Mapping the Matrix: The Ways of Neocortex
Rodney J. Douglas1,* and Kevan A.C. Martin1,*
1Institute of Neuroinformatics, UZH/ETH, Winterthurerstrasse 190, 8057 Zurich, Switzerland
*Correspondence: email@example.com (R.J.D.), firstname.lastname@example.org (K.A.C.M.)
While we know that the neocortex occupies 85% of our brains and that its circuits allow an enormous
flexibility and repertoire of behavior (not to mention unexplained phenomena like consciousness),
a century after Cajal we have very little knowledge of the details of the cortical circuits or their
mode of function. One simplifying hypothesis that has existed since Cajal is that the neocortex con-
sists of repeated copies of the same fundamental circuit. However, finding that fundamental circuit
has proved elusive, although partial drafts of a ‘‘canonical circuit’’ appear in many different guises
of structure and function. Here, we review some critical stages in the history of this quest. In doing
so, we consider the style of cortical computation in relation to the neuronal machinery that supports
it. We conclude that the structure and function of cortex honors two major computational principles:
‘‘just-enough’’ and ‘‘just-in-time.’’
Maps are comforting. They reveal to us the fixed points
of the known world and alert us to the regions that are
‘‘terra incognita.’’ However, maps themselves also map
the changes in our perception of what is the ‘‘known
world’’—and these reveal our perceptions to be unstable.
was first ‘‘discovered’’ in 1578 somewhere between Ire-
land and Frisland and appeared on nautical charts from
then on until it finally sank from consciousness after it last
appeared on a chart in 1856. The island of Madya was the
longest survivor of these phantoms. It first appeared on
maps in about 1400, positioned in the north Atlantic to the
southwest of Ireland. Over the centuries it moved more
westward, so that by 1566 it was located near Newfound-
land, and then took a turn south, and was last seen on a
Rand McNally map of 1906 at the level of the West Indies.
Claude Levi-Strauss (in contrast to William of Occam: ‘‘No
more things should be presumed to exist than are abso-
lutely necessary’’) argued that every culture has a need
for certain concepts and expressions to absorb any ex-
cess of existence that has not yet had a word coined for
it. James Hamilton Paterson (1993) suggests that these
void of ignorance—the terra incognita.
The neocortex is one of the most elaborate maps we
have. Not only does it contain many different areas, but
these areas also contain within themselves multiple maps,
which may reflect directly the sensory periphery or may
has its own floating signifiers, with words like ‘‘column,’’
‘‘module,’’ ‘‘neural representation,’’ ‘‘cortical code,’’ and
‘‘consciousness,’’ which have been coined to absorb the
enormous functional and structural excess of existence
that is evident in every material record of the brain and,
most particularly, in the cortical circuits about whose
mode of organization and operation we are still greatly
ignorant. One fundamental question is whether the neo-
cortex is a unitary structure with a grammar and a logic
of construction and operation that can be understood
in terms of the physical circuits and their physiology, or
whether it is a collective of very many separate modules
with their own specialist ‘‘trick’’ circuitry?
The Languages of Neocortex
To begin at the beginning: like the syntax of human lan-
guages, the structure of the neocortex appears equally
complex in all land mammals. Just as there is no simple
or prototype version of a human language in existence, a
simple or primitive form of neocortex does not exist. Yet,
it is as evident that, like different languages, the neocortex
physiological methods. But just as with languages, we will
claim here, the neocortical areas are also essentially the
same and, like languages, can be translated, one into the
other. Thus, in understanding one area, we can expect to
a ‘‘canonical’’ property of cortical circuits (Douglas et al.,
1989). The immediate challenge is the question, what
defines ‘‘neocortex’’? The usual answer is structural:
genetically older, the neocortex possesses six layers. The
number of layers would, of course, seem a rather fragile
means of defining a structure that varies over five orders
the processing of input from an unlikely range of sensory
systems allowing detection of electromagnetic radiation,
vibration, temperature, sound, and chemicals, and that
then provides output to an equally unlikely range of motor
run. In fact, the ‘‘six-layered’’ neocortex is something of a
unicorn, for the number of layers that can be distinguished
varies greatly between areas and the histological stains
used to reveal the layers. Yet, somehow, neocortex is so
instantly distinguishable from other laminated structures,
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
such as the hippocampus or superior colliculus, that early
anatomists referred to it as ‘‘isocortex.’’
Although it is now clear that language comprehension
and production involves much more of the brain than just
the well-known regions first discovered by Broca and
Wernicke, their 19th century idea of a compartmentaliza-
tion of specific functions has reappeared in modern times,
most prominently in evolutionary biology. The best known
claim is captured by the ‘‘Swiss army knife’’ metaphor for
the functional organization of cortex (Barkow et al., 1992).
In this view, the brain has evolved a series of special-pur-
pose modules, which, like the Swiss army knife, consist of
individual components that have a specific function and
are not designed to work together like the components
of a machine. For humans, the language module is the
most obvious of these special-purpose modules, but
ules are the means by which the neocortex is organized
and works (Fodor, 1983; Zeki, 1993). Implicit in this is the
notion that the neural pathways in the brain subserving
eral-purpose architecture that carries out the neocortical
part of the computations.
Written on the Brain (in Indian Ink)
The era of microcircuit analysis was launched by Camillo
Golgi’s discovery of ‘‘la reazione nera,’’ which allowed in-
dividual neurons to be visualized, and by Santiago Ramon
y Cajal’s law of dynamic polarization, which provided the
critical algorithm for identifying the input and output
regions of individual neurons. Put together, these two
advances made it possible for the first time to show the
probable route of impulses from input to output for a given
structure. As he recorded in his autobiography, the ex-
traordinary claim that Cajal made was that even the high-
est center of the brain, the neocortex, was built of stereo-
typed circuits like those he had discovered in the retina,
cerebellum, hippocampus, spinal cord, and other parts of
the central nervous system (Cajal, 1937). Despite intense
efforts on his part, however, he was unable to define the
basic cortical circuit, but until the end of his life he never-
theless remained convinced that it existed.
