Asymmetric Inhibitory Connections Enhance Directional Selectivity in a Threelayer Simulation Model of Retinal Networks
Amane Koizumi 1,2,3, Misako Takayasu 4, and Hideki Takayasu 5

1. Division of Correlative Physiology, National Institute for Physiological Sciences,
Okazaki, Japan
2. Section of Communications and Public Liaison, National Institute for Physiological
Sciences, Okazaki, Japan
3. Department of Physiological Sciences, School of Life Science, The Graduate
University for Advanced Studies (SOKENDAI), Okazaki, Japan
4. Tokyo Institute of Technology,Interdisciplinary Graduate School of Science andEngineering, Department of Computational Intelligence and Systems Science, Tokyo,
Japan
5. Sony Computer Science Laboratories, Inc, Fundamental Research Laboratory, Tokyo,
Japan

Corresponding to:
Dr. Amane Koizumi,
National Institute for Physiological Sciences, 38 Nishigonaka, Myodaiji, Okazaki, Aichi,
444-8585, Japan;
Phone: +81-564-55-7722; FAX: +81-564-55-7721;
Email: amane@nips.ac.jp

Running title: Asymmetric Inhibition Enhances Directional Selectivity in Retina
Key words: retina; directional selectivity; simulation; asymmetric inhibitionpg. 1

ABSTRACTIn this paper, we found that spatial and temporal asymmetricity of excitatory
connections are able to generate directional selectivity which can be enhanced byasymmetrical inhibitory connections by reconstructing a hexagonally-arranged 3layered simulation model of retina by NEURON simulator. Asymmetric excitatory
inputs to ganglion cells with randomly arborizing dendrites were able to generate
weaker directional selectivity to moving stimuli whose speed was less than 10 μm/msec.
By just adding asymmetric inhibitory connections via inhibitory amacrine cells,
directional selectivity became stronger to respond to moving stimuli at 10 times faster
speed (< 100 μm /msec). In conclusion, an excitatory mechanism appeared to generate
directional selectivity while asymmetric inhibitory connections enhance directional
selectivity in retina..

pg. 2

INTRODUCTION
The directional selectivity is a unique function relating to agility that some portion of
ganglion cells in the retina respond to moving light stimuli with specific direction andspeed [Ariel and Daw, 1982; Barlow et al., 1964]. It has been reported that inhibitory
synaptic outputs from starburst amacrine cells to bistratified directional selective
ganglion cells are playing critical role to make directional selectivity in the rabbit retina[Taylor et al., 2000; Fried et al., 2002]. Starburst amacrine cells have been a favorite
subject for retina researchers since Tauchi and Masland reported [Tauchi and Masland,
1984], and several mechanisms for directional selectivity have been proposed [Fried etal., 2005; He and Masland, 1997; Euler et al., 2002; Hausselt et al., 2007; Poznanski,
2005; Yoshida et al., 2001; Borg-Graham, 2001; Gavrikov et al., 2003; Lee and Zhou,2006]. Recently, especially in rodent retina, several types of retinal ganglion cells were
found to show directional selective light responses [Kim et al., 2008; Weng et al., 2005;
Huberman et al., 2009]. There might be not one, but several directionally selective
ganglion cells involved to generate directional selectivity so that the mechanism forgenerating directional selectivity in retina was thought to be more complicated.
In the present study, to address a common mechanism capable of elucidating
directional selectivity in the retina, we established theoretical hypothesis and conducted3-layer simulation model for directional selectivity by using NEURON simulator [Hines
and Carnevale, 2001].The reconstructed hexagonally-arranged retina consisted ofbipolar cells and ganglion cells as well as inhibitory amacrine cells that sent inhibitory
feed-forward signals to retinal ganglion cells. We proposed the hypothesis thatasymmetric inhibitory inputs from amacrine cells to ganglion cells might play animportant role in enhancing the sensitivity of directional selectivity, although thesepg. 3

inhibitory inputs were not necessarily required to generate directional selectivity. We
have already reported the fundamental idea of this theoretical hypothesis previously
from the theoretical point of view [Takayasu et al., 2005]. Here, we provide details of
our simulation to reinforce our theoretical hypothesis and present further discussion
with recent advances in retinal neurophysiology.

