Direction Selectivity In Primary Visual 
Cortex Using Massive Intracortical 
Connections 
Humbert Suarez 
CNS Program 216-76 
Caltech 
Pasadena, CA 91125 
Christof Koch 
CNS Program 216-76 
Caltech 
Pasadena, CA 91125 
Rodney Douglas 
MRC Anatomical Neuropharmacology Unit 
University of Oxford 
Oxford 
UK 
Abstract 
Almost all models of orientation and direction selectivity in visual 
cortex are based on feedforward connection schemes, where genicu- 
late input provides all excitation to both pyramidal and inhibitory 
neurons. The latter neurons then suppress the response of the for- 
mer for non-optimal stimuli. However, anatomical studies show 
that up to 90 % of the excitatory synaptic input onto any corti- 
cal cell is provided by other cortical cells. The massive excitatory 
feedback nature of cortical circuits is embedded in the canonical 
microcircuit of Douglas & Martin (1991). We here investigate ana- 
lytically and through biologically realistic simulations the function- 
ing of a detailed model of this circuitry, operating in a hysterelic 
mode. In the model, weak geniculate input is dramatically ampli- 
fied by intracortical excitation, while inhibition has a dual role: (i) 
to prevent the early geniculate-induced excitation in the null di- 
rection and (ii) to restrain excitation and ensure that the neurons 
fire only when the stimulus is in their receptive-field. Among the 
4 Humbert Suarez, Christof Koch, Rodney Douglas 
insights gained are the possibility that hysteresis underlies visual 
cortical function, paralleling proposals for short-term memory, and 
strong limitations on linearity tests that use gratings. Properties 
of visual cortical neurons are compared in detail to this model and 
to a classical model of direction selectivity that does not include 
excitatory cortico-cortical connections. The model explain a num- 
ber of puzzling features of direction-selective simple cells, includ- 
ing the small somatic input conductance changes that have been 
measured experimentally during stimulation in the null direction. 
The model also allows us to understand why the velocity-response 
curve of area 17 neurons is different from that of their LGN affer- 
ents, and the origin of expansive and compressive nonlinearities in 
the contrast-response curve of striate cortical neurons. 
1 INTRODUCTION 
Direction selectivity is the property of neurons that fire more strongly for one di- 
rection of motion of a bar (the preferred direction) than the other (null direction). 
It is one of the fundamental properties of neurons in visual cortex and is intimately 
related to the processing of motion by the visual system. LGN neurons that provide 
input to visual cortex respond approximately symmetrically to motion in different 
directions; so cortical neurons must generate that direction specificity. Models of 
direction selectivity in primary visual. cortex generally overlook two important con- 
straints. 1. at least 80% of excitatory synapses on cortical pyramidal cells originate 
from other pyramidal cells, and less than 10 % are thalamic afferents (Peters & 
Payne, 1993). 2. Intracellular in vivo recordings in cat simple cells by Douglas, et 
al. (1988) failed to detect significant changes in somatic input conductance during 
stimulation in the null direction, indicating that there is very little synaptic input 
to direction-selective neurons in that condition, including no massive "shunting" 
inhibition. 
One very attractive solution incorporating these two constraints was proposed by 
Douglas & Martin (1991) in the form of their canonical microcircuit: for motion 
of a visual stimulus in the preferred direction, weak geniculate excitation excites 
cortical pyramidal cells to respond moderately. This relatively small amount of cor- 
tical excitation is amplified via excitatory cortico-cortical connections. For motion 
in the null direction, the weak geniculate excitation is vetoed by weak inhibition 
(mediated via an interneuron) and the cortical loop is never activated. In order 
to test quantitatively this circuit against the large body of experimental data, it 
is imperative to model its operation through mathematical analysis and detailed 
simulations. 
