Balanced cortical microcircuitry for maintaining information in working memory

Abstract

Persistent neural activity in the absence of a stimulus has been identified as a neural correlate of working memory, but how such activity is maintained by neocortical circuits remains unknown. We used a computational approach to show that the inhibitory and excitatory microcircuitry of neocortical memory-storing regions is sufficient to implement a corrective feedback mechanism that enables persistent activity to be maintained stably for prolonged durations. When recurrent excitatory and inhibitory inputs to memory neurons were balanced in strength and offset in time, drifts in activity triggered a corrective signal that counteracted memory decay. Circuits containing this mechanism temporally integrated their inputs, generated the irregular neural firing observed during persistent activity and were robust against common perturbations that severely disrupted previous models of short-term memory storage. These results reveal a mechanism for the accumulation and storage of memories in neocortical circuits based on principles of corrective negative feedback that are widely used in engineering applications.

Fig. 1

Memory networks with negative-derivative feedback. a–c, Simple models of a neural population and their energy surfaces with positive feedback (a), derivative feedback (b), and hybrid positive and derivative feedback (c). Persistent activity can be maintained at different levels (horizontal axis of energy surface) either by a positive feedback mechanism that effectively flattens the energy surface (a, c, bottom) or by a negative-derivative feedback mechanism that acts like a viscous drag force opposing changes in memory activity (b, c, bottom). The wall at the left of the energy surface represents the constraint that activity cannot be negative. d, Illustration of how a negative-derivative feedback mechanism detects and corrects deviations from persistent activity. e–g, Effective time constant of activity from Eq. (2) as a function of the strengths of positive feedback W_pos (e,g) and derivative feedback W_der (f, g). As W_der increases, the network time constant τ_eff becomes less sensitive to changes in W_pos (g).

Fig. 2

Negative-derivative feedback networks of excitatory and inhibitory populations. a, Derivative feedback network structure (top) and component feedback pathways onto the excitatory population (bottom). b, In response to external input that steps the excitatory population between two fixed levels, the recurrent feedback pathways mediate a derivative-like signal resulting from recurrent excitation and inhibition that arrive with equal strength but different timing. c, d, Maintenance of graded persistent firing in response to transient inputs (c) and integration of step-like inputs into ramping outputs (d) with linear (top) and nonlinear (bottom) firing rate (f) vs. input current (I) relationships.

Fig. 3

Negative-derivative feedback with mixture of NMDA/AMPA synapses in all excitatory pathways. a, Derivative feedback network structure. Blue, cyan, and red curves represent NMDA-mediated, AMPA-mediated currents, and GABA-mediated currents, respectively. q_EE and q_IE are the fractions of NMDA-mediated synaptic inputs in each excitatory pathway. b, Time constant of decay of network activity τ_network as a function of the average time constants of excitatory connections, aver(τ_EE ) and aver(τ_IE ). Each average time constant is varied either by varying the fractions or the time constants of NMDA-mediated synaptic inputs in each connection. The region in the red rectangle corresponds to a set of possible aver(τ_EE ) and aver(τ_IE ) obtained when varying q_EE and q_IE while holding the synaptic time constants fixed at values matching the experimental observations in [13]. c, Time constant of decay of network activity τ_network as a function of the connectivity strengths J_ij and the time constants of positive and negative feedback, τ₊ and τ₋. τ_network increases linearly with the balanced amount of positive and negative-derivative feedback J_der ~ J_EE ~ J_IEJ_EI/J_II, and with the difference between τ₊ and τ₋, as W_der~J_der(τ₊ −τ₋).

Fig. 4

Robustness to common perturbations in memory networks with derivative feedback. a–f, Non-robustness of persistent activity in positive feedback models. a, Positive feedback models with recurrent excitatory (left) or disinhibitory (right) feedback loops. b, Effective time constant of network activity, τ_network, as a function of connectivity strength. Green asterisks correspond to 5% deviations from perfect tuning. c–f, Time course of activity in perfectly tuned networks (black) and following small perturbations of intrinsic neuronal gains (c) or synaptic connection strengths (d–f). g–k, Robust persistent firing in derivative feedback models. To clearly distinguish the hybrid models with derivative and positive feedback, purely negative-derivative feedback models with no positive feedback are shown. All excitatory synapses are mediated by both NMDA and AMPA receptors as in Fig. 3, with parameters chosen to coincide with experimental observations [13]. h, τ_network increases linearly with the strength of recurrent feedback J. i–k, Robustness to 5% changes (green asterisks in h) in neuronal gains or synaptic connection strengths. l, Disruption of persistent activity in derivative feedback models following perturbations of NMDA-mediated synaptic currents. m, Hybrid model with positive and derivative feedback. n–q, As the strength of negative-derivative feedback is increased, τ_network decreases less rapidly with mistuning than in purely positive feedback models (n) and the network becomes robust against perturbations (o–q, shown for J_der/J_pos=150). r, Disruption of persistent activity in the hybrid model following perturbations of NMDA-mediated currents.

Fig. 5

Irregular firing in spiking networks with graded persistent activity. a, Experimentally measured irregular firing (coefficients of variation of inter-spike intervals, CV_isi, higher than 1) during persistent activity in a delayed-saccade task. Adapted from [16]. b, Structure of network of spiking neurons with negative-derivative feedback. c–k, Network response to a brief (100 ms) stimulus applied at time 0. c–e, Raster plots illustrating irregular persistent firing of 50 example excitatory neurons. f–h, Instantaneous, population-averaged activity of excitatory neurons, computed within time bins of 1 ms (gray) or 10 ms (black). i–k, Balance between population-averaged excitation and inhibition following offset of external input. l–n, Histogram of CV_isi of active excitatory neurons during the persistent firing. Note that, for activity with strong input, a small subset of neurons fire regularly at high rate and exhibit low CV_isi (n). This reflects that the heterogeneity resulting from our simple assumption of completely randomly connected networks can result in excess positive feedback in some clusters of neurons.

Fig. 6

Synaptic inputs in derivative feedback and common positive feedback models. a–c, Network structures of positive feedback models (a, b) and derivative feedback models (c) with two competing populations. d–f, Relation between firing rates of excitatory and inhibitory neurons. Firing rates of the E₂ (black points) and inhibitory (red points) populations are plotted as a function of E₁ firing rate. g–i, Relation between excitation and inhibition for different levels of maintained firing. X- and y-axes are normalized by the amount of excitation and inhibition received when the left and right excitatory populations fire at equal levels of 30 Hz. j–l, Persistent activity in the two competing excitatory populations (solid: E₁; dashed, E₂). Perturbing the networks by uniformly increasing the intrinsic gain in E₁ leads to gross disruptions of persistent firing in positive feedback models (green curves in j, k), but not negative-derivative feedback models (l). See Supplementary Fig. S5 for robustness to other perturbations.