Comment on ``Critical branching captures activity in living neural networks and maximizes the number of metastable states''

It is shown that, contrary to the claims in a recent letter by Haldeman and Beggs (PRL, 94, 058101, 2005), the branching ratio in epileptic cortical cultures is smaller than one. In addition, and also in contrast to claims made in that paper, the number of metastable states is not significantly different between cortical cultures in the critical state and cultures made epileptic using picrotoxin.Comment: Submitted Comment to PR

Npp1 promotes atherosclerosis in ApoE knockout mice.

Ecto-nucleotide pyrophosphatase/phosphodiesterase 1 (NPP1) generates inorganic pyrophosphate (PP(i)), a physiologic inhibitor of hydroxyapatite deposition. In a previous study, we found NPP1 expression to be inversely correlated with the degree of atherosclerotic plaque calcification. Moreover, function-impairing mutations of ENPP1, the gene encoding for NPP1, are associated with severe, artery tunica media calcification and myointimal hyperplasia with infantile onset in human beings. NPP1 and PP(i) have the potential to modulate atherogenesis by regulating arterial smooth muscle cell (SMC) differentiation and function, including increase of pro-atherogenic osteopontin (OPN) expression. Hence, this study tested the hypothesis that NPP1 deficiency modulates both atherogenesis and atherosclerotic intimal plaque calcification. Npp1/ApoE double deficient mice were generated by crossing mice bearing the ttw allele of Enpp1 (that encodes a truncation mutation) with ApoE null mice and fed with high-fat/high-cholesterol atherogenic diet. Atherosclerotic lesion area and calcification were examined at 13, 18, 23 and 28 weeks of age. The aortic SMCs isolated from both ttw/ttw ApoE(-/-) and ttw/+ ApoE(-/-) mice demonstrated decreased Opn expression. The 28-week-old ttw/ttw ApoE(-/-) and ttw/+ ApoE(-/-) had significantly smaller atherosclerotic lesions compared with wild-type congenic ApoE(-/-) mice. Only ttw/ttw but not ttw/+ mice developed artery media calcification. Furthermore in ttw/+ mice, there was a tendency towards increased plaque calcification compared to ApoE(-/-) mice without Npp1 deficiency. We conclude that Npp1 promotes atherosclerosis, potentially mediated by Opn expression in ApoE knockout mice

Decline of long-range temporal correlations in the human brain during sustained wakefulness

Sleep is crucial for daytime functioning, cognitive performance and general well-being. These aspects of daily life are known to be impaired after extended wake, yet, the underlying neuronal correlates have been difficult to identify. Accumulating evidence suggests that normal functioning of the brain is characterized by long-range temporal correlations (LRTCs) in cortex, which are supportive for decision-making and working memory tasks. Here we assess LRTCs in resting state human EEG data during a 40-hour sleep deprivation experiment by evaluating the decay in autocorrelation and the scaling exponent of the detrended fluctuation analysis from EEG amplitude fluctuations. We find with both measures that LRTCs decline as sleep deprivation progresses. This decline becomes evident when taking changes in signal power into appropriate consideration. Our results demonstrate the importance of sleep to maintain LRTCs in the human brain. In complex networks, LRTCs naturally emerge in the vicinity of a critical state. The observation of declining LRTCs during wake thus provides additional support for our hypothesis that sleep reorganizes cortical networks towards critical dynamics for optimal functioning

Neutral theory and scale-free neural dynamics

Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether such scaling laws stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as systems poised at criticality have been argued to exhibit a number of important functional advantages. Here we employ a well-known model for neural dynamics with synaptic plasticity, to elucidate an alternative scenario in which neuronal avalanches can coexist, overlapping in time, but still remaining scale-free. Remarkably their scale-invariance does not stem from underlying criticality nor self-organization at the edge of a continuous phase transition. Instead, it emerges from the fact that perturbations to the system exhibit a neutral drift --guided by demographic fluctuations-- with respect to endogenous spontaneous activity. Such a neutral dynamics --similar to the one in neutral theories of population genetics-- implies marginal propagation of activity, characterized by power-law distributed causal avalanches. Importantly, our results underline the importance of considering causal information --on which neuron triggers the firing of which-- to properly estimate the statistics of avalanches of neural activity. We discuss the implications of these findings both in modeling and to elucidate experimental observations, as well as its possible consequences for actual neural dynamics and information processing in actual neural networks.Comment: Main text: 8 pages, 3 figures. Supplementary information: 5 pages, 4 figure

Universal Organization of Resting Brain Activity at the Thermodynamic Critical Point

Thermodynamic criticality describes emergent phenomena in a wide variety of complex systems. In the mammalian brain, the complex dynamics that spontaneously emerge from neuronal interactions have been characterized as neuronal avalanches, a form of critical branching dynamics. Here, we show that neuronal avalanches also reflect that the brain dynamics are organized close to a thermodynamic critical point. We recorded spontaneous cortical activity in monkeys and humans at rest using high-density intracranial microelectrode arrays and magnetoencephalography, respectively. By numerically changing a control parameter equivalent to thermodynamic temperature, we observed typical critical behavior in cortical activities near the actual physiological condition, including the phase transition of an order parameter, as well as the divergence of susceptibility and specific heat. Finite-size scaling of these quantities allowed us to derive robust critical exponents highly consistent across monkey and humans that uncover a distinct, yet universal organization of brain dynamics

Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a novel method to solve the self-consistent equations for order parameters by using formal complex-valued phase variables, and apply our theory to networks of in vitro cortical neurons. We find a novel state transition that is not observed in previous oscillator network models.Comment: 4 pages, 3 figure