Dendritic compartmentalization could underlie 
competition and attentional biasing of 
simultaneous visual stimuli 
Kevin A. Archie 
Neuroscience Program 
University of Southern California 
Los Angeles, CA 90089-2520 
Bartlett W. Mel 
Department of Biomedical Engineering 
University of Southern California 
Los Angeles, CA 90089-1451 
Abstract 
Neurons in area V4 have relatively large receptive fields (RFs), so multi- 
ple visual features are simultaneously "seen" by these cells. Recordings 
from single V4 neurons suggest that simultaneously presented stimuli 
compete to set the output firing rate, and that attention acts to isolate 
individual features by biasing the competition in favor of the attended 
object. We propose that both stimulus competition and attentional bias- 
ing arise from the spatial segregation of afferent synapses onto different 
regions of the excitable dendritic tree of V4 neurons. The pattern of feed- 
forward, stimulus-driven inputs follows from a Hebbian rule: excitatory 
afferents with similar RFs tend to group together on the dendritic tree, 
avoiding randomly located inhibitory inputs with similar RFs. The same 
principle guides the formation of inputs that mediate attentional mod- 
ulation. Using both biophysically detailed compartmental models and 
simplified models of computation in single neurons, we demonstrate that 
such an architecture could account for the response properties and atten- 
tional modulation of V4 neurons. Our results suggest an important role 
for nonlinear dendritic conductances in extrastriate cortical processing. 
1 Introduction 
Neurons in higher regions of visual cortex have relatively large receptive fields (RFs): for 
example, neurons representing the central visual field in macaque area V4 have RFs up to 
5  across (Desimone & Schein, 1987). Such large RFs often contain multiple potentially 
significant features in a single image, leading to the question: How can these neurons ex- 
tract information about individual objects ? Moran and Desimone (1985) showed that when 
multiple stimuli are present within the RF of a V4 neuron, attention effectively reduces the 
RF extent of the cell, so that only the attended feature contributes to its output. Desimone 
(1992) noted that one way this modulation could be performed is to assign input from each 
RF subregion to a single dendritic branch of the V4 neuron; modulatory inhibition could 
then "turn off" branches, so that subregions of the RF could be independently gated. 
Recent experiments have revealed a more subtle picture regarding both the interactions be- 
tween simultaneously presented stimuli and the effects of attentional modulation. Record- 
ings from individual V4 neurons have shown that simultanously presented stimuli com- 
pete to set the output firing rate (Luck, Chelazzi, Hillyard, & Desimone, 1997; Reynolds, 
Chelazzi, & Desimone, 1999). For example, consider a cell for which stimulus $, pre- 
sented by itself, produces a strong response consisting of 8 spikes, and stimulus W pro- 
duces a weak response of w spikes. Presenting the two stimuli $ and W together generally 
produces an output less than 8 but more than w. Note that the "weak" stimulus W is ex- 
citatory for the cell when presented alone, since it increases the response from 0 to w, but 
effectively inhibitory when presented together with "strong" stimulus $. Attention serves 
to bias the competition, so that attending to $ would increase the output of the V4 cell 
(moving it closer to 8), while attending to W would decrease the output (moving it closer 
to w). To describe their results, Reynolds et al. (1999) proposed a mathematical model in 
which individual stimuli both excite and inhibit the V4 neuron. The sum of excitatory and 
inhibitory input is acted on by divisive normalization proportional to the total strength of 
input to produce a competitive interaction between simultaneous stimuli. Attention is then 
implemented as a multiplicative gain on both excitatory and inhibitory input arising from 
the attended stimulus. 
In previous work using biophysically detailed compartmental models of neurons with ac- 
tive dendrites, we observed that increasing the stimulus contrast produced a multiplicative 
scaling of the tuning curve of a complex cell (Archie & Mel, 2000, Fig. 6g), suggesting an 
implicit normalization. In the present work, we test the following hypotheses: (1) segrega- 
tion of input onto different branches of an excitable dendritic tree could produce compet- 
itive interactions between simultaneously presented stimuli, and (2) modulatory synapses 
on active dendrites could be a general mechanism for multiplicative modulation of inputs. 