pg. 4

METHODS
Neural network simulation using NEURON simulator
Three layers were reconstructed in the NEURON simulator [Hines and Carnevale,
2001]: bipolar cells layer, amacrine cells layer, and ganglion cells layer (see Figure 2).
In each layer, neurons were located on a triangular lattice, and their somas wereseparated 100 μm apart. Three layers were overlapped with 50 μm distances.
Glutamatergic excitatory synaptic inputs from photoreceptors to the bipolar cells were
imitated by the alpha equation (tau = 2 msec, maximum conductance = 15 mS/cm2). In
order to simplify the model photoreceptors sent only excitatory synaptic outputs tobipolar cells when they received light stimuli. All bipolar cells depolarized withglutamate synaptic inputs in this simulation. Amacrine cells and ganglion cells received
glutamate inputs from bipolar cells (maximum conductance = 400 μS/cm2). Excitatory
receptive fields of amacrine and ganglion cells were assumed to form symmetric somacentered circle of diameter 800 μm. Anatomically, it is known that excitatory bipolarcells connecting to ganglion cells were located in a pattern of asymmetrical mosaic
within a receptive field of ganglion cell. In order to take into account such non-uniform
effect we chosen active connection with probability 50% from 61 input sites in thereceptive filed by connecting these inputs sites with randomly arborizing dendrites ofganglion cells.
In this simulation, we made inhibitory amacrine cells which received excitatory
inputs from 61 bipolar cells and sent feed-forward inhibitory outputs to ganglion cells.
The amacrine cells were assumed to be starburst amacrine cells which have been shownto contribute to directional selectivity [Fried et al., 2002; Tauchi and Masland, 1984;
Euler et al., 2002; Yoshida et al., 2001], although the morphological features were notpg. 5

necessarily consistent with those of real starburst amacrine cells. Inhibitory output
signals from amacrine cells to ganglion cells were determined as GABAergic inhibitory
synapses (maximum conductance = 50 μS/cm2). In our numerical model the length ofdendrites which conveyed inhibitory signal from amacrine cells to ganglion cells werelimited to be less than 1000 μm, and their directions were chosen randomly. A single
amacrine cell possessed three dendrites for inhibitory outputs to release inhibitory
synaptic outputs to ganglion cells. The direction and length of output dendrites of eachamacrine cell were determined randomly. In the model each bipolar cell has soma
(diameter 10 μm, length 31.8 μm) and axon (diameter 3 μm, length 100 μm). An
amacrine cell had soma (diameter 20 μm, length 20 μm) and dendrites (diameter 0.7 μm,
various lengths). A ganglion cell had soma (diameter 20 μm, length 20 μm) anddendrites (diameter 0.7 μm, various lengths).
Electrophysiologically bipolar cells possessed only passive parameters (passive
conductance 50 μS/cm2, membrane capacitance 1 μF/cm2, cytoplasmic resistance 100Ωcm). Amacrine cells possessed passive parameters (passive conductance 50 μS/cm2,
membrane capacitance 1 μF/cm2, cytoplasmic resistance 100 Ωcm) and four types ofionic currents; Hodgkin-Huxley type Na current (maximum conductance, gNa = 10
mS/cm2), K current (gK = 3 mS/cm2), persistent Na current (gNaP = 3 μS/cm2) and Ca
current (gCa = 35 μS/cm2) and their properties were determined to be consistent withelectrophysiological data reported previously [Koizumi et al., 2001]. These mechanisms
and parameters of active conductances were the same as that we used previously[Koizumi et al., 2005]. In this simulation, other types of active conductances, whichwere found in the starburst amacrine cells, were not included because the simulation
represented a caricature model of retinal directional selectivity. In the numerical model

pg. 6

these amacrine cells were able to generate action potentials with temporal delay
preceded by the action potentials of ganglion cells when they received simultaneoussynchronous light stimuli. Ganglion cells possessed passive parameters; two types of
Hodgkin-Huxley type Na current (gNa = 100 mS/cm2) and K current (gK = 10 mS/cm2)
generating the action potential with a certain threshold (around -45 mV). Simultaneous
stimulation of all bipolar cells generated a single action potential in every ganglion cellat the onset of stimulation (ON type response). All ganglion cells had a center-ON(excitatory, 800 μm diameter) and surround-OFF (inhibitory) receptive field.
The total numbers of cells in our numerical simulation are 721, 397 and 397 forbipolar, amacrine and ganglion cells, respectively. This size was assumed to correspondto a retina tissue of radius 1500 μm.

