Modeling of sustained spontaneous network oscillations of a sexually dimorphic brainstem nucleus: the role of potassium equilibrium potential.

Intrinsic oscillators in the central nervous system play a preeminent role in the neural control of rhythmic behaviors, yet little is known about how the ionic milieu regulates their output patterns. A powerful system to address this question is the pacemaker nucleus of the weakly electric fish Apteronotus leptorhynchus. A neural network comprised of an average of 87 pacemaker cells and 20 relay cells produces tonic oscillations, with higher frequencies in males compared to females. Previous empirical studies have suggested that this sexual dimorphism develops and is maintained through modulation of buffering of extracellular K⁺ by a massive meshwork of astrocytes enveloping the pacemaker and relay cells. Here, we constructed a model of this neural network that can generate sustained spontaneous oscillations. Sensitivity analysis revealed the potassium equilibrium potential, E_K (as a proxy of extracellular K⁺ concentration), and corresponding somatic channel conductances as critical determinants of oscillation frequency and amplitude. In models of both the pacemaker nucleus network and isolated pacemaker and relay cells, the frequency increased almost linearly with E_K, whereas the amplitude decreased nonlinearly with increasing E_K. Our simulations predict that this frequency increase is largely caused by a shift in the minimum K⁺ conductance over one oscillation period. This minimum is close to zero at more negative E_K, converging to the corresponding maximum at less negative E_K. This brings the resting membrane potential closer to the threshold potential at which voltage-gated Na⁺ channels become active, increasing the excitability, and thus the frequency, of pacemaker and relay cells.