0.01
0.001 0.02 0.003 0.01 0.005
D3
0.01 O.OOW
0.0007 0.001 0.0002 0.002 0 0.0002
F 0.7 1.7 3 6.2 10 15 I7 29
of Gryllulus domesticus D2
0.007 0.02 0.009 0.01 0.003 0.02 0 0
4
0.002 0.001 0 0.001 0.002 0.003 0 0
PIERRE CARRKABBCRL and P.~LL DLHAL~ TabIs 2. Coefficients
D:
F
D,
0.014 0.015
O.OOY 0.009 0.015 0.014 0.007 Table
oi distortionof Biuhrr~ /US,;
4.
0.0007 O.OQO2 0.0007 0.002 0.0002 0.005 0.002 Coe-flicients
0.7
17 3 6.2 IO I5 17 of
P,
D: 0.09
0.0.
0.017 0.016 0 0.003 0 0
O.uCI’ 0.0) I 0 0.02 0 0
distortion
of
Sarcoahuga
argyrosroma D,
Fig. 1.
0.097 0.18 0.12 0.07 0.04 0.05 0.05 0.005 0.06 0.08 0.04
Bode’s diagram of Gr~~lulusdor~sricus
is strongly affected by carbaryl. Table 3 gives distortion coefficients. 4. Sarcophaga
argyrosroma
Table 4 gives distortion coefficients and Fig 6 Bode’s diagram. In undamaged animals a first maximum of the modulus can be noticed at 1.7 Hz. but that first maximum at a very low frequency exists in all species at frequencies lower than 0.7 Hz. which is the lowest frequency given by the device used for
DA
0.008 0.018 0.0009 0.001 0.003 0.001 0.003 O.OO:! 0.001 0.007 0.0001
F
DI
0.7 1.7 :.z IO 15 17 39 54 89 175
0.06 0.05 0.05 0.01 0.006 0.003 0.003 0.002
D,
0.005 0.002 0.001 0 0 0.0005 0.0006 o.ooQ3
the present work. One can observe three other maxima at 13.28 and 85 Hz. The FFF cannot be obtained with the present device: by extrapolating the curve it is possible to estimate it at about 200 Hz. The phase shift is very large at all frequencies. It reaches Jo’ at 0.7 Hz. and 600” at 175 Hz. Two maxima at 13 and 85 Hz are clearly seen. A third maximum at 28 Hz is dubious. The large phase shift is quite surprising. When the eye of a fly is stimulated by an electronic flash. the response occurs after a time lag of a few msec. With a sinusoidal stimulus. and at a frequency 0.7 Hz. the time lag is as high as 160 msec. At high frequencies the phase shift exceeds 1.5 periods. Carbaryl intoxication results in important modifications. Firstly. the first maximum occurs at a frequency lower than 0.7 Hz. Then. there are two maxima at 13 and 28 Hz. The 85 Hz maximum has disappeared. and the FFF is strongly reduced: it is now of the order of 53 Hz. The phase shift is greatly decreased, with two maxima at 13 and 28 Hz. 5. Labidura
riparia
Table 5 gives the distortion coetTtcients and Fig the FTF. but only for undamaged animals. The modulus has three maxima. at 1.6. 6.5 and 18 Hz. The FFF is 28 Hz. The phase shift is very high. 70’ at 1 Hz and nearly 2 periods at the highest frequency.
7
DtSCLSSlON AZiD COIUCLLSION
Fig. 5. Bode’s diagram of Blahera fusco
The insect visual system is composed of a certain number of levels which are linked with one another. Figure 8 shows schematically the simplest system one can imagine. It comprises three stages. The first stage comprises the photoreceptors. It transforms the htminous stimulus into a nervous signal which is directed to the second stage (intermediate neurons). From that second stage, signals proceed to the third
1501
Dynamic properties of the insect compound eye
-10
m 0
180
720 Fig. 6. Bode’s diagram of Sarcophaga argyrosroma.
,-
I--
l
stage (third neurons) which finally transmits the information to the brain. According to Autrum’s hypothesis there exists a feedback mechanism in that the response of the first stage is modified by the following stages. We indicated it by the arrows going from the third to the second stage, and from the second to the first stage. There may be a feedback from the brain to the third stage. The total ERG is actually the superposition of the electrical responses of the three stages. According to our hypothesis it results from the algebraic sum of three elementary waves. an NR (negative rapid) wave from the first stage, a P (positive) wave from the second, and an NS (negative slow) wave from the third stage (Carricaburu, 1977a. b). After parathion or carbaryl intoxication, the junction between the first and second stages is destroyed, though it is not possible to assess whether Table 5. Coefficients of distortion of Labidura riparia
Fig. 7. Bode’s diagram of Labidura riparia.
