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.
Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215, USA.
J A
JA
White
T
T
Budde
A R
AR
Kay
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