Stochastic Amplification of Fluctuations in Cortical Up-States

Abstract

Cortical neurons are bistable; as a consequence their local field potentials can fluctuate between quiescent and active states, generating slow Hz oscillations which are widely known as transitions between Up and Down States. Despite a large number of studies on Up-Down transitions, deciphering its nature, mechanisms and function are still today challenging tasks. In this paper we focus on recent experimental evidence, showing that a class of spontaneous oscillations can emerge within the Up states. In particular, a non-trivial peak around Hz appears in their associated power-spectra, what produces an enhancement of the activity power for higher frequencies (in the Hz band). Moreover, this rhythm within Ups seems to be an emergent or collective phenomenon given that individual neurons do not lock to it as they remain mostly unsynchronized. Remarkably, similar oscillations (and the concomitant peak in the spectrum) do not appear in the Down states. Here we shed light on these findings by using different computational models for the dynamics of cortical networks in presence of different levels of physiological complexity. Our conclusion, supported by both theory and simulations, is that the collective phenomenon of “stochastic amplification of fluctuations” – previously described in other contexts such as Ecology and Epidemiology – explains in an elegant and parsimonious manner, beyond model-dependent details, this extra-rhythm emerging only in the Up states but not in the Downs.

Geometric structure and information change in phase transitions

“…(22). Since the change in L becomes very small for large fluctuation (i.e., large variance of a PDF) around t = t c , a good estimate on the total L can be obtained by considering the change in L for (i) t < t c during which our results (11)- (19) are valid with Gaussian p(y,t) in Eq.…”

“…(14) and (19) cannot reasonably describe the time evolution of the PDFs. Equation (22) demonstrates that the two peaks form at a finite time which increases with | ln D|. The formation of the two peaks discussed above is accompanied by a large (anomalous) fluctuation.…”

“…We observe the change of the sign H = γ x 2 − x 4 at t ∼ t c in Eq. (22). Unlike x 2 and x 4 which monotonically increase in time, the difference = x 4 − x 2 is not monotonic, but increases to its maximum before decreasing to zero as the PDF settles into its equilibrium (figure not shown).…”

“…[18][19][20][21][22][23]. One of the most striking attributes of some bistable systems is continuous switching between ordered and disordered states, the transition occurring in bursts interspersed by a quiescent period (e.g., see [18]).…”

Noise-controlled bistability in an excitable system with positive feedback

“…They will be useful in interpreting observations of bistable behavior in complex systems such as up-and-down states in neural networks [26,27] and the role of positive feedback, for instance due to autapses [13]. * * * This paper was developed within the scope of IRTG 1740/TRP 2011/50151-0, funded by the DFG / FAPESP and by the BMBF (FKZ: 01GQ1001A).…”