Archives pour l'étiquette EPSP

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

 

 

 

EPSP on a point neuron

What is the relation between the morphology of a neuron and its function? Neurons mostly present large dendritic extensions, the exact role of which largely remains unknown. It could be, as has already been suggested, that dendrites are simply there to increase the membrane surface area of the neurons to enable the binding of 10- or 20 fold more synapses (Mel WB in [2] p421). This being the case, the shape of the dendritic tree and the particular position of the synapses would have only little influence on the computation performed by the neurons. The best model for approximating this dendritic function would be the point neuron. A: the arrival of an action potential at a synapse triggers an EPSP in the post-synaptic neuron. [6] Pages 75-76.

eq1

This function supposes an incoming firing time at t=0 of the presynaptic neuron. In this equation, u is the membrane potential of the dendrite and soma, w is the synaptic weight, delta_ax is the transmission delay between the time the pre-synaptic neuron is active and the time the synapse s becomes active. t is the time constant, t_r is the rising time constant and H is the Heaviside function.

One of the most obvious functions that the point neuron model can perform is coincidence detection: when two neurons are synchronized and both have the same point neuron as output, then the simultaneous arrival of the spikes triggers a summed EPSP that overshoots the spike threshold. This target point neuron then emits an action potential that indicates its coincidence detection. Thus, for a point neuron, the variation of the membrane potential depends exclusively on the synaptic weights and the arrival times of the incoming spikes.

What is less clear however is how this type of neuron, except when integrated in large networks, could detect many spike arrival times, i.e. a specific spike train. To investigate this, we modified the point neuron equation to incorporate a
propagation function along a dendrite.