Timing over Tuning: Overcoming the Shortcomings of a Line Attractor during a Working Memory Task

<div><p>How the brain stores information about a sensory stimulus in working memory is not completely known. Clues about the mechanisms responsible for working memory can be gleaned by recording from neurons during the performance of a delayed response task. I focus on the data recorded during such an experiment, a classic tactile discrimination task. I describe how the observed variability in the firing rate during a trial suggests that the type of attractor that is responsible for holding the stimulus information is not a fixed-point type attractor. I propose an alternate mechanism to a line attractor that allows the network to hold the value of an analog stimulus variable for the duration of the delay period, but rather than maintain a constant level of activity, the cells' firing rate varies throughout the delay period. I describe how my proposed mechanism offers a substantial advantage over a line attractor: The tuning requirements of cell to cell connections are greatly eased from that of a line attractor. To accommodate a change in the length of the delay period, I show that the network can be altered by changing a single parameter - the timing of an executive signal that originates outside of the network. To demonstrate the mechanism, as well as the tuning benefits, I use a well known model of propagation in neuronal networks.</p></div

Distribution of end of delay period activity for a line attractor and two instances of the decay and amplify model.

<p>The first row shows the distributions for a line attractor. The second and third rows show the distributions for models with decay rates of (), and (), respectively. The corresponding amplification rates are also and . The distributions in a single column are very similar, demonstrating that the decay and amplify mechanism integrates noise no better or worse than a line attractor.</p

Model performance.

<p>Shown are the success rates for three decay rates () and four different noise strengths () as a function of the timing of the executive input. For each decay, noise, and input value the simulation was run 200 times. The last 10 persistent cells in the feed forward chain were used in the calculation. The green lines show the boundaries of the timing interval described in the previous section. The noise causes a near symmetric distribution of end of delay period activity levels centered around the mean (the predicted value given in the previous section). At the boundaries, this distribution will be centered around the range required for success, and so the success rate at these boundaries is for all noise strengths.</p

Schematic for the network described by equations (11–12).

<p>The blue circles represent the early and persistent cells through which the traveling wave propagates. The green circles represent the late cells. When the executive input arrives, the late cells are activated by the persistent cells. In this instance, the connections from the persistent to the late are divergent (black arrows). The late cells feed back onto the early and persistent cells in a one-to-one fashion (green arrows). This is only one of many possible implementations of the decay and amplify mechanism.</p

Simulations of the non-feed-forward model.

<p>The upper left panel is an array plot showing all early and persistent cells. Of note is the trailing wavefront that originates at the boundaries. Those cells that this wave front overtakes are the early cells. The upper right, lower left, and lower right panels show the evolution of a persistent, early, and late cell respectively, for a range of stimulus values (the loading phase is not shown). For all of these figures, the connection strength , the feedback strength is , and the executive input arrives at .</p

Time series showing the activity level of a persistent cell (used is the last persistent cell in the chain) undergoing the proposed decay-amplify mechanism.

<p>Shown are time series for stimulus variable values ranging from (black) to (brown). For each of the simulations, the stimulus was removed at , and the executive input arrives at . The connection strengths are and the feedback is . For the noise, .</p

The modified wave.

<p>The panels describe the same things as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003437#pcbi-1003437-g002" target="_blank">figure 2</a>, with the same parameter values. The removal of the stimulus is given by the first dotted line. The arrival time of the task input is represented by the second dotted line. Of note in this figure is that the late cells are held back, and do not participate in the task until the task input arrives.</p