Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning

Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning

Fundamental activity constraints lead to specific interpretations of the connectome

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function.Comment: J. Schuecker and M. Schmidt contributed equally to this wor

Decreasing initial telomere length in humans intergenerationally understates age-associated telomere shortening

Telomere length shortens with aging, and short telomeres have been linked to a wide variety of pathologies. Previous studies suggested a discrepancy in age-associated telomere shortening rate estimated by cross-sectional studies versus the rate measured in longitudinal studies, indicating a potential bias in cross-sectional estimates. Intergenerational changes in initial telomere length, such as that predicted by the previously described effect of a father's age at birth of his offspring (FAB), could explain the discrepancy in shortening rate measurements. We evaluated whether changes occur in initial telomere length over multiple generations in three large datasets and identified paternal birth year (PBY) as a variable that reconciles the difference between longitudinal and cross-sectional measurements. We also clarify the association between FAB and offspring telomere length, demonstrating that this effect is substantially larger than reported in the past. These results indicate the presence of a downward secular trend in telomere length at birth over generational time with potential public health implications

The Contribution of Thalamocortical Core and Matrix Pathways to Sleep Spindles.

Sleep spindles arise from the interaction of thalamic and cortical neurons. Neurons in the thalamic reticular nucleus (TRN) inhibit thalamocortical neurons, which in turn excite the TRN and cortical neurons. A fundamental principle of anatomical organization of the thalamocortical projections is the presence of two pathways: the diffuse matrix pathway and the spatially selective core pathway. Cortical layers are differentially targeted by these two pathways with matrix projections synapsing in superficial layers and core projections impinging on middle layers. Based on this anatomical observation, we propose that spindles can be classified into two classes, those arising from the core pathway and those arising from the matrix pathway, although this does not exclude the fact that some spindles might combine both pathways at the same time. We find evidence for this hypothesis in EEG/MEG studies, intracranial recordings, and computational models that incorporate this difference. This distinction will prove useful in accounting for the multiple functions attributed to spindles, in that spindles of different types might act on local and widespread spatial scales. Because spindle mechanisms are often hijacked in epilepsy and schizophrenia, the classification proposed in this review might provide valuable information in defining which pathways have gone awry in these neurological disorders

Neurogenesis Drives Stimulus Decorrelation in a Model of the Olfactory Bulb

The reshaping and decorrelation of similar activity patterns by neuronal networks can enhance their discriminability, storage, and retrieval. How can such networks learn to decorrelate new complex patterns, as they arise in the olfactory system? Using a computational network model for the dominant neural populations of the olfactory bulb we show that fundamental aspects of the adult neurogenesis observed in the olfactory bulb -- the persistent addition of new inhibitory granule cells to the network, their activity-dependent survival, and the reciprocal character of their synapses with the principal mitral cells -- are sufficient to restructure the network and to alter its encoding of odor stimuli adaptively so as to reduce the correlations between the bulbar representations of similar stimuli. The decorrelation is quite robust with respect to various types of perturbations of the reciprocity. The model parsimoniously captures the experimentally observed role of neurogenesis in perceptual learning and the enhanced response of young granule cells to novel stimuli. Moreover, it makes specific predictions for the type of odor enrichment that should be effective in enhancing the ability of animals to discriminate similar odor mixtures