  A Balance Equation Determines a Switch in Neuronal ExcitabilityFranci, Alessio  ; Drion, Guillaume ; Seutin, Vincent et alin PLoS Computational Biology (in press) We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a ... [more ▼] We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six di erent published conductance based models always nds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological rel- evance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons. [less ▲] Detailed reference viewed: 18 (0 ULg)A novel phase portrait for neuronal excitabilityDrion, Guillaume ; Franci, Alessio ; Seutin, Vincent et alin PLoS ONE (2012), 7(8), Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power ... [more ▼] Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained a core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of FitzHugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability. The revisited model considerably enlarges the modeling power of the original one. In particular, it captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexification of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which calcium channels control the two distinct firing modes of thalamocortical neurons. [less ▲] Detailed reference viewed: 42 (9 ULg)An Organizing Center in a Planar Model of Neuronal Excitability Read More: http://epubs.siam.org/doi/abs/10.1137/120875016?journalCode=sjadayFranci, Alessio ; Drion, Guillaume ; Sepulchre, Rodolphe in SIAM Journal on Applied Dynamical Systems (2012), 11(4), 1698-1722 The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative ... [more ▼] The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables. [less ▲] Detailed reference viewed: 2 (0 ULg)How modeling can reconcile apparently discrepant experimental results: the case of pacemaking in dopaminergic neurons.Drion, Guillaume ; Massotte, Laurent ; Sepulchre, Rodolphe et alin PLoS Computational Biology (2011), 7(5), 1002050 Detailed reference viewed: 110 (35 ULg) M-type channels selectively control bursting in rat dopaminergic neuronsDrion, Guillaume ; ; Waroux, Olivier et alin European Journal of Neuroscience (2010), 31 Detailed reference viewed: 99 (47 ULg) |
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