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In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have also been observed for neural activity, and so it has been proposed that SOC underlies brain organization as well. Surprisingly, for spiking activity in vivo, evidence for SOC is still lacking. Therefore, we analyzed highly parallel spike recordings from awake rats and monkeys, anesthetized cats, and also local field potentials from humans. We compared these to spiking activity from two established critical models: the Bak-Tang-Wiesenfeld model, and a stochastic branching model. We found fundamental differences between the neural and the model activity. These differences could be overcome for both models through a combination of three modifications: (1) subsampling, (2) increasing the input to the model (this way eliminating the separation of time scales, which is fundamental to SOC and its avalanche definition), and (3) making the model slightly sub-critical. The match between the neural activity and the modified models held not only for the classical avalanche size distributions and estimated branching parameters, but also for two novel measures (mean avalanche size, and frequency of single spikes), and for the dependence of all these measures on the temporal bin size. Our results suggest that neural activity in vivo shows a mélange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step. This implies that neural activity does not reflect a SOC state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy.
The neuroanatomical connectivity of cortical circuits is believed to follow certain rules, the exact origins of which are still poorly understood. In particular, numerous nonrandom features, such as common neighbor clustering, overrepresentation of reciprocal connectivity, and overrepresentation of certain triadic graph motifs have been experimentally observed in cortical slice data. Some of these data, particularly regarding bidirectional connectivity are seemingly contradictory, and the reasons for this are unclear. Here we present a simple static geometric network model with distance-dependent connectivity on a realistic scale that naturally gives rise to certain elements of these observed behaviors, and may provide plausible explanations for some of the conflicting findings. Specifically, investigation of the model shows that experimentally measured nonrandom effects, especially bidirectional connectivity, may depend sensitively on experimental parameters such as slice thickness and sampling area, suggesting potential explanations for the seemingly conflicting experimental results.
Dendritic morphology has been shown to have a dramatic impact on neuronal function. However, population features such as the inherent variability in dendritic morphology between cells belonging to the same neuronal type are often overlooked when studying computation in neural networks. While detailed models for morphology and electrophysiology exist for many types of single neurons, the role of detailed single cell morphology in the population has not been studied quantitatively or computationally. Here we use the structural context of the neural tissue in which dendritic trees exist to drive their generation in silico. We synthesize the entire population of dentate gyrus granule cells, the most numerous cell type in the hippocampus, by growing their dendritic trees within their characteristic dendritic fields bounded by the realistic structural context of (1) the granule cell layer that contains all somata and (2) the molecular layer that contains the dendritic forest. This process enables branching statistics to be linked to larger scale neuroanatomical features. We find large differences in dendritic total length and individual path length measures as a function of location in the dentate gyrus and of somatic depth in the granule cell layer. We also predict the number of unique granule cell dendrites invading a given volume in the molecular layer. This work enables the complete population-level study of morphological properties and provides a framework to develop complex and realistic neural network models.
Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of interest in neuroscience. Estimating transfer entropy from two processes requires the observation of multiple realizations of these processes to estimate associated probability density functions. To obtain these necessary observations, available estimators typically assume stationarity of processes to allow pooling of observations over time. This assumption however, is a major obstacle to the application of these estimators in neuroscience as observed processes are often non-stationary. As a solution, Gomez-Herrero and colleagues theoretically showed that the stationarity assumption may be avoided by estimating transfer entropy from an ensemble of realizations. Such an ensemble of realizations is often readily available in neuroscience experiments in the form of experimental trials. Thus, in this work we combine the ensemble method with a recently proposed transfer entropy estimator to make transfer entropy estimation applicable to non-stationary time series. We present an efficient implementation of the approach that is suitable for the increased computational demand of the ensemble method's practical application. In particular, we use a massively parallel implementation for a graphics processing unit to handle the computationally most heavy aspects of the ensemble method for transfer entropy estimation. We test the performance and robustness of our implementation on data from numerical simulations of stochastic processes. We also demonstrate the applicability of the ensemble method to magnetoencephalographic data. While we mainly evaluate the proposed method for neuroscience data, we expect it to be applicable in a variety of fields that are concerned with the analysis of information transfer in complex biological, social, and artificial systems.
Evidence from anatomical and functional imaging studies have highlighted major modifications of cortical circuits during adolescence. These include reductions of gray matter (GM), increases in the myelination of cortico-cortical connections and changes in the architecture of large-scale cortical networks. It is currently unclear, however, how the ongoing developmental processes impact upon the folding of the cerebral cortex and how changes in gyrification relate to maturation of GM/WM-volume, thickness and surface area. In the current study, we acquired high-resolution (3 Tesla) magnetic resonance imaging (MRI) data from 79 healthy subjects (34 males and 45 females) between the ages of 12 and 23 years and performed whole brain analysis of cortical folding patterns with the gyrification index (GI). In addition to GI-values, we obtained estimates of cortical thickness, surface area, GM and white matter (WM) volume which permitted correlations with changes in gyrification. Our data show pronounced and widespread reductions in GI-values during adolescence in several cortical regions which include precentral, temporal and frontal areas. Decreases in gyrification overlap only partially with changes in the thickness, volume and surface of GM and were characterized overall by a linear developmental trajectory. Our data suggest that the observed reductions in GI-values represent an additional, important modification of the cerebral cortex during late brain maturation which may be related to cognitive development.