A flexible cross-correlation based population model of interaural time difference coding in barn owl's midbrain

The cross-correlation model has long served as the standard computational framework for describing interaural time difference (ITD) processing in the barn owls auditory system. While successful in explaining initial sinusoidal responses at the site of coincidence detection in the nucleus laminaris, this previous standard model fails to capture the full diversity of ITD tuning observed in the inferior colliculus (IC), where neurons exhibit sharper-than-sinusoidal ITD tuning, nonlinear frequency integration, level-dependent gain control, and interaural level difference (ILD)-dependent modulation of ITD selectivity. Here we present a modified cross-correlation model that addresses these limitations through the addition of parameterized gain control, linear filters with inhibitory surround structure, static nonlinearities, and ILD-dependent modulation of the cross-correlation computation. We show that divisive gain control produces realistic rate-level functions, including non-monotonic responses. Furthermore, inhibitory weights in the linear filter, combined with a threshold or expansive nonlinearity, generate sharper-than-sinusoidal ITD tuning consistent with experimental observations. This model reproduces both linear and nonlinear two-tone frequency integration and demonstrates that independent variation of filter bandwidth and nonlinearity shape accounts for the experimentally observed lack of correlation between side-peak suppression and frequency tuning width across the neuronal population. In addition, ILD-dependent modifications to the model produce shifts in best ITD and reductions in ITD tuning strength, as observed in the lateral shell of the central nucleus of the IC. The model parameters can be efficiently determined using simulation-based inference, enabling generation of realistic neuronal populations. Thus, this flexible, analytically tractable framework provides a foundation for investigating population coding of auditory space in the owls midbrain.