Brain Noise, Not Wiring, May Explain Why Neural Spectra Shift With Brain State

Every recording of brain activity, whether it comes from electrodes on the scalp, probes buried in cortical tissue, or grids laid over the surface of the brain, carries two intertwined stories. The first is the familiar one of oscillations: the alpha rhythms of a resting mind, the fast gamma bursts of an engaged cortex. The second is quieter and stranger, a broadband aperiodic background whose power falls off steadily with frequency, following a near-1/f pattern that has fascinated physicists and neuroscientists for decades. A new theoretical and computational study argues that much of the variability in this background, including the position of its characteristic spectral knee and the steepness of its decay, can emerge from a single, surprisingly simple source: noise-like fluctuations in neural activity that reshape the effective timescales of entire networks.

The research, published in PLOS Complex Systems by Axel Hutt of the University of Strasbourg and CNRS, Matteus McCulloch and Jérémie Lefebvre of the University of Ottawa, Anthony Hudetz of the University of Michigan, and Aref Pariz of The Royal’s Institute of Mental Health Research, tackles a long-standing puzzle in electrophysiology. The aperiodic component of the power spectral density, or PSD, is not a fixed signature of the brain. Its slope, quantified by an exponent that describes how quickly power decays at higher frequencies, changes systematically with behavioral state. Steep spectra dominated by large-amplitude slow fluctuations appear during sleep and anesthesia, while flatter spectra accompany arousal and wakefulness. The same exponent also tracks cognitive load, task demands, and even aging, making it one of the most widely used spectral biomarkers in modern neuroscience.

Beyond the slope, the aperiodic spectrum is structured by a spectral knee, a bend that separates distinct scaling regimes and is thought to reflect an underlying neuronal timescale. When the knee moves, the frequency range over which the power law can be meaningfully measured moves with it, dragging estimates of the exponent along. Clinically and scientifically, this matters: if the knee shifts, an apparent change in the exponent may say nothing about a change in the actual asymptotic scaling of the signal, and everything about a change in the timescale of the neural population producing it. Yet the biological origin of both the knee and the exponent has remained hotly contested, with proposed explanations ranging from self-organized criticality to the passive filtering of signals by brain tissue and random ion diffusion.

To dissect the problem, the team built a large-scale recurrent neural network with sparse, balanced excitatory and inhibitory connectivity of the kind long used to model interacting neural populations. Each node in the network represents a local population whose mesoscopic synaptic potential evolves under a linear relaxation process, a constant input, and a nonlinear sigmoidal activation function. Crucially, the network was driven by state-dependent fluctuations, modeled as additive Gaussian noise whose variance stands in for the intensity of endogenous broadband activity. Low noise variance corresponded to low-activation states reminiscent of deep anesthesia or slow-wave sleep, while high variance emulated the elevated, irregular activity of awake and aroused cortex, where endogenous fluctuations are particularly prominent thanks to sensory input, brainstem modulation, and inter-area communication.

The simulations revealed a striking pattern. When the noise variance was small, the network settled into epochs of high-amplitude, low-frequency, synchronous activity, and its power spectrum showed strong low-frequency power with a steep high-frequency decay. As the variance increased, low-frequency power was suppressed, higher frequencies gained ground, and the spectral knee visibly shifted toward higher frequencies. At frequencies beyond the knee, however, the asymptotic scaling exponent approached a value that remained largely invariant across noise levels. In other words, the fluctuations were not changing the fundamental scaling law of the network; they were moving the boundary between scaling regimes, reorganizing the spectrum by tuning the effective timescale over which neural populations evolve.

Capturing this behavior mathematically required the researchers to go beyond standard tools. The conventional approach to computing a PSD in a high-dimensional nonlinear network is to linearize the dynamics around a deterministic equilibrium, but this method is computationally awkward for large networks and, more importantly, structurally blind to the phenomenon at hand. A linearized treatment predicts a Lorentzian spectral profile whose knee and slope are fixed regardless of noise intensity; changing the noise merely rescales the overall amplitude of the spectrum. Since both the simulations and the experimental literature show marked state-dependent shifts in knee position and slope, the team concluded that nonlinear effects are essential, and set out to build an analytical framework that could include them.

