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Register a new userBayesian reconstruction of memories stored in neural networks from their connectivity
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The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in a recurrent network of neurons, given its synaptic connectivity matrix. Here, we address this question by determining when solving such an inference problem is theoretically possible in specific attractor network models and by providing a practical algorithm to do so. The algorithm builds on ideas from statistical physics to perform approximate Bayesian inference and is amenable to exact analysis. We study its performance on three different models and explore the limitations of reconstructing stored patterns from synaptic connectivity.
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A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the effective network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (e.g., bursting or non-bursting). We thus demonstrate how conditioning with respect to the global mean activity improves the performance of our method. [...] Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good reconstruction of the network clustering coefficient, allowing to discriminate between weakly or strongly clustered topologies, whereas on the other hand an approach based on cross-correlations would invariantly detect artificially high levels of clustering. Finally, we present the applicability of our method to real recordings of in vitro cortical cultures. We demonstrate that these networks are characterized by an elevated level of clustering compared to a random graph (although not extreme) and by a markedly non-local connectivity.
Neuroscientists are actively pursuing high-precision maps, or graphs, consisting of networks of neurons and connecting synapses in mammalian and non-mammalian brains. Such graphs, when coupled with physiological and behavioral data, are likely to facilitate greater understanding of how circuits in these networks give rise to complex information processing capabilities. Given that the automated or semi-automated methods required to achieve the acquisition of these graphs are still evolving, we develop a metric for measuring the performance of such methods by comparing their output with those generated by human annotators (ground truth data). Whereas classic metrics for comparing annotated neural tissue reconstructions generally do so at the voxel level, the metric proposed here measures the integrity of neurons based on the degree to which a collection of synaptic terminals belonging to a single neuron of the reconstruction can be matched to those of a single neuron in the ground truth data. The metric is largely insensitive to small errors in segmentation and more directly measures accuracy of the generated brain graph. It is our hope that use of the metric will facilitate the broader communitys efforts to improve upon existing methods for acquiring brain graphs. Herein we describe the metric in detail, provide demonstrative examples of the intuitive scores it generates, and apply it to a synthesized neural network with simulated reconstruction errors.
The theory of communication through coherence (CTC) proposes that brain oscillations reflect changes in the excitability of neurons, and therefore the successful communication between two oscillating neural populations depends not only on the strength of the signal emitted but also on the relative phases between them. More precisely, effective communication occurs when the emitting and receiving populations are properly phase locked so the inputs sent by the emitting population arrive at the phases of maximal excitability of the receiving population. To study this setting, we consider a population rate model consisting of excitatory and inhibitory cells modelling the receiving population, and we perturb it with a time-dependent periodic function modelling the input from the emitting population. We consider the stroboscopic map for this system and compute numerically the fixed and periodic points of this map and their bifurcations as the amplitude and the frequency of the perturbation are varied. From the bifurcation diagram, we identify the phase-locked states as well as different regions of bistability. We explore carefully the dynamics emphasizing its implications for the CTC theory. In particular, we study how the input gain depends on the timing between the input and the inhibitory action of the receiving population. Our results show that naturally an optimal phase locking for CTC emerges, and provide a mechanism by which the receiving population can implement selective communication. Moreover, the presence of bistable regions, suggests a mechanism by which different communication regimes between brain areas can be established without changing the structure of the network
Obsessive-compulsive disorder (OCD) is a common psychiatric disorder with a lifetime prevalence of 2-3 percent. Recently, brain activity in the resting state is gathering attention as a new means of exploring altered functional connectivity in psychiatric disorders. Although previous resting-state functional magnetic resonance imaging studies investigated neurobiological abnormalities of patients with OCD, there are concerns that should be addressed. One concern is the validity of the hypothesis employed. Most studies used seed-based analysis of the fronto-striatal circuit, despite the potential for abnormalities in other regions. A hypothesis-free study is a promising approach in such a case, while it requires researchers to handle a dataset with large dimensions. Another concern is the reliability of biomarkers derived from a single dataset, which may be influenced by cohort-specific features. Here, by employing a recently developed machine-learning algorithm to avoid these concerns, we identified the first OCD biomarker that is generalized to an external dataset. We also demonstrated that the functional connectivities that contributed to the classification were widely distributed rather than locally constrained. Our generalizable classifier has the potential not only to deepen our understanding of the abnormal neural substrates of OCD but also to find use in clinical applications.
The $1/f$-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitute evidences of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here we study the relationship between network inhibition and the scaling exponent $beta$ of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality (SOC). We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value $beta = 1$ for a percentage of about 30%. More specifically, $beta$ is close to $2$, namely brownian noise, for purely excitatory networks and decreases towards values in the interval $[1,1.4]$ as the percentage of inhibitory synapses ranges between 20 and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.
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