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Synchronization in neural network

The research project is under the co-supervision of
Nicolas GARNIER                                    LIU Zonghua
(Physics, ENS de Lyon)                          (Physics, ECNU)          

The synchronization of clocks to a unique time has allowed humans in modern societies to be more efficient in their common or cooperative tasks, e.g., by orchestrating activities from different groups and different places. Such cooperative organization is ubiquitous in biological systems : periodic oscillations are observed in their behaviors and functions. In that case the synchronized behavior presents a well identified frequency which is the useful frequency of the biological function, e.g., heart beating, circadian rhythms. Sometimes, synchronization is less obvious, as no period can be measured in the function under study : short-term memory is based on synchronized brain oscillations whereas Parkinson disease has been associated with abnormally synchronized oscillatory activity of the basal gangliacortical loop.

Understanding synchronization phenomena is an active domain in several fields of research, including Physics and Complex Systems. In this context, systems are often organized in terms of networks and the question we are addressing here is how network structure influences the tendency for a network to synchronize (its synchronizability). We are especially interested in neural networks, a network being here an ensemble of coupled cells (the neurons). The network structure can be characterized by several parameters: cells composing the network can be of distinct species, and therefore described by different dynamical equations. It is the case in a vast class of networks and especially in a recent model of the uterus that we have proposed, as well in models of the suprachiasmatic network. The ratio of cells from each specie, as well as the spatial distribution of cells of each specie in an heterogeneous network are relevant parameters to get insight into its functioning. The coupling strength is another important parameter in heterogeneous networks.

- the structure of the network can still be modified by the topology of connections between cells : the coupling between cells is either local or global, and can be located between adjacent or remote cells.

- the behavior of the network is also affected by the presence of intrinsic or extrinsic noise, which can then lead to stochastic synchronization.

While a precise description is obviously important, our experience has been that simple models amenable to the level of analysis and description obtained in statistical mechanics and nonlinear physics, can lead to very important insight. Our research is carried out in this spirit.

The system we study is the the suprachiasmatic nucleus (SCN), which is the primary circadian clock in mammals. It is composed of a large network of 2 × 104 coupled neurons, located in the hypothalamus and receiving information about illumination through the eyes. In the absence of exogeneous periodic forcing (zeitgeber) like the alternance of nights and days, circadian arrhythmicity is observed. Not only the endogeneous periods can then deviate from 24h and scatter in a wide range for different species, but also the SCN neurons may split into two subgroups oscillating with the same endogeneous frequency but in antiphase (phase splitting phenomenon).

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