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NEWS AND VIEWS
Dendritic arithmetic
Nelson Spruston & William L Kath
Pyramidal neurons integrate synaptic inputs arriving on a structurally and functionally complex dendritic tree that has nonlinear
responses. A study in this issue shows that nonlinear computation occurs in individual dendritic branches, and suggests a
possible approach to building neural network models directly connected to the behavior of real neurons and synapses.
Why are real brains so much more powerful
than artificial neural networks? In part this is
a matter of circuit complexity and scale, but it
is also because real neurons are much more
complex than the simple elements used in
neural network models. One strategy for
developing more sophisticated neural networks is to replace simple elements with
sophisticated computational models of neurons, including branching dendritic trees,
thousands of synapses, and dozens of voltagegated conductances. The problem with this
approach is that it is not manageable to use
such computationally expensive neuronal
models in large-scale networks. Another
strategy is to develop abstractions of neurons
that capture the essential processing power of
the real thing. A paper by Polsky and colleagues1 in this issue represents a large step in
this direction by providing experimental
insight into what kinds of computations real
neurons perform and how they do it.
For many decades now, neural network
models have relied on simple neuronal elements called ‘integrate-and-fire neurons’2. In
their simplest form, these abstracted neurons
receive numerous excitatory inputs, each of
which produces an excitatory postsynaptic
potential that decays exponentially. Multiple
inputs sum linearly until a threshold is
reached, whereupon the neuron ‘fires’ and
produces a response that propagates to all of
its targets. Following this virtual action
potential, the membrane potential is reset to
the resting state. Inhibition can be incorpoNelson Spruston is in the Department of
Neurobiology and Physiology and a member of the
Institute for Neuroscience, and William L. Kath is in
the Department of Engineering Sciences and
Applied Mathematics and a member of the Institute
for Neuroscience, Northwestern University,
Evanston, Illinois 60208, USA.
e-mail: [email protected]
rated using units that inhibit, rather than
excite, their targets. Networks combining
integrate-and-fire neurons with synaptic
plasticity carry out powerful computations
that are not easily solved using traditional
approaches3.
Neurophysiologists and neural network
modelers alike have long known that the
integrate-and-fire model is an incomplete
representation of most real neurons4. To
appreciate the complexity of synaptic integration, one need only glance at the structure of neurons with the knowledge that
inputs arriving onto different parts of the
dendritic tree will attenuate differently as
they spread toward the action potential initi-
a
ation zone in the axon. Some mechanisms
may exist to overcome the dendritic disadvantage of synapses on distant dendrites, but
these are unlikely to be effective for all
synapses on all dendrites5. It is natural to
wonder, therefore, to what extent synapses
on the most distant dendrites contribute to
action potential initiation in the axon.
Further obscuring any answer to this question are ion channels with nonlinear
response properties, such as voltage-gated
sodium, calcium and potassium channels, as
well as transmitter-gated channels including
the NMDA receptor, to name a few. These
channels and others are expressed abundantly and often nonuniformly in dendrites,
b
Within branch
3 mV
20 ms
Between branches
Individual EPSPs
Arithmetic sum
Combined EPSP
Figure 1 Spiking in individual dendritic branches implies a three-layer model of synaptic integration.
(a) Schematic representation of the main finding of Polsky et al.1: two multisynaptic inputs onto a
single dendritic branch exhibit superlinear summation (top). Inputs onto separate branches exhibit
roughly linear summation (bottom). (b) Reconstructed layer-5 pyramidal neuron (left) and an
abstracted three-layer network model (right; based on ref. 14). Red branches represent the distal
apical inputs and light blue branches the perisomatic inputs. Together, these inputs constitute the
first layer of the network model, each performing superlinear summation of synaptic inputs as shown
in a (indicated by small circles with sigmoids). The outputs of this first layer feed into two integration
zones: one near the perisomatic branches (dark blue; e.g., soma) and one near the distal apical
branches (purple; e.g., apical spike initiation zone). These integration zones constitute the second
layer of the network model (large circles with sigmoids). The third layer (not shown) is the action
potential initiation zone in the axon. Grey circles indicate connections between layers.
