Coordinated Optimization of Visual Cortical Maps (II) Numerical Studies

In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations. Author Summary: Neurons in the visual cortex of carnivores, primates and their close relatives form spatial representations or maps of multiple stimulus features. In part (I) of this study we theoretically predicted maps that are optima of a variety of optimization principles. When analyzing the joint optimization of two interacting maps we showed that for different optimization principles the resulting optima show a stereotyped, spatially perfectly periodic layout. Experimental maps, however, are much more irregular. In particular, in case of orientation columns it was found that different species show apparently species invariant statistics of point defects, so-called pinwheels. In this paper, we numerically investigate whether the spatial features of the stereotyped optima described in part (I) are expressed on biologically relevant timescales and whether other, spatially irregular, long-living states emerge that better reproduce the experimentally observed statistical properties of orientation maps. Moreover, we explore whether the coordinated optimization of more than two maps can lead to spatially irregular optima.