Complex-Cell Responses Derived from 
Center-Surround Inputs: The Surprising 
Power of Intradendritic Computation 
Bartlett W. Mel and Daniel L. Ruderman 
Department of Biomedical Engineering 
University of Southern California 
Los Angeles, CA 90089 
Kevin A. Archie 
Neuroscience Program 
University of Southern California 
Los Angeles, CA 90089 
Abstract 
Biophysical modeling studies have previously shown that cortical 
pyramidal cells driven by strong NMDA-type synaptic currents 
and/or containing dendritic voltage-dependent Ca ++ or Na + chan- 
nels, respond more strongly when synapses are activated in several 
spatially clustered groups of optimal size in comparison to the 
same number of synapses activated diffusely about the dendritic 
arbor [8]. The nonlinear intradendritic interactions giving rise to 
this "cluster sensitivity" property are akin to a layer of virtual non- 
linear "hidden units" in the dendrites, with implications for the cel- 
lular basis of learning and memory [7, 6], and for certain classes of 
nonlinear sensory processing [8]. In the present study, we show that 
a single neuron, with access only to excitatory inputs from unori- 
ented ON- and OFF-center cells in the LGN, exhibits the principal 
nonlinear response properties of a "complex" cell in primary visual 
cortex, namely orientation tuning coupled with translation invari- 
ance and contrast insensitivity. We conjecture that this type of 
intradendritic processing could explain how complex cell responses 
can persist in the absence of oriented simple cell input [13]. 
84 B. W.. Mel, D. L. Ruderman and K. A. Archie 
I INTRODUCTION 
Simple and complex cells were first described in visual cortex by Hubel and Wiesel 
[4]. Simple cell receptive fields could be subdivided into ON and OFF subregions, 
with spatial summation within a subregion and antagonism between subregions; 
cells of this type have historically been modeled as linear filters followed by a thresh- 
olding nonlinearity (see [13]). In contrast, complex cell receptive fields cannot gen- 
erally be subdivided into distinct ON and OFF subfields, and as a group exhibit 
a number of fundamentally nonlinear behaviors, including (1) orientation tuning 
across a receptive field much wider than an optimal bar, (2) larger responses to 
thin bars than thick bars--in direct violation of the superposition principle, and (3) 
sensitivity to both light and dark bars across the receptive field. 
The traditional Hubel-Wiesel model for complex cell responses involves a hierarchy, 
consisting of center-surround inputs that drive simple cells, which in turn provide 
oriented, phase-dependent input to the complex cell. By pooling over a set of simple 
cells with different positions and phases, the complex cell could respond selectively 
to stimulus orientation, while generalizing over stimulus position and contrast. A 
pure hierarchy involving simple cells is challenged, however, by a variety of more 
recent experimental results indicating many complex cells receive monosynaptic in- 
put from LGN cells [3], or do not depend on simple cell input [10, 5, 1]. It remains 
unknown how complex cell responses might derive from intracortical network com- 
putations that do no depend on simple cells, or whether they could originate directly 
from intracellular computations. 
Previous biophysical modeling studies have indicated that the input-output function 
of a dendritic tree containing excitatory voltage-dependent membrane mechanisms 
can be abstracted as low-order polynomial function, i.e. a big sum of little products 
(see [9] for review). The close match between this type of computation and "energy" 
models for complex cells [12, 11, 2] suggested that a single-cell origin of complex 
cell responses was possible. 
In the present study, we tested the hypothesis that local nonlinear processing in 
the dendritic tree of a single neuron, which receives only excitatory synaptic input 
from unoriented center-surround LGN cells, could in and of itself generate nonlin- 
ear complex cell response properties, including orientation selectivity, coupled with 
position and contrast invariance. 
2 METHODS 
2.1 BIOPHYSICAL MODELING 
Simulations of a layer 5 pyramidal cell from cat visual cortex (fig. 1) were carried 
out in NEURON 1. Biophysical parameters and other implementation details were 
as in [8] and/or shown in Table 2, except dendritic spines were not modeled here. 