pg. 7

RESULTS
The theoretical hypothesis: temporal and spatial asymmetricity of excitatory
connections generate directional selectivity which can be enhanced by inhibitory
asymmetrical connections.
First, we describe theoretical hypothesis that asymmetric excitatory andinhibitory connections can generate directional selectivity, but they have different roles.
Especially, the hypothesis advances the excitatory mechanism for directional selectivity.
The fundamental idea of our hypothesis for directional selectivity [Takayasu etal., 2005] can be understood by a simple diagram of retina’s neural network
schematically shown in Figure 1a. In the schematic drawing, photoreceptors send
excitatory signal when they receive light stimuli. Bipolar cells receive excitatory signals
from photoreceptors and send excitatory signals to both amacrine cells and ganglion
cells. These amacrine cells are inhibitory and send feed-forward inhibitory signals to theganglion cells.
Simplified schema is shown in Figure 1b where only a retinal ganglion cell andits inputs from two bipolar cells and an amacrine cell are shown. The time delay of
inputs from the two bipolar cells (TA and TB) and the amacrine cell (TC) are supposed
to be caused by synaptic delay along the neural network connections fromphotoreceptors and by latency of synaptic integration at each neuron. Spatial distance
between two bipolar cell inputs (A and B) is determined as d and spatial distance
between the bipolar cell (B) and the amacrine cell (C) is determined as d’.
First, we considered responses of the ganglion cell to a moving stimulus at the
speed v, without the inhibitory input (C) to the ganglion cell (Figure 1b). We assumed
that the ganglion cell’s threshold level is a little above one-excitatory-input-level; thepg. 8

ganglion cell can generate action potentials when two excitatory inputs overlap. When amoving stimulus moves from A to B with time difference d/v, the ganglion cell can
respond if the inequality, TA – T0 < d/v + TB < TA+T0, is satisfied, where T0 is theduration time of an excitation (Figure 1c Top, Left). In the case that the moving
stimulus moves from B to A, the condition that ganglion cell can respond is given
similarly as, TB – T0 <d/v + TA<TB+T0, (Figure 1c, Top, Right). When T0 is larger
than TA or TB, the left-hand sides of the previous inequalities are replaced by 0. When
only one of these two conditions is satisfied, directional selective responses can beobserved. For example, when TA>TB the ganglion cell responds only for a moving
stimulus from left to right if the speed of moving stimulus v lies in the range betweend/(T0+TA-TB) and d/(T0+TB-TA), while it does not respond to neither directions if the
speed is smaller than d/(T0+TA-TB). However, the directional selective responses fromthe ganglion cell were lost for a high-speed movement satisfying v > d/(T0+TB-TA)(Figure 1c, Middle).
The case with an asymmetric inhibitory input (C) is shown in Figure 1b (dottedarea). In this case, the ganglion cell receives two excitatory and one inhibitory inputs
with time delays, TA, TB and TC, respectively. As shown in the bottom of Figure 1c
the inhibitory input can shorten the duration time T0 of an excitatory input, and the
directional selective function becomes active for much higher speed because thepractical value of T0 can take a small value by tuning the distance and the time delay
TC. Thus, the asymmetric inhibitory connection can enhance the response speed of
directional selectivity in the retina.
In summary, from this theoretical hypothesis, we concluded that asymmetric
excitatory inputs can generate directional selective responses in ganglion cells to

pg. 9

moving stimuli within a limited range of moving speed. Asymmetric inhibitory input
can shorten the duration of excitation and make the ganglion cell respond to muchhigher speed of moving stimuli.