DI
D3
F
0.13 0.02 0.04 0.09 0.2 0.002 0.01
0.007 0.0002 0.001 0.001 0.01 0.002 0.0005
0.7 1.7 3 6.2 10 I5 17
I502
RERRF
GARRICARURIJ and PALL DCHAZE
hv
ERG
Fig. 8. Model of the insect compound eye.
only the direct connection or both direct and feedback connections are destroyed. The visual system as a whole is a servo-system. in the cybernetics sense. This system is certainly not linear: the response of a linear system to a sinusoidal stimulus is sinusoidal. We have just seen that this was not the case. However. in a preliminary study, we shall liken the eye to a linear servo-system. It is well known that an nth order system can be described by an nth order differential equation. From the equation it is possible to compute its FTF. When the equation is not known. as in the case of the eye. it is possible to determine the FTF by appropriate experiments. as we have done with insect eyes. In these circumstances. and very schematically. the.modulus of FTF of an nth order servo-system shows n - 1 maxima. more or less separated and distinct according to the damping of the system. At high frequencies. the phase shift is n n/2. If several servo-systems are linked. without feedback. we obtain the total FTF by computing. at each frequency. the product of the moduli. and the sum of the phase shifts. As for the eye. a theoretical study is not easy. even in the very simple case of Fig. 8. The experimental FTF is the sum of (at least) three FTF’s: 1. The FTF of the first stage as it is modified by the second stage. 2. The FTF of the second stage. as it is modified by the first and third stages. 3. The FTF of the third stage, as it is modified by the second stage, and perhaps by the brain. The simplest case is that of the intoxicated animals. since we have only the first stage left. without feed-
back from the second stage. That first stage is not exactly linear. but distortion coefficients are lessened by carbaryl. We observed one maximum for the modulus of Locusta. two for Gryllulus and Blabrto. and three for Sarcophagu. With regard to the phase shifts at high frequencies. we measured about 3 n/2 for Locusta and Blabera. and 4~12 for Gryllulus and Sarcophaga. We could liken the first stage of Locusta and Blabera to a third-order servo-system the one of Gryllulus and Sarcophaga to a fourth-order system. The FTF of undamaged animals is much more difficult to interpret. The existence of feedback is perfectly visible in Figs 3-7. In undamaged animals the FFF is much higher: if there existed no feedback. the FFF of the entire eye would be equal or inferior to the FFF of the first stage. As a matter of fact,
the second and third stages could only suppress the highest frequencies transmitted by the first stage: they could not transmit frequencies impeded by the first stage. Moreover. the number of maxima is increased (except in GrJllulus). Lastly. the phase shifts at high frequencies are increased in all cases: n/2 in Locusta. Gryllulus and Blabera. 3 n/2 in Sarcophaga. That affect can be explained by two causes: firstly. the feedback is likely to modify the characteristics and the order of the first stage. Then. as we said above. we pick up on the electrode the superposition of the signals elicited by the three stages. Taking into consideration the values of the phase shifts, we shall admit. for the entirety of the eye, an order equal to 4 in Locusra and Blahera. to 5 in Gr_vllulus. and 7 in Sarcophaga and Labidura.