NATURE NEUROSCIENCE VOLUME 7 | NUMBER 6 | JUNE 2004
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© 2004 Nature Publishing Group http://www.nature.com/natureneuroscience
NEWS AND VIEWS
thus introducing bewildering complexity to
the process of synaptic integration6. Despite
numerous advances in our knowledge of the
distribution and properties of voltage-gated
channels in dendrites, a quantitative understanding of how they influence synaptic
integration and the resulting computational
rules has remained obscure.
Polsky et al.1 illuminate the mechanisms of
dendritic integration by testing a simple
hypothesis: that each terminal dendritic
branch acts as a computational subunit, summing synaptic inputs in a sigmoidal fashion
(that is, a threshold nonlinearity)7. To test
this idea, the authors took advantage of
patch-clamp recording in cortical brain
slices, combined with confocal imaging of
dendritic calcium entry. The imaging
methodology allowed them to identify visually small dendritic branches in the neuron
from which they were recording. They then
placed two small stimulating electrodes near
a single dendritic branch and confirmed,
using calcium imaging, that synapses were
activated locally on the same dendritic
branch. The outcome of the experiments was
simple (Fig. 1a). Stimulation of one dendritic
branch at two locations led to superlinear
summation, supporting the notion that a single dendritic branch performs a sigmoidal
computation with a threshold and a ceiling.
By contrast, when the two stimulating electrodes were positioned near two different
dendritic branches, activation of both inputs
produced roughly linear summation. In fact,
superlinear summation only occurred if the
two activated inputs were less than 100 µm
apart on the same dendritic branch. These
findings support the idea that individual
dendritic branches act as computational subunits, and argue against the notion that dendrites act merely as parking spaces for
randomly distributed, globally summed
synapses.
Further observations in the Polsky et al.
study1 suggest a mechanism for the thresholding nonlinearity in thin dendritic
branches. Blocking glutamate-gated NMDA
receptors largely eliminated the superlinear
summation of inputs onto a single dendritic
branch, suggesting that the voltage-dependent properties of this receptor mediate all-ornone ‘NMDA spikes’ in dendritic branches8.
Other details support the NMDA-spike
mechanism. For example, double stimulation
of each input was most effective at producing
superlinear summation. That longer depolarizations are most effective is consistent
with the slow kinetics of the relief of voltagedependent magnesium blockade of NMDA
receptors9,10. Also, activation of the two
568
inputs with an interval as long as 40 ms produced superlinear summation, which is consistent with the long occupancy of NMDA
receptors by glutamate11. Though the
authors did not completely rule out contributions from voltage-gated sodium and calcium channels to ‘branch spikes’, NMDA
spikes are significantly different from spikes
mediated by voltage-gated channels, because
they cannot actively spread beyond the
region of the dendrites activated by glutamate. Consequently, NMDA receptors provide an excellent mechanism for producing
local spikes.
How does the existence of spiking
branches change our view of synaptic integration? The authors find that a spike in a
single branch of the basal dendrites in a
layer-5 pyramidal neuron produces a depolarization of about 10 mV in the soma.
Because a depolarization of 15–20 mV is
required to span the gap between the resting
potential and the threshold of an axonal
action potential, a small number of these
spiking dendritic branches, activated nearly
simultaneously, might be sufficient to produce an action potential. It is not known,
though, how many synapses are sufficient to
produce a branch spike or whether the depolarization produced by each branch spike
would sum linearly or nonlinearly.
A separate layer of integration is likely to
be imposed by the apical dendritic tree.
Because of the long primary apical dendrite,
synaptic potentials from the apical dendrites
attenuate substantially before reaching the
soma. Polsky et al.1 show that branch spikes
from proximal apical dendrites produce a
somatic depolarization similar to the effect of
basal dendrite activity. More distal branches
on the apical tuft, however, are likely to produce considerably less somatic depolarization. One mechanism for overcoming the
weak influence of apical dendritic branches
in the soma and axon is to have a separate
spike initiation zone in the apical dendrites.
