Cortical Circuit Dynamics Are Homeostatically Tuned to Criticality In Vivo

Abstract

Homeostatic mechanisms stabilize neuronal activity in vivo, but whether this process gives rise to balanced network dynamics is unknown. Here, we continuously monitored the statistics of network spiking in visual cortical circuits in freely behaving rats for 9 days. Under control conditions in light and dark, networks were robustly organized around criticality, a regime that maximizes information capacity and transmission. When input was perturbed by visual deprivation, network criticality was severely disrupted and subsequently restored to criticality over 48 h. Unexpectedly, the recovery of excitatory dynamics preceded homeostatic plasticity of firing rates by >30 h. We utilized model investigations to manipulate firing rate homeostasis in a cell-type-specific manner at the onset of visual deprivation. Our results suggest that criticality in excitatory networks is established by inhibitory plasticity and architecture. These data establish that criticality is consistent with a homeostatic set point for visual cortical dynamics and suggest a key role for homeostatic regulation of inhibition.

Keywords: computation; cortex; criticality; dynamics; homeostasis; homeostatic plasticity; modeling; visual cortex.

Figure 1. DCC, the Deviation from Criticality Coefficient, is an effective, scalar measure of how near a neural network is to criticality.

(A) Discrete relaxation events, i.e. avalanches, are identified in ensemble recordings by the presence of silent periods. Spikes from all neurons in a region of interest can contribute to an avalanche, which is measured as a function of the number of contributing spikes (S) or the event duration (D). (B) (left, center) The probability (PDF, probability distribution function) of observing an avalanche of a given size (gold) or duration (blue) can be fit by power laws, each generating an exponent (τ, α); the exponent is the slope of the line in a log-log plot. Solid gray traces display avalanche distributions in shuffled data. (right) In critical systems, size and duration scale according to the displayed formula. The difference between the predicted exponent (solid gray line) and the observed exponent (dashed gray line) is a quantitative measure of deviation from criticality (Deviation from Criticality Coefficient, DCC). (C) Avalanche size PDF and associated DCC extracted from model networks operating in critical (top left), supercritical (top right), and subcritical regimes (bottom left). (bottom right) Ground truth model testing of DCC. In three model networks (three colors) DCC is compared to the maximum eigenvalue of the adjacency matrix (1.0 indicates a critical regime by definition). (D) Avalanche size PDFs and DCCs extracted from 4 h of single unit data in each of three example animals; examples are a subset of the seven animals used for this study. Data in B and D are derived from control hemisphere ensembles of well-isolated RSUs. Model and empirical data have been fit with power law functions.

Figure 2. Network dynamics are homeostatically tuned to near-criticality, independently of excitatory FR homeostasis.

(A) The FRs of continuously observable excitatory neurons followed across 7 d recordings show a biphasic response to monocular deprivation (MD, 47 units, 7 animals). FRs were normalized to 24 h of baseline recordings prior to the induction of MD. FRs were stable for > 24 h after the light exposure on the first day of MD (0 h). FRs were maximally suppressed at 36 h (blue arrow) and rebounded to baseline levels by 84 h (gold arrow). (B) In the same recordings, critical dynamics were assessed. In the first 4 h of light exposure following lid suture, the mean DCC more than tripled (blue arrow). The mean DCC was restored to baseline levels at 48 h (gold arrow). (C) In the control hemisphere, MD had no significant impact on mean normalized FR of continuously observable units. (D) Likewise, in the control hemisphere MD had no significant impact on DCC. Data from the night before MD1 are not shown as they are subject to artifacts from brief anesthesia and lid suture. Dashed gray line is the baseline mean. Solid green line marks 25% change from baseline. Red arrow is time of lid suture. Blue arrow marks the first bin in which data cross the 25% line. Gold arrow marks the first bin in which data return to within 25% of baseline.

Figure 3. Inhibitory and not excitatory parameters or synaptic plasticity rules are sufficient to recapitulate empirical results in a series of models.

(A) (left) Illustration of model recurrent network with excitatory input (blue) to inhibitory (orange) and excitatory (green) neurons. (right) Illustration of model time course and “successful” results. Firing rates of excitatory (E) and inhibitory (I) neurons and network state with respect to criticality (DCC) were monitored continuously. In successful models, “lid suture” (reduction in excitatory input, blue/gray line) rapidly increased DCC (ω), suppressed inhibitory neuron FRs prior to suppressing excitatory neuron FRs (δ), and each of these measures returned to baseline parameters (ε) despite maintained reduction in input. (B) The inhibitory fraction of the network and the number of excitatory neurons contacted by each inhibitory neuron were systematically varied across three levels of input to inhibitory neurons. Only three discrete combinations of parameters were sufficient to reproduce empirical results (green, blue, and gray). (C) A reasonable (nearby) but unsuccessful arrangement of inhibitory parameters was selected (dashed red line in (B)). With these parameters fixed, no explored region in the three-dimensional space defined by homeostatic plasticity gain (synaptic scaling, SS), spike timing dependent plasticity gain (STDP), and excitatory to excitatory neuron connectivity (%) was capable of rescuing the model. STDP gain factor was applied to both inhibitory and excitatory terms.

Figure 4. Excitatory neuron homeostatic plasticity stabilizes FRs, while inhibitory neuron homeostatic plasticity stabilizes critical dynamics.

Model cortical networks composed of inhibitory and excitatory neurons were subjected to stable input for 20,000 simulation time steps (t₀ to t₁). Spike timing dependent plasticity (STDP) and synaptic scaling (SS; a global multiplicative compensatory change in synaptic strength) were turned on at 50,000 steps (t₁). External input to the network (vertical dashed line, t₂) was reduced as a homeostatic challenge mimicking monocular deprivation. (A through D) Successful models recapitulated empirical results, such that input reduction: suppressed FRs of inhibitory neurons (red) prior to excitatory neurons (green), and both rebounded to baseline levels by t_end(A), and eliminated the critical network state (max eigenvalue equals 1) which rebounded by t_end (B). The mean excitatory synaptic strength (P) across the timecourse of successful models revealed a net increase by t_end (C). The progression of mean P as a function of changes in P due to STDP (orange) and SS (green) (D). (E through H) Successful models were rerun and SS was removed from excitatory neurons at the onset of input reduction. Inhibitory and excitatory FRs exhibited runaway gain (E) and network dynamics became unboundedly supercritical (F). Mean P exhibited a similarly unbounded progressive increase (G) as a result of uncompensated STDP (H). (I through L) Successful models were rerun and SS was removed from inhibitory neurons at the onset of input reduction. Neither excitatory nor inhibitory FRs exhibited runaway gain (I). Near critical network dynamics were eliminated (J). Mean P exhibited a net reduction (K) and alongside stable SS and STDP (L).