Co-emergence of multi-scale cortical activities of irregular firing, oscillations and avalanches achieves cost-efficient information capacity

<div><p>The brain is highly energy consuming, therefore is under strong selective pressure to achieve cost-efficiency in both cortical connectivities and activities. However, cost-efficiency as a design principle for cortical activities has been rarely studied. Especially it is not clear how cost-efficiency is related to ubiquitously observed multi-scale properties: irregular firing, oscillations and neuronal avalanches. Here we demonstrate that these prominent properties can be simultaneously observed in a generic, biologically plausible neural circuit model that captures excitation-inhibition balance and realistic dynamics of synaptic conductance. Their co-emergence achieves minimal energy cost as well as maximal energy efficiency on information capacity, when neuronal firing are coordinated and shaped by moderate synchrony to reduce otherwise redundant spikes, and the dynamical clusterings are maintained in the form of neuronal avalanches. Such cost-efficient neural dynamics can be employed as a foundation for further efficient information processing under energy constraint.</p></div

Multi-scale dynamics of E-I balanced network with various synchrony degree.

<p>Left panel: asynchronous state (<i>τ_{d_e}</i> = 6 ms, <i>τ_{d_i}</i> = 6 ms); Middle panel: moderately synchronized state (<i>τ_{d_e}</i> = 4 ms, <i>τ_{d_i}</i> = 10 ms); Right panel: highly synchronized state (<i>τ_{d_e}</i> = 2 ms, <i>τ_{d_i}</i> = 14 ms). (A, C, E) Time series of membrane potential, input conductances, and input currents of a randomly selected neuron. (B, D, F) Network activity. Top, raster plot of a subset 500 neurons (Exc 400 (blue), Inh 100 (red)); bottom, the average excitatory and inhibitory population activity in 1-ms bins; inset, autocorrelation (AC) of the excitatory population activity. Middle and right panels show that the population rhythm is mainly determined by inhibitory decay time <i>τ_{d_i}</i>, and the delayed negative feedback from inhibitory population suppresses the firing of the excitatory population, leaving a window for integration, whose size controls the burst of individual activities (C, E).</p

Definition of spatiotemporal spike patterns.

<p>(A) Examples of cross-correlogram between neuron pairs for various parameter sets (<i>τ</i>_{<i>d</i>_<i>e</i>}, <i>τ</i>_{<i>d</i>_<i>i</i>}) show that spike coincidence happens within 20-ms windows; the average firing rate of one neuron is plotted relative to the time at which the other neuron spikes, averaged over 2000 pairs of randomly selected excitatory neurons. Black, blue, red points are the respective subcritical, critical supercritical cases as exampled in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005384#pcbi.1005384.g002" target="_blank">Fig 2</a>. Three more cases around the critical region are shown as green points. (B) Schematics of mapping spiking patterns of 10 randomly selected neurons into binary strings; black, patterns without any spike; blue, binary patterns with spikes.</p

Cost-efficient information capacity in the critical region.

<p>(A) Average excitatory firing rate <i>v</i>_<i>E</i>; (B) Energy efficiency <i>η</i>_sim in analog scenario at <i>r</i> = 0; (C, D) Energy efficiency <i>η</i>_sim at various <i>r</i> (colors) and average excitatory firing rate <i>v</i>_<i>E</i> (black) vs. E—E Synchrony in both binary (C) and analog (D) scenarios. Cost-efficiency is achieved robustly in the critical region across the empirical range of <i>r</i>. <i>n</i> = 40 for all patterns. (A, B) in the parameter space (<i>τ</i>_{<i>d</i>_<i>e</i>}, <i>τ</i>_{<i>d</i>_<i>i</i>}) (unit: ms).</p

Spiking neuron number distribution.

<p>Probability distributions of the activated neuron number for the selected states, indicated in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005384#pcbi.1005384.g006" target="_blank">Fig 6A and 6B</a> with the corresponding symbols. <i>n</i> = 40 for all patterns. The distribution in the critical region is close to the experimental data [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005384#pcbi.1005384.ref048" target="_blank">48</a>] (red).</p

Co-existence of multi-scale cortical activities at moderately synchronized states.

<p>(A) Average pairwise 1-ms synchrony between excitatory neurons (E—E Synchrony); (B) Average CV (standard deviation/mean) of the inter-spike intervals (ISIs) over the excitatory population; (C) Power spectra of population activity for 3 different parameter sets indicated in (F); (D) Peak frequency; (E) Peak power. (F) Avalanche size distributions for 3 different parameter sets. (G) Distance of avalanche size distribution from the best-fitted power-law distribution; (H) ISI CV (red), distance from power-law (black) and peak power (blue) <i>vs</i>. E—E Synchrony, showing the co-existence of irregular firing, synchronized oscillations and neuronal avalanches at moderately synchronized states. (A, B, D, E, G) in the parameter space (<i>τ</i>_{<i>d</i>_<i>e</i>}, <i>τ</i>_{<i>d</i>_<i>i</i>}) (unit: ms).</p

Probability of empty patterns.

<p>Dependence of the probability <i>p</i>₀ of empty patterns on the number of spiking neurons <i>m</i>_<i>n</i> for and the subcritical state in our simulations at various sample size <i>n</i>. Dashed line represents the ideal case with all neurons firing randomly. Parameter set (<i>τ</i>_{<i>d</i>_<i>e</i>}, <i>τ</i>_{<i>d</i>_<i>i</i>}) is indicated by the triangle in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005384#pcbi.1005384.g006" target="_blank">Fig 6A and 6B</a>.</p

Schematic representation of network architecture, neuronal integration and spike, synaptic conductance traces.

<p>(A) The local recurrent neuronal network consists of excitatory (Exc) and inhibitory (Inh) spiking neurons with synaptic connections (blue, excitatory; red, inhibitory) and inputs from other neural circuits or external stimuli. (B) The voltage trace of one IF neuron with refractory period and leaky current. (C) The unitary conductance response to a pre-synaptic spike is described by a bi-exponential function with latency <i>τ</i>_<i>l</i>, rise time <i>τ</i>_<i>r</i> and decay time <i>τ</i>_<i>d</i>.</p

Burst firing enhances neural ouput correlation

Neurons communicate and transmit information predominantly through spikes. Given that experimentally observed neural spike trains in a variety of brain areas can be highly correlated, it is important to investigate how neurons process correlated inputs. Most previous work in this area studied the problem of correlation transfer analytically by making significant simplifications on neural dynamics. Temporal correlation between inputs that arises from synaptic filtering, for instance, is often ignored when assuming that an input spike can at most generate one output spike. Through numerical simulations of a pair of leaky integrate-and-fire (LIF) neurons receiving correlated inputs, we demonstrate that neurons in the presence of synaptic filtering by slow synapses exhibit strong output correlations. We then show that burst firing plays a central role in enhancing output correlations, which can explain the above-mentioned observation because synaptic filtering induces bursting. The observed changes of correlations are mostly on a long time scale. Our results suggest that other features affecting the prevalence of neural burst firing in biological neurons, e.g., adaptive spiking mechanisms, may play an important role in modulating the overall level of correlations in neural networks