Establishing Communication between Neuronal Populations through Competitive Entrainment

Abstract

The role of gamma frequency oscillation in neuronal interaction, and the relationship between oscillation and information transfer between neurons, has been the focus of much recent research. While the biological mechanisms responsible for gamma oscillation and the properties of resulting networks are well studied, the dynamics of changing phase coherence between oscillating neuronal populations are not well understood. To this end we develop a computational model of competitive selection between multiple stimuli, where the selection and transfer of population-encoded information arises from competition between converging stimuli to entrain a target population of neurons. Oscillation is generated by Pyramidal-Interneuronal Network Gamma through the action of recurrent synaptic connections between a locally connected network of excitatory and inhibitory neurons. Competition between stimuli is driven by differences in coherence of oscillation, while transmission of a single selected stimulus is enabled between generating and receiving neurons via Communication-through-Coherence. We explore the effect of varying synaptic parameters on the competitive transmission of stimuli over different neuron models, and identify a continuous region within the parameter space of the recurrent synaptic loop where inhibition-induced oscillation results in entrainment of target neurons. Within this optimal region we find that competition between stimuli of equal coherence results in model output that alternates between representation of the stimuli, in a manner strongly resembling well-known biological phenomena resulting from competitive stimulus selection such as binocular rivalry.

Keywords: gamma oscillation; phase coherence; stimulus competition; synchrony.

Figure 1

Schematic of the two-layer feedforward network model used in this study. The source layer consists of two populations of excitatory neurons (E₁, E₂). The target layer contains a single population of excitatory (E₃) and a single population of inhibitory (I₁) neurons. Each excitatory source layer neuron receives oscillating external current and Poisson spiking input, resulting in a random pattern of firing with the stimulus represented by elevated activity within the population at a preferred orientation. Excitatory neurons of the target layer (E₃) receive both stimuli via a set of topographic synaptic connections (S₁, S₂). Within the target layer excitatory and inhibitory populations are fully connected (S₃, S₄).

Figure 2

(A) With no external oscillation applied to the target layer of the top-down model of stimulus selection, both stimuli (E₁, E₂) are equally represented in the activity of the excitatory target population E₃. The average activity in Hertz of the excitatory source (red/blue line) and target (black line) populations are shown in the lower panel of each plot. (C) An external top-down control signal applied to the target population in-phase with arrival of stimuli E₁ results in elevated firing at the orientation of that stimulus and effective filtering of the out-of-phase stimulus E₂. The average firing rate (bar) and fitted Von Mises template for activity of each stimulus (red/blue lines) are shown in (B,D), where each bar is the normalized average firing rate of a single bin of 50 neurons of consecutive preferred orientation.

Figure 3

Properties of QIF model output for stimuli of equal coherence, where oscillation is driven in target neurons by a top-down control signal. (A) Difference in cross-correlation (indicated ρ) of stimuli and target activity enumerated over the range of relative phase values for oscillation in the three excitatory populations. Peaks indicate points of greatest correlation with a single stimulus, and θ₁, θ₂, and θ₃ represent the phase of the two source and target populations respectively. (B) Cumulative values along the axis maintaining θ₃ (upper) exhibit a single maxima where stimuli are directly out-of-phase. At this point, differences in source and target phase (lower) lead to two maxima at points where target oscillation is in-phase with either arriving stimulus accounting for delay. (C) The proportion of decoded trials corresponding to the first stimulus (indicated Φ) over the same range of relative phase values. (D) Cross-section taken at the optimal relative phase for selection of each stimuli (upper panel, the first stimulus shown by a solid line and the second by a dashed line) and cumulative values along the axis of varying stimulus phase (lower).

Figure 4

Membrane potential of a single excitatory (upper) and inhibitory (lower) neuron within the target excitatory (E₃) and inhibitory (I₁) populations, for the (A) QIF and (B) Hodgkin-Huxley bottom-up model of stimulus selection. Neuron firing is indicated by a square at the peak of membrane potential, and the normalized spiking activity of the entire excitatory or inhibitory neuronal population shown as a shaded area. In both cases firing of individual neurons within the model is irregular, with no single neuron firing regularly or at fixed phase offset within the period of oscillation. (C) The normalized distribution of interspike intervals with fitted negative exponential for a single target excitatory neuron, for QIF (upper) and Hodgkin-Huxley (lower) neuron models. (D) Cross-correlation of QIF excitatory target activity to the first (upper) and second (lower) stimulus for varying magnitude and relative stimuli coherence.

Figure 5

Enumeration of the synaptic parameter space for the bottom-up model of stimulus selection. The difference in cross-correlation (ρ) for the QIF neuron model is shown in (A–C), and Hodgkin-Huxley neuron model in (D–F). Hi-lighted regions in (A,D) indicate values of ρ > 0.7 (solid) and ρ > 0.5 (transparent) for the parameters excitatory-inhibitory weight, inhibitory-to-excitatory weight and synaptic delay local to the target later of the network. Delay was increased simultaneously for excitatory-inhibitory and inhibitory-excitatory synapses so both remained equal, the value (λ) indicating delay in a single direction of the recurrent synaptic loop. A cross-section of the difference in cross-correlation is shown in (B,E) for excitatory-to-inhibitory and (C,F) inhibitory-to-excitatory weight relative to synaptic delay. Within the hi-lighted region behavior of both variants of the model is consistent with communication of a single stimulus through phase-coherent oscillation.

Figure 6

(A) The distribution of periods of entrainment of the bottom-up QIF model to a single stimulus with fitted gamma (solid) and log-normal (dashed) probability density functions and (B) auto-correlation of entrainment periods for the same data, both matching empirical results for binocular rivalry. (C) In accordance with Levelt “Proposition II,” when the strength of a single stimulus in the model is reduced, changes in relative duration of entrainment result mainly from a lengthening of periods of entrainment to the unchanged stimulus. (D) Similarly for Levelt “Proposition IV,” increasing the coherence of both stimuli simultaneously leads to an overall decrease in mean dominance time.

Figure 7

(A) Raster plot of alternation in entrainment of target neurons between incoming stimuli of equal coherence for the bottom-up QIF neuron model. Results are shown with synaptic delay (λ) connecting target excitatory and inhibitory populations of 2.2 ms (upper), 2.1 ms (middle), and 2.0 ms (lower) in either direction. (B) The mean duration of dominance intervals shows a non-linear dependence on both synaptic delay and stimulus coherence, while (C) increasing the level of input noise results in progressively faster switching times.