When Cajal applied Golgi’s stain to neonatal brain, he
was able to map, mostly correctly, significant circuits in
the spinal cord, retina, and visual pathways, cerebellum,
hippocampus, olfactory bulb, auditory nuclei, and others.
From this he developed the notion of the ‘‘neural ava-
lanche,’’ which was essentially the inverse of Sherring-
ton’s ‘‘final common path.’’ It stated that the number of
neurons involved in conducting impulses from a sensory
receptor increases progressively from the periphery to
the cortex (Cajal, 1937). De Kock et al. (2007) have calcu-
estimate that a single whisker deflection generates about
4000 impulses in the cortex. This avalanche grows further
through the associated cortical areas, before it is funneled
down the final common path to the motoneuron, but even
with his great skills of preparation, observation, and imag-
ination, Cajal was unable to trace the route from input to
out reward, for he provided a comprehensive description
of the different cell types that inhabit the neocortex of dif-
ferent animals and incorporated the earlier descriptions of
cortical cell types of Retzius, Meynert, Betz, and others.
Lorente de No ´ (1949) pursued Cajal’s dream, also with
Golgi’s stain, and suggested that the functional unit of
cortex consisted of a specific thalamocortical fiber and
a cylindrical group of cells surrounding the fiber, some of
which formed synapses with the thalamocortical fiber.
With succeeding generations, however, this confidence
in a basic circuit became less secure, and there was even
a return, in the 1930s, to the idea that the neocortex was
an equipotential network (Lashley, 1930), an idea demol-
ished by Sperry (Sperry, 1947; Sperry et al., 1955), or
that the connections between cortical neurons were not
at all specific, but perhaps statistical (Sholl, 1956) or semi-
and Schu ¨z, 1991). Thus, proposals that the local circuit of
barrel cortex begins its life as a ‘‘tabula rasa’’ to be written
on by experience (Jeanmonod et al., 1981; Le Be and
Markram, 2006; Kalisman et al., 2005) are simply a contin-
uance of a surprisingly long-lived hypothesis that the
cortex really wants to be a randomly connected neural
In the face of such enormous numbers of possible cir-
cuits that could potentially arise from such random neural
networks, to pursue the concept that all of neocortex has
Figure 1. The Phantom Island of Buss
First ‘‘discovered’’ in 1578, it disappeared from the Nautical charts
after 1856. http://eaudrey.com/myth/Places/buss_island.htm.
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
a uniform basic structure and performs some basic uni-
form operations would seem to be setting oneself up for
yet another instance of Thomas Huxley’s great tragedy
of Science—‘‘the slaying of a beautiful hypothesis by an
ugly fact.’’ Yet, the decade that began in a trough with
Karl Lashley’s despairing account of his search for the en-
for the neocortex, with seminal studies of the physiology
of sensory cortex (Mountcastle, 1957; Hubel and Wiesel,
Architects of the New Cortex
The long hoped for evidence that neocortex had a specific
architecture did not come from anatomists, but from
physiologists working in vivo, who provided the major
new insights into corticalorganization. Mountcastle (1957)
recorded from the somatosensory cortex of cats and
monkeys and found that neurons with common functional
properties lay in a radial column of cells, extending from
white matter to cortical surface. With this discovery, the
anatomists were once again brought into play. Powell,
working at Mountcastle’s side, suggested that the vertical
palisades of cells he saw in stained sections of sensory
cortex were the elementary units that formed of the func-
tional columns (Powell and Mountcastle, 1959). This con-
cept of afunctional columnwas notlost on theirneighbors
at John’s Hopkins, who were just then plotting their first
receptive fields of visual cortical neurons on bed sheets
hung from the ceiling.
Hubel and Wiesel’s ice-cube diagram (Hubel and
the functional architecture of area 17. What had first
seemed to them irregularly shaped ‘‘columns,’’ some-
times ordered, sometimes not, sometimes continuous,
sometimes not (Hubel and Wiesel, 1963, 1968), were
now schematized as parallel slabs, with the thin orienta-
tion slabs cutting the coarser ocular dominance columns
at right angles. Since orientation selectivity is a property
of single cells, it is inevitably discretized, but trivially so,
for in all other respects the map of orientation space
appears to be continuous. In the case of monkey visual
cortex, Hubel and Wiesel (1974b) found that movements
just-detectable shifts in orientation preference (10?) in
monkey V1. From this they reckoned that the orientation
slabs were not discrete, or if they were, they had a width
of less than 25 mm, i.e., the diameter of a large cell
soma. To Hubel and Wiesel this indicated that there was
no correlation between the fine-grain of the physiological
slabs and the coarser grain offered by the orders of mag-
nitudes larger dimensions of the soma, dendrite, and
axon. The recent two-photon imaging of the neurons
that form the orientation map in the cat (Ohki et al., 2005,
2006) confirms in 2D the precision of the progression in
orientation preference seen with the microelectrode and
confronts us again with the puzzle of how this comes
about, given what we now know about the underlying
The anatomical basis of these functional domains was
baffling to Hubel and Wiesel, since the radial fascicles
seen in the light microscope seemed too ubiquitous and
orderly to account for the picture they saw through their
microelectrode (Hubel and Wiesel, 1968). Yet the causal
the functional architecture, the functional architecture has
regularities, and so how do the underlying circuits do it?
The iso-orientation slabs were about 30 mm wide, but
the ocular dominance slabs were 500 mm wide. For other
cortical areas, the picture was even less clear. With re-
spect to the whisker representation in rodents, Hubel
and Wiesel stated, ‘‘Whether they [barrels] should be con-
sidered columns seems a matter of taste and semantics’’
(Hubel and Wiesel, 1974b). The whisker map in rodents
is similar to retinotopic or tonotopic representations in
other sensory cortices, but this map is not the same as
higher-order maps of properties like orientation selectiv-
ity, whose topography is not predictable at the periphery.
Nevertheless, the concept that neocortex consists of ver-
tical arrangements of cells that are interconnected and
have functional properties in common is almost universal.
