Models for contact-mediated pattern formation: cells that form parallel arrays

Kinetic continuum models are derived for cells that crawl over a 2D substrate, undergo random reorientation, and turn in response to contact with a neighbor. The integro-partial differential equations account for changes in the distribution of orientations in the population. It is found that behavior depends on parameters such as total mass, random motility, adherence, and sloughing rates, as well as on broad aspects of the contact response. Linear stability analysis, and numerical, and cellular automata simulations reveal that as parameters are varied, a bifurcation leads to loss of stability of a uniform (isotropic) steady state, in favor of an (anisotropic) patterned state in which cells are aligned in parallel arrays.     

Sparse gamma rhythms arising through clustering in adapting neuronal networks

Gamma rhythms (30-100 Hz) are an extensively studied synchronous brain state responsible for a number of sensory, memory, and motor processes. Experimental evidence suggests that fast-spiking interneurons are responsible for carrying the high frequency components of the rhythm, while regular-spiking pyramidal neurons fire sparsely. We propose that a combination of spike frequency adaptation and global inhibition may be responsible for this behavior. Excitatory neurons form several clusters that fire every few cycles of the fast oscillation. This is first shown in a detailed biophysical network model and then analyzed thoroughly in an idealized model. We exploit the fact that the timescale of adaptation is much slower than that of the other variables. Singular perturbation theory is used to derive an approximate periodic solution for a single spiking unit. This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant. We compare this to a complementary analysis that employs a weak coupling assumption to predict the first Fourier mode to destabilize from the incoherent state of an associated phase model as the external noise is reduced. Both approaches predict the same scaling of cluster number with respect to the adaptation time constant, which is corroborated in numerical simulations of the full system. Thus, we develop several testable predictions regarding the formation and characteristics of gamma rhythms with sparsely firing excitatory neurons.     

Local spatial and temporal processes of influenza in Pennsylvania, USA: 2003-2009

Background

Influenza is a contagious respiratory disease responsible for annual seasonal epidemics in temperate climates. An understanding of how influenza spreads geographically and temporally within regions could result in improved public health prevention programs. The purpose of this study was to summarize the spatial and temporal spread of influenza using data obtained from the Pennsylvania Department of Health''s influenza surveillance system.

Methodology and Findings

We evaluated the spatial and temporal patterns of laboratory-confirmed influenza cases in Pennsylvania, United States from six influenza seasons (2003–2009). Using a test of spatial autocorrelation, local clusters of elevated risk were identified in the South Central region of the state. Multivariable logistic regression indicated that lower monthly precipitation levels during the influenza season (OR = 0.52, 95% CI: 0.28, 0.94), fewer residents over age 64 (OR = 0.27, 95% CI: 0.10, 0.73) and fewer residents with more than a high school education (OR = 0.76, 95% CI: 0.61, 0.95) were significantly associated with membership in this cluster. In addition, time series analysis revealed a temporal lag in the peak timing of the influenza B epidemic compared to the influenza A epidemic.

Conclusions

These findings illustrate a distinct spatial cluster of cases in the South Central region of Pennsylvania. Further examination of the regional transmission dynamics within these clusters may be useful in planning public health influenza prevention programs.     

The mechanisms for compression and reflection of cortical waves

Waves are common in cortical networks and may be important for carrying information about a stimulus from one local circuit to another. In a recent study of visually evoked waves in rat cortex, compression and reflection of waves are observed as the activation passes from visual areas V1 to V2. The authors of this study apply bicuculline (BMI) and demonstrate that the reflection disappears. They conclude that inhibition plays a major role in compression and reflection. We present several models for propagating waves in heterogeneous media and show that the velocity and thus compression depends weakly on inhibition. We propose that the main site of action of BMI with respect to wave propagation is on the threshold for firing which we suggest is related to action on potassium channels. We combine numerical and analytic methods to explore both compression and reflection in an excitable system with synaptic coupling.     

Synchronization in a pool of mutually coupled oscillators with random frequencies

An exact solution to a model of mutually interacting sinusoidal oscillators is found. Limits on the variation of the native frequencies are determined in order for synchronization to occur. These limits are computed for different distributions of native frequencies.This research was supported by NSF Award No. MCS8300885 and the Alfred Sloan Foundation.     

Working Memory Cells' Behavior May Be Explained by Cross-Regional Networks with Synaptic Facilitation

Neurons in the cortex exhibit a number of patterns that correlate with working memory. Specifically, averaged across trials of working memory tasks, neurons exhibit different firing rate patterns during the delay of those tasks. These patterns include: 1) persistent fixed-frequency elevated rates above baseline, 2) elevated rates that decay throughout the tasks memory period, 3) rates that accelerate throughout the delay, and 4) patterns of inhibited firing (below baseline) analogous to each of the preceding excitatory patterns. Persistent elevated rate patterns are believed to be the neural correlate of working memory retention and preparation for execution of behavioral/motor responses as required in working memory tasks. Models have proposed that such activity corresponds to stable attractors in cortical neural networks with fixed synaptic weights. However, the variability in patterned behavior and the firing statistics of real neurons across the entire range of those behaviors across and within trials of working memory tasks are typical not reproduced. Here we examine the effect of dynamic synapses and network architectures with multiple cortical areas on the states and dynamics of working memory networks. The analysis indicates that the multiple pattern types exhibited by cells in working memory networks are inherent in networks with dynamic synapses, and that the variability and firing statistics in such networks with distributed architectures agree with that observed in the cortex.