There is now substantial evidence for such a
mechanism and for interesting interactions
between the axonal and apical dendritic
action potential initiation zones12,13.
Based on these findings, the authors suggest that a single layer-5 pyramidal neuron
may act like a three-layer neural network14
(Fig. 1b). The first layer consists of individual
dendritic branches (roughly 50–100 in a typical pyramidal neuron), each of which performs a sigmoidal computation. The output
of each element in the first layer is then
passed to an element in the second layer,
which in the simplest case consists of two
integration zones (for example, one near the
perisomatic branches and one near the distal
apical branches). A more complex case might
consist of multiple elements in the second
layer, corresponding to multiple integration
zones on the main apical dendrite. Finally,
the output of the second-layer elements
would be passed to the third layer, consisting
of a single action potential initiation zone
(the axon).
What is exciting about this proposal is that
individual neurons could be modeled using a
framework that is widely implemented in
current neural network models. In particular,
the ‘abstracted’ integrate-and-fire elements
used by neural network modelers may come
full circle and be the key components needed
to understand how real neurons perform
synaptic integration. With a better idea of
how pyramidal neurons function, moreover,
it might now be conceivable to build neural
networks directly connected to the behavior
of real neurons and real synaptic connections. Additional details regarding synaptic
integration could be layered on top of the
pyramidal neuron abstraction. For example,
inhibitory interneurons targeting different
domains of the dendritic tree could be modeled by inputs to subdomains of the threelayered pyramidal neuron, and interactions
between multiple spike-initiation zones
could be modeled by interactions between
elements in the second layer.
Despite these exciting results and their
wide-reaching implications, the pyramidal
neuron is not yet completely solved. To name
just a few of the many remaining mysteries:
we still do not fully understand the mechanism of branch-spike initiation and spread,
or the mechanisms for spike initiation in
larger dendrites. We still do not know how
many integration zones might lie in the
larger branches of apical dendrites or precisely how they interact. We still do not fully
understand the significance and implications
of the nonuniform distribution of some
channels in dendrites, such as the high density of hyperpolarization-activated channels
in distal dendrites15. We do not understand
the multitude of modulatory and plastic
influences that affect somatic, axonal and
dendritic ion channels and shape dendritic
integration. And, importantly, we still do not
understand how neurons in other brain
regions (hippocampal pyramidal neurons,
cerebellar Purkinje cells, myriad inhibitory
interneurons) differ from the layer-5 pyramidal neuron of neocortex with respect to
synaptic integration. Research in these areas
will continue, but in the meantime, the paths
of neural network modelers and experimental neuroscientists have crossed, and a golden
VOLUME 7 | NUMBER 6 | JUNE 2004 NATURE NEUROSCIENCE
NEWS AND VIEWS
© 2004 Nature Publishing Group http://www.nature.com/natureneuroscience
opportunity exists for an effective exchange
of ideas leading to new advances in our
understanding of dendritic arithmetic and
neural computation.
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Deconstructing a navigational neuron
Günther M Zeck & Richard H Masland
Flies show remarkable flight control, aided partly by motion-sensitive neurons in the visual ganglia. Haag and Borst now unravel
the microcircuitry of some of these motion-analyzing cells, and suggest a mechanism for their receptive field tuning.
The brain of a fly is small but powerful.
Although we do not know much about a fly’s
thoughts, everyday experience teaches us
plenty about another of its brain functions,
the control of flight. Flies move fast, they
avoid (most) obstacles, and they are remarkably good at dodging predators, such as birds
and rolled-up newspapers. These visual
stunts are possible in part because of the fly’s
unusually large eyes (Fig. 1), but the most
interesting computations are carried out by a
small set (∼120) of visually driven neurons
located within the head ganglia. In this issue,
Jürgen Haag and Alexander Borst get into the
middle of this machinery—to a place roughly
halfway between light detection and wing
movement—and unravel the microcircuitry
that controls the activity of one of the
motion-analyzing cells1.
