A neural field model with dual glutamatergic-GABAergic action neurons
Abstract
In this work, we consider a neural field model that describes the mean synaptic activity of a population of excitatory and inhibitory hippocampal granule cells. In comparison to traditional formulations we consider the clinical evidence observed in this cerebral structure in which neurons manifest themselves in a dual glutamatergic-GABAergic action. That is, excitatory neurons transform their influence into inhibitory neurons. In this work we study the existence conditions for spatiotemporal patterns of activity in the form of stationary bumps, fronts and traveling waves for a neural field model. The comprehension of the biological
mechanisms behind spatio-temporal patterns of brain activity provides an eort towards the understanding of the complex synaptic interaction present in cerebral activity.
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Bressloff PC, Cowan JD, Golubitsky M, Thomas PJ and Wiener M, Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex Phil.Trans.R.Soc. B 356, 299-330, doi: 10.1098/rstb.2000.0769 (2001)
Bressloff, PC, Spatiotemporal dynamics of continuum neural fields J Phys A Math Theor 45, doi: 10.1088/1751-8113/45/3/033001 (2012)
Butler, TC and Benayoun, M and Wallace, W and van Drongelen, W and Goldenfeld, and Cowan, J. Evolutionary constraints on visual cortex architecture from the dynamics of hallucinations. PNAS 109, 2,606-609, https://doi.org/10.1073/pnas.1118672109 (2012)
Desfeux A, El Ghazi F, Jegou S, Legros H, Marret S, Laudenbach V, Gonzalez BJ, Dual Effect of Glutamate on GABAergic Interneuron Survival during Cerebral Cortex Development in Mice Neonates Cerebral Cortex 20, 1092-
, doi: 10.1093/cercor/bhp181 (2010)
Ermentrout, B, Neural networks as spatio-temporal pattern-forming systems Rep Prog Phys 61, 353-430 (1998)
Ermentrout, GB and Cowan, J, A mathematical theory of visual hallucination patterns Biol Cybern 34, 137-150 (1979)
Ermentrout, GB and Cowan, J, The role of multiple-scale modelling of epilepsy in seizure forecasting J Clin Neurophysiol 32, 220-226, doi:10.1097/WNP.0000000000000149 (2016)
Foster, BL and Boja, I and Liley, DTJ, Understanding the Effects of Anesthetic Agents on the EEG through Neural Field Theory Conf Proc IEEE Eng Med Biol Soc 652, 4709-12, doi: 10.1109/IEMBS.2011.6091166 (2011)
Gonz´alez-Ram´ırez, LR and Ahmed, OJ and Cash, SS and Wayne, CE and Kramer, MA, A biologically constrained, mathematical model of cortical wave propagation preceding seizure termination PLoS Comput Biol 11, doi:
1371/journal.pcbi.1004065 (2015)
Guti´errez R, MA, The dual glutamatergic-GABAergic phenotype of hippocampal granule cells Trends Neurosci 28, 297-303 (2005)
Liley, DTJ and Cadusch, PJ and Dafilis, MP, A spatially continuous mean field theory of electrocortical activity Network 13,67-113,https://doi.org/10.1080/net.13.1.67.113 (2002)
Ottem EN, Godwin JG, Krishnan S, Petersen SL, Dual-Phenotype GABA/Glutamate Neurons in Adult Preoptic Area: Sexual Dimorphism and Function J of Neurosci 37, 8097-8105, doi: 10.1523/JNEUROSCI.2267-
2004 (2004)
Proix, T and Jirsa, VK and Bartolomei, F and Guye, M and Truccolo, W, Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy Nat Commun 9, doi: 10.1038/s41467-018-02973-y
(2018)
Root DH, Zhang S, Barker DJ, Miranda-Barrientos J, Liu B, Wang HL, Morales M, Selective Brain Distribution and Distinctive Synaptic Architecture of Dual Glutamatergic-GABAergic Neuron Cell Rep 23, 3465-3479,
