autapse - Journal of Computational Neuroscience 9 171185 2000 c 2000 Kluwer Academic Publishers Manufactured in The Netherlands The Autapse A Simple

Journal of Computational Neuroscience 9, 171–185, 2000 c 2000 Kluwer Academic Publishers. Manufactured in The Netherlands. The Autapse: A Simple Illustration of Short-Term Analog Memory Storage by Tuned Synaptic Feedback H. SEBASTIAN SEUNG Brain and Cognitive Sciences Department, Massachusetts Institute of Technology, Cambridge, MA 02139; Lucent Technologies, Bell Laboratories, Murray Hill, NJ 07974 [email protected] DANIEL D. LEE, BEN Y. REIS AND DAVID W. TANK Lucent Technologies, Bell Laboratories, Murray Hill, NJ 07974 Received May 20, 1999; Revised November 30, 1999; Accepted December 2, 1999 Action Editor: John Rinzel Abstract. According to a popular hypothesis, short-term memories are stored as persistent neural activity main- tained by synaptic feedback loops. This hypothesis has been formulated mathematically in a number of recurrent network models. Here we study an abstraction of these models, a single neuron with a synapse onto itself, or autapse. This abstraction cannot simulate the way in which persistent activity patterns are distributed over neural populations in the brain. However, with proper tuning of parameters, it does reproduce the continuously graded, or analog, nature of many examples of persistent activity. The conditions for tuning are derived for the dynamics of a conductance-based model neuron with a slow excitatory autapse. The derivation uses the method of averag- ing to approximate the spiking model with a nonspiking, reduced model. Short-term analog memory storage is possible if the reduced model is approximately linear and if its feedforward bias and autapse strength are precisely tuned. Keywords: short-term memory, persistent neural activity, synaptic feedback, reverberating circuit 1. Introduction In parts of the central nervous system ranging from the spinal cord (Prut and Fetz, 1999) to the neocortex (Fuster, 1995), transient inputs have been observed to cause persistent changes in the rate of action poten- tial firing. By now, there is no doubt that this general phenomenon is closely related to short-term memory, but its physiological mechanisms remain unknown. According to one long-standing hypothesis, persis- tent neural activity is maintained by synaptic feed- back loops (Lorente de No, 1933; Hebb, 1949; Amit, 1995). This hypothesis has found precise mathematical formulation in a number of recurrent network mod- els (Cannon et al., 1983; Seung, 1996; Georgopoulos et al., 1993; Zipser et al., 1993; Griniasty et al., 1993; Amit et al., 1994; Zhang, 1996; Camperi and Wang, 1998). Not only do these models maintain persistent activity patterns, but they also reproduce the experi- mentally observed ways in which neural firing rates encode computational variables. In this article we analyze an abstraction of these re- current network models: a single neuron that makes a synapse onto itself, or autapse. In this model, feed- back is localized to a single loop, rather than distributed over a complex web of connections. This simplification