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H. R. (1971) Flicker fusion frequency of the compound eye of Hekoris zea (Lepidoptera: Noctuidae). Ann. enr. Sot. Am. 64. 942-945. Arsac J. (1961) Trunsforrnarion de Fourier et Thhorie des Distrihurions.Dunod. Paris. Autrum H. (1948a) tjber das zeitliche Auflosungsvermogen des Insektenauges. Nachr. Akad. Wiss. Giirr. 1948. 8-12. Autrum H. (1948bl Zur Analyse des zeitlichen At&sungsvermijgens des Insektenauges. Nachr. Akad. Wiss. Giirr. 1948. 8-12. Autrum H. (1949) Neue Versuche zum optischen Auflosungsvermogen fliegender Insekten. Experienria 5. 271277. Autrum H. and Stoecker M. (1950) Die Verschmelzungsfrequenz des Bienenauges. Z. Noturf: Sb. 38-43. Autrum H. and Stoecker M. (1952) Qber optische Verschmehungsfrequenzen und stroboskopisches Sehen bei Insekten. Biol. Zenrralbl. 71. 129-152. Benguerrah A. and Carricaburu P. (1976) L’electroretinostramme cheez les Crustaces Isooodes. Vision Res. 16. T173-1177. Best W. and Bohnen K. (1957) Altemierende Potentiale im Elektroretinogramm des Menschen bei Flimmerbelichttmg. Acra ophthaL35. 273-278. Blest A. D. and Coibtt T. S. (1965a) Micro-electrode studies of the medial protoeerebrum of some Lepidop tera. I. Responses to simple binocular visuaI stimulation. J. Insect PkJsiol. 11. 1079-I 103. Blest A. D. and Collett T. S. (196Sb) Micro-electrode studies of the medial protocerebrum of some Lepidoptera. 2. Responses to visual flicker. J. Insect Phyriol. 11. 1289-1306. Campan R.. Gallo A. and Queinnec Y. (1965) Dttermination eleetroritinogaphique de la frtquence critique de
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Dynamic properties of the insect compound eye fusionnement visuel: etude comparative ponant sur les yeux composes de dix sept especes d’lnsectes. C.r. Sot. Biol.. Paris 159. 2521-2526. Carricaburu P. (1971) Action du parathion sur l’electroretinogramme de la Mouche Muscu domestica. C.r. hebd. Sr’anc. Acad. Sci.. Paris 273 D. 25762578. Carricaburu P. (1972a) Intoxication organo-phosphoree et fonction de transfert des friquences des yeux composes des Mouches. Cr. hebd. Seunc. Acad. Sci.. Paris 275 D. 69 I-694. Carricaburu P. (1972b) Action du parathion sur la fonction de transfert des frequences des yeux composes de I’Abeille Apis melrifica. C.r. hebd. S&c. Acad. Sci.. Paris 275 D. 2029-2031. Carricaburu P. (1977a) Intoxication par le carbaryl et structure de I’ilectroretinogramme des Insectes. C.r. hebd. Seanc. Acad. Sci.. Paris 284 D. 2365-2368. Carricaburu P. (1977b) Installation pour Clectrorttinographie. Archs origin. C.N.R.S.. Paris. No. A.0.580. Carricaburu P. and Fouchard R. (1969) Mode d’etablissement de la reponse electrique synch&e de l’oeil de I’Insecte iclairi en lumiere mod&e. C.r. hebd. Shanc. Acad. Sci.. Paris 268 D. 1955-1957. Carricaburu P. and Lacroix R. (1973) Effet du parathion sur I’electroretinogramme de la Souris blanche. Vision Res. 13. 793-796. Colemann D. B. and Renninger G. H. (1976) Theory of the response of the Limulus retina to periodic excitation. J. math. Biol. 3. 103-119. Fouchard R. and Carricaburu P. (1970) La reponse electrorttinographique oscillante chez cinq especes de Mouches. Vision Res. 10. 655-669. Fouchard R. and Carricaburu P. (1972a) Analyse de l’electroritinogramme de l’lnsecte. Vision Res. 12. l-15. Fouchard R. and Carricaburu P. (1972b) Flicker altemating potentials in the ERGS of Insects in response to two different stimuli. J. camp. Physiol. 77. 341-355. Gemperlein R. and Smola U. (1972a) Ubertragungseigenschaften der Sehzelle der Schmeissfliege CoDiphora erythrocephala. I Abhlngigkeit vom Ruhepotential. J. Physiol. 78. ‘30-52.