With the enormous success of the cortical physiologists
in defining a basic architecture of cortex, the ball was
back in the anatomists’ court to explain the underlying
Anatomists in the Garden
Although Golgi’s stain had provided generations of anato-
mists with a powerful tool, it also had a major limitation,
which Cajal had recognized and used to his advantage:
it worked best in immature material. Because multiple
cellswere impregnated, itwas virtuallyimpossible totrace
the same axon from one section to the next. Thus, the cell
structures illustrated were obtained from reconstructions
of single sections of perhaps 100 mm thick. A hint that
this picture of the cortical axons was very incomplete
came from degeneration studies in which small lesions
had been made within the cortical gray matter. When the
resulting degeneration was traced, it was clear that intra-
mm (Fisken et al., 1975; Gatter and Powell, 1978; Creutz-
feldt et al., 1977). What is most surprising was how similar
the pattern of fiber degeneration was across different spe-
cies and different areas. Figure 2 shows the close similar-
ities between the striate visual cortex and the primary mo-
tor cortex of monkey cortex, which, in cytoarchitectonic
and functional respects, differ the most. It was evidence
like this that encouraged Powell to pursue the concept
of cortical uniformity. Later, bulk injections of tracers like
horseradish peroxidase into the cortex confirmed this pat-
tern of spread (Blasdel et al., 1985) and also revealed the
existence of widespread lateral connections of pyramidal
The lateral fibers detected in the degeneration studies
and the first complete picture of mature cortical neurons
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
intracellularly with horseradish peroxidase (HRP; Gilbert
and Wiesel, 1979, 1983; Martin and Whitteridge, 1984).
These pictures were a revelation (Figure 3).
It was as if the Golgi stain had been given growth hor-
mone, for the black spindly trees had now extended their
branches and sprouted bushy terminal thickets. It was ev-
ident that even the ‘‘projection neurons’’ were substantial
players in the local cortical circuits. However, what consti-
tuteda localcircuitwas nowevenlessclear. Whatwasthe
elementary unit of structure that formed the vertical func-
tional column? The palisades of cell bodies still formed
their neat columns, but not only did the dendrites originat-
ing from these cell bodies spread well beyond these ele-
mentary columns, so did their axonal arbors. It became
impossible on anatomical grounds to define the columnar
structure of a given area, let alone explain how the visible
structure gave rise to the functional phenomenon of col-
umns.Thedifficulty of defining the columnhas alsogener-
ated the opinion that the concept has failed as a unifying
principle forcerebral cortex (Purves etal.,1992;Swindale,
1998; Horton and Adams, 2005). However, the idea of
elementary modules that could, by repetition, generate
an entire cortex, could not so easily be quashed by these
Modules and Maps
Critics of the column concept have to deal with the reality
that the very long history of microelectrode recordings
from the primary visual cortex seemed to give the same
results, regardless of where exactly the electrode was
placed. If it were not so, progress would have been ach-
ingly slow, and the visual cortex would never have be-
come the model system it has. This reliable repetitiveness
is most convincingly made for the many areas that contain
topographic mapsof the sensory periphery. Here, the cor-
tical area represents in 2D a map of audible frequencies,
or a whisker, or one patch of visual field, and the actual
shape of the cortical surface is determined by this primary
map (Daniel and Whitteridge, 1961). Within this map is the
machinery studied so intensively by recording from single
neurons and analyzing the receptive field properties. This
realization that within the topographic map there was
another dimension, the vertical distance between pial sur-
face and white matter, prompted the deep thought that
‘‘the machinery may be roughly uniform over the whole
striate cortex, the difference being in the inputs. A given
region of cortex simply digests what is brought to it, and
is a great developmental advantage in designing such
machinery once only, and repeating it over and over
Figure 2. Similarity in the Patterns of Local Degeneration
after a Narrow Cut Through the Layers of Cortex in Area 17
(Top) and Area 4 (Bottom) in the Monkey
From Fisken et al. (1975) and Gatter and Powell (1978).
Figure 3. Pyramidal Cell of Layer 3 of Cat Visual Cortex
Showing Dendrite (Green) and Axon (Red) Forming Multiple
Clusters of Boutons (Black) in Layer 3 and 5
Scale bar, 500 mm. The neuron was intracellulary injected with horse-
radish peroxidase and reconstructed in 3D (Anderson, Binzegger,
Douglas, and Martin, unpublished data).
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
monotonously, like a crystal’’ (Hubel and Wiesel, 1974a,
in the paper that they considered their most important af-
ter their 1962 paper).
Contrariwise, Hu ¨bener et al. (1997), on the basis of 2D
optical imaging of the intrinsic signal evoked by various
stimuli, suggested instead that the cortex ‘‘could not be
ules, but rather it is composed of ‘mosaics’ of functional
domains for the different properties.’’ This latter view of
functional mosaics, however, does not capture the fact
that all recording methods show that there is continuity
in many of the maps and that each neuron expresses
not just one property, but a number of properties. These
multidimensional receptive fields of single neurons means
that different properties that map onto a given cortical
surface can never be simply segregated into separate
‘‘modules.’’ However, the same multidimensionality is
represented in orderly 3D mappings, forcing us back to
the central conundrum of how this multidimensionality is
generated in the physical circuits.
The Mismatch of the Minicolumns
Although the concept of an identifiable ‘‘minicolumn’’ has
a wide currency (Mountcastle, 1997; Peters and Yilmaz,
1993; Rockland and Ichinohe, 2004), to suppose that
there is some acreage of gray matter that sensible scien-
tists will agree contains an essence of their ‘‘cortical
column’’ seems doubtful. There is simply a mismatch be-
tween the anatomy and the functional maps. The notion of
the minicolumn or module does not properly capture the
granularity ortheverticalandlateralinterdigitation ofcom-
ponent neurons that seems to be the essence of the cor-
tical circuit. This means that even in a highly specialized
‘‘column’’ such as those evident in the rodent barrel cor-
tex, one cannot simply clip out a cylinder of tissue that
contains the whole local circuit, for later reconstruction
‘‘in silico’’ (Markram, 2006; Helmstaedter et al., 2007).
able connection matrix. If you don’t know what is there,
then you cannot hope to simplify intelligently for your
models. We are convinced that there is a local circuit, one
that we have referred to as a ‘‘canonical’’ circuit for neo-
2004). This elemental circuit has been elaborated quanti-
tatively for cat visual cortex (Binzegger et al., 2004, see
below). It has also been demonstrated through detailed
simulations that the quantitative circuit derived from cat
visual cortex can, with few modifications, perform the op-
erations of the prefrontal cortical area called frontal eye
fields (FEF) in the monkey brain (Heinzle et al., 2007),
thus importantly demonstrating the property of generality.
