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                                  1                                      2
        Miha PELKO, Grega REPOVŠ
1   Jožef Stefan international Postgraduate School, Ljubljana, Slovenia
2   Department of Psychology, Faculty of Arts, University of Ljubljana, Slovenia

           INTRODUCTION                                                                                                          Target                  Delay               Response             The subjects maintain fixation on a
                                                                                                                                                                                                  central point while a peripheral target
                                                                                                                                      Fix X                X

                                                                                                                                                                                                  is flashed for 200ms at a certain angle.
            Sustained firing of neurons observed in neuropsychological                                                                                                                            Following a delay of 2-5s, the fixation
            experiments in monkeys is thought to be the neuronal correlate of the                                                                                                                 point is extinguished and the subjects
                                                                                                                                                                                                  make a memory-guided saccade to
            representations in working memory. Those representations are                                                                                                                          the original location of the target.
            temporary, where the proposed mechanisms for the degradation of
            working memory are temporal decay and interference [1,2]. We                                                                                                                          While only behavioral information
                                                                                                                                                                                                  (angle of the saccade) is measured in
            specifically focus on the computational modeling of visuospatial                                                                                                                      the experiments involving humans [3],
            delayed-response experiments, where the experiments on humans                                                                                                                         also singe-cell measurements are
                                                                                                                                                                                                  taken in the experiments with monkeys
            [3] and monkeys [4], performing a memory-guided saccade task show                                                                    200ms
                                                                                                                                                                                                  [4], more precisely the neural activity of
            stable accuracy, but decreased precision of with time. An appropriate                                               Fix
                                                                                                                                                                                                  the cells corresponding to a specific
            computational model should:                                                                                                                                                           angle.
            ? to encode persistent stable activity with decreased
              Be able
            precision even in the absence of stimuli.
                                                                                                                                                                   Excitatory neurons
              Include a
            ? system of memory degradation coherent with the findings
            in the single-cell studies.
                                                                                                                                 Inhibitory neurons


                                                                                                                            To simulate the neuronal activity of the prefrontal cortex during the delayed-response task we use one
                                                                                                                            of the most frequently found model in the literature from Compte et al. [5]. This is conductance based
                                                                                                                            integrate-and-fire model, including GABA (inhibitory), AMPA and NMDA (both excitatory) mediated
                                                                                                                            synaptic currents.

                                                                                                                            The neural network in the model is composed of the populations of inhibitory and excitatory neurons
                                                                                                                            (EN), and external noisy stimulus representing the input from other brain areas. All the neurons are
                                                                                                                            fully interconnected.

                                                                                                                            EN are encoding the information of the target angle (the memory). Each neuron represents a specific
                                                                                                                            target angle. The connections among EN are formed in a way that the neurons encoding similar
                                                                                                                            angles are better connected (higher synaptic connectivity), then the ones encoding different angles.
                                                                                                                            The chart in the upper right shows such an exemplary profile of connectivity for a neuron encoding
                                                                                                                            angle 180°.

                                                                                                                            The simulations were preformed using the Brian Simulator [6].

                                                                                                                            The tested model successfully produces a stable persistent

                                                                                                                            Using the
                                                                                                                            ? model we were unable to fully simulate the decrease of
                                                                                                                            the neural activity in accordance with the single-cell measurements.

                                                                                                                            More thorough systematic approach in the search within the mode
                                                                                                                            connectivity parameters is required.

           The sequences of two of the performed simulations for different sets of connectivity parameters are
           shown above (top and bottom).

           The simulated neurons (N=2560) are constantly receiving random external stimuli. At t=200ms we induce
           a current to the neurons encoding the primary direction (PD = 180°) and the neighboring neurons for the
           period of 200ms, representing visual stimulus. This is followed by the delay period, when the neurons are
           again only receiving the background stimulation and the input from each other (fully interconnected
           network), which enables the persistent encoding.
            The raster plots on the left represent the activity (spike frequency) of the excitatory neuronal population     [1] Portrat, S., Barrouillet, P., & Camos, V. (2008). Time-related decay or interference-based forgetting in
           encoding the target angle over time. The recorded spikes are averaged over the time interval t=240ms             working memory? Journal of Experimental Psychology. Learning, Memory, and Cognition, 34(6), 1561-
           and the angle of 6°. The left figures present the activity of the neurons encoding the primary direction (PD -   1564. doi: 10.1037/a0013356.
           red lines) and the neurons encoding the two other angles (155°- green lines, 135° - blue lines ). The dotted
           lines roughly represent the schematic expected activity from the single-cell measurements.                       [2] Oberauer, K., & Lewandowsky, S. (2008). Forgetting in Immediate Serial Recall: Decay, Temporal
                                                                                                                            Distinctiveness, or Interference? Psychological Review, 115(3), 576, 544.
           For the first simulation (top) we set a strong excitatory interconnectivity. The network encodes the target
           angle and holds this stable encoding over the whole delay period. The lack of any degradation of neural          [3] Ploner, C. J., Gaymard, B., Rivaud, S., Agid, Y., & Pierrot-Deseilligny, C. (1998). Temporal limits of spatial
                                                                                                                            working memory in humans. The European Journal of Neuroscience, 10(2), 794-797.
           activity can be observed on the right figure.
                                                                                                                            [4] White, R.L. & Snyder, L.H. (2005). Dynamics of Memory-related Spatial Tuning in the Frontal Eye Field.
           The second simulation employs a more conservative parameter setting, generally resulting in lower
           activity. However, as we can see on the right figure, the activity for all observed neurons only drops           [5] Compte, A., Brunel, N., Goldman-Rakic, P. S., & Wang, X. (2000). Synaptic Mechanisms and Network
           immediately after we shut down the cue current, after which it remains constant on average.                      Dynamics Underlying Spatial Working Memory in a Cortical Network Model. Cereb. Cortex, 10(9), 910-923.
                                                                                                                            doi: 10.1093/cercor/10.9.910.