Gemperlein R. and Smola U. (1972b) Ubertragungseigenschaften der Sehzelle der Schmeissfliege Colliphora crrrhrocepholu. 3. Verbesserung des Signal-StGrungs-Verhaltnisses durch prkynaptische Summation in der Lamina ganglionaris. J. camp. Physiol. 79. 393-409. Hamdorf K.. Beckh F. and Lowe B. (1969) Das Elektroretinogramm (ERG) der weiss;iugigen Fliege (Colliphoru eryrhrocephaln) im Bereiche der Verschmelzungsfrequenz. Z. uergl. Physiol. 63, 91-l 12. Meyer H. W. (1971a) Visuelle Schliisselreize fur die Auslosung der Beutefangheit beim Bachwasserllufer k’elia co@. (Hemiptera, Enteroptera) I. Untersuchung der raumlichen und zeitlichen Reizparameter mit formverschieden Attrappen. Z. wrgl. Physiol. 72. X0-297. Meyer H. W. (1971 b) Visuelle Schlilsselreize fur die Auslosung der Beutefangheit beim Bachwasserllufer Velia coproi. 2. Untersuchung der Wirkung zeitlicher Reizmuster mit Flimmerlicht. 2. very/. Physiol. 72. 298-341. Michieli S. (1965) Zur Kenntnis der zeitlichen Auslosungsvermiigen der Insektenaugen. Bull. SC. Consril Acad. R. S. F. jugoslac Sec. A. IO. I80-180. Ruck P. (1961) Photoreceptor cell response and flicker fusion frequency in the compound eye of the Fly Lucilio sericara (Meigen). Biol. Bull. 120. 375-383. Ruck P. and Jahn T. L. (1954) Electrical studies on the compound eye of Ligia occidentalis (Crustacea; Isopoda). J. gen.
Physiol.
37,
825-849.
Smola U. and Gemperlein R. T. (1972) Ubertragungseigenschaften der Sehzelle der Schmeissfliege Calliphora eryrhrocephala. 2. Die Abhiingigkeit vom Ableitort: Retina-Lamina ganglionaris. J. camp. Physiol. 79. 363-392.
Swihart S. L. (1973) Retinal duality in the Butterfly Heliconis charironius. J. Insect Physiol. 19. 2035-2051. Wu C. F. and Wong F. (1977) Frequency characteristics in the visual system of Drosophila. J. gen. PhysioL 69. 705-724.
Zettler F. (1969) Die Abhlngigkeit des Ubertragungsverhaltens von Frequenz und Adaptationzustand gemessen am einzelnen Lichtreceptor von Calliphora eryrhrocephala.
Z.
uergl.
Physiol.
64.
432-449.
OF THE INSECT COMPOUND
EYE
PIERRE CARRICABURU and PAUL DUHAZ~ Department
of Physiology. Faculty of Medicine. 45 rue des Saints-Peres. F-75270 Paris. Cedex 06. France (Receioed 25 January
1978)
Abstract-l. The ERG’s of five species of Insects were studied. the stimulus being a white flux modulated in sinusoidal function of time. 2. The amplitudes. phase shifts and Fourier coefficients of distortion were measured and Bode’s diagrams were plotted. 3. Carbaryl intoxication resulted in an important decrease of the flicker fusion frequencies. a decrease of the phase shifts at high frequencies. and a decrease of the coefficients of distortion. 4. A model of the electrical response is propounded, consisting in three linked servo-systems. The order of the system depends on the species, and carbaryl intoxication results in a decrease of that order.
INTRODUCTION
Since the first work by Autrum (1948a. b). on the flicker fusion frequency of insects, several workers have studied the dynamic properties of compound eyes of crustaceans and insects: Agee, 1971; Autrum, 1952; Autrum and Stoecker. 1950. 1952; Benguerrah and Carricaburu, 1976; Blest and Collett. 1965b; Campan, Gallo and Queinnec, 1965; Carricaburu and Fouchard. 1969; Fouchard and Carricaburu, 1972a. b; Gemperlein and Smola 1972a. b; Hamdorf, Beckh and Lowe, 1969; Ruck and Jahn, 1954; Wu and Wang. 1977. The flicker fusion frequencies were found to be severely affected by organo-phosphorous intoxication. as much in insects (Carricaburu, 1972a. b) as in mammals (Carricaburu and Lacroix, 1973). In the present article we consider the insect compound eye as a servo-system, and we study its frequency transfer function, firstly in undamaged animals, then in animals intoxicated by carbaryl, a carbamate insecticide.