The hexagonally-arranged 3-layered simulation model of retina
In order to confirm these basic results of directional selectivity in the theoretical
hypothesis, we reconstructed properties of retina as an ensemble of huge number ofneurons by using NEURON simulator[Hines and Carnevale, 2001]. The NEURON
simulator is a well-established numerical simulator of neural networks, in whichelectrophysiological properties of neurons can be described accurately. Here, wereconstructed a hexagonally-arranged 3-layered retinal neural network with 721 bipolarcells, 397 amacrine cells and 397 ganglion cells (Figure 2, see Methods in detail). We
incorporated passive and active properties into these neurons. In order to simplify themodel, we assumed that photoreceptors were just a receptor of light stimuli and sent
glutamergic outputs to depolarize bipolar cells. Bipolar cells were non-spiking neurons,
while ganglion cells were determined as spiking neurons. A bipolar cell sent excitatory
outputs when it was excited. The bipolar cells had synaptic connections directly withganglion cells and/or with amacrine cells. In this simulation, the speed of the signal
spread on dendrites of inhibitory amacrine cells was determined as approximately 100
μm/msec according to previous models of cultured cells [Koizumi et al., 2005; Y
Yamada et al., 2002]. In fact, in starburst amacrine cells, the speed of cytosolic calcium
spread has been reported to reach 100 μm per 100 msec [Poznanski, 2010a]. (We will
discuss the effect of the speed of signal spread on dendrites of amacrine cells later inFigure 5 and Discussion). Thus, initiation and spread of signals on dendrites of thesepg. 10amacrine cells made temporal delay in synaptic outputs to ganglion cells. In addition,
asymmetric expansion of dendrites of amacrine cells made asymmetric synaptic outputs
to ganglion cells.
Asymmetricity of excitatory inputs was achieved by randomly arborizing
dendrites of ganglion cells. Ganglion cells received excitatory inputs from bipolar cells
which were only from bipolar cells above the randomly arborizing dendrites. The spatial
randomness due to randomly arborizing dendrites caused time delays such as TA and
TB with various distribution of distance d in the simulation model. Connections
between ganglion cells and amacrine cells were randomly chosen. These randomly
chosen inhibitory connections made temporal and spatial asymmetricity of inhibitory
inputs to ganglion cells.

Asymmetric excitatory inputs were able to generate weaker directional selectivity
Figure 3a shows an example of spatial distribution of bipolar cells connectedwith a ganglion cell having asymmetric dendritic arbor receiving excitatory inputs but
not with any inhibitory inputs from amacrine cells. Responses of this ganglion cell tomoving stimuli at 5 μm/msec were displayed in Figure 3b for 6 directions. As expected
the directional symmetry was broken due to the randomly arborizing dendrites.
However, the strength of directional selectivity was rather small. Directional Selectivity
Index (DSI) was calculated by dividing the length of the vector sum by the summed
lengths of the component vectors [Taylor et al., 2000]. DSI value of 1 would indicatecomplete directional selectivity. In Figure 3c, the distribution of DSI for 397 ganglion
cells represented in a polar coordinate in the case of no inhibitory connections. Virtually
all of ganglion cells showed less than 0.2 DSI.

pg. 11Asymmetric inhibitory inputs enhanced the strength of directional selectivity
By adding an inhibitory connection as shown in Figure 4a the ganglion cell's
response became more sensitive to the direction difference as demonstrated in Figure 4b.
In Figure 4a, an inhibitory amacrine cell’s dendritic field was surrounded by the blue
dotted circle, while a blue line represents the connection between the amacrine cell andthe ganglion cell. Responses of this ganglion cell to moving stimuli at 10 μm/msec weredisplayed in Figure 4b for 6 directions. In Figure 4b, blue shaded area in the circulargraph represented the case with the inhibitory connection, and the red line in the circulargraph represented the case without the inhibitory connections of the same ganglion cell.
We found that the strong directional selective function of the ganglion cell disappeared
only by neglecting the inhibitory connections. Comparing the distribution of thestrength of DSI of all 397 ganglion cells in Figure 4c with Figure 3c where every
ganglion cell had the same parameters except the inhibitory connections, it is clear thatthe inhibitory connections drastically enhanced the selective function.