By integrating recent advances in random matrix theory, and in particular the circular law that constrains the eigenvalues of random connectivity matrices within a disk in the complex plane, the researchers derived a variational equation inspired by Floquet theory and the master stability function. Rather than linearizing about a deterministic fixed point, they analyzed stability about the stochastic system’s evolution, assuming a Gaussian stationary probability density for the network activity, an approximation validated by extensive simulations. This yielded an effective spectral radius that depends explicitly on the noise variance: increasing the noise contracts the spectral disk, steering the network away from the May-Wigner instability threshold and reinforcing linear, stable behavior. Noise, in this framework, is not merely a nuisance but a stabilizing control parameter.

Substituting this effective spectral radius back into the expression for the mean power spectrum produced an analytical prediction with an explicit, nonlinear dependence on noise variance, and it matched the simulations with remarkable fidelity. The theory predicted, and the numerics confirmed, that the characteristic knee frequency increases with noise variance, indicating a reduction in the effective neuronal timescale. The resulting displacement of the knee flattened the spectrum within fixed frequency bands, decreasing the apparent exponent exactly as observed empirically. These results held across multiple orders of magnitude of noise variance, across different levels of connectivity heterogeneity, in networks conforming to Dale’s law, and in the presence of temporally correlated colored noise, though the magnitude of the effect declined as the noise autocorrelation time grew.

To connect theory with biology, the team revisited local field potential recordings from rats under the anesthetic desflurane, comparing light and deep anesthesia. The spectra were steeper under deep anesthesia, and a paired bootstrap analysis across seven trials found a statistically significant increase in the exponent with anesthetic depth. This aligns with the hypothesis that deeper anesthesia suppresses endogenous fluctuations, potentially through dampening of the ascending reticular arousal system, and thus corresponds to a lower intrinsic noise level, a slower knee frequency, and a steeper spectrum. The experimental trend qualitatively mirrors the model’s central prediction.

The broader implication is provocative: shifts in widely used spectral biomarkers may reflect noise-driven, nonlinear transitions in recurrent neural systems rather than the action of any single biophysical mechanism. Variations in the statistics of endogenous neural activity alone, without any change in connectivity, could account for spectral changes previously attributed to rewiring or altered microarchitecture. The authors are careful to note that their model is deliberately simplified, using random Erdős–Rényi connectivity rather than the hierarchical, small-world architectures of real brains, and that tissue filtering, synaptic filtering, and ion diffusion likely act as complementary mechanisms shaping spectra across different frequency ranges and recording modalities. Still, the message is clear: the brain’s broadband background is dynamic, its characteristic features are generic properties of nonlinear recurrent networks, and the noise that neuroscientists so often average away may be one of the very levers by which the brain reorganizes itself across sleep, wakefulness, and every state in between.

Subject of Research: Mechanisms by which noise-like neural fluctuations drive state-dependent shifts in neuronal timescales and 1/f power spectra

Article Title: Noise-like fluctuations drive shifts in neuronal timescales and 1/ f power spectra across brain states

Article References: Hutt, A., McCulloch, M., Hudetz, A. G., Pariz, A., & Lefebvre, J. (2026). Noise-like fluctuations drive shifts in neuronal timescales and 1/f power spectra across brain states. PLOS Complex Systems, 3(9), e0000133. https://doi.org/10.1371/journal.pcsy.0000133

Image Credits: AI Generated

DOI: 10.1371/journal.pcsy.0000133

Keywords: neuroscience, 1/f power spectrum, spectral knee, neural noise, brain states, recurrent neural networks, random matrix theory, EEG, anesthesia, neuronal timescales, power spectral density, criticality