316
A. Sedlackova et al.
The resulting dynamics of a neuron can be written as
τ m ·
dU
dt
= −U + I app + I tonic +
n
i=1
G s,i ·
E s,i − U
(1)
if U ≥ θ, U (t) ← 0,
(2)
where τ m is the membrane time constant, I app is an applied current, I tonic is a constant
intrinsic current, n is the number of incoming synapses, G s,i is the instantaneous conductance of the i th synapse (computed below), and E s,i is the reversal potential of the i th
incoming synapse relative to the postsynaptic neuron’s resting potential. Each synapse’s
instantaneous conductance is reset to its maximum value g s,i when the presynaptic
neuron spikes:
τ s ·
dG
dt
= −G
(3)
if presynaptic neuron spikes, G ← g.
(4)
In the following sections, we describe the desired function of connections within the
network in terms of “gain” k, that is, the ratio between the postsynaptic and presynaptic
neurons’ spiking frequencies. Using our functional subnetwork approach for designing
dynamical neural models, we can relate the gain to the neural and synaptic parameters,
and directly tune their values [15].
2.3 Structure and Function of the Optic Lobe Model
Retina. The retina layer encodes visual information into the neural system. The retina
cells respond to changes in light intensity in the visual field. The compound eye of the
retina has a hexagonally-arranged structure of ommatidia, i.e. photoreceptors that lie
below the lens. Insects have multiple retina cells per ommatidium [16]. However, to
keep the model tractable, our model simply possesses one retina cell per ommatidium.
The retina layer in our network consists of 64 neurons that each take input from
the corresponding angular bins described in Sect. 2.1 (Fig. 1E, white rectangles) Each
neuron’s applied current is a linear function of the average grayscale intensity of its
corresponding optical bin. For simplicity, our retina only encodes increases in brightness,
the so-called ON-ON pathways [3]. How this selection affects the performance of the
motion detector is further explained in the medulla section. The retina neurons in our
model have a time constant τ m = 200 ms and a tonic current I tonic = 0.5 nA. These values
ensure that the lamina neurons do not fire any spikes at the minimum input intensity and
fire spikes at 100 Hz at the maximum input intensity.
Lamina. The lamina neurons function as a spatial filter, increasing the dynamic range
of retina activity. Every neuron is excited by retina cells in its own column and inhibited
by those from the adjacent columns, a connectivity pattern called lateral inhibition. This
connectivity increases the contrast of the image.
A. Sedlackova et al.
The resulting dynamics of a neuron can be written as
τ m ·
dU
dt
= −U + I app + I tonic +
n
i=1
G s,i ·
E s,i − U
(1)
if U ≥ θ, U (t) ← 0,
(2)
where τ m is the membrane time constant, I app is an applied current, I tonic is a constant
intrinsic current, n is the number of incoming synapses, G s,i is the instantaneous conductance of the i th synapse (computed below), and E s,i is the reversal potential of the i th
incoming synapse relative to the postsynaptic neuron’s resting potential. Each synapse’s
instantaneous conductance is reset to its maximum value g s,i when the presynaptic
neuron spikes:
τ s ·
dG
dt
= −G
(3)
if presynaptic neuron spikes, G ← g.
(4)
In the following sections, we describe the desired function of connections within the
network in terms of “gain” k, that is, the ratio between the postsynaptic and presynaptic
neurons’ spiking frequencies. Using our functional subnetwork approach for designing
dynamical neural models, we can relate the gain to the neural and synaptic parameters,
and directly tune their values [15].
2.3 Structure and Function of the Optic Lobe Model
Retina. The retina layer encodes visual information into the neural system. The retina
cells respond to changes in light intensity in the visual field. The compound eye of the
retina has a hexagonally-arranged structure of ommatidia, i.e. photoreceptors that lie
below the lens. Insects have multiple retina cells per ommatidium [16]. However, to
keep the model tractable, our model simply possesses one retina cell per ommatidium.
The retina layer in our network consists of 64 neurons that each take input from
the corresponding angular bins described in Sect. 2.1 (Fig. 1E, white rectangles) Each
neuron’s applied current is a linear function of the average grayscale intensity of its
corresponding optical bin. For simplicity, our retina only encodes increases in brightness,
the so-called ON-ON pathways [3]. How this selection affects the performance of the
motion detector is further explained in the medulla section. The retina neurons in our
model have a time constant τ m = 200 ms and a tonic current I tonic = 0.5 nA. These values
ensure that the lamina neurons do not fire any spikes at the minimum input intensity and
fire spikes at 100 Hz at the maximum input intensity.
Lamina. The lamina neurons function as a spatial filter, increasing the dynamic range
of retina activity. Every neuron is excited by retina cells in its own column and inhibited
by those from the adjacent columns, a connectivity pattern called lateral inhibition. This
connectivity increases the contrast of the image.