The sensitivity for the speed of the moving stimuli was also enhanced by inhibitory
connections.
Asymmetric inhibitory connections also enhanced the sensitivity for the speed ofmoving stimuli as well as the strength of DSI. In the case of no inhibitory connection
the characteristic speed of directional selective function was estimated by the ratio of
the interval of bipolar cells connecting to the same ganglion cell over the excitation
input duration time, i.e., 100 μm (the minimum distance between bipolar cells) / 10
msec (an approximate duration time of excitation) = 10 μm/msec, in this simulation. In

pg. 12

our model retina the directional selective function could not be found for the moving
speed faster than this characteristic speed for the case without the inhibitory bypass asshown in Figure 5a (red line).
In contrast, the directional selective function became active for more than 10times higher speed by simply adding the inhibitory connections (blue curve in Figure5a). The time delay of inhibitory connections, namely TC in Figure 1, was a key factor
for making the wide range of speed sensitivity in this simulation. The main part of timedelay TC consisted of two types of time delays in amacrine cells: excitation time delay
and signal spread time delay (Figure 5b). In our simulation, excitation time delay wasestimated as almost 10 msec. Time delay of signal spread depended on the speed ofsignal spread on dendrites of amacrine cells. Because in this simulation, the speed of thesignal spread on dendrites of amacrine cells was approximately 100 μm/msec. When the
speed of moving stimuli exceeded the speed of the signal spread on dendrites, thedirectional selectivity should disappear. Taken together, that is a reason why, in our
simulation, the maximum speed of moving light stimuli was approximately 100
μm/msec (see Figure 5a).

DISCUSSION
We have found that temporal and spatial asymmetricity of excitatory inputs andinhibitory inputs have different roles in shaping directional selectivity in retina.
First, asymmetricity of excitatory inputs was enough to generate directional
selectivity. However its generation was limited to moving stimuli at a certain range of
speed. In addition, directional selective index was lower. Second, the inhibitory
asymmetricity had important role in enhancing the agility of directional selective

pg. 13

responses. Inhibitory connection made ganglion cells more sensitive to moving stimuli
with wide range of speed, about 10 times more agile. However, in our hypothesis, thespeed of signal spread on dendrites of inhibitory amacrine cells determined the
maximum speed of moving stimuli that were able to make directional selective
responses in ganglion cells. These kinds of limitations probably were not in real retina.
There should be more factors, which we ignored in this simulation, to enhance
directional selectivity in retina.
In this simulation, we determined the speed of the signal spread on dendrites ofamacrine cells as approximately 100 μm/msec. In starburst amacrine cells, Poznanski(2010a) has shown that speeds of cytosolic calcium spread can reach 100 μm per 100
msec under the hypothesis of the starburst amacrine cell having continuous endoplasmic
reticulum. Of course, these speeds are not as fast as those used in this simulation;
however, this suggests that calcium-mediated potentials might be propagating withinsuch a speed in the dendrites of starburst amacrine cells given that cytosolic calcium isalways an order or two slower than voltage.
One of the factors to potentially enhance the agility which we ignored here inthis theoretical simulation was presynaptic feed-back inhibition from amacrine cells tobipolar cells. For example, transient local feed-back inhibitory mechanism was found in
dendritic varicosities of A17 amacrine cells [Chavez et al., 2006; Grimes et al., 2010]
and in starburst amacrine cells [E S Yamada et al., 2003]. If such a transient local feedback inhibitory mechanism works in between bipolar cells and amacrine cells which
contribute to generate directional selectivity, the time delay in amacrine cells, namely
Tc, could be much shorter and excitatory inputs themselves could be asymmetricallymodulated. Anatomical and nerurophysiological evidences also supported thispg. 14

prediction of the effect of presynaptic feed-back inhibition on directional selectivity[Fried et al., 2005; Borg-Graham, 2001; Poznanski, 2010b]. These mechanisms very
possibly also contribute to enhance directional selectivity in real retina.