2 Methods 
We used both biophysically detailed compartmental models and a simplified model of a 
single cortical neuron to test whether competition and attentional biasing could arise from 
interactions between excitatory and inhibitory inputs in a nonlinear dendritic tree. An 
overview of the input segregation common to both classes of model is shown in Fig. 1. 
Biophysically detailed compartmental model. The detailed model included 4 layers of 
processing: (1) an LGN cell layer with center-surround RFs; (2) a virtual layer of simple- 
cell-like subunits which were drawn from elongated rows of ON- and OFF-center LGN 
cells -- virtual in that the subunit computations were actually carded out in the dendrites 
of the overlying complex cells, following Mel, Ruderman, and Archie (1998) and Archie 
and Mel (2000); (3) an 8 x 8 grid of complex cells, each of which contained 4 subunits 
with progressively shifted positions/phases; and (4) a single V4 cell in the top layer, which 
received input from the complex cell layer. Layers 3 and 4 are shown in Fig. 2. 
The LGN was modeled as 4 arrays (ON- and OFF-center, left and right eye) of difference- 
of-Gaussian spatial filters, as described in Archie and Mel (2000). Responses of the corti- 
cal cells were calculated using the NEURON simulation environment (Hines & Carnevale, 
1997). Complex cells contained 4 basal branches, each 1 /zm in diameter and 150 
long; one apical branch 5 /zm in diameter and 250/zm long; a spherical soma 20 
in diameter; and an axon 0.5 /zm in diameter and 1000 /zm long with an initial seg- 
ment 1 /zm in diameter and 20/zm long. Hodgkin-Huxley-style Na + and K + conduc- 
tances were present in the membrane of the entire cell, with 10-fold higher density in 
the axon (Na = 0.120 S/cm2,K = 0.100 S/cm 2) than in the soma and dendrites 
(ma = 0.012 S/cm2,K = 0.010 S/cm2). The V4 cell was modeled with the same 
parameters as the complex cells, but with 8 basal branches instead of 4. 
I I 
A1 
A2 
S1 S2 
Figure 1: Segregation of excitatory and inhibitory inputs. Two sources of stimulus-driven 
input are shown, S1 and S2, each corresponding to an independently attendable subregion 
of the RF of the V4 cell. Note that each source of stimulus-driven input makes both exci- 
tatory projections to a specific branch on the V4 cell, and inhibitory projections (through 
an interneuron) to other branches. Similarly, the modulatory inputs A1 and A2 each di- 
rect attention to a particular branch; for example, A1 adds excitatory modulation to the 
branch corresponding to the S1 RF subregion and (indirectly) inhibitory modulation to 
other branches. 
V4 
cell 
/. inhibitory 
interneurons 
complex 
cells 
_ 
- . 
RF subregion 
Figure 2: Design of the biophysically detailed model. Complex cells were arranged in a 
grid with overlapping RFs and similar orientation preferences. Each vertical stripe of cells 
formed an RF subregion to which attention could be directed. Each complex cell within 
a subregion formed one excitatory and one (indirect) inhibitory connection onto the V4 
cell. Synapse locations were assigned at random within a given V4 branch. All excitatory 
connections for a given subregion were targeted to a single branch, while the corresponding 
inhibitory synapses were distributed across all of the other branches of the cell. Attentional 
modulatory and background synapses, both described in the text, are not shown. 
Excitatory synapses were modeled as having both voltage-dependent (NMDA) and voltage- 
independent (AMPA/kainate) components, while inhibitory synapses were fast and voltage- 
independent (GABA-A). All synapses were modeled using the kinetic scheme of Destexhe, 
Mainen, and Sejnowski (1994), with peak conductance values scaled inversely by the local 
input resistance to reduce the dependence of local EPSP size on synapse location. 
