Propagation of bursts through noisy heterogeneous synfire chains: A theoretical study with application to the songbird nucleus HVC

Recent experiments on the songbird nucleus HVC (high vocal center) show the presence of sparse brief high-frequency bursts that are believed to play an important role in sequential timing of syllables. To explain the generation of the bursts, we first study a feed-forward chain-like network containing a single neuron on each node based on a single-compartment Hodgkin-Huxley neuronal model with five conductances. We find that bursts similar to those observed experimentally as well as single spikes can propagate stably on the chain with carefully chosen parameters. We next study the propagation of bursts through a synfire chain consisting of feed-forward pools of multiple neurons with noise currents and network heterogeneity. The noise current is an Ornstein-Uhlenbeck (OU) process with mean zero and standard deviation sigma from 0 to 50 pA and the heterogeneity is established by random connections between successive pools with a fixed connecting probability c from 0.2 to 0.9. We show that bursts---not individual spikes---can propagate robustly for moderate amounts of noise (≥ 30 pA) and heterogeneity (c ≤ 0.9). We analyze the spike firing probability of an integrate-and-fire neuron based on the pool size, the noise and the heterogeneity, and show that the simulations agree with the analyses in that the stable synfire propagation needs strong synchronous signals to resist the perturbations from noise and heterogeneity. As a consequence of strong synchronous signals, bursting propagation can only be carried by large-pool chains. In conclusion, our simulations support the hypothesis of bursting synfire chains in the songbird nucleus HVC.