The matrix of cortical neurons scales in interesting ways
ample, Elston and colleagues have shown a rostro-caudal
gradient in the size of pyramidal cells and their dendritic
elaborations (Elston, 2002). An intriguing scaling across
species is also apparent for the lateral collaterals of the
layer 3 pyramidal cells, which collectively form a series
of small clusters, which we have called a ‘‘daisy’’ (Douglas
and Martin, 2004). Daisies seem to be present in all corti-
their work in the old world primate, Lund and colleagues
(Lund et al., 1993; Pucak et al., 1996) pointed out that
thereisa simple correlation between the spacingbetween
the clusters and the cluster size in the macaque monkey
cortex. It turns out that this relationship may be universal
across areas and species (Douglas and Martin, 2004).
This is a remarkable and unexpected example of some
underlying organizing principle, but supports the idea
that there are common rules whereby the cortical circuits
organize themselves in 3D.
Cajal and the Quantitative Circuits
There are many different levels at which we can begin to
understand the cortical circuit. One of the simplest steps
is to catalog the elements of the circuits: which types of
neurons exist and in which layers and their relations. How-
ever, this in itself is not definitive; for the neocortex, it has
allowed the full spectrum of interpretations of the local cir-
cuit, from tabula rasa to specified circuits. A second step,
and one that has proved exceedingly difficult, is determin-
ing who talks to whom and how much. Thus, there are at
least two levels of connection diagrams that can be dis-
tinguished. One connection diagram, lets call it the ‘‘Cajal
circuit,’’ shows the average pattern of connections be-
tween the different neuronal types that make up the cir-
cuit. This circuit does not take into account any quantita-
tive aspects and shows only the most essential functional
connections of the circuit. So for the retina, for example,
the Cajal circuit shows the connection from photorecep-
tors to bipolar cells to ganglion cells. This is an essential
step, but sequence of processing through neuronal ele-
ments provides a logic of the circuit and not the relative
influence of the elements. The ‘‘quantitative circuit’’ cap-
tures the essential magnitude of the relations between
Figure 4. Canonical Cortical Circuit Based on
Electrophysiological and Modeling Studies in the Cat Visual
From Douglas and Martin (1991).
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
the elements. In the case of the retina, this would be the
number of photoreceptors and horizontal cells that con-
nect to a bipolar cell and the number of bipolar cells that
connect to amacrine and to ganglion cells. In the retina,
these numbers change greatly with distance from the area
centralis or fovea, and so these changing numbers reflect
essential properties of the receptive fields. For the cortex,
the assumption is that the proportions of different types of
neurons remain uniform across an area and that their pat-
terns of connections are constant. However, the principle
purpose of the quantitative circuit is to understand the
functional consequences of the circuit, which are given by
the details of the connectivity. No wonder then that there
is currently a worldwide initiative to develop automated
methods for solving the structure of brain circuits at syn-
aptic resolution (Briggman and Denk, 2006).
The anatomist Tom Powell, a major modern proponent
of cortical uniformity, had previously explored this quanti-
tative aspect of cortical circuitry in a very imaginative way.
His case for cortical uniformity rested on several observa-
tions, one of which was the stereotyped pattern of degen-
eration after a focal lesion, mentioned above (reviewed in
Powell, 1981). Another was that at electron microscope
level, he could distinguish three basic cell types, which
were in the same proportions in all of the cortical areas
that he studied in the monkey, cat, and rat (Sloper et al.,
1978; Winfield et al., 1981; see below). A third, more con-
troversial observation was that he simply counted the
number of neurons in an arbitrary box (25 3 30 mm) that
extended from layer 1 to white matter. With one exception
(and despite 3-fold variations in cortical thickness) the
number of neurons in the box was astonishingly similar
and man. The exception was area 17 in primates, which
areas (Rockel etal., 1974, 1980). Thislatter result begs the
at face value it suggests that there are major differences in
the way that area 17 is assembled compared to all other
cortical areas, but there are not (for review see Dehay
ticalcytoarchitectonics, wherethenonuniformity of cortex
is distinguished on the basis of various cellular staining
At the very high magnifications of the electron micro-
scope, these cytoarchitectonic differences vanish in the
apparently relentless gray wallpaper of an electron micro-
graph. Nevertheless, skilled anatomists, like Gray, Szen-
ta ´gothai, Powell, Jones, and Peters, were able to discover
in the welter of ultrastructural detail clear differences in
synapse morphology and associated targets, as well as
ultrastructural correlates of the smooth and spiny neurons
that had first been seen by Cajal in Golgi-stained neocor-
tex. When applied to the neocortex, the electron micro-
scope also greatly encouraged quantification, and now,
with modern stereological methods, unbiased estimates
can be made of numbers of the structures of choice: neu-
rons, glia, or synapses. This at least removes the quirky
selectivity inherent in Golgi stains, or the biases inherent
in intracellular staining in vivo or in vitro. The quantitative
aspects of the cortical circuits revealed clear consisten-
cies across species and cortical areas (Douglas and Mar-
tin, 2004). About 80% of neurons are spiny and excitatory
and form 85% of the synapses, while about 20% of the
neurons are smooth and inhibitory, and they form about
15% of the synapses, because of their smaller axonal ram-
ifications. One equally consistent finding is that in forming
in turn it will provide output to thousands of target neurons.
