Communication through resonance in spiking neuronal networks

Abstract

The cortex processes stimuli through a distributed network of specialized brain areas. This processing requires mechanisms that can route neuronal activity across weakly connected cortical regions. Routing models proposed thus far are either limited to propagation of spiking activity across strongly connected networks or require distinct mechanisms that create local oscillations and establish their coherence between distant cortical areas. Here, we propose a novel mechanism which explains how synchronous spiking activity propagates across weakly connected brain areas supported by oscillations. In our model, oscillatory activity unleashes network resonance that amplifies feeble synchronous signals and promotes their propagation along weak connections ("communication through resonance"). The emergence of coherent oscillations is a natural consequence of synchronous activity propagation and therefore the assumption of different mechanisms that create oscillations and provide coherence is not necessary. Moreover, the phase-locking of oscillations is a side effect of communication rather than its requirement. Finally, we show how the state of ongoing activity could affect the communication through resonance and propose that modulations of the ongoing activity state could influence information processing in distributed cortical networks.

Figure 1. Architecture and ongoing activity of the diluted FFN model.

(a) Scheme of a 3-layer FFN. The color code is preserved across figures: red/blue/black represent // neurons. (b) Pulse packet response in an isolated layer. A pulse packet (; ) was presented after . Gray shaded rectangle: ongoing activity region. Subpanels: raster plot of the spiking activity (top); membrane potential traces of two example neurons (upper-middle); output rate histogram (lower-middle); and input rate histogram (bottom).

Figure 2. Ongoing dynamics and impulse response of an isolated FFN layer.

(a–c) Ongoing activity statistics computed in absence of pulse packet stimulation (gray region in Figure 1b) from a simulation of . Color code as in Figure 1. Filled/empty inverted triangles: mean/s.d.. (a) Mean rate distribution of individual neurons. (b) Distribution of values. (c) Distribution of pairwise correlation coefficients (inset: auto-covariance function of the population spike train). (d) Pulse packet amplitude transfer map. Black trace: membrane potential distribution of neurons in its c.d.f. form plotted as a function of the distance to spike threshold (; “Jump”). Gray lines: average voltage depolarization (“Jump”) caused by a pulse packet of . Dark gray line: depolarization when which is the value used in this work. Light gray line: depolarization when . Red dots and dotted lines: trajectory of a pulse starting from a fully activated layer (). (e) Effect of stimulation with a single pulse packet (; ). Subpanels: time evolution of inhibitory and excitatory conductances ( and ) averaged across neurons (upper); and evolution of the membrane potential distribution for and neurons (lower). Gray region: optimal time window for the arrival of a hypothetical second pulse packet. Cyan dot: arrival time of the actual pulse packet. Magenta/green dot: hypothetical arrival of a second pulse outside/inside of the optimal time window. Dotted lines: mean s.d. across neurons. Black dashed line: Same as blue trace in Figure 4b bottom (), resonance curve plotted as a function of time interval instead of frequency.

Figure 3. Resonance in an isolated FFN layer.

(a) Network activity during stimulation with a train of pulse packets (; ; ). Color code as in Figure 1. Subpanels: raster plot of the spiking activity (top); membrane potential traces of two example neurons (upper-middle); output rate histogram (lower-middle); and input (to neurons) rate histogram (bottom). (b) Increased mean firing rate at the layer's resonance frequency within 20 ms after the pulse packet arrival. neurons were stimulated with trains of periodic pulses packets (; ; ). Error bars: average s.d. across trials (c) Increased activation caused by dis-inhibition. Red/black line: average mean of the membrane potential distribution of / neurons sampled prior to the arrival of the pulse. Train of pulses as in b with frequency . Inset: average s.d. of the membrane potential distribution across neurons. Light gray bars: rate response calculated as in (b). Dark gray bars: firing rate within before the pulse packet arrival. (d) Spiking and membrane potential statistics measured during of stimulation. Stimulus statistics as in (c). Subpanels: distribution of individual mean firing rates in Hz (; ; mean s.d. across population; upper left); distribution of (; ; upper right); distribution of pairwise correlation coefficients (; ; lower left); and auto-covariance function of the population spike train (lower right).

Figure 4. Communication through resonance in diluted FFNs.

(a) Example simulations illustrate the transmission of synchrony in 5-layer diluted FFNs for three different stimulus frequencies: 1 Hz (top), 28 Hz (middle) and (bottom; resonance frequency for this network). Pulse packets: and . In all three subpanels: stimulus time histogram in kHz (bottom) and raster plot of spiking activity (top). Gray/white stripes: different layers. Color code as in Figure 1. (b) Propagation of synchronous activity in 10-layer FFNs as a function of the stimulus frequency (). Activity of the first layer (blue trace in bottom subpanel and top subpanel) and the last layer (red trace in bottom subpanel and middle subpanel) during periodic stimulation at different frequencies (pulses: and ). Top/middle subpanels: /. Bottom subpanel: (blue trace) and (red trace). White circles: significantly larger than . Note that was previously depicted in Figure 2e as a function of the inter-pulse interval for comparison with the average network response to an isolated synchronous pulse.

Figure 5. Robustness of CTR against deviations from periodicity.

(a) Effect of jittered arrival times on CTR. Resonance curves () of / (blue/red) as a function of the amount of jitter. Pulse packets: and . Jitter is expressed as a fraction of the input's interval . White circles: significantly larger than . (b) Non-periodic Poisson input to neurons in a 5-layer FFN triggers CTR. Subpanels: Raster plot of the spiking activity (top); and input (to only) rate histogram in kHz (bottom). Color code as in Figure 1. (c) Last layer reached by the propagating synchronous activity as a function of the additional input rate to . Solid circle: stimulus as in b.

Figure 6. Effect of the dynamical network state on CTR.

(a) Population spiking statistics as a function of drive. Blue line: mean ; red line: population Fano factor (pFF); and green line: mean firing rate. Dashed red line: separation between synchronous and asynchronous state based on the pFF. (b) Effect of drive on . (c) with . Blue/Red trace: average /; dotted traces: maximum (upper) and minimum (lower) power values computed across input frequencies for each case. (d) SNR measured in as a function of drive.

Figure 7. Propagation speed within the resonance frequency range.

Simulations were conducted in 5-layer FFNs. Propagation speed measured in cycles per layer as a function of the inter-pulse interval. Bottom/center/top box lines: first/second/third quartiles of the speed distributions. Top/bottom whiskers: largest/smallest value within 1.5 IQR of the upper/lower quartile. Crosses: values observed outside the 1.5 IQR.