  Cortical slow oscillations occur in the mammalian brain during deep sleep and
have been shown to contribute to memory consolidation, an effect that can be
enhanced by electrical stimulation. As the precise underlying working
mechanisms are not known it is desired to develop and analyze computational
models of slow oscillations and to study the response to electrical stimuli. In
this paper we employ the conductance based model of Compte et al. [J
Neurophysiol 89, 2707] to study the effect of electrical stimulation. The
population response to electrical stimulation depends on the timing of the
stimulus with respect to the state of the slow oscillation. First, we reproduce
the experimental results of electrical stimulation in ferret brain slices by
Shu et al. [Nature 423, 288] from the conductance based model. We then
numerically obtain the phase response curve for the conductance based network
model to quantify the network's response to weak stimuli. Our results agree
with experiments in vivo and in vitro that show that sensitivity to stimulation
is weaker in the up than in the down state. However, we also find that within
the up state stimulation leads to a shortening of the up state, or phase
advance, whereas during the up-down transition a prolongation of up states is
possible, resulting in a phase delay. Finally, we compute the phase response
curve for the simple mean-field model by Ngo et al. [Europhys Lett 89, 68002]
and find that the qualitative shape of the PRC is preserved, despite its
different mechanism for the generation of slow oscillations.
