Model-free reconstruction of neuronal network connectivity from calcium imaging signals

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.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted for publicatio

Diameter of the spike-flow graphs of geometrical neural networks

Full article is available at Springerlink: http://link.springer.com/chapter/10.1007%2F978-3-642-31464-3_52 DOI: 10.1007/978-3-642-31464-3_52Average path length is recognised as one of the vital characteristics of random graphs and complex networks. Despite a rather sparse structure, some cases were reported to have a relatively short lengths between every pair of nodes, making the whole network available in just several hops. This small-worldliness was reported in metabolic, social or linguistic networks and recently in the Internet. In this paper we present results concerning path length distribution and the diameter of the spike-flow graph obtained from dynamics of geometrically embedded neural networks. Numerical results confirm both short diameter and average path length of resulting activity graph. In addition to numerical results, we also discuss means of running simulations in a concurrent environment

Scale-freeness and small-world phenomenon in information-flow graphs of geometrical neural networks

In this dissertation we set out to study a simplified model of activation flow in artificial neural networks with geometrical embedding. The model provides a mathematical description of abstract neural activation transfer in terms, which bear resemblances to multi-value Boltzmann-like evolution. The activation-preserving constraint mimics a critical regime of the dynamics and, along with accounting for geometrical location of the neurons, makes the system more feasible for modelling of real-world networks. We focus on scale invariance or scale-freeness and small-world phenomena in the said networks. Our results clearly confirm presence of both features at the functional level of the activity-flow graph. We show that the degree distribution preserves a power-law shape with the exponent value approximately equal to -2. In addition, we present our results concerning characteristic path length in the said graphs, which grows roughly logarithmically with the size of the network, while the clustering coefficient turns out to be relatively high. Taken together, the clustering and path length ratios are surprisingly high, and thus confirm large both local and global efficiency of the network. Finally, we compare the properties of activation-flow model to those reported in neurobiological analyses of brain networks recorded with functional magnetic resonance imagining (fMRI). There is a strong agreement between the shape and exponent value of degree distribution also the clustering and characteristic path lengths are comparable in both the model and medical data.Celem niniejszej rozprawy jest analiza uproszczonego modelu przepływu aktywności w sztucznych sieciach neuronowych zanurzonych w przestrzeni geometrycznej. Przedstawiony model dostarcza matematycznego opisu transferu aktywności w terminach zbliżonych do wielowartościowych maszyn Boltzmanna. Wymóg zachowania stałej sumarycznej aktywności odzwierciedla krytyczność dynamiki i wraz z uwzględnieniem wpływu lokalizacji geometrycznej neuronów sprawia, że system jest bardziej adekwatny do modelowania rzeczywistych sieci. Badania koncentrują się na bezskalowości oraz fenomenie małego świata w wyżej wymienionych sieciach. Uzyskane rezultaty potwierdzają obecność obu własności w omawianych grafach. Pokażemy, że rozkład stopni wejściowych wierzchołków zachowuje się jak funkcja potęgowa z wykładnikiem równym -2. Ponadto prezentujemy wyniki dotyczące charakterystycznej długości ścieżki, który rośnie logarytmicznie wraz z wielkością systemu, podczas gdy współczynnik klasteryzacji okazuje się dość duży. W konsekwencji stosunek klasteryzacji do długości ścieżek jest zaskakująco wysoki, co jest dystynktywną własnością sieci małego świata. Wreszcie, dokonujemy porównania cech omawianego modelu przepływu aktywności z neuro-biologicznymi rezultatami, przedstawionymi w badaniach grafów mózgowych z danych uzyskanych z funkcjonalnego obrazowania z wykorzystaniem rezonansu magnetycznego (fMRI). Wskazujemy silną odpowiedniość pomiędzy kształtem i wartością wykładnika rozkładu stopni, zaś klasteryzacja i charakterystyczna długość ścieżki są porównywalne w modelu i danych medycznych

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Fundamental activity constraints lead to specific interpretations of the connectome

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function.Comment: J. Schuecker and M. Schmidt contributed equally to this wor

Linear response for spiking neuronal networks with unbounded memory

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how linear response is explicitly related to neuronal dynamics with an example, the gIF model, introduced by M. Rudolph and A. Destexhe. This example illustrates the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike statistics. We illustrate our results with numerical simulations.Comment: 60 pages, 8 figure

A combined experimental and computational approach to investigate emergent network dynamics based on large-scale neuronal recordings

Sviluppo di un approccio integrato computazionale-sperimentale per lo studio di reti neuronali mediante registrazioni elettrofisiologich