Putting the theory into 'burstlet theory' with a biophysical model of burstlets and bursts in the respiratory preBötzinger complex

Inspiratory breathing rhythms arise from synchronized neuronal activity in a bilaterally distributed brainstem structure known as the preBötzinger complex (preBötC). In in vitro slice preparations containing the preBötC, extracellular potassium must be elevated above physiological levels (to 7 - 9mM) to observe regular rhythmic respiratory motor output in the hypoglossal nerve to which the preBötC projects. Reexamination of how extracellular K⁺ affects preBötC neuronal activity has revealed that low amplitude oscillations persist at physiological levels. These oscillatory events are sub-threshold from the standpoint of transmission to motor output and are dubbed burstlets. Burstlets arise from synchronized neural activity in a rhythmogenic neuronal subpopulation within the preBötC that in some instances may fail to recruit the larger network events, or bursts, required to generate motor output. The fraction of subthreshold preBötC oscillatory events (burstlet fraction) decreases sigmoidally with increasing extracellular potassium. These observations underlie the burstlet theory of respiratory rhythm generation. Experimental and computational studies have suggested that recruitment of the non-rhythmogenic component of the preBötC population requires intracellular Ca²⁺ dynamics and activation of a calcium-activated non-selective cationic current. In this computational study, we show how intracellular calcium dynamics driven by synaptically triggered Ca²⁺ influx as well as Ca²⁺ release/uptake by the endoplasmic reticulum in conjunction with a calcium-activated non-selective cationic current can reproduce and offer an explanation for many of the key properties associated with the burstlet theory of respiratory rhythm generation. Altogether, our modeling work provides a mechanistic basis that can unify a wide range of experimental findings on rhythm generation and motor output recruitment in the preBötC.