Certain studies have showed that synapses have a stable

influence that is independent of their distance to the soma, a

phenomenon referred to as “equal vote” or “dendritic

democracy” [12], [13]. In this setting, the synaptic weights

and time constant would be modified in order to obtain the

same EPSP at the soma level for all the synapses i.e.

distance-dependent scaling [14]. If we consider that the

propagation times remain different, we can calculate a

composite EPSP with stable amplitude of several tens of

milliseconds. To obtain this type of effect in the soma it is

necessary to organize the synapses in a regular manner along

the dendrite with the synaptic weights increasing with

distance to the soma. We will call this particular

configuration the “frequency sensitive setting” and all the

others “spatio-temporal sensitive”. Here we demonstrate that

neurons organized in a frequency sensitive manner (hereafter

named frequential neurons) are able to « count » the spikes

that arrive within a specific time interval, a phenomenon

which itself depends on the dendritic length and the

propagation speed. With a constant EPSP shape, the neuron

becomes particularly sensitive to the average firing rate of

the global pattern but reacts little to changes in the precise

timing of each spike

# Archives pour la catégorie article

For published journal article or conference article

# 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:

# 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:

**, or synapse position.**

*lambda_s*Accounting for this dendritic effect, equation 1 then

becomes

**(**

*u***,**

*t***,**

*p***) with**

*lambda_s**relating to the position on the*

**p**dendrite relative to the soma:

** μ** represents the maximum value of u expressed without

considering the synaptic weight

**. It is only used to**

*w*normalize

**, making**

*u***equal the synaptic weight**

*u***at the**

*w*EPSP peak.

**is expressed by the following equation:**

*μ*

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:

# Fig : point neuron and neuron with a dendrite

- A: a point neuron model can only trigger a simple EPSP everytime it receives an incoming spike. EPSPs are combined solely on the basis of the spike arrival time.
- B: A neuron with a dendrite and a single input synapse.
- C: a spatio-temporally sensitive setting. All the synapses together can form a composite EPSP based on the combination of several single EPSPs generated by each synapse.

# 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.

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,

**is the transmission delay between the time the pre-synaptic neuron is active and the time the synapse s becomes active.**

*delta_ax***is the time constant,**

*t***is the rising time constant and**

*t_r***is the Heaviside function.**

*H*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.

# Introduction of Temporal and rate decoding in spiking neurons with dendrites

ULTIMATELY understanding the role of dendrites in neural computation requires a theory. This theory must identify the benefits of having dendrites and reveal the basic principles used to provide these benefits” [1]. In the conclusion of the book entitled “Dendrites”, the editors Nelson Spruston, Greg Stuart and Michael Häusser wrote:

“Despite this tremendous progress, the most exciting times in dendrite research lie ahead of us. Much of the knowledge we have accumulated to date has been descriptive […] Two key questions that now need addressing are:

- What computations does each neuron perform within its neuronal network?
- And, which features of dendrites are most relevant to how neurons perform these computations? [2]

Concerning neuronal functions, a first element was given by Rieke et al in 1999 [3]:

“When we see, we are not interpreting the pattern of light intensity that falls on our retina; we are interpreting the pattern of spikes that the million cells of our optic nerve send to the brain. […] Spike sequences are the language for which the brain is listening, the language the brain uses for its internal musings, and the language it speaks as it talks to the outside world.”

There is also much evidence showing that biological neurons are able to interpret firing rate [4] and temporal codes [5]. Here we show that the addition of a single dendrite to a point neuron model considerably extends its possible range of functions, in particular, enabling it to detect a precise spatio-temporal pattern of spikes or, conversely, to have an undifferentiated response to precise spike timing but to react to average firing rate. We also show that these two distinct types of behavior characterized either by spatio-temporal or frequency sensitivity depend solely on the morphology of the « synapse-dendrite » system and in particular on the position of synapses on the dendrite. These findings provide an additional element necessary to our global understanding of the features required by dendrites that enable biological neurons to perform these computations.

# Abstract of TempUnit Rules

How could synapse number and position on a dendrite affect neuronal behavior with respect to the decoding of firing rate and temporal pattern? I developed a model of a neuron with a passive dendrite and found that dendritic length and the particular synapse positions directly determine the behavior of the neuron in response to patterns of received inputs. I revealed two distinct types of behavior by simply modifying the position and the number of synapses on the dendrite. In one setting – spatio-temporally sensitive – the neuron responds to a precise spatio-temporal pattern of spikes, but shows little change following an increase in the average frequency of the same input pattern. In the other setting – frequency sensitive – the neuron is insensitive to the precise arrival time of each spike but responds to changes in the average firing rate. This would allow neurons to detect different spatio-temporal patterns.