Modulating the Granularity of Category Formation by Global Cortical States

The unsupervised categorization of sensory stimuli is typically attributed to feedforward processing in a hierarchy of cortical areas. This purely sensory-driven view of cortical processing, however, ignores any internal modulation, e.g., by top-down attentional signals or neuromodulator release. To isolate the role of internal signaling on category formation, we consider an unbroken continuum of stimuli without intrinsic category boundaries. We show that a competitive network, shaped by recurrent inhibition and endowed with Hebbian and homeostatic synaptic plasticity, can enforce stimulus categorization. The degree of competition is internally controlled by the neuronal gain and the strength of inhibition. Strong competition leads to the formation of many attracting network states, each being evoked by a distinct subset of stimuli and representing a category. Weak competition allows more neurons to be co-active, resulting in fewer but larger categories. We conclude that the granularity of cortical category formation, i.e., the number and size of emerging categories, is not simply determined by the richness of the stimulus environment, but rather by some global internal signal modulating the network dynamics. The model also explains the salient non-additivity of visual object representation observed in the monkey inferotemporal (IT) cortex. Furthermore, it offers an explanation of a previously observed, demand-dependent modulation of IT activity on a stimulus categorization task and of categorization-related cognitive deficits in schizophrenic patients

Reconstruction and simulation of neocortical microcircuitry

We present a first-draft digital reconstruction of the microcircuitry of somatosensory cortex of juvenile rat. The reconstruction uses cellular and synaptic organizing principles to algorithmically reconstruct detailed anatomy and physiology from sparse experimental data. An objective anatomical method defines a neocortical volume of 0.29 ± 0.01 mm3 containing ∼31,000 neurons, and patch-clamp studies identify 55 layer-specific morphological and 207 morpho-electrical neuron subtypes. When digitally reconstructed neurons are positioned in the volume and synapse formation is restricted to biological bouton densities and numbers of synapses per connection, their overlapping arbors form ∼8 million connections with ∼37 million synapses. Simulations reproduce an array of in vitro and in vivo experiments without parameter tuning. Additionally, we find a spectrum of network states with a sharp transition from synchronous to asynchronous activity, modulated by physiological mechanisms. The spectrum of network states, dynamically reconfigured around this transition, supports diverse information processing strategies

Geometric measurements of the scleractinian coral <i>Madracis</i> and neuronal dendritic bifurcations show that bifurcations are mostly planar, but bifurcation angles are not always Steiner tree optimal.

<p>Measurements were done on bifurcations composed of a parent (P) and two daughter branches (D₁, D₂). For each case an example of the very different coral and dendritic tree morphologies is shown (left), the distribution of cone angles <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002474#pcbi.1002474-Uylings2" target="_blank">[22]</a> as a quantification of the shape of a bifurcation (center) and the distribution of the angles between the branches (right). <b>A.</b> Samples of coral bifurcations from 4 coral species. <b>B.</b> Samples of dendritic bifurcations of 8 neuron types. The cone angle values are marked in color in the range of 0 to 180° on the samples themselves (see scale at the bottom right). The histogram of cone angle distributions peaks at 180°, showing a marked tendency towards planarity. The bifurcation angle (2DB) distribution for both corals and neurons shows that only a small proportion of angles are close to 120°.</p

Geometric Theory Predicts Bifurcations in Minimal Wiring Cost Trees in Biology Are Flat

<div><p>The complex three-dimensional shapes of tree-like structures in biology are constrained by optimization principles, but the actual costs being minimized can be difficult to discern. We show that despite quite variable morphologies and functions, bifurcations in the scleractinian coral <em>Madracis</em> and in many different mammalian neuron types tend to be planar. We prove that in fact bifurcations embedded in a spatial tree that minimizes wiring cost should lie on planes. This biologically motivated generalization of the classical mathematical theory of Euclidean Steiner trees is compatible with many different assumptions about the type of cost function. Since the geometric proof does not require any correlation between consecutive planes, we predict that, in an environment without directional biases, consecutive planes would be oriented independently of each other. We confirm this is true for many branching corals and neuron types. We conclude that planar bifurcations are characteristic of wiring cost optimization in any type of biological spatial tree structure.</p> </div

Random bifurcations have a tendency to be planar.

<p><b>A.</b> Diagram showing how random bifurcations can be mapped onto a unit sphere. The bifurcation point is fixed at the center of the sphere and non-bifurcation points are projected onto its surface. Intuitively, the probability of finding a cone with cone angle can be thought of in terms of choosing three non-bifurcating points that fall onto the base circle of this cone, i.e. the intersection of the cone with the sphere. <b>B.</b> The circumference of the base circle gets larger as the cone angle increases. <b>C.</b> Overlay of the random bifurcations' distribution of cone angles with the biological distributions shows that the distribution of all biological bifurcations deviates significantly from the random one (KS test, p-value = 10⁻⁵). <b>D.</b> The probability distribution for random bifurcations is (where is in radians). The probability of cone angles >160° is 26%.</p

A bifurcation in an optimal wiring cost tree has to lie on a plane and consecutive planes are independent of each other.

<p><b>A.</b> Projecting the red bifurcation point () onto the blue bifurcation plane reduces the costs of all three edges involved, and therefore the total cost of the entire tree. Note that in this example the bifurcation plane is defined by neighboring bifurcation points (), but some or all of these could be replaced by fixed or terminal points. <b>B.</b> Most of the distributions of angles between consecutive bifurcation planes approximate the uniform distribution, except for Purkinje cells, L5 PFC pyramidal cells and <i>M. mirabilis</i>. Data from the other 6 neuron types and 3 coral species were statistically consistent with a uniform distribution (p>0.05, one-sample Kolmogorov-Smirnov test, considering only basal dendrites for L2/3 pyramidal neurons). <b>C.</b> Example of bifurcation planes in a L2/3 somatosensory cortex pyramidal cell. The bifurcation planes are color coded according to their cone angles.</p