The complex cells received input from the LGN, using the spatial arrangement of exci- 
tatory and inhibitory inputs described in Archie and Mel (2000), with inhibitory inputs 
distributed throughout the input branches (rather than, e.g., being restricted to the proximal 
part of the branch). We have previously shown that this arrangement of inputs produces 
phase- and contrast-invariant tuning to stimulus orientation, similar to that seen in cortical 
complex cells. All 64 complex cells had the same preferred orientation, which we will for 
convenience call vertical. For each stimulus image, each complex cell was simulated for 1 
second and the resulting firing rate was used to set the activity level of one excitatory and 
one inhibitory synapse onto the V4 cell. The inhibition was assumed to emanate from an 
implicit inhibitory interneuron in V4. The stimulus-driven inputs to the V4 neuron were 
modeled as Poisson trains whose mean rate was set to the corresponding complex cell fir- 
ing rate for excitatory synapses, and 1.3 times the corresponding complex cell firing rate 
for inhibitory synapses. The inputs were arranged on the V4 cell so that all of the com- 
plex cells with RFs distributed along a vertical stripe of the V4 RF (i.e., aligned with the 
preferred orientation of the complex cells) formed one subregion and made their excitatory 
projections to a single branch (Fig. 2). The inhibitory synapse from each complex cell was 
placed on a different branch than the corresponding excitatory synapse, with the specific 
location chosen at random. 
Attention was implemented by placing two modulatory synapses on each branch, one exci- 
tatory and one inhibitory. In the absence of attention, all modulatory synapses had a mean 
event rate of 0.1 Hz. Attention was directed to a particular subregion by increasing the fir- 
ing rate of the excitatory modulation on the corresponding branch to 100 Hz, and increasing 
the inhibitory modulation on all other branches to 67 Hz. Each branch of the V4 cell also 
received a single excitatory synapse with mean firing rate 25 Hz, representing background 
(non-stimulus driven) input from the cortical network. These synapses provided most of 
the input needed for the cell to fire action potentials, while the stimulus-driven inputs mod- 
ulated the firing rate. 
The rationale for the spatial arrangement of synapses was that coaligned complex cells with 
overlapping RFs would have correlated responses over the ensemble of images seen during 
early postnatal development, and would thus tend to congregate within the same dendritic 
subunits according to Hebbian developmental principles. Similarly, excitatory synapses 
would tend to avoid inhibitory synapses driven by the same stimuli, since if the two are 
near each other on the dendrite, the efficacy of the excitation is systematically reduced by 
the corresponding inhibition. 
Sum of squared filters model. We have previously proposed that an individual cortical 
pyramidal neuron may carry out high-order computations that roughly fit the form of an 
energy model, i.e., a sum of half-squared linear filters, with electrotonically isolated regions 
of the dendritic tree performing the quadratic subunit computations. Only excitatory inputs 
were previously considered, leaving open the question of how inhibition might fit in such a 
model. An obvious implementation of inhibition is to simply subtract the mean firing rates 
of inhibitory inputs, just as excitatory inputs are added. The sum-of-squares model thus 
has the form: f(x) = Ej((Eij wixi)+) 2, where /+ denotes /if / _> 0, 0 otherwise; 
Bj is the set of inputs i that project to branch j; and wi is +1 if input i is excitatory, -1 
if inhibitory. We considered both a "paper-and-pencil" model, in which we hand-selected 
input values for each stimulus with an eye towards ease of interpretation; and also a model 
in which the tabulated complex cell output rates (from layer 3 of the detailed model) were 
strong stimulus weak stimulus attention away attention to strong attention to weak 
35 
3 
o 
E 25 
o 
o 2 
o_ 
 15 
'. 
(/) 1 
05 
_I 
strong weak away to strong to weak 
single stimulus attention 
(no attention) 
Figure 3: Results from the biophysically detailed model. In the top row, strong and weak 
visual stimuli are shown at left, and combined stimuli in three attentional conditions are 
indicated at right. Bar graph shows response of simulated V4 cell under each of these 5 
conditions, averaged over 192 runs. Combined stimulus in the absence of attention yields 
output between the responses to either stimulus alone. Attention to either the strong or the 
weak stimulus pushes the cell's response toward the individual response for that stimulus. 
used as input. 