These conversations between pairs of neurons have
been monitored by cross-correlation or intracellular re-
cording methods. However, aftermanyyears ofworkfrom
many laboratories, we still do not yet have a comprehen-
sive picture of the Cajal circuit for even one cortical area,
let alone a quantitative circuit of all the connections. Thus,
the first priority for neocortex is still to understand com-
prehensively what actually exists in a cortical area. For
most of the 20th century, anatomists like Cajal and Lor-
ente de No ´ would be able to count the number of different
types of cortical neurons on the fingers of both hands.
These types were based only on their morphology. Now,
with the advent of molecular markers and physiological
methods for examining the biophysics and synaptic
methods, the combinatorial possibilities of all the different
parameters that can be measured are enormous, and the
number of types presently hangs more on inclination than
on any commonly agreed criteria, as Crick has long com-
plained (Crick, 1999). In some hands, there is an immense
diversity of neuron types, whether classified by morphol-
ogy, cytochemistry, physiology, or gene expression (see
reviews by Monyer and Markram, 2004; Nelson et al.,
2006; Yuste, 2005). In others’ hands, there were just two:
simple and complex cells (Hubel and Wiesel, 1962). Per-
haps a taxonomy of cortical neurons will only be properly
Given that each neuron is polyneuronally innervated,
whether physiological or anatomical, are simply unable to
do this. Although significant steps have been taken to de-
velop transsynaptic tracers for resolving the total input to
quantitative problems remains for the future (Wickersham
et al., 2007). Thus, in the absence of a direct means of
tracing quantitatively the total circuit, alternative theory-
based estimates have had to do. This process began with
the statistical approaches of Sholl (1956) and Braitenberg
and Luria (1960) and persists into the modern era.
Mapping the Matrix
The most determined attempt to assign a source to every
synapse in a single cortical area was made by Binzegger
et al. (2004) for the cat’s area 17. Starting with high-fidelity
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
reconstructions of completeaxons and dendrites of single
neurons obtained fromintracellular recordings in vivo, and
continuing with a large database gleaned from the litera-
ture of cell counts and synaptic counts, Binzegger et al.
applied ‘‘Peter’s rule’’ (Braitenberg and Schu ¨z, 1991),
contribution to the neuropil of their dendrites and axonal
synaptic boutons. This of course is an approximation that
in the connections between types of neurons, there is an
exception to Peter’s rule. However, on average both spiny
and smooth cell types follow Peter’s rule in their connec-
tions intheneuropil, asseenfromthequantitative electron
microscopic analysis described above. The analysis of
Binzegger et al. (2004) for cat visual cortex showed that
for some layers at least, it was possible to account for
most of the synapses in a given layer on the basis of the
known content of the local circuits (Figure 5).
In other layers, however, there was an embarrassment
of riches: there were far more synapses than could be
accounted for by the known neuronal composition of
area 17. These synapses, the ‘‘dark matter’’ of the cortex,
constituted a colossal 90% of all the synapses in layer 1
and 40% of all the synapses in layer 6. This latter number
translates to about 3000 synapses per layer 6 pyramidal
neuron. One may speculate at the sources of these
synapses, but it is slightly disturbing to think that their
very existence was unknown until the attempt was made
to account for every one. Unfortunately, such an analysis
has not yet been attempted for any other cortical area.
What the source is of the ‘‘dark matter’’ is not clear. One
simple way of accounting for them is to suppose that they
arise from an as yet unidentified type of local neuron. This
seems unlikely, because many studies using a variety of
different techniques have time and again turned up the
same set of neuronal types. Thus, while there may be Yeti
or Bigfoot neurons, large numbers of them are unlikely to
be found. A more likely source of the dark matter synap-
ses are interareal or subcortical sources, such as the
claustrum or basal forebrain nuclei, which of course
were not included in the original solution of Binzegger
et al. (2004), who considered only the local neurons and
must certainly account for some of the dark matter,
particularly for those in layer 1, which is a target of the
so-called ‘‘feedback’’ projections. Whether such large
numbers of unaccounted synapses can be made up by
the long-distance connections remains an open experi-
The reasons for the shadow of doubt about whether
these interareal sources will be sufficient to soak up the
dark matter are the quantitative experimental studies of
Kennedy and cohorts on the monkey cortex. They have
mapped by retrograde tracing the source of all the inputs
to a point in a cortical area, such as V1 or V4 (reviewed in
Vezoli et al., 2004; A. Falchier et al., 2006, Soc. Neurosci,
abstract). They find consistently that over 80% of the neu-
rons labeled by the retrograde tracer lay within the same
cortical area in which the tracer injection was made. The
next largest group, about 10%, was in the neighboring
cortical area. With progressive distances from the areas in
were found, indicating progressively weaker connections
between the two areas. For comparison, the lateral genic-
ulate nucleus, which provides the major sensory drive to
V1 and, relatively speaking, is a strong connection, con-
tributed less than 1% of the total number of neurons that
project to a point in V1. It is clear from these quantitative
studies that if the dark matter is formed by neurons that
lie outside the cortical area then each different projection
contributes only a small fraction of the total additional
synapses that are needed to account for the dark matter.
Thus, long-distance projections from many different areas
are needed to make up these numbers. This is a key impli-
cation in the light of the proposed functional roles of the
long-distance projections on the neurons of the local
Modeling the Map of Synapses
Most modeling solutions to the cortical circuits are one-
dimensional, because they reflect connectivity maps
obtained from in vitro recordings or in vivo anatomical
tracing studies. However, in the visual system, the two-
dimensional receptive fields and cortical maps have given
rise to more elaborate model circuits. Most of these have
considered how properties like feature selectivity are gen-
erated, or how responses of cortical neurons become
invariant. There are very large-scale simulations and
often-ingenious expressions of these models, but these
are almost without exception designed to accomplish
their intended monistic goal, such as explaining orienta-
tionselectivity. Fewhavebeen generalizedtoencapsulate
the generic computations that are carried out in any
cortical area (Douglas et al., 1996; Douglas and Martin,
Figure 5. Quantitative Analysis of Excitatory Connections of
Local Neurons and Thalamic Afferents in Cat Visual Cortex
Numbers are percentages of total excitatory synapses inarea 17 of cat
visual cortex contributed by the particular cell type. (See Binzegger
et al., 2004.)
