Mathematical models provide insight into the role of interneurons in hippocampal CA1 network theta rhythm generation

The theta rhythm, a network rhythm oscillating between 3-12 Hz, is one of the most prominent clocking mechanisms detected in the mammalian brain. These rhythms are recorded in the hippocampus during exploratory behaviour and R.E.M. sleep, and are associated with episodic memory and spatial navigation (Buzsรกki, 2002). A "classic" theta model predicts that pacemaker neurons in the medial septum drive the hippocampal rhythm. However, Goutagny et al. (2009) recently showed that the hippocampal formation possesses the necessary and sufficient circuitry to generate its own theta rhythm, implying that different subregions of the hippocampus can perform separate computational tasks simultaneously. Mathematical models have been used to investigate the possibility of independent hippocampal theta generators, but in general rely on a population of pacemaking interneurons to drive the system (Wulff et al., 2009; Rotstein et al., 2005; Tort et al., 2007), a mechanism that may not be physiologically relevant (Kispersky et al., 2012). In an attempt to understand the underlying dynamics of this rhythm, a number of experimentally constrained mathematical network models are developed with a focus on the CA1 hippocampus. We first describe the development of simple models of individual CA1 parvalbumin-positive (PV+) interneurons, oriens-lacunosum-moleculare (OLM) interneurons, and pyramidal cells (PYR), as derived from an intact, whole hippocampus preparation in vitro expressing population oscillations. These single cell models are used to construct thousands of network models, and we investigate the role of these different cell types in CA1 network oscillations. Networks of PV+ interneurons alone exhibited sharp transitions into coherent high frequency firing (> 100 Hz), providing insight into how these fast oscillations could become nested in theta rhythms. We predict that the dis-inhibitory effect of OLM cells on bistratified cell (BSC) to PYR interactions plays a critical role in the power of network theta oscillations. Additionally, our network models demonstrated that without a phasic drive, PYR network models alone could not exhibit coherent oscillations while maintaining sparse firing - a feature of our PYR recordings during theta. However, when PV+ cell networks were incorporated into the PYR networks, PYR sparsely fired, and network frequency and stability was increased. Thus, our experimentally constrained network models suggest that PV+ interneurons play a key role in the frequency and stability of network oscillations, and that OLM-BSC interactions may influence network theta power.Ph.D