Modeling Relays and Rhythms of the Granular Retrosplenial Cortex

Abstract

In this thesis, we study mathematical models of two experimentally observed phenomena in granular retrosplenial cortex (RSg). First, we consider short-term synaptic depression of thalamocortical inputs to RSg, expected to convey head direction (HD) information. We show depressing synapses enable extraction of a head speed signal from the HD population representation and that anticipatory firing of thalamic HD cells sharpens this head speed signal. By semi-analytical methods, we establish how anticipatory time interval and synaptic depression kinetics should be related to optimize head speed coding, and we describe the expected scaling of postsynaptic activity with head speed. This provides one possible explanation for the widespread tuning of RSg neurons to angular head velocity. Second, we construct a model of cross-hemispheric oscillatory patterning seen in extracellular recordings of RSg: in-phase gamma (30-80 Hz) and anti-phase spline (100-160 Hz) oscillations, coupled to distinct phases of a background theta (4-12 Hz) rhythm. We show this type of patterning can result from simple, four-population interhemispheric connectivity motifs and examine numerically the associated bifurcation structures. We compare the spectral statistics of the model output with those computed from data, revealing that delayed excitatory to inhibitory cross-hemispheric projections, known to exist in this particular circuit, may suffice to generate the observed oscillations.