Numerical Simulation Analysis of a Mathematical Model of Circadian Pacemaker Neurons
Author(s)
Takaaki Shirahata
ABSTRACT
Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of nonlinear ordinary differential equations. An important feature of the SCN neurons observed in electrophysiological recording is spontaneous repetitive spiking, which is reproduced using this model. In the present study, numerical simulation analysis of this model was performed to evaluate variations in two system parameters of this model: the maximal conductance of calcium current (gCa) and the maximal conductance of sodium current (gNa). Simulation results revealed the spontaneous repetitive spiking states of the model in the (gCa, gNa)-pa-rameter space.
Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of nonlinear ordinary differential equations. An important feature of the SCN neurons observed in electrophysiological recording is spontaneous repetitive spiking, which is reproduced using this model. In the present study, numerical simulation analysis of this model was performed to evaluate variations in two system parameters of this model: the maximal conductance of calcium current (gCa) and the maximal conductance of sodium current (gNa). Simulation results revealed the spontaneous repetitive spiking states of the model in the (gCa, gNa)-pa-rameter space.
Cite this paper
Shirahata, T. (2015) Numerical Simulation Analysis of a Mathematical Model of Circadian Pacemaker Neurons. Applied Mathematics, 6, 1214-1219. doi: 10.4236/am.2015.68113.
Shirahata, T. (2015) Numerical Simulation Analysis of a Mathematical Model of Circadian Pacemaker Neurons. Applied Mathematics, 6, 1214-1219. doi: 10.4236/am.2015.68113.
References
[1] Ermentrout, G.B. and Terman, D. (2010) Mathematical Foundations of Neuroscience (Interdisciplinary Applied Mathematics). Springer, New York.
http://dx.doi.org/10.1007/978-0-387-87708-2 [2] Sim, C.K. and Forger, D.B. (2007) Modeling the Electrophysiology of Suprachiasmatic Nucleus Neurons. Journal of Biological Rhythms, 22, 445-453.
http://dx.doi.org/10.1177/0748730407306041 [3] Ashrafuzzaman, M. and Tuszynski, J. (2012) Membrane Biophysics (Biological and Medical Physics, Biomedical Engineering). Springer, New York. [4] Drion, G., Massotte, L., Sepulchre, R. and Seutin, V. (2011) How Modeling Can Reconcile Apparently Discrepant Experimental Results: The Case of Pacemaking in Dopaminergic Neurons. PLoS Computational Biology, 7, e1002050.
http://dx.doi.org/10.1371/journal.pcbi.1002050 [5] Shirahata, T. (2011) The Effect of Variations in Sodium Conductances on Pacemaking in a Dopaminergic Retinal Neuron Model. Acta Biologica Hungarica, 62, 211-214.
http://dx.doi.org/10.1556/ABiol.62.2011.2.11 [6] Shirahata, T. (2014) Effect of Sodium Conductance Variations on Electrical Behavior of a Neocortical Neuron Model. Acta Biologica Hungarica, 65, 379-384.
http://dx.doi.org/10.1556/ABiol.65.2014.4.2 [7] Shirahata, T. (2015) Numerical Study of a Mathematical Model of Vibrissa Motoneurons: The Relationship between Repetitive Spiking and Two Types of Sodium Conductance. International Journal of Theoretical and Mathematical Physics, 5, 48-52.
[1] Ermentrout, G.B. and Terman, D. (2010) Mathematical Foundations of Neuroscience (Interdisciplinary Applied Mathematics). Springer, New York.
http://dx.doi.org/10.1007/978-0-387-87708-2 [2] Sim, C.K. and Forger, D.B. (2007) Modeling the Electrophysiology of Suprachiasmatic Nucleus Neurons. Journal of Biological Rhythms, 22, 445-453.
http://dx.doi.org/10.1177/0748730407306041 [3] Ashrafuzzaman, M. and Tuszynski, J. (2012) Membrane Biophysics (Biological and Medical Physics, Biomedical Engineering). Springer, New York. [4] Drion, G., Massotte, L., Sepulchre, R. and Seutin, V. (2011) How Modeling Can Reconcile Apparently Discrepant Experimental Results: The Case of Pacemaking in Dopaminergic Neurons. PLoS Computational Biology, 7, e1002050.
http://dx.doi.org/10.1371/journal.pcbi.1002050 [5] Shirahata, T. (2011) The Effect of Variations in Sodium Conductances on Pacemaking in a Dopaminergic Retinal Neuron Model. Acta Biologica Hungarica, 62, 211-214.
http://dx.doi.org/10.1556/ABiol.62.2011.2.11 [6] Shirahata, T. (2014) Effect of Sodium Conductance Variations on Electrical Behavior of a Neocortical Neuron Model. Acta Biologica Hungarica, 65, 379-384.
http://dx.doi.org/10.1556/ABiol.65.2014.4.2 [7] Shirahata, T. (2015) Numerical Study of a Mathematical Model of Vibrissa Motoneurons: The Relationship between Repetitive Spiking and Two Types of Sodium Conductance. International Journal of Theoretical and Mathematical Physics, 5, 48-52.