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Temporal and rate decoding in spiking neurons with dendrites

The temporal DC neuron specifically recognizes a spatio-temporal pattern of spikes. Any modification to the temporal or the spatial scheme of this pattern leads to a much attenuated response even when the global number of spikes remains unchanged.
On the other hand, the maximum membrane potential reached by a frequential DC neuron, for which the synapses are placed at regular intervals on its dendrite, depends primarily on the number of spikes in the input train (the average frequency) and is less influenced by the precise timing of each spike.
This study has successfully shown that dendrites play a much greater role in transmission than simply increasing the surface area of membrane able to accommodate more synapses. By regarding dendrites as an integration line with time delay, one can understand that the addition of only one dendrite can considerably increase the processing capacities of the point neuron, the main function of which is coincidence detection. Consequentially, the synchronization between neurons becomes the fundamental information medium in a neural network of spiking point neurons. Indeed, synchronization has been the subject of extensive research aimed at understanding information processing in the nervous system. In the case of dendritic computation as presented in this study, synchronization phenomena lose their importance, since a neuron with a dendrite can identify any spatio-temporal pattern specifically, or respond to a defined average spiking rate. It is thus unnecessary to use a network of synchronized point neurons to make this detection; only a single neuron with a dendrite is enough to achieve the same goal.
This study demonstrates that a single neuron with only one dendritic segment can perform either frequency decoding or temporal decoding of spatio-temporal spike patterns. The position and number of synapses on the dendrite are enough to determine this function. With this model of dendritic computation, one is thus left wondering as to whether a biological neuron codes/decodes average frequency or temporal sequences, since now it has now been shown that a neuron with only one dendrite can do both, the choice of which likely depends on the needs of the central nervous system. The nervous system would hence have two functional bricks used according to the required tasks. For instance, to carry out a task of sound or image recognition: the image or sound is recoded by the primary cortices, A1 in the case of sound or V1 in the case of an image, as spatio-temporal patterns of spikes. The identification of a particular spatio-temporal pattern of spikes becomes a key task to recognizing specific schemes or objects in this image or sound. This can be done using the temporal neuron presented in this study. To identify the intensity of a stimulus, as is needed to determine if a sound is close or distant, it would be more interesting to use in this case the frequential neuron since intensities are often coded by firing rate in the central nervous system.

Influence of the average firing rate on a temporal neuron.

Using the original input of 34 spikes in A as a reference,
the average frequency was then decreased by increments of
1 spike by randomly removing the corresponding number of
spikes to reach the desired average frequency. Ten input
patterns were tested per frequency level. For each of these
patterns the maximal response was simulated and an average
calculated per frequency level. The results are shown in Fig
5B dark triangles.

The frequency was then increased from 35 to 70 spikes by
randomly adding the desired number of spikes to the input
pattern. Ten input patterns were tested for each frequency
level. For each of these patterns the maximal response was
simulated and an average calculated per frequency level. The
results are shown in Fig 5B open triangles. We see that
when the input frequency is double (100%) that of the
original, an increase in response of only 7.2% is observed
compared to the original response.

Influence of the precise timing of each spike on a temporal neuron

To obtain the input represented in C, a temporal noise
filter of ±3ms was applied to the original spatio-temporal
pattern shown in A. The total number of spikes remained
constant as well as the number of spikes emitted from each
RF neuron; therefore the average frequency remained
unchanged as before. D depicts the response for this input:
the membrane activity remained relatively weak throughout
most of the input duration then increased sharply to a
maximum of 94.3mV above the resting potential, 28% less
than the response to the original spike pattern. The response
of this temporal neuron decreased as the temporal noise
increased on the input: Fig 5A triangle signs.

Influence of the precise timing of each spike on a frequential neuron

Using the spike pattern represented in B and applying a
random noise filter of maximum ±3ms gave the
configuration represented by D. This filter involved the
random modification of the firing times within a maximum
range of 3ms before or after the original spike timing. The
total number of spikes remained constant and hence also the
average firing rate. Fig 3E shows the response for this
particular input. The membrane potential increased gradually
until reaching a maximum of about 115mV above the resting
potential.

Frequential neuron, qualitative results.

I developed a C++ software to simulate the dendritic computation implemented by equations 1 to 5. This software simulates a single neuron with a single dendrite. This neuron receives inputs from a neuronal layer called receptive field (RF) neurons all of which are spiking point neurons. Using this software, we calculated the membrane potential at each position on the dendrite and at the soma for differing numbers of synapses, synaptic positions and spike input patterns.

The configuration tested first was that of a frequential neuron with an 80μm long dendrite, a passive propagation velocity: v=1 μm.ms-1, and one RF neuron as input projecting 20 regularly spaced synapses. Each synapse had a synaptic weight of 6 mV, a rise time constant of 1ms and a general time constant of 2ms.

A first spike train of 33 spikes was used to stimulate the dendrite computing (DC) neuron: B. C shows the response for this particular input. The membrane potential increased gradually until reaching a maximum at about 115mV above the resting potential that was arbitrarily set to 0mV.

Temporal neuron, qualitative results

11 RF neurons were used as the input, all projecting to the
same DC neuron with a total of 42 synapses on its dendrite.
The precise morphology of this network has been elaborated
according to the rules explained in section II.D and Fig 2. A
depicts the original input activity. Each line of the raster plot
represents the temporal activity of one of the 11 RF neurons.
The bottom-most line represents the sum of the 11 lines
above. A depicts the response of the DC neuron for this
input: the membrane activity remained relatively weak
during most of the input duration then increased sharply to a
maximum of 130.9 mV above the resting potential.

Temporal decoding principle

fig6

A temporal neuron like in C can detect specific spatio-temporal spike
patterns. On the top, an example of a spatio-temporal spike pattern based on three neurons N1 to N3 and 6 spikes. On the bottom, the specific organization of synapses along the dendrite corresponding to the detected spike pattern given above.

A neuron for which the behavior can be described by eq. 4
(hereafter named temporal neuron) is able to detect a
specific spatio-temporal pattern of spikes. The general idea
of this form of detection is that all the EPSPs created by the
different spikes in the spike train will converge at the same
moment at the soma using the different propagation times to
counter-balance the different spike arrival times at each
synapse; all this creating a maximal depolarization in the
soma. A different version of the same general idea was
suggested by Gerstner et al. ([7] page 144) with the notable
difference that instead of using different propagation times,
they implemented different rise times.