2 MODEL DESCRIPTION AND ANALYSIS 
The model consists of a retino-geniculate and a cortical stage (Fig. 1). The former 
includes a center-surround receptive field and bandpass temporal filtering (Victor, 
1987). We simulate a 1-D array of ON LGN neurons, with 208 LGN neurons at each 
of 6 spatial positions in this array. The output of the LGN--action potentials--feeds 
Direction Selectivity in Primary Visual Cortex 5 
into the cortical module consisting of 640 pyramidal (excitatory) and 160 inhibitory 
neurons. Each neuron is modeled using 3~4 compartments whose parameters reflect, 
in a simplified way, the biophysics and morphology of cortical neurons; the somatic 
compartment produces action potentials in response to current injection. There are 
excitatory connections among all pyramidal neurons, and inhibitory confiections 
from the inhibitory population to itself and to the pyramidal population. The 
receptive field of the geniculate input to the inhibitory cortical neurons is displaced 
in space from the geniculate input to the pyramidal neurons, so that in the null 
direction inhibition overlaps with geniculate excitation in the pyramidal neurons, 
resulting in direction selectivity in the pyramidal neurons. The time courses of 
the post-synaptic potentials (PSP's) are consistent with physiologically recorded 
PSP's. The EPSP's in our model arise exclusively from non-NMDA synapses, and 
the IPSP's originate from both GABAA and GABAr synapses. 
There are two operating modes of this cortical amplifier circuit, depending on pa- 
rameter values. In the first mode, the pyramidal neurons' response increases pro- 
portionally to the stimulus strength over a substantial range of input values, before 
saturating. In the second mode, the response increases much faster over a narrow 
range of stimulus strengths, then saturates. Analytically, one can define a steady- 
state transfer function for the network of pyramidal neurons; then, in the first mode, 
the transfer function has a slope that is less than 1, so that the network's firing rate 
at equilibrium increases proportionally to the input strength and the network dy- 
namics are rather slow. In the second mode the initial slope is larger than 1, so 
that the network can discharge briskly at equilibrium even without any input, show 
hysteresis, and has rather fast dynamics. The network does not fire without any 
input, because of the neuron's threshold. In this paper, we will show responses in 
that second, hysteretic mode of operation. 
We will compare the cortical amplifier model's response properties to a pure feed- 
forward model, that has no excitatory connections between pyramidal neurons. In 
order to maintain strong responses in that model, the LGN was connected more 
strongly to the pyramidal neurons, and in order to maintain direction selectivity, 
the weights of the connections of the inhibitory neurons to the pyramids were in- 
creased as well. 
3 
AMPLIFICATION AND CONDUCTANCE CHANGE 
IN THE NULL DIRECTION 
The input conductance of pyramidal neurons, a measure of total synaptic input, 
changes by only 50 % in the cortical amplifier model versus 400 % in the feedfor- 
ward model, and so is more consistent with physiology (Fig. 2). Indeed, most of 
the current causing firing in the preferred direction originates from other pyrami- 
dal neurons, so the connection weight from the LGN is small. Consequently, the 
inhibitory weight is also small, since it needs only be large enough to balance out 
the LGN current in the null direction. Since there is little firing in other pyramidal 
neurons in the null direction, there is also little total synaptic input to the fiducial 
cell. The cortical amplifier circuit provides substantial amplification of the LGN 
input. In the preferred direction, excitatory intracortical connections amplify the 
LGN input, providing a feedback current that is about 2.2 times larger than the 
6 Humbert Suarez, Christof Koch, Rodney Douglas 
AREA 1 7 
LGN 
640 
pyramidal 
cells 
! x I 
160 
smooth 
cells 
208 
neurons 
at each 
position 
+  s.patial 
RETINA IIIIIIIII111111111_---II11111111111111111 
pixels 
Figure 1: Wiring diagram of the direction selectivity model. Input to LGN neu- 
rons comes from a one-dimensional array of retinal pixels. There are 208 LGN 
neurons at each of six spatial positions. The LGN neurons connect slightly differ- 
ently with the two populations of cortical neurons (pyramidal and inhibitory) so 
that as a group the LGN inputs to the pyramids are displaced spatially by 5  from 
those to the inhibitory neurons. The open triangle symbols denote excitatory con- 
nections, the filled triangles inhibitory GABAA-mediated synapses, and the filled 
circles inhibitory GABAB-mediated synapses. The capital sigma symbol indicates 
convergence of inputs from many LGN neurons onto cortical neurons. 
