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Biophysical Journal 69: 1203-1217 (1995)
© 1995 the Biophysical Society

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A bifurcation analysis of neuronal subthreshold oscillations.

J A White, T Budde and A R Kay

Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215, USA.

ABSTRACT

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.




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