Brain rhythms have been proposed to facilitate brain function, with an especially important role attributed to the phase of low-frequency rhythms. Understanding the role of phase in neural function requires interventions that perturb neural activity at a target phase, necessitating estimation of phase in real-time. Current methods for real-time phase estimation rely on bandpass filtering, which assumes narrowband signals and couples the signal and noise in the phase estimate, adding noise to the phase and impairing detections of relationships between phase and behavior. To address this, we propose a state space phase estimator for real-time tracking of phase. By tracking the analytic signal as a latent state, this framework avoids the requirement of bandpass filtering, separately models the signal and the noise, accounts for rhythmic confounds, and provides credible intervals for the phase estimate. We demonstrate in simulations that the state space phase estimator outperforms current state-of-the-art real-time methods in the contexts of common confounds such as broadband rhythms, phase resets, and co-occurring rhythms. Finally, we show applications of this approach to in vivo data. The method is available as a ready-to-use plug-in for the Open Ephys acquisition system, making it widely available for use in experiments.

Olfactory receptor repertoires exhibit remarkable functional diversity, but how these proteins have evolved is poorly understood. Through analysis of extant and ancestrally-reconstructed drosophilid olfactory receptors from the Ionotropic receptor (Ir) family, we investigated evolution of two organic acid-sensing receptors, Ir75a and Ir75b. Despite their low amino acid identity, we identify a common 'hotspot' in their ligand-binding pocket that has a major effect on changing the specificity of both Irs, as well as at least two distinct functional transitions in Ir75a during evolution. Moreover, we show that odor specificity is refined by changes in additional, receptor-specific sites, including those outside the ligand-binding pocket. Our work reveals how a core, common determinant of ligand-tuning acts within epistatic and allosteric networks of substitutions to lead to functional evolution of olfactory receptors.