3 Results 
Detailed model. A strong stimulus (a vertical bar) and a weak stimulus (a bar of the same 
length, turned 60  from vertical) were selected. Figure 3 shows the stimulus images and 
simulated V4 cell response for each stimulus alone and for the combined stimulus in various 
attentional states. In the absence of attention within the receptive field (attention away), the 
response of the cell to the combined image lay between the responses to the strong image 
alone or the weak image alone. This intermediate response is consistent with the responses 
of many V4 cells under similar conditions, and is the result of the competition between 
excitatory and inhibitory inputs: because of the spatial segregation, inhibitory synapses 
driven by one stimulus selectively undermine the effectiveness of excitation due to the 
other. 
This competition between stimuli was also biased by attentional modulation (Fig. 3). At- 
tending to the strong stimulus elevated the response to the combined image compared to 
the condition where attention was directed away, thus bringing the response closer to the 
response to the strong stimulus alone. Similarly, attention to the weak stimulus lowered the 
response to the combined stimulus. 
Sum of squared filters. We used a 4-subunit sum-of-squares model for illustrative pur- 
poses. A stimulus in this model is a 4-dimensional vector, with each component repre- 
senting the total input (excitatory positive, inhibitory negative) to a single subunit. Most 
stimuli tested had equal excitatory and inhibitory influence, so that the sum of the compo- 
nents was zero, and had excitatory influence confined to one subunit (i.e., the features were 
small compared to the entire V4 RF). One example set of stimulus vectors follows, with  
indicating that stimulus x is attended (implemented by adding a modulatory value of + 1 to 
the attended branch, and -1 to all others): 
s= [5, -2, -1, -2] > 25+0+0+0 =25 
w= [-1,-1,-1,3] > 0+0+0+9 =9 
s+w= [4, -3, -2, 1] > 16+0+0+1 =17 
+w= [5, -4, -3,0] > 25+0+0+0 =25 
s+= [3, -4, -3, 2] > 9+0+0+4 =13 
This simple model gave qualitiatively correct results. Some stimulus combinations we 
considered gave results inconsistent with the biased-competition model -- e.g., the above 
situation with w = [-1,-1, 3,-1]. The most common type of failure was that attending 
to the strong stimulus in the combined image led to a larger response than that produced 
by the strong stimulus alone. We also saw this happen for certain parameter sets in the 
biophysically detailed model, as described below; a similar result is seen in some of the 
data of Reynolds et al. (1999). Nonetheless, this simple model gives qualitatively correct 
results for a surprisingly large set of input combinations. 
When the complex-cell output from the detailed model was used as input to a sum-of- 
squared-filters model with 8 subunits, results qualitatively similar to the detailed simulation 
results were obtained. For the stimuli shown in Fig. 3, the following results were seen (all 
responses in arbitrary units): with no attention, strong: 109, weak: 2.57, combined: 84.3; 
combined, attention to strong: 106; to weak: 80. This simplified model, like the biophysi- 
cally detailed model, is rather sensitive to the values used for the modulatory inputs: with 
slightly different values, for example, attending to the strong stimulus makes the response 
to the combined image higher than the response to the strong stimulus alone. In continuing 
studies, we are working to determine whether this parameter sensitivity is a general feature 
of such models. 
4 Discussion 
A variety of previous models for attention have considered how the RF of cortical neurons 
can be dynamically modulated (Olshausen, Anderson, & Van Essen, 1993; Niebur & Koch, 
1994; Salinas & Abbott, 1997; Lee, Itti, Koch, & Braun, 1999). Our model, an extension 
of the proposal of Desimone (1992), specifies a biophysical mechanism for the multiplica- 
tive gain used in previous models (Salinas & Abbott, 1997; Reynolds et al., 1999), and 
suggests that both the stimulus competition and attentional effects seen in area V4 could be 
implemented by a straightforward mapping of stimulus-driven and modulatory afferents, 
both excitatory and inhibitory, onto the dendrites of V4 neurons. The results from the sum- 
of-squared-filters models demonstrate that even a crude model of computation in single 
neurons can account for the complicated response properties of V4 neurons, given sev- 
eral quasi-independent nonlinear dendritic subunits and a suitable spatial arrangement of 
synapses. In continuing work, we are exploring the large space of parameters (e.g., density 
of various ionic conductances, ratio of inhibition to excitation, strength of modulatory in- 
puts) to determine which aspects of the response properties are fundamental to the model, 
and which are accidents of the particular parameters chosen. This work should help to 
identify strong vs. weak experimental predictions regarding the contributions of dendritic 
subunit computation to the response properties of extrastriate neurons. 
