Mathematical modelling of stability and dynamics of localized activity in biological cell networks
The project is finanzed by
The Research Council of Norway,
under the
BeMatA programme. The project started January 2004.
Cortex
The cortex in mammalian brains consists of billions of neurons interconnected
in a complex neural network. These neurons communicate predominantly via action
potentials, standarized pulse-like disturbances of the neuron membrane potential.
Neurons are generally grouped into two main categories:
- Excitatory - tend to increase the probability of action potentials firing in the neurons they project to.
- Inhibitory - tend to decrease the probability of action potentials firing in the neurons they project to.
The firing dynamics of cortical neurons is thus governed
by a competition between the exciting and inhibiting inputs from the other neurons.
Two neuron populations, marked red and blue, where each population connects to it self and the other population.
Experimental observations of persistent activity
Experimental observations have established persistent neuronal
activity in prefrontal cortex
as a neural process underlying short-term, working memory
(for a review, see Ref. X.-J. Wang,
Synaptic reverbation underlying mnemonic
persistent activity, Trends in Neuroscience 24 (2001), pp. 455-463).
In particular, localized persistent activity, or ''bumps'', in cortical
networks may serve as
memory storage. Numerous modelling studies have examined the existence
and stability of such
bumps, and both firing-rate and spiking-neuron models have been
considered.
Our study
The present project focuses on mathematical models for networks of coupled
excitatory and inhibitory neuron populations using a firing rate model
approach. In particular, we study the existence and stability of localized
activity levels as well as pattern formation.
Publications
- Ø. Nordbø, J. Wyller and G.T. Einevoll:
Neural network firing-rate models on integral form
- Effects of temporal coupling kernels on equilibrium-state stability,
Biological Cybernetics (2007).
[preprint, PDF, 393kB]
- J. Wyller, P. Blomquist, and G.T. Einevoll:
On the origin and properties of two-population neural field models
- a tutorial introduction
Biophysical Reviews & Letters 2, 79-98 (2007).
[preprint, pdf, 618KB]
- J. Wyller, P. Blomquist and G. T. Einevoll,
Turing instability and pattern formation in a two-population
neuronal network model, Physica D 225 pp. 75-93 (2007) [preprint,
PDF]
- P. Blomquist, J. Wyller and G.T. Einevoll,
Localized activity patterns in two-population neuronal networks,
Physica D 206 pp. 180-212 (2005)
[reprint, PDF]
Presentations
- P. Blomquist, U. G. Indahl, A. Devor, I. Ulbert, G. T. Einevoll and A. M.
Dale, Estimation of cortical microcircuit model from joint thalamic
singleunit and cortical laminar-electrode recordings in rat
whisker-barrel, Poster presentation Barrel XIX meeting, Atlanta, 12.-13.10
2006.
- P. Blomquist, U. G. Indahl, A. Devor, I. Ulbert, G. T. Einevoll and A. M.
Dale, Estimation of cortical microcircuit model from joint thalamic
singleunit and cortical laminar-electrode recordings in rat
whisker-barrel, Poster presentation Society for Neuroscience, Atlanta,
14.-18.10 2006.
- P. Blomquist, U. G. Indahl, A. Devor, I. Ulbert, G. T. Einevoll and A. M.
Dale, Estimation of cortical microcircuit model from joint thalamic
singleunit and cortical laminar-electrode recordings in rat
whisker-barrel, Poster presentation Conference on Mathematical
Neuroscience, Andorra, 1.-4.09.2006.
- P. Blomquist, J. Wyller and G.T. Einevoll,Pattern formation in
simplified cortical network models, Oral presentation
Biofysikk-møtet 2006, Kongsvold Fjeldstue, 15.-17.03.2006.
- P. Blomquist, J. Wyller and G.T. Einevoll,Pattern formation in simplified cortical network models, Oral presentation 3rd. Nordic Workshop on Neuroinformatics, Stockholm, 9.-11.09 2005.
- P. Blomquist, J. Wyller and G.T. Einevoll,Pattern Formation in a Two-Population Cortical Neural Network Model, Poster presentation ICMS Mathematical Neuroscience Meeting, Edinburgh, 21.-23.3 2005.
- P. Blomquist, J. Wyller and G.T. Einevoll, Neuronal Activity in Synaptically Coupled Network of Excitatory and Inhibitory neurons, Poster presentation SIAM Nonlinear Waves and Coherent Structures, Orlando, 2.-5.10. 2004.
- P. Blomquist, J. Wyller and G.T. Einevoll, Population Models for Neural Activity in Cortex, Poster presentation Biofysikermtet 2004, Kongsvold,17.-19.3. 2004.
- P. Blomquist, J. Wyller and G.T. Einevoll, Mathematical Models for Interacting Neuron Populations, Poster presentation Fysikermtet 2003, Sundvollen, 9.-12.8. 2003.
