Modeling [Ca²⁺]_o- and [K⁺]_o-dependent oscillations in spinal Hb9 interneurons

The spinal interneurons in newborn rodents, when synaptically isolated by removing the extracellular calcium ([Ca²⁺]_o), demonstrate intrinsic rhythmic bursting activity that can be suppressed by riluzole, a blocker of the persistent sodium current (I_NaP) [2]. This finding led to the suggestion that lowering of [Ca²⁺]_o may enhance I_NaP by shifting its activation threshold toward more negative voltages, and raised the question of functional relevance of this finding to generation of locomotor rhythm. To assess this issue, a series of experiments was performed in vitro using the isolated spinal cord preparation from the neonatal rat with measurements of [Ca²⁺]_o and extracellular potassium concentration ([K⁺]_o) during pharmacologically induced fictive locomotion. We demonstrated that with the onset of fictive locomotion, [Ca²⁺]_o reduced from 1.2 up to 0.9 mM whereas [K⁺]_o increased from 4 up to 6 mM. At the same time, a special study performed on the isolated genetically identified Hb9 excitatory interneurons showed that, at [Ca²⁺]_o= 1 mM and [K⁺]_o=5 mM, 12% of Hb9 cells expressed intrinsic I_NaP-dependent bursting, and at the concentrations typical for fictive locomotion ([Ca²⁺]_o= 0.9 mM and [K⁺]_o=6 mM), as many as 50% of identified Hb9 interneurons expressed I_NaP-dependent bursting. Importantly, the threshold of [Ca²⁺]_o to generate bursting decreased as [K⁺]_o increased. The analysis of Hb9 neuron behavior during slow ramp increase of voltage revealed that lowering [Ca²⁺]_o from 1.2 to 0.9 mM induced a negative shift (~ -3 mV) in the I_NaP half-activation voltage (V_1/2NaP). In contrast, V_1/2NaP was not changed when [K⁺]_o increased from 4 to 6 mM.

To theoretically investigate the effect of changing [Ca²⁺]_o and [K⁺]_o on the Hb9’s pacemaker properties and firing behavior, we developed a single-compartment computational model of Hb9 neuron. In this model, we explicitly simulated a negative shift of V_1/2NaP occurring with the reduction of [Ca²⁺]_o.. At [K⁺]_o=6 mM, our model exhibited tonic activity at V_1/2NaP = –50 mV (Fig. 1A, left). The rhythmic bursting emerged at V_1/2NaP = –51 mV, and further shifting V_1/2NaP to the left produced stable bursting (Fig. 1A, right). In turn, an increase in [K⁺]_o reduced the potassium reversal potential and hence all voltage-gated potassium currents (I_K), which provided an additional augmentation of I_NaP-dependent bursting [1]. To study a synergistic effect of [Ca²⁺]_o and [K⁺]_o on the emergence of bursting activity, we modeled a population of 50 uncoupled neurons with randomly distributed parameters (see Fig. 1B). Our simulations have shown that shifting V_1/2NaP towards more negative values induced by reducing [Ca²⁺]_o may play a major role in emergence of bursting activity in the population of spinal interneurons. We have also demonstrated that accumulation of [K⁺]_o can facilitate the emergence of I_NaP-dependent bursting via the reduction of I_K.

In summary we suggest that co-regulation of I_NaP and I_K by the corresponding changes in [Ca²⁺]_o and [K⁺]_o may convert activity of spinal interneurons from asynchronous/tonic to the synchronized bursting. This activity-dependent switching in firing behavior may represent a fundamental mechanism for locomotor rhythm generation in the spinal cord.