Date : 21/06/2011

Internship proposal for : Master 1 or Master 2

Laboratory
Matières et systèmes Complexes
UMR 7056 Paris Diderot
Université Denis Diderot Paris 7
10 rue Alice Domon et Léonie Duquet
Case courrier 7056 - pièce 813A Bâtiment Condorcet
75205 Paris Cedex 13
Website : www.msc.univ-paris-diderot.fr
Main discipline : Physics
Lab director : Loic Auvray

Mentor
Samuel Bottani
email : Cet e-mail est protégé contre les robots collecteurs de mails, votre navigateur doit accepter le Javascript pour le voir
phone : +33 6 60 52 94 87

Subjects
1.: Computational biology
2.: Neurobiology
3.: Networks

Tools and methodologies
1.: Programming
2.: Simulation
3.: Maths

Summary of lab's interests

Characterization, modeling and simulation of biological regulation networks (signal transduction, gene-expression, metabolism). Transcription factor functions, gene expression dynamics and gene dosage effects (polyploidy). Systems and Synthetic Biology. Quantitative Biology. Networks related science.

Summary of project

Investigation of a quorum percolation model for neural networks This internship proposes to explore a theoretical model recently proposed to explain the architecture of large two dimensional neural networks (Quorum percolation in living neural networks, O. Cohen et al. EPL, 89 , 18008, 2010). Neurons form complicate webs of connections, where dentrites and axons ramify and are interlinked through synapses with their neighbors. The natural architecture of these networks, eg in the brain, display astonishing robust features, tolerating damage and removal of many neurons and synapses preserving the global behavior. An approach to characterize the complexity of these wiring diagram and explain their structural properties uses physical analogies with percolation problems. Numerical simulations enable to study the network dynamics and it's dependence with the connectivity structure. As accurate large scale charts of real neuronal network are not available, connection between macroscopic observables measurements and counterparts on simulation results allow to infer conclusions on the network properties. Questions that can be addressed by percolation models include for instance, the neurons size and branching properties that enable the interconnection of the whole network (percolation), the connectivity (number of links) and cells that can be removed without altering the behavior. In the simplest view, an active neuron emits spikes towards connected neighbors. Receiver neurons integrate input signals and fire once a signal threshold is reached, cascading a signal to the other neurons. The quorum percolation model requires that a given quorum "m" of input nodes is necessary to determine the firing of a target neuron. Using "m" as the control parameter one can investigate with given network connectivities, the transition to a giant component of connected neurons that fire together and span a significant fraction of the network. Similar mechanisms may be at play in other systems such as propagation of epidemics, or creation of public opinions, where people may need to hear the opinions of many views before making up their mind. In the framework of a prospective collaboration with the authors of the cited paper, the purpose of this internship is first to get familiar with neuronal network percolation models and reproduce the simulation results of the cited paper above before introducing new ingredients, such as different assumptions on the networks structures.