A Symmetry Approach for the Layout of Orientation Preference Maps

Experimental and theoretical evidence suggests that the development of orientation preference maps (OPMs) constitutes an activity-dependent self-organization process. The formation of OPMs in the visual cortex can be modelled by dynamic field equations [1,2]. Key features of such models strongly depend on the symmetries of the dynamics [2]. We presented a new class of Gaussian random maps which allows to study the consequences of shift-twist symmetry (STS), a fundamental symmetry of visual cortical circuitry [3], on the layout of orientation maps. This symmetry mathematically describes that the position of stimuli in the visual field and the preferred orientation of visual cortical neurons ought to be represented in a common coordinate system. Here we use this approach to identify signatures of this new symmetry which are accessible to experimental testing. We find that STS predicts a locking of the layout of the OPM to the retinotopic map. We calculate the joint probability density of the relative orientation preference of separate columns, as a function of their relative distance and direction. We find that this distribution exhibits a characteristic cloverleaf-like shape. The theoretical predictions are compared to OPMs obtained from tupaia and galago visual cortex.

[1] Swindale, N.V. Network, 7:161 (1996)
[2] Wolf & Geisel, Nature (1998) 395:73
[3] Bressloff, Cowan, Golubitsky, Thomas, Wiener, Phil.Trans.R.Soc.London.B (2001) 356:299