transistor. and the other from the eye. Eleven frequencies were used. almost in geometrical progression from 0.7 to I75 Hz. After processing the films were studied with a photographic enlarger. For each frequency, the amplitude of the eye’s response and its phase shift with respect to the stimulus were measured. The ERG’s were found roughly sinusoidal only at high frequencies. At low frequencies. for the amplitudes of the responses, we took the total amplitudes between peaks, and for the phase-shifts. the gaps between the lowest points.of the phototransistor’s signals (extinction of the stimulus) and the lowest (most positive) points of the eye’s response (Fig. I). The amplitudes (in millivolts) at a given frequency obviously depend on the species. As we were only interested in the variations of the amplitudes according to the frequencies, we ran the experimental data through the following mathematical transformations. Calling A, the amplitude (in mV) of the eye’s response at frequency 0.7 Hz. and A, the amplitude at frequency n Hz, we computed: M = 20 log &/A@ where M is the modulus of the frequency transfer function
TECHNIQUE
(FTF) expressed in decibels.
AND IMIXHODS
The animals were placed on holders specially made for
each species. The ERG’s were recorded through stainless steel electrodes attached to the eyes by means of a micromanipulator. The indifferent electrode was a stainless steel plate on which the animals lay. The signals were amplified by a direct current amplifier made by us, displayed on the screen of a cathode ray oscilloscope. and photographed. The stimulus was a white flux modulated in a sinusoidal function over time. It was very simply provided by a quartz iodine bulb whose real image was projected by an elliptical mirror on one extremity of a light guide. Between the bulb and the light guide were placed filters stopping ultraviolet and infrared, and two polaroids; the first was given a rotary movement of variable speed by an electric motor: the second was fixed. Near the input of the tight guide was placed a phototransistor which delivered a sinusoidal electric signal in phase with the stimulus. On the screen of the cathode ray tube, two curves were displayed. one above the other: one from the photo-
The phase shifts. which were functions of frequencies. were expressed in degrees. Figure I shows the way we computed the phase shifts. Curve P is the response of the
Fig 1. Responses of the phototransistor (curve P) and of the eye (curve E) Locusta migratoria. f = IO Hz.
1497
PIERRE CARRICABLRL
1198 phototransistor. with of the eye. obviously
and PALL
period T Curbe E is the response with the same period iY We deter-
classical formulae. Actually. period r was dlbided mtti :x intervals. and we measured the ordinates of the cur\-’ for each of those 18 points. The 18 figures *ere then introduced into a Tektronix model 32 computer. which corn-
mined the positions of the lowest points of E. namely R. R’ and so on. We measured SR = d. the time lag of the response. The phase shifts were computed by:
puted the coefficients. It should be noticed that the computer computed the coefficients with unnecessary accurac) In fact. the accuracy was limited on one hand by the width of the cathode ray spot. and on the other hand by the noise of the animal. In reality. the e)e’s response IO a strictly sinusoidal stimulus is not strict!> periodic in the mathematical sense. but rather pseudo-periodic (Fig. 2). We computed Fourier coefficients for different frequencies. As the figures are not very explicit. we preferred lo gi\e distortion coefficients. defined III the following manner:
cp=?#dsT expressed in degrees. Finally. we drew Bode’s diagrams (Figs 3-7) by plotting on the abscissae the logarithms of frequencies. and on the ordinates the moduli M in the upper part of the drawing. and the phase-shifts I$ at the lower part. Another mathematical study was the decomposition of the ERG’s in Fourier series. If the stimulus has the form B = BO (I + sin w r) then
the eye’s response V=
+ E, Coefficients
Srcontl-order
V, + .-l, sinwr + B,cosc~r + AzsinZwr A,sin3w;-t B,cos3&r + ..... B,.
tlisrorrion:
has the form
coi2wr + A,.