Direction Selectivity in Prirna Visual Cortex 7 
0.5 
04 
0.3 
0.2 
0.1 
o 
400 
30O 
200 
lOO 
o 
0 0.1 0.2 0.3 0.4 0.5 
1 2 
Time (seconds) 
150 
125 
100 
75 
o 1 2 
Figure 2: (a) Total synaptic current in a simulated pyramidal cell from the LGN 
(with symbols) and from other pyramidal cells (continuous without symbols), during 
stimulation by a bar moving in the preferred direction. For the same stimulus 
moving in the null direction, somatic input conductance as a function of time, (b) 
for a direction-selective pyramidal neuron (data from Douglas et al., 1988); (c) 
feedforward model; (d) cortical amplifier model; 
LGN current at 60 % contrast (Fig. 2). 
4 CONTRAST-RESPONSE CURVES 
Contrast-response curves plot the peak firing rate to a grating moving in the pre- 
ferred direction as function of its contrast, or stimulus amplitude (Albrecht & Hamil- 
ton, 1982). The cortical amplifier's contrast-response curve is very different from 
the LGN inputs' and is similar to those that have been described experimentally in 
cortex (Albrecht & Geisler 1991), having a steep power-function portion followed 
by abrupt saturation (Fig. 3). The network firing saturates at the fixed point of 
the transfer function mentioned above (see section 2) and the steep portion results 
from the fast rise to that fixed point when the stimulus has exceeded the neurons' 
threshold. In contrast, the feedforward model's contrast-response curve is similar 
to the LGN inputs' and does not match physiology. The response is very small in 
the null direction, resulting in very good direction selectivity at all contrasts (i.e., 
the average direction index is above 0.9). 
5 VELOCITY-RESPONSE CURVES 
8 Humbert Suarez, Christof Koch, Rodney Douglas 
lOO 
lO 
1 
lO 100 
Gonrast (%) 
lOO 
lO 
1 
10 lOO 
Gonrast (%) 
10o 
 o 
LL 
1 
d 
10 100 
Contrast (%) 
Figure 3' Peak firing rate versus contrast during stimulation by a moving grating. 
(a) Visual cortical neuron. Data from Albrecht/z Hamilton, 1982. (b) LGN model. 
(c) Feedforward model. (d) Cortical amplifier model. 
Velocity-response curves plot the peak response to a bar moving in the preferred 
direction as a function of its velocity . Again, the cortical amplifier 's velocity- 
response curve is very different from the LGN inputs' and is similar to physiology 
(Orban, 1984; Fig. 4). The LGN model is firing strongly at high velocities but 
the model pyramidal neurons are totally silent, due to a combination of GABAA 
inhibition, neuron threshold, and membrane low-pass filtering. At low velocities, 
the LGN model does not fire much, while the cortical neurons respond strongly. 
Indeed, the network firing has enough time to reach the fixed point of the transfer 
function and will reach it as long as the input is suprathreshold. In contrast, the 
feedforward model's velocity-response curve is again similar to the LGN input's 
and does not match physiology. Also shown in Fig. 4 is the response in the null 
direction for the cortical amplifier model. There is very good direction selectivity at 
all velocities, consistent with physiological data (Orban, 1984). The persistence of 
direction selectivity down to low velocities depends critically on the time constant 
of GABAB and the presence of a very small displacement between the LGN inputs 
to the pyramidal and inhibitory neurons. 
