Kinetic properties of persistent Na⁺ current orchestrate oscillatory bursting in respiratory neurons

The rhythmic pattern of breathing depends on the pre-Bötzinger complex (preBötC) in the brainstem, a vital circuit that contains a population of neurons with intrinsic oscillatory bursting behavior. Here, we investigate the specific kinetic properties that enable voltage-gated sodium channels to establish oscillatory bursting in preBötC inspiratory neurons, which exhibit an unusually large persistent Na⁺ current (I_NaP). We first characterize the kinetics of I_NaP in neonatal rat brainstem slices in vitro, using whole-cell patch-clamp and computational modeling, and then test the contribution of I_NaP to rhythmic bursting in live neurons, using the dynamic clamp technique. We provide evidence that subthreshold activation, persistence at suprathreshold potentials, slow inactivation, and slow recovery from inactivation are kinetic features of I_NaP that regulate all aspects of intrinsic rhythmic bursting in preBötC neurons. The slow and cumulative inactivation of I_NaP during the burst active phase controls burst duration and termination, while the slow recovery from inactivation controls the duration of the interburst interval. To demonstrate this mechanism, we develop a Markov state model of I_NaP that explains a comprehensive set of voltage clamp data. By adding or subtracting a computer-generated I_NaP from a live neuron via dynamic clamp, we are able to convert nonbursters into intrinsic bursters, and vice versa. As a control, we test a model with inactivation features removed. Adding noninactivating I_NaP into nonbursters results in a pattern of random transitions between sustained firing and quiescence. The relative amplitude of I_NaP is the key factor that separates intrinsic bursters from nonbursters and can change the fraction of intrinsic bursters in the preBötC. I_NaP could thus be an important target for regulating network rhythmogenic properties.