Leader neurons in leaky integrate and fire neural network simulations

Several experimental studies show the existence of leader neurons in population bursts of 2D living neural networks. A leader neuron is, basically, a neuron which fires at the beginning of a burst (respectively network spike) more often that we expect by looking at its whole mean neural activity. This means that leader neurons have some burst triggering power beyond a simple statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model. Our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themself. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends a signal to many excitatory neurons as well as to a few inhibitory neurons and a leader neuron receives only a few signals from other excitatory neurons. Our linear analysis exhibits five essential properties for leader neurons with relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron can be a good leader neuron and which cannot. Our prediction formula gives us a good statistical prediction even if, considering a single given neuron, the success rate does not reach hundred percent.Comment: 25 pages, 13 figures, 2 table

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465-8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311-345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063-1070, 2004; Gerstner and Naud, Science 326:379-380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neuron

Leaders of neuronal cultures in a quorum percolation model

We present a theoretical framework using quorum-percolation for describing the initiation of activity in a neural culture. The cultures are modeled as random graphs, whose nodes are excitatory neurons with kin inputs and kout outputs, and whose input degrees kin = k obey given distribution functions pk. We examine the firing activity of the population of neurons according to their input degree (k) classes and calculate for each class its firing probability \Phi_k(t) as a function of t. The probability of a node to fire is found to be determined by its in-degree k, and the first-to-fire neurons are those that have a high k. A small minority of high-k classes may be called "Leaders", as they form an inter-connected subnetwork that consistently fires much before the rest of the culture. Once initiated, the activity spreads from the Leaders to the less connected majority of the culture. We then use the distribution of in-degree of the Leaders to study the growth rate of the number of neurons active in a burst, which was experimentally measured to be initially exponential. We find that this kind of growth rate is best described by a population that has an in-degree distribution that is a Gaussian centered around k = 75 with width {\sigma} = 31 for the majority of the neurons, but also has a power law tail with exponent -2 for ten percent of the population. Neurons in the tail may have as many as k = 4, 700 inputs. We explore and discuss the correspondence between the degree distribution and a dynamic neuronal threshold, showing that from the functional point of view, structure and elementary dynamics are interchangeable. We discuss possible geometric origins of this distribution, and comment on the importance of size, or of having a large number of neurons, in the culture.Comment: Keywords: Neuronal cultures, Graph theory, Activation dynamics, Percolation, Statistical mechanics of networks, Leaders of activity, Quorum. http://www.weizmann.ac.il/complex/tlusty/papers/FrontCompNeuro2010.pd

Flux de chaleur dans des systèmes stochastiques hors équilibre

Dans ce document, nous nous sommes intéressés à un modèle de conduction de chaleur. Celui-ci est constitué de cellules, supposées ergodiques, qui stockent de l'énergie par la rotation mécanique d'un disque. L'énergie parcourt le système à l'aide de particules qui n'interagissent pas entre elles, mais qui peuvent interagir avec le disque contenu dans chaque cellule. Notre modèle est purement stochastique, toutefois, il peut être vu comme une modélisation simplifiée d'un modèle hamiltonien dans lequel les règles de collisions élastiques entre les disques et les particules sont bien définies. Ce modèle contient peu d'hypothèses mais est intéressant puisqu'il permet de retrouver des lois comme la loi de Fourier. Dans notre travail, conformément à ce que prédisent les lois de la thermodynamique, nous montrons que la chaleur circule naturellement du chaud vers le froid. Nous mettons aussi en évidence le fait que pour construire une pompe à chaleur, il faut apporter un travail mécanique. Ce travail peut être produit à l'aide d'un surplus de pression de la source froide par rapport à la source chaude. Mais, nous montrons aussi que ce travail peut être produit par deux sources de chaleur indépendantes

Leader neurons in living neural networks and in leaky integrate and fire neuron models

This thesis is devoted to complex systems, more particularly to neural networks. Disassociated in vitro rat brain neuron cultures show, under a variety of experimental contexts, a spontaneous electrical activity. This activity manifests itself by a rapid succession of ignitions of a large fraction of neurons named collective bursts. The study of the initiators of these bursts is one of the conceptual problems underlying the spontaneous electrical activity. A study of Eytan and Marom showed that some "first to fire" cells exist. In this thesis, we study these particular neurons, through a detailed analysis of data obtained by the multi-electrode array methods and simulations. We have established that some cells are triggering bursts beyond a simple statistical effect of being the first. These particular cells are called leaders. The analysis of experimental data indicates that the long term dynamics of the leaders is relatively robust and that these leaders are not only the main initiators of bursts, but, the burst itself carries traces indicating which of the leaders has initiated the burst. The study of simulations using the leaky integrate and fire neuron model permitted us to find out that leaders form naturally from a balanced combination of inputs, outputs, their local neighborhood and their own properties. Basically, a leader is an excitatory neuron, has a low membrane potential firing threshold, sends a signal to a lot of excitatory neurons as well as to a few inhibitory neurons and a leader receives only a few signals from other excitatory neurons

Leader neurons in population bursts of 2D living neural networks

Eytan and Marom recently showed that the spontaneous burst activity of rat neuron cultures includes `first to fire' cells that consistently fire earlier than others. Here we analyze the behavior of these neurons in long term recordings of spontaneous activity of rat hippocampal and rat cortical neuron cultures from three different laboratories. We identify precursor events that may either subside (`aborted bursts') or can lead to a full-blown burst (`pre-bursts'). We find that the activation in the pre-burst typically has a first neuron (`leader'), followed by a localized response in its neighborhood. Locality is diminished in the bursts themselves. The long term dynamics of the leaders is relatively robust, evolving with a half-life of 23-34 hours. We show that the leaders carry information about the identity of the burst, as measured by the signature of the number of spikes per neuron in a burst. The number of spikes from leaders in the first few spikes of a precursor event is furthermore shown to be predictive with regard to the transition into a burst (pre-burst versus aborted burst). We conclude that the leaders play a role in the development of the bursts