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      A balanced memory network

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          Abstract

          A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate mechanism is the attractor network, and a great deal of effort has gone toward investigating it theoretically. Yet, despite almost a quarter century of intense work, attractor networks are not fully understood. In particular, there are still two unanswered questions. First, how is it that attractor networks exhibit irregular firing, as is observed experimentally during working memory tasks? And second, how many memories can be stored under biologically realistic conditions? Here we answer both questions by studying an attractor neural network in which inhibition and excitation balance each other. Using mean field analysis, we derive a three-variable description of attractor networks. From this description it follows that irregular firing can exist only if the number of neurons involved in a memory is large. The same mean field analysis also shows that the number of memories that can be stored in a network scales with the number of excitatory connections, a result that has been suggested for simple models but never shown for realistic ones. Both of these predictions are verified using simulations with large networks of spiking neurons.

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          Most cited references85

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          Mnemonic coding of visual space in the monkey's dorsolateral prefrontal cortex.

          1. An oculomotor delayed-response task was used to examine the spatial memory functions of neurons in primate prefrontal cortex. Monkeys were trained to fixate a central spot during a brief presentation (0.5 s) of a peripheral cue and throughout a subsequent delay period (1-6 s), and then, upon the extinction of the fixation target, to make a saccadic eye movement to where the cue had been presented. Cues were usually presented in one of eight different locations separated by 45 degrees. This task thus requires monkeys to direct their gaze to the location of a remembered visual cue, controls the retinal coordinates of the visual cues, controls the monkey's oculomotor behavior during the delay period, and also allows precise measurement of the timing and direction of the relevant behavioral responses. 2. Recordings were obtained from 288 neurons in the prefrontal cortex within and surrounding the principal sulcus (PS) while monkeys performed this task. An additional 31 neurons in the frontal eye fields (FEF) region within and near the anterior bank of the arcuate sulcus were also studied. 3. Of the 288 PS neurons, 170 exhibited task-related activity during at least one phase of this task and, of these, 87 showed significant excitation or inhibition of activity during the delay period relative to activity during the intertrial interval. 4. Delay period activity was classified as directional for 79% of these 87 neurons in that significant responses only occurred following cues located over a certain range of visual field directions and were weak or absent for other cue directions. The remaining 21% were omnidirectional, i.e., showed comparable delay period activity for all visual field locations tested. Directional preferences, or lack thereof, were maintained across different delay intervals (1-6 s). 5. For 50 of the 87 PS neurons, activity during the delay period was significantly elevated above the neuron's spontaneous rate for at least one cue location; for the remaining 37 neurons only inhibitory delay period activity was seen. Nearly all (92%) neurons with excitatory delay period activity were directional and few (8%) were omnidirectional. Most (62%) neurons with purely inhibitory delay period activity were directional, but a substantial minority (38%) was omnidirectional. 6. Fifteen of the neurons with excitatory directional delay period activity also had significant inhibitory delay period activity for other cue directions. These inhibitory responses were usually strongest for, or centered about, cue directions roughly opposite those optimal for excitatory responses.(ABSTRACT TRUNCATED AT 400 WORDS)
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            The glutamate receptor ion channels.

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              Chaos in neuronal networks with balanced excitatory and inhibitory activity.

              Neurons in the cortex of behaving animals show temporally irregular spiking patterns. The origin of this irregularity and its implications for neural processing are unknown. The hypothesis that the temporal variability in the firing of a neuron results from an approximate balance between its excitatory and inhibitory inputs was investigated theoretically. Such a balance emerges naturally in large networks of excitatory and inhibitory neuronal populations that are sparsely connected by relatively strong synapses. The resulting state is characterized by strongly chaotic dynamics, even when the external inputs to the network are constant in time. Such a network exhibits a linear response, despite the highly nonlinear dynamics of single neurons, and reacts to changing external stimuli on time scales much smaller than the integration time constant of a single neuron.
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                Author and article information

                Journal
                10.1371/journal.pcbi.0030141
                0704.3005
                1971123
                17845070

                Theoretical physics,Neurosciences
                Theoretical physics, Neurosciences

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