DI_HAZE
etc. can
be computed
by
Third-order
tlisrorrion:
Fourier’s
0.7
1.7
6.2
Fig. 2. Responses
of Locusta
miyratoria
at different cated
frequencies. animal.
Left:
undamaged
animal.
Right:
intoxi-
1499
Dynamic properties of the insect compound eye If the eye was a linear system. the response to a sinusoidal stimulus would be sinusoidal. and we would have: D, = D, = 0. The less linear the system. the higher the distortion coefficients. Five insect species were studied: Locustcl migraroria and Gryllulus domesticus(Orthoptera). Blahera fusca (Dictyoptera). Sarcophaga argyrostoma (Diptera) and Labiduru riparia (Dermaptera). All these animals had been raised in various laboratories of the University of Paris. For each species. we studied the FTF of undamaged animals, then the FTF of the same animal intoxicated by carbaryl. We showed that this insecticide had an effect on the ERG by the synaptical junctions (Carricaburu. sectionning 1977a. b). In this way we could determine the FTF for the entire eye and for the photoreceptor. It should be observed that we could not study the action of carbaryl in Labidurn riparia because of the very high sensitivity of that species to insecticides. The animals used to die within I min after application of carbaryl. In other animals carbaryl intoxication was processed by pouring a few drops of a l/lOO.OOOacetonic solution onto the head and thorax.
RESULTS
Fig. 3. Bode’s diagram of Locusra Myraroria.
I. Locusta migratoria
Figure 2 shows the responses at different frequencies. on the left for undamaged animals, on the right for intoxicated animals. All the responses of undamaged animals are very far from being sinusoidal. On the other hand. the responses after intoxication are simpler, and have a sinusoidal aspect at frequencies as low as 10 Hz. Table 1 gives the corresponding distortion coefficients. Figure 3 gives Bode’s diagrams, in a continuous line for undamaged animals and in dots for intoxicated animals. In undamaged animals, the modulus of the FTF decreases from 0.7 to 17 Hz, passes through a maximum at 28 Hz, and decreases again. The phase shift is very high, even at the lowest frequencies. It increases regularly up to the flicker fusion frequency (FFF) at about SOHz. The curve shows an inflexion point at 15 Hz. Intoxicated animals have a quite different FTF. The modulus increases from 0.7 Hz to a maximum at 1.6 Hz, and then decreases to the FFF at 27Hz. The phase shift is lower than in undamaged animals. 2. Gryllulus domesticus The shape of the responses is similar to that of Locusta migratoria. It is very different from a sinusoid
in undamaged animals and at low frequencies. Table 2 gives the distortion coefficients. Here again, carbaryl Table 1. Coefficients of distortion
intoxication results in a simplification of the responses, a modification of the FTF with a marked decrease of the FFF. Figure 4’is Bode’s diagram. In undamaged animals the modulus decreases from 0.7 Hz to the FFF at 51 Hz, with a maximum at 15 Hz. It is not exactly a mathematical maximum. but an area situated between two points of inflexion. The phase shift shows a very marked inflexion at about 15 Hz. After intoxication, the modulus shows a maximum at 13 Hz. The phase shift is slightly increased. with a point of inflexion at 18 Hz.
