A Synthetic Nervous System Model of the Insect Optomotor Response
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In our model, the lamina layer consists of 64 neurons (Fig. 1E, violet circles). Every
neuron in the lamina is excited by a corresponding neuron in the retina, and inhibited
by the retina neurons of the neighboring columns (Fig. 1E). The lamina neurons have
the same parameter values as the retina neurons. To cancel the lamina’s response to a
spatially uniform image, we wish for the gain of the incoming synapses to add to 0.
Since each lamina cell receives excitation from one retina cell but inhibition from two,
we designed the excitatory synapses to have a gain of 1.5 and the inhibitory synapses to
have a gain of −0.25. For the excitatory synapses, E s = 160 mV and g s = 1.064 µS;
for the inhibitory synapses, E s = −80 mV and g s = 0.3072μ S. Both synapse types
have time constants τ s = 2.17 ms.
Medulla. The cells in the medulla respond to visual motion in a direction-dependent
manner. The classical Reichardt detector structure computes the correlation of one column’s activity with a time-delayed copy of a neighboring column’s activity. This twocolumn comparison excites the medulla neuron in the “preferred direction”. This model
successfully predicts many gross features of motion vision in insects [3]. Recent neurophysiology suggests a new, “three-arm detector” model that combines preferred direction
enhancement (the Reichardt detector) and null direction suppression (the Barlow-Lewick
detector) [17]. Combining these mechanisms not only accurately replicates the response
properties of the T4 and T5 cells in the medulla, but also accounts for the non-negative
nature of signal transmission throughout the nervous system (i.e. neurons only spike
when depolarized, not when hyperpolarized).
Our medulla model is based on the “three-arm detector” model [3]. Each layer
possesses 126 neurons, half of which are excited by rightward visual motion, and half of
which are excited by leftward motion. These correspond to the medulla’s T4 neurons [3].
Figure 1E shows the medulla neurons (blue and orange circles), each of which receives
an excitatory input from its corresponding lamina neuron, a delayed excitatory signal
from its neighboring column’s lamina neuron, and a delayed inhibitory signal from the
contralateral lamina neuron. To perform the multiplication inherent to the Reichardt
model, each medulla neuron operates as a logical AND gate. Specifically, it can only fire
action potentials if is depolarized by both excitatory inputs simultaneously. The duration
of its spiking encodes the speed of visual motion across those two columns of the optic
lobe. To enforce AND gate functionality and prevent the medulla neurons from firing
when only one excitatory input is present, each neuron’s tonic stimulus I tonic = −19.5
nA. Otherwise, all parameter values are the same as the other neurons. All excitatory
synapses have k = 1 and all inhibitory synapses have k = −1. For the excitatory
synapse, E s = 160 and g s = 0.658μ S. The neighboring column’s excitatory synapse
additionally has a delay t = 100 ms. For the inhibitory synapse, E s = −80 mV and
g s = 1.536μ S.
Lobula Plate Tangential Cells. The lobula plate tangential cells (LPTCs) are large,
motion-sensitive neurons that reside in the posterior lobula plate. They can be separated
into four different layers, each activated by large-field motion in one of the four cardinal
motion directions. They pool the output signals on their dendrites from many thousands
317
In our model, the lamina layer consists of 64 neurons (Fig. 1E, violet circles). Every
neuron in the lamina is excited by a corresponding neuron in the retina, and inhibited
by the retina neurons of the neighboring columns (Fig. 1E). The lamina neurons have
the same parameter values as the retina neurons. To cancel the lamina’s response to a
spatially uniform image, we wish for the gain of the incoming synapses to add to 0.
Since each lamina cell receives excitation from one retina cell but inhibition from two,
we designed the excitatory synapses to have a gain of 1.5 and the inhibitory synapses to
have a gain of −0.25. For the excitatory synapses, E s = 160 mV and g s = 1.064 µS;
for the inhibitory synapses, E s = −80 mV and g s = 0.3072μ S. Both synapse types
have time constants τ s = 2.17 ms.
Medulla. The cells in the medulla respond to visual motion in a direction-dependent
manner. The classical Reichardt detector structure computes the correlation of one column’s activity with a time-delayed copy of a neighboring column’s activity. This twocolumn comparison excites the medulla neuron in the “preferred direction”. This model
successfully predicts many gross features of motion vision in insects [3]. Recent neurophysiology suggests a new, “three-arm detector” model that combines preferred direction
enhancement (the Reichardt detector) and null direction suppression (the Barlow-Lewick
detector) [17]. Combining these mechanisms not only accurately replicates the response
properties of the T4 and T5 cells in the medulla, but also accounts for the non-negative
nature of signal transmission throughout the nervous system (i.e. neurons only spike
when depolarized, not when hyperpolarized).
Our medulla model is based on the “three-arm detector” model [3]. Each layer
possesses 126 neurons, half of which are excited by rightward visual motion, and half of
which are excited by leftward motion. These correspond to the medulla’s T4 neurons [3].
Figure 1E shows the medulla neurons (blue and orange circles), each of which receives
an excitatory input from its corresponding lamina neuron, a delayed excitatory signal
from its neighboring column’s lamina neuron, and a delayed inhibitory signal from the
contralateral lamina neuron. To perform the multiplication inherent to the Reichardt
model, each medulla neuron operates as a logical AND gate. Specifically, it can only fire
action potentials if is depolarized by both excitatory inputs simultaneously. The duration
of its spiking encodes the speed of visual motion across those two columns of the optic
lobe. To enforce AND gate functionality and prevent the medulla neurons from firing
when only one excitatory input is present, each neuron’s tonic stimulus I tonic = −19.5
nA. Otherwise, all parameter values are the same as the other neurons. All excitatory
synapses have k = 1 and all inhibitory synapses have k = −1. For the excitatory
synapse, E s = 160 and g s = 0.658μ S. The neighboring column’s excitatory synapse
additionally has a delay t = 100 ms. For the inhibitory synapse, E s = −80 mV and
g s = 1.536μ S.
Lobula Plate Tangential Cells. The lobula plate tangential cells (LPTCs) are large,
motion-sensitive neurons that reside in the posterior lobula plate. They can be separated
into four different layers, each activated by large-field motion in one of the four cardinal
motion directions. They pool the output signals on their dendrites from many thousands