A mechanism for persistent memory in oscillatory networks

I just finished the Methods in Computational Neuroscience "bootcamp". It was intense, but valuable—I can recommend that any student/postdoc who wants to get started in the field take it. 

For a course project, I extended previous work, which showed that oscillatory drive can excite patterned instabilities in visual cortex. These patterns constitute attractor states that are stabilized by an external oscillatory drive. The project explored the idea that similar oscillation-stabilized attractors might serve as a flexible working memory. 

(Unfortunately, these notes are rather brief and incomplete as I never had the time to write this up properly. )

Selective, short-term maintenance of attractor states is important for working memory in neural systems. Neural networks, however, are typically stabilized by feedback inhibition. The delays in this inhibition lead to unavoidable oscillations. 

This project demonstrate a scenario where the attractor dynamics associated with a working memory are not fixed points, but instead fixed limit cycles embedded within a population oscillation. 

External oscillatory drive, perhaps e.g. an attention signal, can switch such a network from a "read-in" mode, in which the system responds to external input, and a "hold" model, in which the system retains a memory of its past states. These concepts may underlie flexible working memory solutions that can coexist with population oscillations.

To better understand the mechanisms underlying this, we explored a switched piece-wise linear model that captured the qualitative dynamics of the original system. We found that firing-rate nonlinearities with positive curvature are important for allowing a synchronous (non-selective) external signal to excite the asymmetric network states associated with a memory trace. 

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[get presentation slides]

Preview: Figure 4

Figure 4: Many-population generalization of the two-population model of Rule et al. (2011), serving as a working memory. Starting from rest, a stimulus is delivered to the first oscillator (green) for $t\in[300,500)$ ms. We test the stability of this stimulus-driven network response during a hold period $t\in[500,1500)$ ms. Without oscillatory drive (top), the memory fades in a few cycles. Periodic stimulation (bottom) preserves the memory. Rightmost plots show the phase-plane dynamics during the readout period $t\in[1000,1500)$. The top system, without drive, has returned to rest. The driven system shows a stable limit cycle, with higher firing rates in the population that initially received the stimulus.