3. Blabera fusca We have previously pointed out that neither organo-phosphorous insecticides (parathion) nor carbamates (carbaryl) seemed to act on the ERG of cockroaches. The ERG in response to an electronic flash suffers no modification after intoxication. Actually, the action of carbaryl is very marked on the FTF. as can be seen in Fig. 5. The modulus of undamaged animals shows two maxima. at 9.5 and 16 Hz. whereas the phase shift increases with a point of inflexion at 13 Hz and a maximum at 16 Hz. After intoxication the modulus shows only one very marked maximum at 6 Hz. The phase shift increases with the frequency. passes through a maximum at 3.5 Hz, through a minimum at 6 Hz, then increases. Here again. the FFF
of Locusta migrutoria Table 2. Coefficients of distortion
D2
D3
F
D2
D3
0.7 1.7 3 6.2 10 15 17 29 54
0.13 0.04 0.02 0.02 0.007 0.0004 0.0025 0.012 0
0.0078 0.002 0.0003 0.0009 OX004 0 0 0 0
D2
0.17 0.10 0.11 0.04 0.03 0.002 0.09 0.09 0.01
0.03 0.005 0.008 0.002 0.001 0.0007 0.009 0.002 0.001
0.17 0.05 0.01
0.001 0.02 0.003 0.01 0.005
D3
0.01 O.OOW
0.0007 0.001 0.0002 0.002 0 0.0002
F 0.7 1.7 3 6.2 10 15 I7 29
of Gryllulus domesticus D2
0.007 0.02 0.009 0.01 0.003 0.02 0 0
4
0.002 0.001 0 0.001 0.002 0.003 0 0
PIERRE CARRKABBCRL and P.~LL DLHAL~ TabIs 2. Coefficients
D:
F
D,
0.014 0.015
O.OOY 0.009 0.015 0.014 0.007 Table
oi distortionof Biuhrr~ /US,;
4.
0.0007 O.OQO2 0.0007 0.002 0.0002 0.005 0.002 Coe-flicients
0.7
17 3 6.2 IO I5 17 of
P,
D: 0.09
0.0.
0.017 0.016 0 0.003 0 0
O.uCI’ 0.0) I 0 0.02 0 0
distortion
of
Sarcoahuga
argyrosroma D,
Fig. 1.
0.097 0.18 0.12 0.07 0.04 0.05 0.05 0.005 0.06 0.08 0.04
Bode’s diagram of Gr~~lulusdor~sricus
is strongly affected by carbaryl. Table 3 gives distortion coefficients. 4. Sarcophaga
argyrosroma
Table 4 gives distortion coefficients and Fig 6 Bode’s diagram. In undamaged animals a first maximum of the modulus can be noticed at 1.7 Hz. but that first maximum at a very low frequency exists in all species at frequencies lower than 0.7 Hz. which is the lowest frequency given by the device used for
DA
0.008 0.018 0.0009 0.001 0.003 0.001 0.003 O.OO:! 0.001 0.007 0.0001
F
DI
0.7 1.7 :.z IO 15 17 39 54 89 175
0.06 0.05 0.05 0.01 0.006 0.003 0.003 0.002
D,
0.005 0.002 0.001 0 0 0.0005 0.0006 o.ooQ3
the present work. One can observe three other maxima at 13.28 and 85 Hz. The FFF cannot be obtained with the present device: by extrapolating the curve it is possible to estimate it at about 200 Hz. The phase shift is very large at all frequencies. It reaches Jo’ at 0.7 Hz. and 600” at 175 Hz. Two maxima at 13 and 85 Hz are clearly seen. A third maximum at 28 Hz is dubious. The large phase shift is quite surprising. When the eye of a fly is stimulated by an electronic flash. the response occurs after a time lag of a few msec. With a sinusoidal stimulus. and at a frequency 0.7 Hz. the time lag is as high as 160 msec. At high frequencies the phase shift exceeds 1.5 periods. Carbaryl intoxication results in important modifications. Firstly. the first maximum occurs at a frequency lower than 0.7 Hz. Then. there are two maxima at 13 and 28 Hz. The 85 Hz maximum has disappeared. and the FFF is strongly reduced: it is now of the order of 53 Hz. The phase shift is greatly decreased, with two maxima at 13 and 28 Hz. 5. Labidura
riparia
Table 5 gives the distortion coetTtcients and Fig the FTF. but only for undamaged animals. The modulus has three maxima. at 1.6. 6.5 and 18 Hz. The FFF is 28 Hz. The phase shift is very high. 70’ at 1 Hz and nearly 2 periods at the highest frequency.