6 OTHER PROPERTIES 
Recently, direction-selective cortical neurons have been tested for !inearity using 
an intracellular grating superposition test and found to be quite linear (Jagadeesh 
et al., 1993). Despite that amplification in the present model is so nonlinear, the 
model is also linear according to that superposition test. An analysis of the test in 
the context of the model shows that such a test has limited usefulness and suggests 
improvements. 
Given that the network transfer function has a fixed point at high firing without any 
Direction Selectivity in Primary Visual Cortex 9 
120 
100 
80 
60 
40 
4O 
20 20 
0 0 
0.1 0.1 
LGN 
FF 
1 10 100 
Velocity (deg/sec) 
lOO 
 80 
'. 60 
d 
NP. . .... 
I lO lOO 
Velocity (deg/sec) 
Figure 4: Peak firing rate versus velocity during stimulation by a bar. (a) LGN 
neuron in cat (Frishman e! al., 1983). (b) area 17 visual cortical neuron in cat 
(Orban, 1984). (c) LGN model neuron (curve labelled "LGN") and feedforward 
model (rr). (d) Cortical amplifier model in the preferred (curve labelled "P") and 
null directions (NP). 
10 Humbert Suarez, Christof Koch, Rodney Douglas 
input (see section 2), hysteresis may occur, whereby the network's discharge persists 
after the initial stimulus is withdrawn. Because of hysteresis, it is imperative to reset 
the network by presenting a negative, or inhibitory, input. A parallel can be drawn 
to several recent proposals for the mechanisms underlying short-term memory. 
7 CONCLUSIONS 
From early on, neurophysiologists have proposed that the LGN provides most of the 
input to visual cortical neurons and shapes their receptive properties (Hubel and 
Wiesel, 1962). However, direction selectivity and several other stimulus selectivities 
are not present in LGN neurons, and other important discrepancies have appeared 
between the receptive field properties of cortical neurons and those of their LGN 
afferents. Anatomically, synaptic inputs from the LGN account for less than 10 % 
of synapses to pyramidal neurons in visual cortex; the remaining 90 % could clearly 
prqvide a substrate for these receptive field transformations. Although intracortical 
inhibition has often been invoked to explain various cortical properties, excitation 
is usually not mentioned, despite that most cortico-cortical synapses are excitatory. 
In this paper, we show that intracortical excitation can better account for several 
key properties of cortical neurons than a purely feedforward model, including the 
magnitude of the conductance change in the null direction, contrast-response curves, 
and velocity-response curves. Furthermore, surprinsingly, other key cell properties 
that are appear to point to feedforward models, such as linearity measured by 
superposition tests, are also properties of a model based on intracortical excitation. 
Acknowledgements 
This research was supported by the Office of Naval Research, the National Science 
Foundation, the National Eye Institute, and the McDonnell Foundation. 
References 
Albrecht, D.G., and Geisler, W.S. (1991) Visual Neuroscience 7, 531-546. 
Albrecht, D.B., and Hamilton, D.B. (1982) J. Neurophysiol. 48, 217-237. 
Douglas, R.J., and Martin, K.A.C. (1991) J. Physiol. 440, 735-769. 
Douglas, R.J., Martin, K.A.C., and Whitteridge, D. (1988) Nature 332, 642-644. 
Frishman, L.J., Schweitzer-Tong, D.E., and Goldstein, E.B. (1983) J. Neurophysiol. 
50, 1393-1414. 
Hubel, D.H., and Wiesel, T.N. (1962) J. Physiol. 165,559-568. 
Jagadeesh, B., Wheat, H.S. and Ferster, D. (1993) Science 262, 1901-1904 
Orban, G.A. (1984) Neuronal operations in the visual cortex. Springer, Berlin. 
Peters, A. and Payne, B. R. (1993) Cerebral Cortex 3, 69-78. 
Victor, J.D. (1987) J. Physiok 386, 219-246. 
