Metastability and inter-band frequency modulation in networks of oscillating spiking neuron populations

Abstract

Groups of neurons firing synchronously are hypothesized to underlie many cognitive functions such as attention, associative learning, memory, and sensory selection. Recent theories suggest that transient periods of synchronization and desynchronization provide a mechanism for dynamically integrating and forming coalitions of functionally related neural areas, and that at these times conditions are optimal for information transfer. Oscillating neural populations display a great amount of spectral complexity, with several rhythms temporally coexisting in different structures and interacting with each other. This paper explores inter-band frequency modulation between neural oscillators using models of quadratic integrate-and-fire neurons and Hodgkin-Huxley neurons. We vary the structural connectivity in a network of neural oscillators, assess the spectral complexity, and correlate the inter-band frequency modulation. We contrast this correlation against measures of metastable coalition entropy and synchrony. Our results show that oscillations in different neural populations modulate each other so as to change frequency, and that the interaction of these fluctuating frequencies in the network as a whole is able to drive different neural populations towards episodes of synchrony. Further to this, we locate an area in the connectivity space in which the system directs itself in this way so as to explore a large repertoire of synchronous coalitions. We suggest that such dynamics facilitate versatile exploration, integration, and communication between functionally related neural areas, and thereby supports sophisticated cognitive processing in the brain.

Figure 1. PING oscillatory architecture and behaviour.

(A) The pyramidal inter-neuronal gamma (PING) architecture used for the neural oscillator nodes in the simulation experiments. To generate oscillator nodes of different frequencies for different neural models this base architecture was used with a genetic algorithm evolving the weights and delays for the synaptic connections. (B) Example of the firing behaviour of an evolved QIF PING node oscillating at 30 Hz.

Figure 2. Extraction of frequencies from population firings (A) Scalogram of the excitatory layer of a neural PING node that has been connected to 9 other nodes each oscillating at a different frequency.

(B) Firing behaviour of the same excitatory layer between 1000 ms to 1500 ms in the simulation. Note how the spacing in between the burst of firing is reflected as different frequencies in the scalogram in panel A. (C) Time slice of the scalogram in panel A taken at 1460 ms. The red line shows the time slice and the green lines show different Gaussians, the sum of which fits the red line.

Figure 3. Synchrony, coalition entropy, and the number of coexisting frequencies.

Each simulation uses 10 neural PING oscillator nodes with the connection probability and weight being the same between all nodes on a single simulation run. Each separate simulation uses a different connection probability and weight drawn from a uniform distribution between 0 and 1. (A) The overall synchrony in the networks using the QIF neuron model, (B) same as panel A for the HH neuron model. (C) The coalition entropy in the networks using the QIF neuron model, (D) same as panel C for the HH neuron model. (E) The average number of coexisting frequencies per oscillator at each time point in the networks using the QIF neuron model, (F) the same as panel E for the HH neuron model.

Figure 4. The number of correlations found.

The setup is the same as for figure 3. (A) The average number of mean intermittent frequency correlations found for networks using the QIF neuron model, (B) same as panel A for the HH neuron model. (C) The average number of phantom mean intermittent frequency correlations found for networks using the QIF neuron model, (D) the same as panel C for the HH neuron model.

Figure 5. Mean intermittent frequency correlation.

The setup is the same as for figure 3 and subsequent figures. (A) The mean intermittent frequency correlation for networks using the QIF neuron model, (B) the same as panel A for the HH neuron model. (C) The phantom mean intermittent frequency correlation for networks using the QIF neuron model, (D) the same as panel C for the HH neuron model. The mean intermittent frequency metric selects correlations where the coefficient > = 0.5 and p < = 0.05, and all correlations are normalised by the length of the time series strands.

Figure 6. Average number of correlations, and the peak of modulated exploration.

The setup is the same as for figure 3 and subsequent figures. (A) The average number of mean intermittent frequency correlations found for networks using the QIF neuron model, (B) the same as panel A for the HH neuron model. The number of correlations found has been normalized by the number of coexisting frequency time series in all oscillators on each simulation run. The figure shows, on average, how many frequencies in other oscillators each individual frequency is interacting with at each time point. (C) and (D) show from two different angles a combination of mean intermittent frequency correlation and coalition entropy for the QIF neuron model. The values of both metrics have been normalised before multiplying them together. The graphs emphasise a peak area, and in this area there is also a linear relationship between weight and connection probability. This peak area facilitates modulated exploration of a large repertoire of different coalitions.