Abstract
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.
Highlights
IntroductionIn the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]
We consider a model for the coordinated optimization of general real and complex valued order parameter fields we view z(x) as the field of orientation preference (OP) throughout this article to aid comparison to the biologically observed patterns
In the visual cortex of species widely separated in mammalian evolution we previously found virtually indistinguishable layout rules of orientation columns that are quantitatively fulfilled with a precision of a few percent [42]
Summary
In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. We used symmetry considerations to derive a classification and parametrization of conceivable inter-map coupling energies and identified a representative set of inter-map coupling terms: a gradient-type and a product-type coupling energy which both can enter with different power in the dynamics. We examined the impact of these coupling energies in a system of coupled SwiftHohenberg equations These were constructed such that without coupling stripe patterns emerge for the complex valued order parameter field. For solutions that can become optima of the model, pinwheels are arranged on regular periodic lattices such as rhombic pinwheel crystals (rPWCs) or hexagonal pinwheel crystals (hPWCs) These analyses focused on the optimization of a single pair of feature maps in which the complex valued map represented the OP map and the real map the OD map. For this case we presented a complete characterization of the stable OP and OD
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