Neural Computation of Motion in the Fly Visual System: Quadratic
Nonlinearity of Responses Induced by Picrotoxin in the HS and CH Cells.
Kondoh, Y., Y. Hasegawa, J. Okuma, and F. Takahashi.
Honda R&D Co. Ltd., Wako Research Center, Chuo 1-4-1, Wako, Saitama 351-01,
Japan.
APStracts 2:0201N, 1995.
SUMMARY AND CONCLUSIONS
1. A computational model accounting for motion detection in the fly was
examined by comparing responses in motion-sensitive, horizontal system (HS)
and centrifugal horizontal (CH) cells in the fly's lobula plate with computer
simulation implemented on a motion detector of the correlation type, the
Reichardt detector. First- (linear) and second- order (quadratic nonlinear)
Wiener kernels from intracellularly recorded responses to moving patterns were
computed by cross-correlating with the time-dependent position of the
stimulus, and were used to characterize response to motion in those cells. 2.
When the fly was stimulated with moving vertical stripes with a spatial
wavelength of 5-40, the HS and CH cells showed basically a biphasic first-
order kernel, having an initial depolarization which was followed by
hyperpolarization. The linear model matched well with the actual response,
with a mean square error of 27% at best, indicating that the linear component
comprises a major part of responses in these cells. The second-order
nonlinearity was insignificant. When stimulated at a spatial wavelength of
2.5, the first-order kernel showed a significant decrease in amplitude, and
was initially hyperpolarized; the second-order kernel was, on the other hand,
well defined, having 2 hyperpolarizing valleys on the diagonal with 2 off-
diagonal peaks. 3. The blockage of inhibitory interactions in the visual
system by application of 10 -4 M picrotoxin, however, evoked a nonlinear
response that could be decomposed into the sum of the first- (linear) and
second-order (quadratic nonlinear) terms with a mean square error of 30-50%.
The first-order term, comprising 10-20% of the picrotoxin- evoked response, is
characterized by a differentiating first-order kernel. It thus codes the
velocity of motion. The second-order term, comprising 30-40% of the response,
is defined by a second-order kernel with 2 depolarizing peaks on the diagonal
and 2 off- diagonal hyperpolarizing valleys, suggesting that the nonlinear
component represents the power of motion. 4. Responses in the Reichardt
detector, consisting of 2 mirror-image subunits with spatiotemporal low-pass
filters followed by a multiplication stage, were computer- simulated and then
analyzed by the Wiener kernel method. The simulated responses were linearly
related to the pattern velocity (with a mean square error of 13 % for the
linear model), and matched well with the observed responses in the HS and CH
cells. After the multiplication stage, the linear component comprised 15-25%
and the quadratic nonlinear component 60-70% of the simulated response, which
was similar to the picrotoxin- induced response in the HS cells. The quadratic
nonlinear components were balanced between the right and left sides, and could
be eliminated completely by their contralateral counterpart via a subtraction
process. On the other hand, the linear component on one side was the mirror-
image of that on the other side as expected from the kernel configurations. 5.
These results suggest that responses to motion in the HS and CH cells depend
on the multiplication process in which both the velocity and power components
of motion are computed, and that a putative subtraction process selectively
eliminates the nonlinear components, but amplifies the linear component. The
nonlinear component is directionally insensitive due to its quadratic
nonlinearity. Therefore, the subtraction process allows the subsequent cells
integrating motion (such as the HS cells) to tune, more sharply, the direction
of motion.
Received 1 August 1995; accepted in final form 10 July 1995.
APS Manuscript Number J471-4.
Article publication pending J. Neurophysiol.
ISSN 1080-4757 Copyright 1995 The American Physiological Society.
Published in APStracts on 30 July 1995.