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
A big step forward in understanding the circuits of cor-
tex came with the ingenious formulation of a processing
devised by Hubel and Wiesel (1962). Now 45 years old,
their back-of-the-envelope sketch of serial processing in
the cat visual cortex has shown an admirably tenacious
grip on life, to the extent that no alternative yet appears in
the undergraduate textbooks, and it is still at the heart of
much more elaborate computational models (see reviews
by Ferster and Miller, 2000; Sompolinsky and Shapley,
1997). The enormous barriers to putting structure to
function are illustrated by the stark fact that, although
the connection between the LGN and layer 4 of cat
visual cortex is one of the most studied connections in
the central nervous system, it has taken decades to accu-
mulate sufficiently detailed structural and physiological
data to now be able to build biologically realistic models
of the thalamic afferent input to spiny stellate cells
(Banitt et al., 2007).
However, the experimental difficulties of determining
quantitatively the actual numbers that should be put in
the models cannot be exaggerated. One simple example
is illustrated by the brief history of attempts to determine
the fraction of thalamic synapses in layer 4 of cat visual
cortex. Estimates of the proportion of thalamic synapses
in layer 4 of cat visual cortex have varied over a factor of
ten, depending on the experimental method used. The
highest estimate was 28%, which was made by LeVay
and Gilbert (1976), who used tritiated proline as the tracer
and made their counts of autoradiographs of thin EM sec-
tions. LeVay (1986) later repeated the experiment with
wheat-germ agglutinin as the tracer and obtained a mark-
edly lower value of 5%, which, however, was much more
in agreement with the estimates of Garey and Powell
(1971), who used degeneration methods, and with those
of Ahmed et al. (1994), who mapped the entire synaptic
input to the dendrites of layer 4 spiny stellate cells (Ander-
son et al., 1994) and then used ultrastructural criteria to
identify which were the LGN synapses. It seems likely
that technical issues, such as background activity, gener-
atedthe inflatedfigures obtained withtritiated proline.The
consensus figure from the anatomy is that the thalamus
provides around 5% of the excitatory synapses in its main
target layer. This estimate is supported by electrophysio-
logical studies using cross-correlation, where about 30
geniculate neurons are estimated to converge on a single
simple cell in layer 4 (Usrey et al., 2000). Similar estimates
White, 1978). The majority of the remaining synapses in
layer 4 of the cat come from other neurons in the local cor-
tical circuit, such as the layer 6 pyramidal cells and spiny
to its principal thalamic nucleus by such a fragile long-dis-
tance link? The answer, we believe, lies in understanding
with its strongly recurrent excitatory and inhibitory subcir-
cuits, and the long-distance connections that arise from
many sources, including thalamus and cortex.
That’s Just Enough!
The small number of thalamic synapses in relation to the
excitatory synapses from intracortical sources may seem
puzzling to the generations who have relied on the text-
book model of the simple cell, which shows no other in-
puts than those from the thalamus. However, this number
raises a key question that has never really been seriously
asked: how many synapses should be made for a given
projection? Because itisso wellstudied,thethalamicpro-
jection offers our best case study for establishing a likely
number. If the thalamic afferents are the dominant excit-
atory input to the cortical simple cells, they clearly cannot
be too dominant for the following reason: the synaptic
mapping experiments showed that the just over 4000 ex-
citatory synapses are formed with the dendritic tree of a
spiny stellate cell (Ahmed et al., 1994). The simulations
of a very detailed biophysical model show that the syn-
chronous activation of about 100 thalamocortical synap-
ses can drive the voltage of the spiny stellate cell mem-
brane from resting potential through the spike threshold,
assuming no inhibitory inputs are coactivated and there
is no strong synaptic depression (Banitt et al., 2007). If the
thalamic synapses are a substantial fraction of the excit-
that even the activity of a small fraction of these would be
sufficient to excite the postsynaptic cell. This means that
even at the nonoptimal orientations, more than sufficient
excitation would arrive from the thalamus to drive the
spiny stellate cell through threshold, and so degrade the
observed selective response of these neurons.
The classical solution to the problem of strong excita-
tion is always: use strong inhibition. Thus, one argument
has been that it is intracortical inhibition that prevents
the cell from firing at the nonoptimal orientations. How-
ever, the case for so-called ‘‘cross-orientation inhibition’’
is weak, because direct measurements show that cortical
inhibition is tuned to the same orientation as the excitation
and is weak or absent at the nonoptimal orientations (Fer-
son et al., 2000). Thus, the fact that the layer 4 neurons do
not fire at nonoptimal orientations must be because the
relatively small numbers of thalamocortical synapses are
tion needed to drive the spiny stellate membrane through
its spike threshold. If the thalamic drive is insufficient, then
therecurrentconnections ofthelocalcircuit willnotbeen-
gaged. But when the thalamic relay cells drive the spiny
stellate cell,thentherecurrentcircuitsof thecanonical cir-
cuit amplify to the synaptic drive initiated by the thalamic
afferents (Douglas et al., 1989, 1996). In fact, the simula-
tions of Banitt et al. (2007) indicate that some sort of back-
ground activity is required to help the thalamic afferents to
drive their postsynaptic neurons. Thus, we are led inexo-
rably to the conclusion that the thalamus contributes
‘‘just-enough’’ excitation to the spiny stellate cell to drive
it when the appropriate stimulus configuration is pre-
sented. Similar mechanisms have been proposed for the
thalamocortical link in the rodent barrel cortex, which is
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
similarly modest in its contribution to a single layer 4 neu-
ron (White, 1978; Bruno and Sakmann, 2006).
