Models of respiratory rhythm generation in the pre-Botzinger complex. II. Populations of coupled pacemaker neurons

We have proposed models for the ionic basis of oscillatory bursting of resp iratory pacemaker neurons in the pre-Botzinger complex. In this paper, we i nvestigate the frequency control and synchronization of these model neurons when coupled by excitatory amino-acid-mediated synapses and controlled by convergent synaptic inputs modeled as tonic excitation. Simulations of pair s of identical cells reveal that increasing tonic excitation increases the frequency of synchronous bursting while increasing thp strength of excitato ry coupling between the neurons decreases the frequency of synchronous burs ting Low levels of coupling extend the range of values of tonic excitation where synchronous bursting is found. Simulations of a heterogeneous populat ion of 50-500 bursting neurons reveal coupling effects similar tn those fou nd experimentally in vitro: coupling increases the mean burst duration and decreases the mean burst frequency. Burst synchronization occurred over a w ide range of intrinsic frequencies (0.1-1 Hz) and even in populations where as few as 10% of the cells were intrinsically bursting. Weak coupling, ext reme parameter heterogeneity, and low levels of depolarizing input could co ntribute to the desynchronization of the population and give rise to quasip eriodic states. The introduction of sparse coupling did not affect the burs t synchrony, although it did make the interburst intervals more irregular f rom cycle to cycle. At a population level, both parameter heterogeneity, an d excitatory coupling synergistically combine to increase the dynamic input range: robust synchronous bursting persisted across a much greater range o f parameter space (in terms of mean depolarizing input) than that of a sing le model cell. This extended dynamic range for rhp bursting cell population indicates that cellular heterogeneity is functionally advantageous. Our mo deled system accounts for the range of intrinsic frequencies and spiking pa tterns of inspiratory (I) bursting cells found in the pre-Botzinger complex in neonatal rat brain stem slices in vitro. There is a temporal dispersion in the spiking onset times of neurons in the population, predicted to be d ue to heterogeneity in intrinsic neuronal properties, with neurons starting to spike before (pre-I), with (I), or after (late-I) the onset of the popu lation burst. Experimental tests for a number of the model's predictions ar e proposed.