Slow EEG waves reflect a slow oscillation in cortical neurons, between a depolarized state (UP-State) and hyper polarized state (DOWN-state; Steriade et al., 1993a, 1993b). During the down-state, neurons are disfacilitated (they can't really be activated by external stimuli or depolarized; Contreras et al., 1996). As the brain progress into deep sleep (lots of large-amplitude slow waves), not only cortical but also thalamic neurons becomes more and more hyper polarized (Amzica & Steriade, 2001). Steriade (2006) proposed that this progressive hyper polarization that is occurring during deep sleep might protect the brain from interference from the external world and facilitate memory consolidation, because the brain becomes "non-responsive" to the external environment. Indeed, this thalamo-cortical hyper polarization occuring during the down-state might "gate" the brain from external influence.
Recent neuroimaging studies in humans (Schabus et al., 2012) indeed showed that during the DOWN state, there was no cortical response to auditory stimuli in fMRI. Thus we think that those waves, either in N2 (K-Complex) or N3 (SW), protect the sleep brain from external influence.
Sources :
Steriade M, Nuñez A, Amzica F. A novel slow (< 1 Hz) oscillation of neocortical neurons in vivo: depolarizing and hyperpolarizing components. Journal of Neuroscience. 1993;13(8):3252–3265.
Steriade M, Contreras D, Curró Dossi R, Nuñez A. The slow (< 1 Hz) oscillation in reticular thalamic and thalamocortical neurons: scenario of sleep rhythm generation in interacting thalamic and neocortical networks. J Neurosci. 1993;13(8):3284–3299.
Contreras D, Timofeev I, Steriade M. Mechanisms of long-lasting hyperpolarizations underlying slow sleep oscillations in cat corticothalamic networks. J Physiol (Lond). 1996;494 ( Pt 1):251–264.
Amzica F, Steriade M. Electrophysiological correlates of sleep delta waves. Electroencephalography and Clinical Neurophysiology. 1998;107(2):69–83. doi:10.1016/S0013-4694(98)00051-0.
Steriade M. Grouping of brain rhythms in corticothalamic systems. Neuroscience. 2006;137(4):1087–1106. doi:10.1016/j.neuroscience.2005.10.029.
Schabus M, Dang Vu TT, Heib DPJ, et al. The Fate of Incoming Stimuli during NREM Sleep is Determined by Spindles and the Phase of the Slow Oscillation. Front Neurol. 2012;3:40. doi:10.3389/fneur.2012.00040.