Modelling Fly Motion Vision - Computational Neuroscience: A Comprehensive Approach - page 410

different velocities, different saturation plateaus are found. This latter phenomenon
has also been called gain control and was observed at the behavioral level in flies,
too [76]. In general, modelling studies along with measurements of motion induced
changes of input conductances revealed that the circuit model of a single tangential
cell and its presynaptic array of motion detectors is fully sufficient to produce the
observed saturation of membrane response.
For understanding the phenomenon of gain control, one needs to realize that a) the
tangential cells receive excitatory and inhibitory synaptic input from elements equiv-
alent to the subunits of the correlation detector, and b) these presynaptic elements
have only a weak direction selectivity: they not only respond to motion along their
preferred direction but also, to a lesser extent, to motion along the opposite direction
(see panel 2 1 in Figure 14.6) . These conclusions are based on various electrophysio-
logical, calcium-imaging and pharmacological experiments [7, 9, 11, 70, 71, 83, 85].
Given that, motion along one direction leads to a joint, though differently weighed
activation of excitatory and inhibitory input, resulting in a mixed reversal potential
at which the postsynaptic response settles for large field stimuli. This can be seen
by the following calculation where the membrane potential ( V ) of a tangential cell
is approximated as an isopotential compartment ( E e ,

g e denoting excitatory reversal
potential and conductance, respectively, subscript i for inhibitory, E leak = 0 ) :

V =( E e g e + E i g i ) / ( g e + g i + g leak ) (14.12)

= − = /

g e to denote the ratio of inhibitory
and excitatory conductances being co-activated during preferred direction motion,
one obtains:

Assuming E e E i and introducing c g i

V = E e g e ( 1 − c ) / ( g e + cg e + g leak ) (14.13)

With increasing pattern size, g e become large compared to g leak : The membrane
potential tends towards a saturation level. This level can be expressed as:

g e → ∞ (

lim V )= E e ( 1 − c ) / ( 1 + c ) (14.14)

As can be calculated from such correlation-type input elements, the activation
ratio of these opponent inputs is a function of pattern velocity:

c =

cos ( R − Φ ( ω )) / cos ( R + Φ ( ω )) (14.15)

with R denoting 2 π times the ratio of the EMD's sampling base and the spatial

pattern wavelength λ , Φ denoting the phase response of the EMD's temporal filter

and . Consequently, motion in one direction jointly activates excitatory

and inhibitory inputs with a ratio that depends on velocity. This explains how the
postsynaptic membrane potential saturates with increasing pattern size at different
levels for different pattern velocities.
Taking into account the membrane properties of real tangential cells ( Figure 14.12a) ,
simulations of detailed compartmental models indeed revealed the phenomenon of
gain control. Stimulating the neuron by pattern motion of increasing size lead to a

ω = 2 π v / λ