Maintaining information in short-term memory (STM), a crucial aspect of various cognitive and non-cognitive functions, relies on biophysical mechanisms that are still not fully understood. While persistent neuronal activation correlates with memory maintenance, simple recurrent network feedback models face challenges. These models either exhibit implausible sensitivity to parameter adjustments or can only maintain a single, unrealistically high firing rate, limiting information capacity to a single bit. This limitation is referred to as the "low firing rate problem". Separately, research has revealed distinct oscillatory activity bands during working memory maintenance, originating from various mechanisms (cell-intrinsic, local circuitry, or long-range interactions). The functional role of these oscillations, however, remains unclear—ranging from essential components to mere epiphenomena. This study explores a potential mechanistic role for oscillations, showing how oscillatory inputs to recurrent feedback circuits can enable low-firing-rate persistent activity and multiple distinct firing rates, thus enhancing memory network information capacity.

The paper reviews existing models of persistent neural activity, highlighting the limitations of simple recurrent network feedback models in realistically representing both stimulus identity and amplitude. These models, based on positive feedback, either fail to maintain activity at biologically plausible firing rates (the low firing rate problem) or require implausibly precise parameter tuning. The role of oscillatory activity in working memory is also discussed, acknowledging conflicting viewpoints: some studies propose a crucial role for oscillations in various memory functions (generating/maintaining persistent activity, structuring spatial codes, coordinating activity), while others consider oscillations as incidental to other mechanisms. The authors cite relevant research on oscillations in working memory and their potential relationship to memory functions.

The authors utilize several mathematical models to investigate their hypothesis. Initially, they illustrate the limitations of simple recurrent feedback circuits in achieving biologically plausible persistent activity using an idealized circuit model with a memory neuron and positive feedback. They explore both linear and nonlinear firing rate functions, revealing the challenges of achieving stable, low-firing-rate persistent activity without exact parameter tuning. Subsequently, a more biologically realistic conductance-based spiking neuron model (Wang-Buzsaki model) is employed to demonstrate the effects of adding a subthreshold oscillatory drive. This model incorporates potassium, sodium, and leak conductances. The oscillatory input's effects on generating persistent activity and multiple firing rates are analyzed. The authors investigate the requirements for this mechanism, including oscillation strength, synaptic time constants, and the nonlinearity of the neuron model to facilitate phase-locking to the external oscillation. Further analysis involves a simplified integrate-and-fire model neuron to better understand the phase-locking mechanism and its relation to discretely graded persistent activity. Both non-leaky and leaky integrate-and-fire models are examined, highlighting how the restorative decay in membrane potential influences phase-locking and robustness to perturbations. To investigate the robustness of the mechanism, the authors compare their oscillatory autapse memory model with a traditional approximately linear autapse model known to produce graded persistent activity without oscillations. The effects of mistuning recurrent feedback weights on the performance of both models are examined. Finally, the basic principle is extended to more complex network architectures: a spatially uniform (all-to-all) network for temporal integration, a ring-like architecture for encoding both spatial location and graded levels, and a chain-like architecture for generating sequences of activity with multiple graded amplitudes. The robustness of the all-to-all network to various sources of noise (input noise, weight noise, shuffled phases, noisy oscillation parameters) is also evaluated.

The core finding is that adding a subthreshold oscillatory input to recurrent excitatory networks allows for the robust maintenance of multiple, discretely graded levels of persistent activity. This contrasts with non-oscillatory models which either exhibit the low-firing-rate problem or require implausible parameter tuning. The mechanism relies on phase-locking of neuronal spiking to the oscillatory input, creating stable fixed points at integer multiples of the oscillation frequency. The authors demonstrate this mechanism in various network models: * **Single Neuron Model:** Adding oscillatory input to a conductance-based spiking neuron model (Wang-Buzsaki model) enables the maintenance of multiple discretely graded persistent activity levels that are robust to small changes in parameters. Small input perturbations cause transient phase shifts that quickly decay, ensuring stability in spiking activity. This feature is absent in non-leaky integrate-and-fire neurons. * **All-to-All Network:** A large-scale network (1000 neurons) with all-to-all connectivity demonstrates robust multi-level persistent activity even with various sources of noise (input noise, weight noise, random phase shifts, noisy oscillation frequency and amplitude). The network is shown to effectively temporally integrate its inputs. * **Ring Network:** A ring network model, commonly used for studying spatial working memory, maintains multiple graded levels of activity at specific locations. This capacity surpasses traditional ring models limited to binary representations. * **Chain Network:** A chain-like network, suitable for modelling sequential activity, exhibits sequences of activity with multiple discretely graded amplitudes, unlike traditional sequential activity models which have only a single activity level. The robustness of the multi-level storage mechanism is attributed to the phase-locking process. Mistuning of feedback weights has minimal effects on the multi-level storage in the oscillatory models, unlike traditional models that are highly sensitive to these parameter changes. This finding highlights the resilience of the proposed mechanism to biological variability.

The findings address the limitations of traditional models of persistent activity in working memory by demonstrating a mechanism that enables multi-level storage without requiring precise parameter tuning. The introduction of subthreshold oscillatory inputs transforms networks from binary to discretely graded activity representations, significantly increasing their information capacity. This mechanism is robust to various types of noise and parameter variations. The proposed model provides a potential explanation for the observed oscillatory activity during working memory tasks and suggests a new role for oscillations in enhancing short-term memory capacity. The discretely graded nature of the representation could potentially be further refined by pooling across multiple discretized representations with different staircase step locations, potentially resolving the trade-off between the number of storable levels and robustness to noise. The findings call for further experimental investigations to verify the phase-locking predictions of the model, which requires high-resolution recordings capable of capturing both population-wide and cellular-resolution activity.

This paper presents a novel mechanism for multi-level information storage in short-term memory using oscillatory inputs. This mechanism, tested across various network architectures and noise conditions, overcomes limitations of existing models by enabling robust multi-stable representations without the need for fine-tuning. Future research should focus on experimental validation of the model's predictions regarding phase-locking and the potential for pooling multiple representations to enhance resolution, and exploring the implications of this mechanism for other brain functions relying on persistent neural activity.

The study relies heavily on computational models. While the models are biologically inspired, translating the findings to real biological systems requires further experimental validation. The high-resolution recording techniques needed to test the phase-locking prediction are currently limited. The model assumes a homogeneous oscillatory input; the effect of more realistic heterogeneous oscillatory inputs needs further investigation. Also, the method of terminating persistent activity is not explicitly modeled.