The Effects of Potassium Currents on the Synchronization of Electrically Coupled Neural Oscillators

Synchronous oscillatory activity in cortical neurons is thought to be important for higher order cognitive functions [Gray et al., 1992]. It is believed that electrical coupling between inhibitory neurons is at least partially responsible for synchronization. This is supported by both experimental [e.g. Galarreta and Hestrin, 2001; Gibson et al., 1999; Beierlein et al., 2000; Amitai et al., 2002] and theoretical [Chow and Kopell, 2000; Lewis and Rinzel, 2003; Pfeuty et al., 2003; Bem et al., 2005; Di Garbo et al., 2005; Mancilla et al., 2007] studies. Mathematical models of electrically coupled neural oscillators show that electrical coupling also can support stable antisynchronous activity [Skinner et al., 1999; Pfeuty et al., 2003; Nomura et al., 2003; Lewis and Rinzel, 2004; Di Garbo et al., 2005; Mancilla et al., 2007]. However, antisynchronous activity in pairs of neurons connected solely by electrical coupling has not been found Colin B. Middleton University of California, Davis 2011 experimentally [Mancilla et al., 2007, see also Merriam et al., 2005; Gibson et al, 2005]. It is not understood why only robust synchrony is observed to the exclusion of antisynchrony. In fact, several model studies have investigated the roles of intrinsic membrane conductances on phase-locking in electrical coupled cells and found seemingly contradictory results. Pfeuty et al. (2003) showed that potassium currents promoted synchrony while Mancilla et al. (2007) found that potassium currents promoted anti-phase behavior. In this thesis, we seek to explain these results and to further understand how potassium currents influence the synchronization of electrically coupled neural oscillators.