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The preB\"otzinger Complex, the mammalian inspiratory rhythm generator,encodes inspiratory time as motor pattern. Spike synchronization throughoutthis sparsely connected network generates inspiratory bursts albeit withvariable latencies after preinspiratory activity onset in each breathing cycle.Using preB\"otC rhythmogenic microcircuit minimal models, we examined thevariability in probability and latency to burst, mimicking experiments. Amongvarious physiologically plausible graphs of 1000 point neurons withexperimentally determined neuronal and synaptic parameters, directedErd\H{o}s-R\'enyi graphs best captured the experimentally observed dynamics.Mechanistically, preB\"otC (de)synchronization and oscillatory dynamics areregulated by the efferent connectivity of spiking neurons that gates theamplification of modest preinspiratory activity through input convergence.Furthermore, to replicate experiments, a lognormal distribution of synapticweights was necessary to augment the efficacy of convergent coincident inputs.These mechanisms enable exceptionally robust yet flexible preB\"otC attractordynamics that, we postulate, represent universal temporal-processing anddecision-making computational motifs throughout the brain.

Microcircuit synchronization and heavy tailed synaptic weight distribution in preB\"otzinger Complex contribute to generation of breathing rhythm