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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.

Composite EPSP

The term Single Fiber EPSP or composite EPSP was first
introduced by Burke [11], and later used by Sheppard [6]
page 91 and calculated by Larkum et al [8]. The single fiber
EPSP is the result in the soma of the simultaneous activation
of a pool of synapses located at different positions on the
same dendritic branch. This co-activation is deterministic as
long as they are all synapses from the same pre-synaptic
neuron. In this setting, a single spike in a presynaptic cell
activates its entire pool of synapses. The generated EPSPs
are combined to create a composite EPSP in a deterministic
fashion, with S representing the number of synapses in the
pool and F the total number of incoming spikes arriving at tf
times. Using the previous equations 1 to 4 we can write the
equation of the composite EPSP, for each time t and for each
position p on the dendrite:

eq5

 

 

Effect of a dendrite on the EPSP

Location of a synapse on a dendrite will modulate the
arrival time of the EPSP at the soma level due to the
propagation time of the EPSP in the dendrite [8] and will
also modulate the shape of the alpha function. Fig 1B.

The soma arrival time depends logically on the
propagation velocity v within the dendrite, on the spike
arrival time at the synapse and on the distance to be
traversed by the EPSP to the soma: lambda_s, or synapse position.
Accounting for this dendritic effect, equation 1 then
becomes u(t ,p,lambda_s) with p relating to the position on the
dendrite relative to the soma:

eq2

 

 

μ represents the maximum value of u expressed without
considering the synaptic weight w. It is only used to
normalize u, making u equal the synaptic weight w at the
EPSP peak. μ is expressed by the following equation:eq3

 

The amplitude of the EPSP is also attenuated during its
somatopetal propagation (from the synapse to the soma) [8],
[9], [10]. This attenuation at a particular position p on the
dendrite depends on the distance to the synapse:( ) and
on a chosen attenuation rate α. We used the following
attenuation function:

eq4