Search

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), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps.

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.

[This corrects the article DOI: 10.1371/journal.pcbi.1008259.].

Human Immunodeficiency Virus 1 uses for entry into host cells a receptor (CD4) and one of two co-receptors (CCR5 or CXCR4). Recently, a new class of antiretroviral drugs has entered clinical practice that specifically bind to the co-receptor CCR5, and thus inhibit virus entry. Accurate prediction of the co-receptor used by the virus in the patient is important as it allows for personalized selection of effective drugs and prognosis of disease progression. We have investigated whether it is possible to predict co-receptor usage accurately by analyzing the amino acid sequence of the main determinant of co-receptor usage, i.e., the third variable loop V3 of the gp120 protein. We developed a two-level machine learning approach that in the first level considers two different properties important for protein-protein binding derived from structural models of V3 and V3 sequences. The second level combines the two predictions of the first level. The two-level method predicts usage of CXCR4 co-receptor for new V3 sequences within seconds, with an area under the ROC curve of 0.937+/-0.004. Moreover, it is relatively robust against insertions and deletions, which frequently occur in V3. The approach could help clinicians to find optimal personalized treatments, and it offers new insights into the molecular basis of co-receptor usage. For instance, it quantifies the importance for co-receptor usage of a pocket that probably is responsible for binding sulfated tyrosine.