The soma contained modified Hodgkin-Huxley channels with peak somatic conduc- 
tances of.sa and ODR 0.20 S/cm 2 and 0.12 S/cm 2, respectively; dendritic membrane 
was electrically passive. Each synapse included both an NMDA and AMPA-type 
XNEURON simulation environment courtesy Michael Hines and John Moore; synaptic 
channel implementations courtesy Alan Destexhe and Zach Mainen. 
Complex-cell Responses Derived from Center-surround Inputs 85 
Figure 1: Layer 5 pyramidal neuron used in the simulations, showing 100 synaptic 
contacts. Morphology courtesy Rodney Douglas and Kevan Martin. 
excitatory conductances (see Table 1). Conductances were scaled by an estimate 
of the local input resistance, to keep local EPSP size approximately uniform across 
the dendritic tree. Inhibitory synapses were not modeled. 
2.2 MAPPING VISUAL STIMULI ONTO THE DENDRITIC TREE 
A stimulus image consisted of a 64 x 64 pixel array containing a light or dark 
bar (pixel value kl against a background of 0). Bars of length 45 and width 7 
were presented at various orientations and positions within the image. Images were 
linearly filtered through difference-of-Gaussian receptive fields (center width: 0.6, 
surround width: 1.2, with no DC response). Filtered images were then mapped 
onto 64 x 64 arrays of ON-center and OFF-center LGN cells, whose outputs were 
thresholded at k0.02 respectively. In a crude model of gain control, only a random 
subset of 100 of the LGN neurons remained active to drive the modeled cortical 
cell. 
Each LGN neuron gave rise to a single synapse onto the cortical cell's dendritic 
tree. In a given run, excitatory synapses originating from the 100 active LGN cells 
were activated asynchronously at 40 Hz, while all other synapses remained silent. 
The spatial arrangement of connections from LGN cells onto the pyramidal cell 
dendrites was generated automatically, such that pairs of LGN cells which are co- 
active during presentations of optimally oriented bars formed synapses at nearby 
sites in the dendritic tree. The activity of the LGN cell array to an optimally 
oriented bar is shown in fig. 3. Frequently co-activated pairs of LGN neurons are 
hereafter referred to as "friend-pairs", and lie in a geometric arrangement as shown 
in fig. 4. Correlation-based clustering of friend-pairs was achieved by (1) choosing 
a random LGN cell and placing it at the next available dendritic site, (2) randomly 
86 B. W. Mel, D. L. Ruderman and K. A. Archie 
Parameter Value 
Rm 10kcm 2 
R, 200cm 
Cm 1.0/F/cm  
Vrest -70 mV 
Somatic Na 0.20 S/cm 2 
Somatic DR 0.12 S/cm 2 
Synapse count 100 
Stimulus frequency 40 Hz 
TAMPA (on, off) 0.5 ms, 3 ms 
AMPA 0.27 nS - 2.95 nS 
7MDA (on, off) 0.5 ms, 50 ms 
NMDA 0.027 nS - 0.295 nS 
Esyn 0 mV 
Figure 2: Table 1. Simulation Parameters. 
choosing one of its friends and placing it at the next available dendritic site, and so 
on, until until either all of the cell's friends had already been deployed, in which case 
a new cell was chosen at random to restart the sequence, or all cells had been chosen, 
meaning that all of the 8192 (= 64 x 64 x 2) LGN synapses had been successfully 
mapped onto the dendritic tree. In previous modeling work it was shown that this 
type of clustering of correlated inputs on dendrites is the natural outcome of a 
balance between activity-independent synapse formation, and activity dependent 
synapse stabilization [6]. 
This method guaranteed that an optimally oriented bar stimulus activated a larger 
number of friend-pairs on average than did bars at non-optimal orientations. This 
led in turn to relatively clustery distributions of activated synapses in the dendrites 
in response to optimal bar orientations, in comparison to non-optimal orientations. 
In previous work, it was shown that synapses activated in clusters about a dendritic 
arbor could produce significantly larger cell responses than the same number of 
synapses activated diffusely about the dendritic tree [7, 8]. 
3 Results 
Results for two series of runs are shown in fig. 5. For each bar stimulus, average 
spike rate was measured over a 250 ms period, beginning with the first spike initiated 
after stimulus onset (if any). This measure de-emphasized the initial transient climb 
off the resting potential, and provided a rough steady-state measure of stimulus 
effectiveness. Spike rates for 30 runs were averaged for each input condition. 
