Michael Schnabel

Universality in the Evolution of Orientation Columns in the Visual Cortex

Orientation Columns In the brains visual cortex, certain neurons respond to vertical lines and others to horizontal lines, with a range in between. Such orientation of neurons tends to be organized in columns reflecting similar responses, and the columns are organized in pinwheels representing the range of responses. Kaschube et al. (p. 1113, published online 4 November; see the Perspective by Miller) looked at the organization of orientation columns in diverse placental mammals and discovered a similarity of organizational principles. Analysis of evolutionarily divergent species highlights constraint on brain structure imposed by self-organizing neural networks. The brain’s visual cortex processes information concerning form, pattern, and motion within functional maps that reflect the layout of neuronal circuits. We analyzed functional maps of orientation preference in the ferret, tree shrew, and galago—three species separated since the basal radiation of placental mammals more than 65 million years ago—and found a common organizing principle. A symmetry-based class of models for the self-organization of cortical networks predicts all essential features of the layout of these neuronal circuits, but only if suppressive long-range interactions dominate development. We show mathematically that orientation-selective long-range connectivity can mediate the required interactions. Our results suggest that self-organization has canalized the evolution of the neuronal circuitry underlying orientation preference maps into a single common design.

Self-organization and the selection of pinwheel density in visual cortical development

Self-organization of neural circuitry is an appealing framework for understanding cortical development, yet its applicability remains unconfirmed. Models for the self-organization of neural circuits have been proposed, but experimentally testable predictions of these models have been less clear. The visual cortex contains a large number of topological point defects, called pinwheels, which are detectable in experiments and therefore in principle well suited for testing predictions of self-organization empirically. Here, we analytically calculate the density of pinwheels predicted by a pattern formation model of visual cortical development. An important factor controlling the density of pinwheels in this model appears to be the presence of non-local long-range interactions, a property which distinguishes cortical circuits from many non- living systems in which self-organization has been studied. We show that in the limit where the range of these interactions is infinite, the average pinwheel density converges to . Moreover, an average pinwheel density close to this value is robustly selected even for intermediate interaction ranges, a regime arguably covering interaction ranges in a wide range of different species.

Interareal coordination of columnar architectures during visual cortical development

The formation of cortical columns is often conceptualized as a local process in which synaptic microcircuits confined to the volume of the emerging column are established and selectively refined. Many neurons, however, while wiring up locally are simultaneously building macroscopic circuits spanning widely distributed brain regions, such as different cortical areas or the two brain hemispheres. Thus, it is conceivable that interareal interactions shape the local column layout. Here we show that the columnar architectures of different areas of the cat visual cortex in fact develop in a coordinated manner, not adequately described as a local process. This is revealed by comparing the layouts of orientation columns (i) in left/right pairs of brain hemispheres and (ii) in areas V1 and V2 of individual brain hemispheres. Whereas the size of columns varied strongly within all areas considered, columns in different areas were typically closely matched in size if they were mutually connected. During development, we find that such mutually connected columns progressively become better matched in size as the late phase of the critical period unfolds. Our results suggest that one function of critical-period plasticity is to progressively coordinate the functional architectures of different cortical areas—even across hemispheres.

Dynamic Transcription Factor Networks in Epithelial-Mesenchymal Transition in Breast Cancer Models

The epithelial-mesenchymal transition (EMT) is a complex change in cell differentiation that allows breast carcinoma cells to acquire invasive properties. EMT involves a cascade of regulatory changes that destabilize the epithelial phenotype and allow mesenchymal features to manifest. As transcription factors (TFs) are upstream effectors of the genome-wide expression changes that result in phenotypic change, understanding the sequential changes in TF activity during EMT provides rich information on the mechanism of this process. Because molecular interactions will vary as cells progress from an epithelial to a mesenchymal differentiation program, dynamic networks are needed to capture the changing context of molecular processes. In this study we applied an emerging high-throughput, dynamic TF activity array to define TF activity network changes in three cell-based models of EMT in breast cancer based on HMLE Twist ER and MCF-7 mammary epithelial cells. The TF array distinguished conserved from model-specific TF activity changes in the three models. Time-dependent data was used to identify pairs of TF activities with significant positive or negative correlation, indicative of interdependent TF activity throughout the six-day study period. Dynamic TF activity patterns were clustered into groups of TFs that change along a time course of gene expression changes and acquisition of invasive capacity. Time-dependent TF activity data was combined with prior knowledge of TF interactions to construct dynamic models of TF activity networks as epithelial cells acquire invasive characteristics. These analyses show EMT from a unique and targetable vantage and may ultimately contribute to diagnosis and therapy.

Fake symmetry transitions in lattice Dirac spectra

In a recent lattice investigation of Ginsparg-Wilson-type Dirac operators in the Schwinger model, it was found that the symmetry class of the random matrix theory describing the small Dirac eigenvalues appeared to change from the unitary to the symplectic case as a function of lattice size and coupling constant. We present a natural explanation for this observation in the framework of a random matrix model, showing that the apparent change is caused by the onset of chiral symmetry restoration in a finite volume. A transition from unitary to symplectic symmetry does not occur.

Stock fluctuations are correlated and amplified across networks of interlocking directorates

Traded corporations are required by law to have a majority of outside directors on their board. This requirement allows the existence of directors who sit on the board of two or more corporations at the same time, generating what is commonly known as interlocking directorates. While research has shown that networks of interlocking directorates facilitate the transmission of information between corporations, little is known about the extent to which such interlocking networks can explain the fluctuations of stock price returns. Yet, this is a special concern since the risk of amplifying stock fluctuations is latent. To answer this question, here we analyze the board composition, traders’ perception, and stock performance of more than 1,500 US traded corporations from 2007-2011. First, we find that the fewer degrees of separation between two corporations in the interlocking network, the stronger the temporal correlation between their stock price returns. Second, we find that the centrality of traded corporations in the interlocking network correlates with the frequency at which financial traders talk about such corporations, and this frequency is in turn proportional to the corresponding traded volume. Third, we show that the centrality of corporations was negatively associated with their stock performance in 2008, the year of the big financial crash. These results suggest that the strategic decisions made by interlocking directorates are strongly followed by stock analysts and have the potential to correlate and amplify the movement of stock prices during financial crashes. These results may have relevant implications for scholars, investors, and regulators.

Pattern selection, pinwheel stability and the geometry of visual space

Address: 1Department of Nonlinear Dynamics, Max-Planck-Institute for Dynamics and Self-Organization, D37073 Göttingen, Germany, 2Bernstein Center for Computational Neuroscience, D37073 Göttingen, Germany, 3Faculty of Physics, University of Göttingen, D37073 Göttingen, Germany, 4Lewis-Sigler Institute for Integrative Genomics, Princeton, NJ, USA and 5Medical Center, Duke University, Durham, NC, USA