The eye of a blowfly consists of a precise
array of photosensitive cells, arranged in
groups of eight. These cells converge via several way-stations onto higher-order cells
within a central structure called the lobula
plate. The responses of photoreceptor cells
signal only the presence or absence of light,
but at later stages, more interesting properties begin to appear, one of which is that
some neurons become direction-selective,
passing along a signal that depends on the
direction of stimulus motion. This is, however, only the beginning of the story. Cells of
the lobula plate have a much larger and more
Günther M. Zeck and Richard H. Masland are at
the Howard Hughes Medical Institute,
Massachusetts General Hospital and Harvard
Medical School, 50 Blossom Street, Wellman 429,
Boston, Massachusetts 02114, USA.
e-mail: [email protected]
puzzling repertoire, which Haag and Borst
now set out to explain, focusing on neurons
responsive to vertical motion, termed VS or
‘vertical system’ cells.
There are ten distinguishable VS cells in
each hemisphere of the blowfly. Each of them
has a region of visual space upon which it
reports, its receptive field. In general, the
receptive field of a neuron of the visual system roughly corresponds to the extent of the
input neurons sampled by its dendritic arbor,
but the receptive fields of the VS neurons
instead cover a huge area, representing a
visual angle of more than 100 degrees.
Instead of surveying a narrow segment of the
world, each VS cell somehow views an area
bigger than the area scanned by its own set of
photoreceptor cells. The VS cells have a
remarkable second feature2. Not only do they
have a bias for upward or downward motion
(as their name implies); they are also particularly sensitive to rotational flow fields (Fig. 1;
see also Supplementary Fig. 1 of the paper by
Haag and Borst1). A rotating visual stimulus
is what is seen when one looks at the center of
a propeller; a rotational flow field is the visual
stimulus generated during the act of tilting
one’s head, when the whole visual world
rotates.
It turns out that the VS cells’ complex
response properties can be explained by lateral connections among the VS1–VS10 neurons. Haag and Borst used two electrodes to
record from pairs of VS cells. Passing current
into one cell was found to depolarize nearby
cells. The connection was bidirectional, so
that current could flow from either cell of the
pair to the other. The coupling between pairs
of cells became weaker as the distance
between the cells increased. The connection
NATURE NEUROSCIENCE VOLUME 7 | NUMBER 6 | JUNE 2004
could be analyzed as a low-pass filter, and had
kinetics of increasing order for cells that were
more separated in distance. These results
indicate that the cells are coupled by gap
junctions, in a chain-like fashion such that
depolarizing one cell depolarizes its neighbor, which then depolarizes the next neighbor and so on. Interestingly, two-photon
imaging of multiple VS cells injected with
fluorescent dyes gave no convincing evidence
of contact among the dendrites; the gap junctions instead seem to be axo-axonal.
Coupling between the cells can create the
observed broadening of any individual cell’s
receptive field. Each individual VS cell
responds to the set of photoreceptor cells
surveyed by that VS cell’s dendrites. The dendrites of neighboring VS cells survey nearby
patches of photoreceptor cells, and thus sample neighboring regions of visual space. If the
cells are coupled, the receptive field of any
individual cell expands to include the region
of visual space monitored by the neighboring
(coupled) VS cells.
For the most distant VS cells, and for other
(horizontal system) cells of the lobula plate,
the coupling relationships were more complicated. The authors studied the VS7/8 cell
in detail. This cell responds broadly to downward motion, adding to the direct output of
local direction-selective cells a graded excitation from VS6 and VS9, neighboring cells
that are also downward-sensitive but cover
additional visual space. The VS7/8 cell is also
tuned to two more directions. From a neuron
called HSN (which conveys information
about horizontal motion), the VS7/8 cell
gains sensitivity to horizontal motion, this
time via a chain comprising an excitatory
synapse from HSN on an unknown cell X
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