43 research outputs found
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
The locally-linked neuronal network model and external asynchronous stimulus currents.
<p>(a) The locally-linked neuronal network model on two-dimensional square having neurons and layers. Here, we take , and label neural number (1 – 1000) from left to right layers. (b) To train the network, the input pulse current with duration is injected alternately into each pair of layers with the left-right sequence having the same inter-stimulus interval , respectively. After each training trial, there is a long enough time to let network activity recover to the rest state for the next training. We perform training for all the pair of layers with the same number of trials. (c) To test the resulting feedforward structure and its propagative capacity, a steady current is injected into a certain layer (here, we choose the 3rd layer, i.e., L3).</p
Cost-efficient information capacity in the critical region.
<p>(A) Average excitatory firing rate <i>v</i><sub><i>E</i></sub>; (B) Energy efficiency <i>η</i><sub>sim</sub> in analog scenario at <i>r</i> = 0; (C, D) Energy efficiency <i>η</i><sub>sim</sub> at various <i>r</i> (colors) and average excitatory firing rate <i>v</i><sub><i>E</i></sub> (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><sub><i>d</i>_<i>e</i></sub>, <i>τ</i><sub><i>d</i>_<i>i</i></sub>) (unit: ms).</p
Probability of empty patterns.
<p>Dependence of the probability <i>p</i><sub>0</sub> of empty patterns on the number of spiking neurons <i>m</i><sub><i>n</i></sub> 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>Ï„</i><sub><i>d</i>_<i>e</i></sub>, <i>Ï„</i><sub><i>d</i>_<i>i</i></sub>) 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>Ï„</i><sub><i>l</i></sub>, rise time <i>Ï„</i><sub><i>r</i></sub> and decay time <i>Ï„</i><sub><i>d</i></sub>.</p
Average synaptic weights as a function of the stimulus interval for STDP with temporal asymmetry.
<p>The same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g006" target="_blank">Fig. 6</a>, but for the temporally asymmetric form of STDP. Here, the parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a>, except for , ms, ms.</p
Definition of spatiotemporal spike patterns.
<p>(A) Examples of cross-correlogram between neuron pairs for various parameter sets (<i>Ï„</i><sub><i>d</i>_<i>e</i></sub>, <i>Ï„</i><sub><i>d</i>_<i>i</i></sub>) 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
Average synaptic weights as a function of the number of training trials.
<p>Average synaptic weights for three different connection types: feedforward (squares), feedback (circles) and recurrent (upward triangles) as a function of the trial number for temporally symmetric form of STDP ( and ms) (a) and for temporally asymmetric form of STDP ( and ms) (b). The other parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a> except for ms. Also, we show the average synaptic weights for the connections including both feedforward and feedback types (downward triangles) in (a) and (b).</p
Multi-scale dynamics of E-I balanced network with various synchrony degree.
<p>Left panel: asynchronous state (<i>Ï„<sub>d_e</sub></i> = 6 ms, <i>Ï„<sub>d_i</sub></i> = 6 ms); Middle panel: moderately synchronized state (<i>Ï„<sub>d_e</sub></i> = 4 ms, <i>Ï„<sub>d_i</sub></i> = 10 ms); Right panel: highly synchronized state (<i>Ï„<sub>d_e</sub></i> = 2 ms, <i>Ï„<sub>d_i</sub></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>Ï„<sub>d_i</sub></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
Dependance of exponents for the resulting structure on exponents of STDP after 20 training trials.
<p>(a) vs. for different (b) vs. for different . For comparison, and are shown as solid lines in (a) and (b), respectively. The other parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a>.</p