A bifurcation analysis of neuronal subthreshold oscillations.
The conditions under which a noninactivating sodium current and either a potassium current or an inwardly rectifying cation current can generate subthreshold oscillations were analyzed using nonlinear dynamical techniques applied to a neuronal model consisting of two differential equations. Mathematical descriptions of the membrane currents were derived using voltage-clamp data collected from entorhinal cortical neurons. A bifurcation analysis was performed using applied current as the control parameter to map the range of magnitudes of the sodium, potassium/cation, and leakage conductances over which subthreshold oscillations exist. The threshold of the potassium/cation current was an important determinant of the robustness of oscillatory behavior. The activation time constant of the potassium/cation current largely determined the frequency range of emergent oscillations. This result implicates the slow inward rectifier or an as yet undescribed slow outward current in entorhinal cortical oscillations; the latter explanation, while more speculative, is more consistent with the pharmacological properties of subthreshold oscillations and gives oscillations over a larger current range. The shallowness of the sodium activation curve confined emergent oscillations to rise gradually rather than abruptly and extended the current range over which the model oscillated.
White
J A
JA
Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215, USA.
Budde
T
T
Kay
A R
AR
D000818:Animals; D001921:Brain / Q000502:physiology*; D066298:In Vitro Techniques; D008297:Male; D008433:Mathematics; D008564:Membrane Potentials; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D009991:Oscillometry; D015221:Potassium Channels / Q000502:physiology; D051381:Rats; D015222:Sodium Channels / Q000502:physiology; D013997:Time Factors
D015221:Potassium Channels; D015222:Sodium Channels