Acknowledgements 
Supported by NSF. 
Reference 
Archie, K. A., & Mel, B. W. (2000). A model for intradendritic computation of binocular 
disparity. Nature Neurosci., 3(1), 54-63. 
Connor, C. E., Preddie, D.C., Gallant, J. L., & Essen, D.C. V. (1997). Spatial attention 
effects in macaque area V4. J. Neurosci., 7(9), 3201-3214. 
Desimone, R., & Schein, S. J. (1987). Visual properties of neurons in area V4 of the 
macaque: sensitivity to stimulus form. J. Neurophysiol., 57(3), 835-868. 
Desimone, R. (1992). Neural circuits for visual attention in the primate brain. In Carpenter, 
G. A., & Grossberg, S. (Eds.), Neural Networks for Vision and Image Processing, 
chap. 12, pp. 343-364. MIT Press, Cambridge, MA. 
Desimone, R. (1998). Visual attention mediated by biased competition in extrastriate visual 
cortex. Phil. Trans. R. Soc. Lond. B, 353, 1245-1255. 
Destexhe, A., Mainen, Z., & Sejnowski, T. J. (1994). Synthesis of models for excitable 
membranes, synaptic transmission and neuromodulation using a common kinetic for- 
malism. J. Cornput. Neurosci., 1,195-230. 
Destexhe, A., & Parr, D. (1999). Impact of network activity on the integrative properties 
of neocortical pyramidal neurons in vivo. J. Neurophysiol., 81, 1531-1547. 
Hines, M. L., & Carnevale, N. T. (1997). The NEURON simulation environment. Neural 
Comput., 9, 1179-1209. 
Lee, D. K., Itti, L., Koch, C., & Braun, J. (1999). Attention activates winner-take-all 
competition among visual filters. Nature Neurosci., 2(4), 375-381. 
Luck, S. J., Chelazzi, L., Hillyard, S. A., & Desimone, R. (1997). Neural mechanisms 
of spatial selective attention in areas V1, V2, and V4 of macaque visual cortex. J. 
Neurophysiol., 77, 24-42. 
McAdams, C. J., & Maunsell, J. H. R. (1999). Effects of attention on orientation-tuning 
functions of single neurons in macaque cortical area V4. J. Neurosci., 19(1), 431- 
441. 
Mel, B. W. (1999). Why have dendrites? A computational perspective. In Stuart, G., Sprus- 
ton, N., & Hiusser, M. (Eds.), Dendrites, chap. 11, pp. 271-289. Oxford University 
Press. 
Mel, B. W., Ruderman, D. L., & Archie, K. A. (1998). Translation-invariant orientation 
tuning in visual "complex" cells could derive from intradendritic computations. J. 
Neurosci., 18(11), 4325-4334. 
Moran, J., & Desimone, R. (1985). Selective attention gates visual processing in the ex- 
trastriate cortex. Science, 229, 782-784. 
Motter, B.C. (1993). Focal attention produces spatially selective processing in visual 
cortical areas V1, V2, and V4 in the presence of competing stimuli. J. Neurophysiol., 
70(3), 909-919. 
Niebur, E., & Koch, C. (1994). A model for the neuronal implementation of selective 
visual attention based on temporal correlation among neurons. J. Cornput. Neurosci., 
1,141-158. 
Olshausen, B. A., Anderson, C. H., & Van Essen, D.C. (1993). A neurobiological model 
of visual attention and invariant pattern recognition based on dynamic routing of 
information. J. Neurosci., 13(11), 4700-4719. 
Reynolds, J. H., Chelazzi, L., & Desimone, R. (1999). Competitive mechanisms subserve 
attention in macaque areas V2 and V4. J. Neurosci., 9(5), 1736-1753. 
Salinas, E., & Abbott, L. F. (1997). Invariant visual responses from attentional gain fields. 
J. Neurophysiol., 77, 3267-3272. 
