An oscillatory mechanism for multi-level storage in short-term memory

The study addresses how neural circuits maintain information over seconds-long intervals characteristic of short-term/working memory. Traditional recurrent positive-feedback models can produce persistent activity that encodes stimulus identity spatially, but they typically suffer either from the low-firing-rate problem (nonlinear models that yield only binary on/off states with unrealistically high sustained rates) or from a fine-tuning requirement (linear models that allow graded rates but demand exact balance between decay and feedback). Concurrently, oscillatory activity is frequently observed during working memory, yet its causal role remains debated. The authors hypothesize that adding subthreshold oscillatory input to recurrent circuits enables storage not only of spatial identity but also of discretized amplitude levels via phase-locking, thereby increasing information capacity without implausible fine-tuning.

The paper reviews evidence for persistent activity as a correlate of working memory and classical recurrent feedback mechanisms for its generation, noting limitations such as the low firing rate problem and fine-tuning in analog integrators. It surveys observations of oscillatory activity (theta, alpha, beta, gamma) during maintenance and prior proposals for roles of oscillations in generating persistent activity, structuring codes through cross-frequency coupling, and coordinating/gating memory. Some work posits oscillations as epiphenomenal. Prior spatial bump attractor models can store locations but typically support binary amplitudes unless finely tuned. The present work builds on and complements these by proposing a mechanistic role for oscillations to create discretely graded, robust states without exact tuning.

The authors use computational modeling with conductance-based spiking neurons and simplified integrate-and-fire models. Primary model: Wang–Buzsáki (W-B) conductance-based neuron with sodium, potassium, and leak currents receiving: (1) recurrent synaptic feedback I_s via weight(s) w, (2) a tonic bias current I0, (3) a subthreshold oscillatory input I_osc(t) = A cos(ωt), and (4) transient external inputs to set memory levels. Spike times are defined by AP peaks exceeding 0 mV. Numerical integration uses 4th-order Runge–Kutta with 0.01 ms time step. A slow NMDA-like synaptic activation variable s provides inter-cycle persistence; in multi-neuron networks, heterogeneous oscillation phases can reduce the required synaptic time constant by bridging cycles through staggered spiking. Single-neuron analyses: An autapse (self-excitation) W-B neuron illustrates the low-rate problem without oscillations and the emergence of discretely graded persistent activity with oscillations via phase-locking. Perturbation analyses show that phase advances/delays during suprathreshold phases are reset during subthreshold troughs, stabilizing spikes-per-cycle. Integrate-and-fire analyses: Non-leaky IF (no subthreshold decay) lacks phase resetting; small input changes accumulate phase shifts across cycles, yielding continuously graded spiking per cycle. Leaky IF (membrane time constant 10 ms) exhibits exponential decay of phase perturbations during subthreshold periods, enabling phase-locking and discrete spikes-per-cycle. Example parameters: I_osc amplitude −1.0 µA/cm^2, ω = 0.05 ms^−1, constant current I = −0.4 µA/cm^2; spike threshold −59.9 mV; reset −68 mV; no refractory. Network architectures of W-B neurons: (a) All-to-all network (N=1000) with uniform synaptic weights, extended to examine robustness to perturbations: input noise (independent Ornstein–Uhlenbeck noise per neuron, σ specified), static weight noise (Gaussian noise added to each synapse), sparsity, shuffled oscillation phases, and time-varying oscillation frequency/amplitude (Ornstein–Uhlenbeck drift). (b) Ring network with local excitation and broader inhibition; connectivity approximated by w_ij = A + B cos(2π(θ_i − θ_j)) to generate spatial ‘bumps’. (c) Directed/chain-like network adding asymmetric term (e.g., Heaviside-weighted offset) to induce drift of activity bumps and produce sequences. Comparison model: An approximately linear spiking autapse model (per Seung et al. 2000; Shriki et al. 2003) that supports analog persistent activity only under fine-tuned feedback balancing decay, used to contrast robustness to synaptic weight detuning. Implementation details and parameter values for neurons, synapses, oscillations, and noise processes are provided in Supplementary Notes and Tables. Code and data are available via GitHub/Zenodo.