Of course, it is trivially true that a threshold-crossing
stimulus must provide just enough stimulation to evoke a
response. But notice that our use of ‘‘just-enough’’ means
that the total effect of input projections is also capped by
the small number of synapses that are available to drive
the target neuron from any particular source, such as thal-
amus or another cortical area. That is, the input projec-
tions are critically small. This feature has particular signif-
icance in relation to the pathways between cortical areas,
which are thought to provide the essential ‘‘top-down
modulation’’ or ‘‘bottom-up driving’’ of their targets. The
significant effects of these connections are now taken for
granted, for example in the celebrated distributed hierar-
chical processing network of the primate cerebral cortex
(Felleman and Van Essen, 1991). But how is all this driving
and modulation to be achieved with projections that pro-
vide at most a few percent of synapses to their target
areas (Anderson et al., 1998; Vezoli et al., 2004)? It ap-
pears that these tiny long-distance projections must pro-
vide ‘‘just-enough’’ to guarantee a significant effect on
their target under some spatiotemporal configurations
of their input spikes, but on the other hand, theirmaximum
effect is also capped by design. Thus, the ‘‘just-enough’’
principle may be true for all cortical circuits, because
these long projections are the only ones that can provide
the biases for the recurrent excitatory operations of the
local canonical circuits (Douglas and Martin, 2007). The
functional maps of cortex should then be seen not as the
static units suggested by Hubel and Wiesel’s ice-cube
model, but dynamic ensembles (Basole et al., 2003, 2006;
Tsodyks et al., 1999; Kenet et al., 2003) whose state re-
flects not only the spatial interaction of local and long-dis-
tance circuits, but also their spatiotemporal interactions.
The flip side of the ‘‘just-enough’’ coin is the problem of
punctuality. In conventional computation, time enters in
a very different way to that used by the nervous system.
Conventional computing is organized according to two
pological ordering that describes the sequence of trans-
formations of the process. The second is the temporal
property of the underlying physical circuit that implements
the communications and transformations. The values of
the input data must be held steady for some minimum
time before and after the clock signal that activates the
transformation is applied. Beyond this technical require-
ment of the transformation, there is also the question of
how the topological sequence of the algorithm is bound
to the physical time of the underlying machine. There are
two basic models: systems that operate synchronously
and those that operate asynchronously. In the first case,
the communication and transformation actions are syn-
chronized by a global clock, while in the second case,
each transformation element times only its local transfor-
input before emitting its output. This means that all trans-
formation elements that take input from the waiting ele-
ment must also wait until that output is available. In both
cases, the physical time at which transitions occur have
no role in the representation of the data being processed.
It is only the sequence number of the transformation that
is relevant, and physical time is simply the medium that
permits data exchange and transformations to be coordi-
nated at each step for the process (on either the global
or the local scale). In contrast to these styles of machine
computation, it appears that spiking neurons follow a
rather different strategy, in which physical time is intrinsic
to the data processing and representation.
Generally, neurons are quiescent, providing an output
only on demand when driven by suitable input. Estimates
based on power requirements for neuronal signaling and
the power actually consumed by the brain suggest that
only a few percent of neurons are significantly active at
any time, an estimate that supports notions of sparse
2003). In the cerebral cortex, the output of neurons is not
synchronized by a global clock, although synchronization
to a local oscillating field potential such as hippocampal
theta and cortical gamma oscillations has been inter-
preted as providing a local clock (Hopfield and Brody,
2001). Unlike their silicon counterparts, neurons are ready
to process at any time and will emit asynchronous output
provided that some spatiotemporal input conditions on its
dendrites are approximately met within some sliding time
window of output excitability.
Because neurons are not waiting for a clock-tick, they
are always prepared to process, and because neuronal
processing is everywhere intimately linked to physical
time, there is no need for a global clock to provide for syn-
chronous processing steps. All that is required is that just
enough signals rendezvous at a given location just-in-time
to perform the transformation at that location, otherwise
processing along that branch will die. Moreover, the pro-
cessing in the brain is then intrinsically synchronized with
the natural dynamics of the events in the external world
that it strives to characterize and predict. How many
spikes should rendezvous? The simulations of Banitt et al.
(2007) indicate that a quiescent soma requires between
100–200 synaptic events within a window determined by
the synaptic time constant in order to honor an output
computation. That is, a few percent (a few hundred) of its
excitatory inputs should be active during a window whose
time constant is about 10–20 ms.
Is it possible for neurons to compute on such patterns?
In principle, yes. Hopfield and others have described such
mechanisms (Hopfield, 1995; Hopfield and Brody, 2001;
Gu ¨tig and Sompolinsky, 2006). The ‘‘Tempotron’’ of Gu ¨tig
and Sompolinsky (2006) isamodel integrate-and-fire neu-
ron that is able to learn decisions based on the spatiotem-
poral pattern of the spikes input to its simple dendrite. The
Tempotron can learn to detect the presence of a particular
spatiotemporal pattern anywhere in a time interval that
is significantly longer than the duration of the patterns
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
themselves. Their model performs best for synaptic time
constants of about 10 ms, provided the number of pat-
terns that must be detected is no more than about twice
the number of input synapses. A Tempotron signals its
recognition of an input pattern by generating an output
spike. So a model composed of parallel Tempotrons
with some common inputs would offer a simple circuit
element that detects and transforms temporal patterns.
An important property of the Tempotron is that it is robust
input patterns. So the signal is restored, and signals that
do not arrive in time can be neglected.
When just-enough and just-in-time are combined in the
cortical circuits, the result is a rich matrix of possible out-
comes. Their manner of interaction is illustrated schemat-
ically in Figure 6, which shows how a computation evolves
in time in a network of neurons, represented here for only
a single spatial dimension. The network illustrated con-
sists of three spatiotemporal ‘‘rendezvous nodes’’ (Rab,
Rcd, Rbd). Each node represents a temporal window
over a clusters of neurons within the same orientation
domain or within the same whisker barrel, for example.
The rendezvous nodes receive input from distant sites,
such as thalamus or another cortical area. These distant
sites are represented by nodes Ra and Rb, which emit
messages composed of spatiotemporal spike patterns
along the communication edges indicated as red arrows.
