Homogenization by homeostatic synaptic plasticity in a recurrent cortical network model of continuous bump attractors
Experiments on spatial working memory and head direction cells indicate that the memory of a spatial direction or position is encoded by neuronal circuits with a continuous family of spatially localized persistent firing patterns (`bump attractors'). These circuits are very sensitive to heterogeneities (Zhang, J. Neurosci. 1996). We have investigated this issue through both numerical simulations and mean field analysis of a large-scale network model of spiking neurons (Compte et al. Cereb. Cortex 2000). In the absence of heterogeneity the network possesses a continuum of bump attractors. When a small heterogeneity (a Gaussian distribution of the leak potential with mean -70 mV and standard deviation 1 mV) is added, only a small number (two or three) number of these attractors remain stable, so that activity patterns elicited by most locational cues show a fast systematic drift, reaching one of these 2 or 3 privileged positions in a few seconds after the cue offset. We then incorporate an activity-dependent synaptic scaling mechanism (Turrigiano et al. Nature 1999), under the assumption that, on a long timescale (days), bumps are equally likely to occur at any position. When the scaling dynamics reaches a steady state, the synaptic scaling factor for each cell is a function of its leak potential. Using this function in the full network simulations the drift becomes random and unbiased, i.e. the network is effectively homogenized. We propose that synaptic scaling provides a mechanism for realizing a continuous family of bump attractors in an inhomogeneous cortical network.