The phase response of the cortical slow oscillation
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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 89:2707–2725, 2003) 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 423:288–293, 2003) 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. (EPL Europhys Lett 89:68002, 2010) and find that the qualitative shape of the PRC is preserved, despite its different mechanism for the generation of slow oscillations.
KeywordsSleep Cortex Phase response Slow oscillation Synchronization
This work was supported by the Deut-sche Forschungsgemeinschaft (DFG) within SFB 654 “Plasticity & Sleep” and the Graduate School for Computing in Medicine and Life Sciences funded by Germany’s Excellence Initiative [DFG GSC 235/1].
- Granada A, Hennig R, Ronacher B, Kramer A, Herzel H (2009) Phase response curves: elucidating the dynamics of coupled oscillators. In: Michael L. Johnson and Ludwig Brand (eds) Methods in enzymology, vol 454. Elsevier, pp 1–27Google Scholar
- Kuramoto Y (2003) Chemical oscillations, waves, and turbulence. Chemistry series, Dover Publications (originally published: Springer Berlin, 1984)Google Scholar
- Mattia M, Sanchez-Vives M (2012) Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity. Cogn Neurodyn 6(3):239–250Google Scholar
- Petersen CC, Hahn TT, Mehta M, Grinvald A, Sakmann B (2003) Interaction of sensory responses with spontaneous depolarization in layer ii/iii barrel cortex. Proc Natl Acad Sci USA 100(23):13638Google Scholar
- Tass PA (1999) Phase resetting in medicine and biology: stochastic modelling and data analysis. Springer, BerlinGoogle Scholar
- Winfree AT (2001) The geometry of biological time, 2nd edn. Springer, BerlinGoogle Scholar