pg. 15

Acknowledgement
The authors appreciate collaboration with Shiraishi, Y, Hayashida, Y., Kiuchi, T.,
Yoshitake, Y., Yagi, T. and Kaneko, A. on developing the numerical simulation byusing NEURON simulator.

pg. 16

Figure legends
Figure 1 Theoretical hypotheses: how asymmetric excitatory and inhibitory
connections make directional selectivity in the retina.
(a) Schematic view of information flow in the retina. Photoreceptors (dark rectangles)
send synaptic outputs to bipolar cells (red circles) responding to moving stimuli. A
bipolar cell has synaptic connections either directly with a ganglion cell (brown circle)
or with an amacrine cell (blue circle) that makes an inhibitory output to the ganglion
cell. (b) Simplified figure of the information paths. Two direct paths A and B, eachhaving time delays TA and TB respectively, are located at distance d. An amacrine
cell’s inhibitory connection C located at distance d’ from B transmits an inhibitory
signal to the ganglion cell with time delay TC. (c) Time evolution of responses tomoving stimuli at A, B and C paths, and the amplitude of integrated response at theganglion cell (A+B+C). Each dark triangle indicates the time that the photoreceptor
receives moving stimulus. Top: (Left): In the case the stimulus moves from A to B thesum of synaptic inputs exceeds the ganglion's threshold level (dotted line) and theganglion cell fires (shaded area), however, in the opposite direction case the ganglion
cell does not fire (Right). Middle: (Left and Right) When the speed of the stimulus ishigh enough the ganglion cell fires for both directions. Bottom: Adding the inhibitory
synaptic input through path C the ganglion cell fires for the stimulus moving from A to
B to C as before, however, it does not respond to the high speed stimulus motion from C
to A, namely, the directional selectivity recovers.

Figure 2. The hexagonally-arranged 3-layered simulation model of retina.

pg. 17

(a) Three layers, bipolar, amacrine and ganglion cells, were reconstructed. This figure
simply shows partial connections between cells, ignoring dendritic structure of each cell.
(b) In each layer, cells were located on a triangular lattice, and their somas wereseparated 100 μm apart. Three layers were overlapped with 50 μm distances. See
Methods in detail.

Figure 3. Response of ganglion cells without inhibitory connections.
(a) An example of randomly arborizing dendrites of a ganglion cell and resulting
asymmetric spatial distribution of connecting bipolar cells. (b) Direction dependence ofthe ganglion cell’s responses. The speed of the moving stimulus was 5 μm/msec on theretina. The circular graph shows a polar coordinate representation of the numbers of
output pulses for each direction. For comparison, the case that all bipolar cells were
stimulated simultaneously the ganglion generated action potential (Synchronous). (c)The distribution of directional selectivity indices (DSI) for 397 ganglion cells
represented in a polar coordinate. Each DSI is defined by the vector sum of the polar
diagram in (b) normalized by the total spike numbers. The DSI value is 1 when the
ganglion cell fires in only one direction.

Figure 4. Response of ganglion cells with inhibitory connections.
(a) An example of randomly arborizing dendrites of a ganglion cell and an inhibitory
input via an amacrine cell. (b) Direction dependence of the ganglion cell’s response.
The speed of the moving stimulus was 10 μm/msec on the retina. The blue shaded partin the circular graph shows the case with inhibitory connections and the red line

pg. 18

represents the case neglecting the inhibitory connection with identical bipolar cells’
connection. (c) The distribution of DSI for 397 ganglion cells.

Figure 5. The maximum DSI values as functions of speed of the moving stimuli.
(a) A blue line shows an typical example of ganglion cell’s directional selective
response with the inhibitory connection and a red line is that with no inhibitory
connection.(b) Schematic vertical view of an amacrine cell. Time delay in amacrine
cells, namely TC in Figure 1b, consisted of two components: excitation time delay andsignal spread time delay. In this simulation, the speed of directional selective moving
stimuli could not exceed that of the signal spread on dendrites (100 μm/msec).

pg. 19

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