Orientation tuning curves for a thin bar (7 x 45 pixels) are shown in fig. 5. The 
orientation tuning peaks sharply within about 10  of vertical, and then decays 
slowly for larger angles. Tuning is apparent both for dark and light bars, and 
remains independent of location within the receptive field. 
Complex-cell Responses Derived from Center-surround Inputs 87 
eeeeel 
eeeeel 
eeeeel 
eeeeel 
eeeeel 
eeeeel 
eeeeel 
..... Active On 
; 
; 
Oe eeeeeeeO 
..... Active Off 
! 
! 
! 
eeeee 
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eeeee 
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..... Inactive 
Figure 3: LGN cell activities in response to a vertical light bar of width w - 10 
presented against a dark background. Large white circles: active on-center cells; 
large dark circles: active off-center cells; small gray circles: inactive cells. Only a 
22 x 7 section of the array is shown. 
4 Discussion 
The results of fig. 5 indicate that a pyramidal cell driven exclusively by excitatory 
inputs from ON- and OFF-center LGN cells, is at a biophysical level capable of pro- 
ducing the hallmark nonlinear response property of visual complex cells. Further- 
more, the cell's translation-invariant preference for light or dark vertical bars was 
established by manipulating only the spatial arrangement of connections from LGN 
cells onto the pyramidal cell dendrites. Since exactly 100 synapses were activated in 
every tested condition, the significantly larger responses to optimal bar orientations 
could not be explained by a simple elevation in the total synaptic activity imping- 
ing on the neuron in that condition. The origin of the cell's orientation-selective 
response resulted from nonlinear pooling of a large number of minimally-oriented 
subunits, i.e. consisting of pairs of ON and OFF cells that were co-consistent with 
an optimally oriented bar. We have achieved similar results in other experiments 
with a variety of different friend-neighborhood structures including ones both sim- 
pler and more complex than were used here, for LGN arrays with substantially 
different degrees of receptive field overlap, with random subsampling of the LGN 
array, with graded LGN activity levels, and for dendritic trees containing active 
sodium channels in addition to NMDA channels. 
Thus far we have not attempted to relate physiologically-measured orientation and 
width tuning curves, and other detailed aspects of complex cell physiology, to our 
model cell, as we have been principally interested in establishing whether the most 
salient nonlinear features of complex cell physiology were biophysically feasible at 
the single cell level. Detailed comparisons between our results and empirical tuning 
curves, etc., must be made with caution, since our model cell has been "explanted" 
from the network in which it normally exists, and is therefore absent the normal 
recurrent excitatory and inhibitory influences the cortical network provides. 
88 B. W. Mel, D. L. Ruderman and K. A. Archie 
I 
w 
I 
w 
00 
w 
 0 % O* 
w 
Figure 4: Layout of friends for an ON-center LGN cell for vertically oriented thin 
bars (top). The linear friendship linkage for a given ideal vertical bar of width w 
was determined as follows. Suppose an LGN cell is chosen at random, e.g. an ON- 
center cell at location (i, j) within the cell array. When a vertical bar is presented, 
LGN cells along the two vertical edges of the bar become active. The ON-center 
cell at position (i, j) is active to a light bar when it is in a column of cells just inside 
either edge of the bar. Those cells which are co-active under this circumstance are: 
(a) other on-center cells in the same vertical column, (b) on-center cells in vertical 
columns a distance w - I to the right and left (depending on the bar position), 
(c) off-center cells in columns a distance 4-1 away (due to the negative-going edge 
adjacent), and (d) off-center cells a distance w to the right and left (due to the 
opposite edge). As "friend-pairs" we take only those LGN cells a distance 4-(w - 1) 
and +w away. Those in the same and neighboring columns are not included. The 
friends of an off-center cell are shown in the bottom figure. It and its friends are 
optimally stimulated by bars of width w placed as shown. The width selected for 
our friend-pairs was w - 7, the same width as all bars presented as stimuli. 
Experimental validation of these simulation results would imply a significant change 
in our conception of the role of the single neuron in neocortical processing. 
Acknowledgments 
This work was funded by grants from the National Science Foundation and the 
Office of Naval Research. 
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