7
DtSCLSSlON AZiD COIUCLLSION
Fig. 5. Bode’s diagram of Blahera fusco
The insect visual system is composed of a certain number of levels which are linked with one another. Figure 8 shows schematically the simplest system one can imagine. It comprises three stages. The first stage comprises the photoreceptors. It transforms the htminous stimulus into a nervous signal which is directed to the second stage (intermediate neurons). From that second stage, signals proceed to the third
1501
Dynamic properties of the insect compound eye
-10
m 0
180
720 Fig. 6. Bode’s diagram of Sarcophaga argyrosroma.
,-
I--
l
stage (third neurons) which finally transmits the information to the brain. According to Autrum’s hypothesis there exists a feedback mechanism in that the response of the first stage is modified by the following stages. We indicated it by the arrows going from the third to the second stage, and from the second to the first stage. There may be a feedback from the brain to the third stage. The total ERG is actually the superposition of the electrical responses of the three stages. According to our hypothesis it results from the algebraic sum of three elementary waves. an NR (negative rapid) wave from the first stage, a P (positive) wave from the second, and an NS (negative slow) wave from the third stage (Carricaburu, 1977a. b). After parathion or carbaryl intoxication, the junction between the first and second stages is destroyed, though it is not possible to assess whether Table 5. Coefficients of distortion of Labidura riparia
Fig. 7. Bode’s diagram of Labidura riparia.
DI
D3
F
0.13 0.02 0.04 0.09 0.2 0.002 0.01
0.007 0.0002 0.001 0.001 0.01 0.002 0.0005
0.7 1.7 3 6.2 10 I5 17
I502
RERRF
GARRICARURIJ and PALL DCHAZE
hv
ERG
Fig. 8. Model of the insect compound eye.
only the direct connection or both direct and feedback connections are destroyed. The visual system as a whole is a servo-system. in the cybernetics sense. This system is certainly not linear: the response of a linear system to a sinusoidal stimulus is sinusoidal. We have just seen that this was not the case. However. in a preliminary study, we shall liken the eye to a linear servo-system. It is well known that an nth order system can be described by an nth order differential equation. From the equation it is possible to compute its FTF. When the equation is not known. as in the case of the eye. it is possible to determine the FTF by appropriate experiments. as we have done with insect eyes. In these circumstances. and very schematically. the.modulus of FTF of an nth order servo-system shows n - 1 maxima. more or less separated and distinct according to the damping of the system. At high frequencies. the phase shift is n n/2. If several servo-systems are linked. without feedback. we obtain the total FTF by computing. at each frequency. the product of the moduli. and the sum of the phase shifts. As for the eye. a theoretical study is not easy. even in the very simple case of Fig. 8. The experimental FTF is the sum of (at least) three FTF’s: 1. The FTF of the first stage as it is modified by the second stage. 2. The FTF of the second stage. as it is modified by the first and third stages. 3. The FTF of the third stage, as it is modified by the second stage, and perhaps by the brain. The simplest case is that of the intoxicated animals. since we have only the first stage left. without feed-
back from the second stage. That first stage is not exactly linear. but distortion coefficients are lessened by carbaryl. We observed one maximum for the modulus of Locusta. two for Gryllulus and Blabrto. and three for Sarcophagu. With regard to the phase shifts at high frequencies. we measured about 3 n/2 for Locusta and Blabera. and 4~12 for Gryllulus and Sarcophaga. We could liken the first stage of Locusta and Blabera to a third-order servo-system the one of Gryllulus and Sarcophaga to a fourth-order system. The FTF of undamaged animals is much more difficult to interpret. The existence of feedback is perfectly visible in Figs 3-7. In undamaged animals the FFF is much higher: if there existed no feedback. the FFF of the entire eye would be equal or inferior to the FFF of the first stage. As a matter of fact,
the second and third stages could only suppress the highest frequencies transmitted by the first stage: they could not transmit frequencies impeded by the first stage. Moreover. the number of maxima is increased (except in GrJllulus). Lastly. the phase shifts at high frequencies are increased in all cases: n/2 in Locusta. Gryllulus and Blabera. 3 n/2 in Sarcophaga. That affect can be explained by two causes: firstly. the feedback is likely to modify the characteristics and the order of the first stage. Then. as we said above. we pick up on the electrode the superposition of the signals elicited by the three stages. Taking into consideration the values of the phase shifts, we shall admit. for the entirety of the eye, an order equal to 4 in Locusra and Blahera. to 5 in Gr_vllulus. and 7 in Sarcophaga and Labidura.
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