Rapid switching of in-phase and anti-phase interhemispheric rhythms within a single theta cycle: a mechanistic explanation

The granular retrosplenial cortex (RSG) supports memory consolidation and spatial navigation. In vivo recordings of local field potential (LFP) from RSG reveal coexisting gamma (30-80 Hz) and spline (100-160 Hz) oscillations, coupled to distinct phases of the background theta ([~]8 Hz) rhythm. Remarkably, bilateral recordings reveal that gamma and splines exhibit divergent interhemispheric phase relationships: gamma is in-phase across hemispheres, while splines are anti-phase. Here, using numerical bifurcation analysis of next-generation neural mass models, we show that RSG oscillations within a single hemisphere can be understood as alternation of PING (pyramidal-interneuron gamma) and ING (interneuron gamma) mechanisms in an excitatory-inhibitory network. Theta-frequency external drive to the inhibitory population switches the network between these two rhythms. Next, we build canonical interhemispheric circuits, composed of two such excitatory-inhibitory modules, delay-coupled across hemispheres. These circuits switch between in-phase gamma and anti-phase splines within a single theta cycle, reproducing the cross-spectral statistics of experimental RSG recordings. Finally, we present analytical results for threshold-linear neural mass models, showing cross-hemispheric phase patterning is governed by the ratio of cross-hemispheric delay to local inhibitory delay; we obtain explicit ranges of this ratio for which RSG-like patterning could be expected. Our work establishes that the unique oscillatory profile of RSG can be explained parsimoniously by minimal interhemispheric circuit configurations and provides a framework for experimental interrogation of interhemispheric rhythms.