- Oscillatory input enables discretely graded persistent activity: Adding a subthreshold oscillatory drive to a recurrently excited neuron or network transforms binary/bistable responses into multiple stable levels corresponding to an integer number of spikes per oscillation cycle. Phase-locking creates a ‘staircase’ in firing rate versus feedback strength. - Resolution–robustness trade-off across frequencies: Lower frequency oscillations (e.g., 8 Hz) yield more closely spaced, more numerous levels; higher frequencies (e.g., 24 Hz, 40 Hz) yield fewer, more robust levels with wider basins of attraction. - Mechanistic requirements: (1) Oscillation amplitude must be sufficient to eliminate the no-spike fixed point near peaks and the runaway high-rate fixed point near troughs; (2) a process bridging cycles (e.g., slow NMDA-like synapses or network phase heterogeneity) is needed; (3) neuronal nonlinearity with restorative subthreshold dynamics enables phase-locking and correction of small perturbations. - Robustness to mistuning and noise: Unlike linear, tuned integrators, oscillation-based memory maintains discretized levels despite ±5% synaptic weight detuning. In 1000-neuron all-to-all networks, performance remains accurate under moderate perturbations: input noise with σ ≈ 0.1 µA·ms^0.5/cm^2 (point at which degradation begins), static weight noise with σ ≈ 0.055 µA/cm^2 (≈10× mean weight; onset of degradation), shuffled oscillation phases, and OU-drifting oscillation parameters. Perfectly correlated frequency noise across neurons degrades performance further but still supports multi-second persistence in typical realizations. - Spatial and sequential extensions: In a ring network, oscillations allow maintenance of discretely graded bump amplitudes and temporal integration of location-specific inputs without fine-tuning. In a directed/chain-like network, oscillations enable sequences with discretely graded amplitudes; without oscillations, activity decays or saturates to a single level. - Experimental prediction: Neural spikes should phase-lock to ongoing oscillations with discretized spikes-per-cycle that increase stepwise with input strength; EEG shows parametric power variations, but cellular-resolution recordings are likely needed to test discretization.

The findings resolve core issues in persistent activity models by exploiting oscillation-induced phase-locking: the low-firing-rate problem is overcome by cyclic termination of runaway feedback at oscillation troughs, while the fine-tuning requirement is alleviated because small feedback errors do not accumulate across cycles unless they change the integer spike count per cycle. This phase-reset mechanism yields multi-stable, discretely graded levels that increase working memory capacity beyond binary states without requiring precise parameter tuning. The framework generalizes across network architectures—uniform, spatial bump (ring), and chain-like sequential networks—supporting richer memory codes (amplitude plus spatial position or sequence timing). The model delineates a principled trade-off: higher-frequency rhythms enhance robustness and noise tolerance but limit the number of stable levels; lower frequencies afford higher resolution but demand longer bridging processes and are more noise-sensitive. These principles suggest potential roles of diverse brain rhythms in working memory and motivate experimental tests of discretized, phase-locked spike counts per cycle in population recordings during parametric memory tasks.

Oscillatory input can convert recurrent circuits from storing binary activity levels to maintaining multiple discretely graded, robust levels via phase-locking. This mechanism applies to persistent and sequential memory representations and extends to spatial bump networks, increasing information capacity without exact tuning. It predicts discretized spikes-per-cycle codes locked to oscillations. Future work should: (1) test for discrete spike counts per cycle with population-scale cellular-resolution recordings; (2) examine how multiple oscillation frequencies and heterogeneous phases jointly support capacity and robustness; (3) explore readout mechanisms that pool across discretized codes to achieve finer analog estimates; and (4) investigate biological substrates (e.g., NMDA/dendritic plateaus, circuit-level phase heterogeneity) that bridge oscillation cycles.

- Computational modeling study without direct experimental validation; empirical tests need cellular-resolution data to detect discretization. - Requires an inter-cycle bridging mechanism (e.g., slow synapses or network phase heterogeneity); insufficient bridging at low frequencies can degrade stability. - Some degree of feedback tuning is still needed to realize multiple stable levels; stability is limited by step widths in the spike-per-cycle staircase. - Performance degrades with sufficiently strong noise, especially with perfectly correlated oscillation-frequency fluctuations across neurons and at lower frequencies. - Assumes availability of subthreshold oscillatory inputs; the model does not specify the biological origin of these oscillations or termination signals for persistent activity.