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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.

Livre : Codage spatio-temporel des neurones cortico-motoneuronaux

Codage spatio-temporel des neurones cortico-motoneuronaux

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Résumé

Le système Cortico-Motoneuronal (CM) est composé de populatio+ns de neurones situées dans le Cortex Moteur qui réalisent des prolongements axoniques directs vers les motoneurones de la moelle épinière. Il participe à la réalisation de mouvements volontaires de la main et particulièrement pour les mouvements qui nécessitent un haut degré de dextérité. Les cellules CM réalisent des connexions monosynaptiques avec les motoneurones impliqués dans ces mouvements. Il est par conséquent particulièrement pertinent de s’intéresser au codage de l’information en relation avec l’activité musculaire dans l’activité de ces neurones.

Le but de ce travail de thèse a été de comprendre à la fois, i) Quelle est l’information transmise par le système CM ? ii) Comment est codée cette information ? Pour cela nous avons utilisé des enregistrements de neurones CM et des enregistrements de l’activité musculaire (EMG) chez le Macaque lors de la réalisation d’une tâche de préhension entre le pouce et l’index. Pour déterminer le codage utilisé par les neurones CM, nous avons utilisé un perceptron multi-couches à délai temporel (TDMLP) que nous avons entraîné afin de déterminer la fonction de transfert donnant l’EMG à partir de l’activité CM.

Les résultats obtenus montrent qu’il existe 2 types de codage de l’activité EMG par le neurone CM : Un codage en fréquence et un codage temporel. Le codage en fréquence a la particularité d’être défini dans l’activité binaire du neurone avec un délai correspondant à la latence entre le pic d’activité CM et le pic EMG. Le codage en fréquence défini les grandes variations de l’activité EMG. A cela s’ajoute un codage temporel des petites variations de l’EMG avec un délai de l’ordre du délai de transmission. En effet, de nombreux indices ont corrélé la fréquence moyenne des PAs dans une fenêtre avec les grandes variations de l’EMG. De plus, nous avons trouvé des patrons temporels de PAs en relation avec l’amplitude des petites variations de l’EMG mesuré par le post-spike variation (PSV). Le PSV est la dérivée de l’EMG centrée sur un PA. Un codage temporel a été observé dans l’activité de 28 neurones CM sur les 45 analysés. Ces patrons, une fois utilisés comme entrée de TDMLP entraînés ont influencé l’EMG d’une manière prédictible selon le type de patron. L’occurrence des patrons est plus importante pendant la période de maintien que pendant les périodes de mouvement. Or, la fréquence moyenne de décharge des neurones CM est généralement supérieure pendant la période de mouvement, ceci révèle une indépendance dans la modulation en temporel et en fréquentielle de l’activité CM. De plus, une meilleure utilisation du codage temporel par les neurones CM peut permettre de transmettre une plus grande quantité d’information par ces neurones à chaque instant et donc être mise en relation avec une meilleure réalisation de la tâche comportementale. Tous ces résultats expérimentaux ont été regroupés dans un modèle formel et explicatif, le TempUnit, se basant sur le principe de la sommation temporelle. Le modèle TempUnit a montré de meilleures capacités que le TDMLP pour prédire l’activité EMG à partir de l’activité CM.

Codage spatio-temporel des neurones cortico-motoneuronaux

Constant EPSP

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

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

 

 

 

Fig : point neuron and neuron with a dendrite

fig1

 

  • 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.

delay line neural network as precise spikes sequence detector

delay line I&F neural network
delay line I&F neural network

This neural network has been done with the Animatlab software using only firing realistic neurons.

Here, to simplify, there is only one input neuron, in red. But the principle is the same with several input neurons. Each input neuron has to project to the delay line neurons, in orange. The last neuron of the delay line, in orange, has to project to the output neuron with a conduction weight depending on the number of spikes in the pattern to be recognize.

With this specific connectivity, the input neuron creates 3 links to the conduction delay neurons, hence the pattern to be recognize will contain 3 spikes. I have used a conduction delay of 10ms. This network will then recognize a spike pattern of 3 spikes with the following arrival time t1=0, t2=30ms and t3=40ms.

Composite EPSP

Everytime a spike input the delay line neural network, it creates a particular composite EPSP in the output neuron.

composite EPSP
the particular network architecture creates a predictable composite EPSP

This particular shape of the membrane potential is created by the propagation times the different spikes take to go through the conduction line neural network. Because the propagation time are predictable  as well as the axonic connections, the composite EPSP in the output neuron is hence predictable.

temporal decoding : precise spike sequence detection.

when a specific spike pattern arrives with a particular timing the output neuron integrates the composite EPSPs and fire.
when a specific spike pattern arrives with a particular timing the output neuron integrates the composite EPSPs and fire.

when the input have the particular timing of the network:  t1=0, t2=30ms and t3=40ms, the output neuron recognize the sequence and fire.

the precise spike timing is also important even in the case of 3 input spikes.

Even with 3 spikes, the precise spike timing is important to make the output neuron fire.
Even with 3 spikes, the precise spike timing is important to make the output neuron fire.

if the timing is not good, the composite EPSPs do not combine well in the output neuron that cannot reach the membrane potential threshold to fire.

The precision of the timing can be modulated by tuning the decay time of each EPSP. With a longer duration of the EPSP it is possible to be less exigent on the precision of the timing.

We have seen here that with a conduction line neural network and only realistic neurons it is possible to make a temporal decoder: the output neuron can fire only when a precise spatio-temporal spike pattern is in input.

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.

Perception : spatio-temporal spikes patterns

http://neuroxidence.com/

All our perceptions from the world are coded in our brain by spatio-temporal patterns of spikes : In a mathematical word there are binary matrices. Those data look like the raster plot figure on the left.

When we recognize an object the brain recognize in fact a specific spatio-temporal spikes pattern (STSP) or a sequence of STSPs or a set of STSPs.

If the brain is not able to recognize any memorized STSP, our actions manipulate the object in all directions in order to enter a specific configuration of stimuli which in turn create a specific STSP that can be recognized.

The TempUnit model showed in this website will demonstrate that it can:

  • detect (recognize) a specific STSP
  • detect a noisy STSP
  • detect an incomplete STSP

What Artificial Intelligence would look like when it is only about manipulation of STSPs ?

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:

  1. What computations does each neuron perform within its neuronal network?
  2. 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.