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0.4 s asymmetrical IF response for the left MOT. Because of the expanded timescale, the stripe slew rate is about 3007s. When the stripe slews to the right, there is a single, impulse-like dip in IF of the left MOT of about 5 Hz peak, or about -6.25% (20 responses are averaged synchronously with the stimulus in each case). When the stripe slews back to the left, there is a distinct doublet response; a broad positive peak of about 5 Hz, followed by a narrow, negative peak of the same amplitude. The more complex waveform may be in response to the slight overshoot of the object over the left eye. Clearly, the animal's CSEM system responds to high angular velocities, in this case, ±300°/s.

right

10Hz

FIGURE 5.4-5 Responses of both muscles to a horizontal step displacement of the vertical stripe object. Upper trace, IF change of the right MOT; middle trace, IF change of the left MOT; bottom trace, stripe position. Note that the right MOT IF spikes positive as the stripe slews to the right, as the right eye's medial ommatidia attempt to track the stripe. Also note the overshoot in the stripe position; this is an electromechanical artifact that the insect sees. (From Qi, 1989. With permission.)

I5 Hz

0.1s

FIGURE 5.4-6 Averaged response of a left MOT to a 30° step displacement of a bar object subtending 0.75° (100 mm x 1.5 mm, 11.5 cm from the eye). Left plots, stripe stepped to right; right plots, stripe stepped to left. Note transient increase in the left MOT frequency, as the fly contracts the left MOT in an attempt to track the stripe. The transient decrease in frequency of left MOT spikes is thought to be a response to the overshoot transient in stripe position. The negative slope in the stripe position is about 25 ms in length. (From Qi, 1989. With permission.)

FIGURE 5.4-7 Schematic of a one-dimensional model for closed-loop control of slip speed, ve, of an object moving in front of anterior (medial) ommatidia. See text for discussion.

Qi (1989a, b) did many tests using the ipsilateral (right) eye with the object (stripe) centered over a point 37° from the anterior axis, over the right eye. The object was a stripe moved ±15° around 37°. To test the hypothesis that the fly's CSEM system uses feedback to slew the optical axes of the lateral ommatidia of the ipsilateral eye to follow an object moving from front to rear, Qi "opened the loop" of the feedback system by cutting the ipsilateral MOT. He recorded from the ipsilateral NMOT. Because the muscle was cut, the medial ommatidia assumed a fixed position with regard to the head, and obviously could not track an object moving from front to rear, and vice versa. Qi observed two results as a result of cutting the muscle: (1) The peak-to-peak amplitude of the change in frequency decreased about 17% (average of three preparations) for the same ±10° triangular stripe oscillation amplitude over the ipsilateral eye. (2) The time constant of the ipsilateral NMOT square wave rise increased by about 34.5%, signifying that opening the feedback loop caused the system response to slow, i.e., have a lower, dominant natural frequency. Unfortunately, these two observations are incompatible with a simple negative feedback model for the CSEM system. To understand this dichotomy better, refer to Figure 5.4-7, which shows the system schematically in one dimension to facilitate understanding. A one-dimensional array of ommatidia send analog signals from their retinula cells to a "black box" DS processor. There are one or more neuron outputs from the DS processor whose spike frequency is proportional to f0 - |v0| [1 + cos(29)]/2, |9|< 90° 542

that is, the product of object speed times the directional factor. 8 is the angle between the PD of the DS unit and the velocity, vo of the object. Note that the DSU output, fo, goes to zero for vo directed ±90° to the PD. fo > 0 causes the NMOT frequency to increase, shortening the MOT, and scanning the medial ommatidia in the PD (in this case, toward the rear). In the case where vo is aligned with the PD, 8 = 0, fo is maximum, and the optical axes of the medial ommatidia track the object with vr < vo. Thus, the medial array of receptors experiences a reduced apparent object velocity, ve = vo - vr. The DS unit now responds to ve < vo, producing a reduced fo', etc. This feedback action is summarized for the 8 = 0 case in Figure 5.4-8. In the closed-loop case, the change in NMOT frequency is given by

FIGURE 5.4-8 Block diagram of a putative model for a closed-loop, MOT control system that attempts to minimize slip speed. See text for discussion.

When the loop is opened,

Clearly, for the same object velocity, Afmn(OL) > Afmn(CL), which is incompatible with Qi's observation. If the DS system is single-order low-pass, Kds(s) = Kds/(xs + 1), then the closed-loop gain is

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