Period Concatenation Underlies Interactions between Gamma and Beta Rhythms in Neocortex

The neocortex generates rhythmic electrical activity over a frequency range covering many decades. Specific cognitive and motor states are associated with oscillations in discrete frequency bands within this range, but it is not known whether interactions and transitions between distinct frequencies are of functional importance. When coexpressed rhythms have frequencies that differ by a factor of two or more interactions can be seen in terms of phase synchronization. Larger frequency differences can result in interactions in the form of nesting of faster frequencies within slower ones by a process of amplitude modulation. It is not known how coexpressed rhythms, whose frequencies differ by less than a factor of two may interact. Here we show that two frequencies (gamma – 40 Hz and beta2 – 25 Hz), coexpressed in superficial and deep cortical laminae with low temporal interaction, can combine to generate a third frequency (beta1 – 15 Hz) showing strong temporal interaction. The process occurs via period concatenation, with basic rhythm-generating microcircuits underlying gamma and beta2 rhythms forming the building blocks of the beta1 rhythm by a process of addition. The mean ratio of adjacent frequency components was a constant – approximately the golden mean – which served to both minimize temporal interactions, and permit multiple transitions, between frequencies. The resulting temporal landscape may provide a framework for multiplexing – parallel information processing on multiple temporal scales

Rhythm Generation through Period Concatenation in Rat Somatosensory Cortex

Rhythmic voltage oscillations resulting from the summed activity of neuronal populations occur in many nervous systems. Contemporary observations suggest that coexistent oscillations interact and, in time, may switch in dominance. We recently reported an example of these interactions recorded from in vitro preparations of rat somatosensory cortex. We found that following an initial interval of coexistent gamma (∼25 ms period) and beta2 (∼40 ms period) rhythms in the superficial and deep cortical layers, respectively, a transition to a synchronous beta1 (∼65 ms period) rhythm in all cortical layers occurred. We proposed that the switch to beta1 activity resulted from the novel mechanism of period concatenation of the faster rhythms: gamma period (25 ms)+beta2 period (40 ms) = beta1 period (65 ms). In this article, we investigate in greater detail the fundamental mechanisms of the beta1 rhythm. To do so we describe additional in vitro experiments that constrain a biologically realistic, yet simplified, computational model of the activity. We use the model to suggest that the dynamic building blocks (or motifs) of the gamma and beta2 rhythms combine to produce a beta1 oscillation that exhibits cross-frequency interactions. Through the combined approach of in vitro experiments and mathematical modeling we isolate the specific components that promote or destroy each rhythm. We propose that mechanisms vital to establishing the beta1 oscillation include strengthened connections between a population of deep layer intrinsically bursting cells and a transition from antidromic to orthodromic spike generation in these cells. We conclude that neural activity in the superficial and deep cortical layers may temporally combine to generate a slower oscillation

Cholinergic neuromodulation controls directed temporal communication in neocortex <i>in vitro</i>

Acetylcholine is the primary neuromodulator involved in cortical arousal in mammals. Cholinergic modulation is involved in conscious awareness, memory formation and attention &ndash; processes that involve intercommunication between different cortical regions. Such communication is achieved in part through temporal structuring of neuronal activity by population rhythms, particularly in the beta and gamma frequency ranges (12 &ndash; 80 Hz). Here we demonstrate, using in vitro and in silico models, that spectrally identical patterns of beta2 and gamma rhythms are generated in primary sensory areas and polymodal association areas by fundamentally different local circuit mechanisms: Glutamatergic excitation induced beta2 frequency population rhythms only in layer 5 association cortex whereas cholinergic neuromodulation induced this rhythm only in layer 5 primary sensory cortex. This region-specific sensitivity of local circuits to cholinergic modulation allowed for control of the extent of cortical temporal interactions. Furthermore, the contrasting mechanisms underlying these beta2 rhythms produced a high degree of directionality, favouring an influence of association cortex over primary auditory cortex

S-adic characterization of dendric languages

Dendric shift spaces or langages generalize Arnoux-Rauzy words and have interesting properties related to return words. It is known that we can build particular S-adic representations of any given dendric system. In this talk, I explain how we can understand to properties of these representations to obtain a characterization. The main result is the description of a graph such that a system is dendric if and only if it has a primitive S-adic representation labeling an infinite path in this graph