Thesemessages aresimilar to the synfire chains of Abeles
(Abeles, 1982). The arrows represent the axonal projec-
tions between the nodes, while the blue-gray paths flank-
ing each arrowed edge represent the spatial dimension (y
axis) of the anatomical projection (just-enough) and the
temporal window (x axis) dimensions of the effective spike
pattern being transmitted. Messages A and B pass
through the rendezvous node Rab, where as a result of
a local interaction in the node, Rab emits spatiotemporal
messages B0and C. C, in this example, consists of a small
number of neurons that hold their outputs steady for some
The interaction of C and D leads to dynamic switching
withinnode Rcd, which resultsin the emission of message
E and the quenching of a potential progress of D to D0. As
aresultof thisdynamicswitching in nodeRcd,theinterac-
tion of B0and D0in node Rbd cannot occur with the conse-
quence that the potential emission B00from node Rbd will
not be honored. This scheme obviously places emphasis
on the role of populations of neurons in collectively trans-
forming multineuronal input messages, rather than on the
input-output relations of single neurons.
Whether by single neuron or by collective computation,
how is it that inputs which are barely enough and nearly in
time can be used to compute a reliable output? It is here,
we believe, that the recurrent connections of the cortical
circuits play their role, providing the signal gain necessary
for actively reorganizing the relatively small contributions
of long-range afferents. It is this collective processing of
transformations that could provide the signal restoration
properties sought by von Neumann, who pondered how
the brain was able to transform data through many suc-
cessive stages without degradation of significant signal
(von Neumann, 2000). The positive feedback between
neurons of the cooperating population can be used to
enhance the features of the input that match patterns em-
bedded in the weights of the excitatory feedback connec-
tions. At the same time, the overall strength of the excit-
atory response of the population is used to suppress
outliers via the dynamical inhibitory threshold imposed
by inhibitory neurons. In this sense, the network can ac-
tively impose an interpretation on an incomplete or noisy
input signal by restoring it toward some activity distribu-
tion across a ‘‘permitted set’’ of neurons (Hahnloser
et al., 2002; Douglas and Martin, 2007).
Thus,thepotential instability ofthestrongpositive feed-
back, which is a cardinal feature of the recurrent cortical
circuits, is exploited during the transient behavior of the
networks, because the network can use this instability to
explore new interpretations (partitions of active neurons)
Figure 6. Schematic Representation of Just-Enough and
Just-in-Time Computation in a Cortical Network
The computation is shown evolving in time in a network of neurons,
represented here spatially in one dimension. Two local populations
of neurons located at computational ‘‘rendezvous’’ nodes Ra and Rb
emit messages composed of spatiotemporal spike patterns along
the communication edges (‘‘axons’’) indicated as red arrows. The
‘‘widths’’ of the connection pathways (the number of connections)
and the temporal window during which they can be effective are indi-
cated by the blue-gray paths flanking each arrowed edge (widths ‘‘je’’
and ‘‘jit’’). Messages A and B are shown passing through a rendezvous
node Rab. As a result of that local interaction, Rab emits messages B0
and C. C in this case consists of a small number of neurons that hold
their outputs steady for some interval until the arrival of message D
at rendezvous node Rcd. The interaction of C and D then leads to
the emission of message E from Rcd. As a result of this interaction,
another possible output, D0, from node Rcd does not occur, which
means that a possible interaction between B0and D0in rendezvous
node Rbd does not occur, and B00is not emitted.
Neuron 56, October 25, 2007 ª2007 Elsevier Inc.
until a suitable (stable) interpretation, which is consistent
with the input pattern, is found (Hahnloser et al., 2000).
The computational primitives found in the neocortex in-
clude linear operations such as summation, division, and
sign inversion, and also nonlinear operations such as win-
ner-take-all, invariance, and multistability, in which lateral
interactions of excitation and inhibition play a key role
(Douglas et al., 1996; Douglas and Martin, 2007). These
that have been observed in different cortical areas. It is
perhaps important to point out that these computational
primitives arise through the collective action of the whole
circuit and are not carried out within the dendritic tree of
single neurons. As a consequence of this collective action
of many thousands of neurons, the neural avalanche of
Cajal, which begins at the peripheral sense organs and
rolls on through the matrix of canonical cortical circuits,
is not out of control, but is constrained such that it gener-
ates a coherent activity consistent with the context in
which the animal finds itself. The cortical output along
the final common path of Sherrington then generates an
adaptive motor action.
Lost (and Found) in Translation
Our understanding of the organization of specific neocor-
tical circuits derives in large part from electrophysiological
in the work in visual cortex where the results from single-
electrode recordings were the basis for inferring a func-
tional architecture for the visual cortex. Details of this
functional architecture were expressed in circuits, most
famously those for simple and complex cells in area 17 of
the cat (Hubel and Wiesel, 1962). Because the specificity
of the connections inferred was on a very fine grain, it
has proved impossible to translate any of these functional
models into an anatomically proven circuit. Thus, the
translation of structure into function remains elusive for
neocortex, and Francis Crick’s dictum that, ‘‘if you do not
make headway understanding a complex system, study
matically’’ has yet to be realized for the neocortex.
As is by now a familiar pattern, new floating signifiers
have been coined to soak up the excess of existence, as
ger et al. (2004) to explain the existence of large numbers
of synapsesof nofixedaddress.Nevertheless, ourcurrent
knowledge of the structural richness of cortical neurons
ogies and patterns of connection in many different cortical
areas and in different species challenges us to provide
a far more comprehensive translation of structure into
function. This challenge is now being addressed by the
development of methods for large-scale solutions of neo-
cortical circuits at synaptic resolution. But in translating
structure into function we need more than the weight
matrix of the connectivity or even the complete wiring
diagram. To understand the syntax of cortex is going to
be a major advance, but we also need to understand
deeply the semantics of the many areas of neocortex and
the conversations they have with each other. As a wise
person once remarked: the great difference between the
telephone directory and a play of Shakespeare is that,
while both have a grand cast of characters, only the play
has a plot.
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