4 research outputs found
Leaders of neuronal cultures in a quorum percolation model
We present a theoretical framework using quorum-percolation for describing
the initiation of activity in a neural culture. The cultures are modeled as
random graphs, whose nodes are excitatory neurons with kin inputs and kout
outputs, and whose input degrees kin = k obey given distribution functions pk.
We examine the firing activity of the population of neurons according to their
input degree (k) classes and calculate for each class its firing probability
\Phi_k(t) as a function of t. The probability of a node to fire is found to be
determined by its in-degree k, and the first-to-fire neurons are those that
have a high k. A small minority of high-k classes may be called "Leaders", as
they form an inter-connected subnetwork that consistently fires much before the
rest of the culture. Once initiated, the activity spreads from the Leaders to
the less connected majority of the culture. We then use the distribution of
in-degree of the Leaders to study the growth rate of the number of neurons
active in a burst, which was experimentally measured to be initially
exponential. We find that this kind of growth rate is best described by a
population that has an in-degree distribution that is a Gaussian centered
around k = 75 with width {\sigma} = 31 for the majority of the neurons, but
also has a power law tail with exponent -2 for ten percent of the population.
Neurons in the tail may have as many as k = 4, 700 inputs. We explore and
discuss the correspondence between the degree distribution and a dynamic
neuronal threshold, showing that from the functional point of view, structure
and elementary dynamics are interchangeable. We discuss possible geometric
origins of this distribution, and comment on the importance of size, or of
having a large number of neurons, in the culture.Comment: Keywords: Neuronal cultures, Graph theory, Activation dynamics,
Percolation, Statistical mechanics of networks, Leaders of activity, Quorum.
http://www.weizmann.ac.il/complex/tlusty/papers/FrontCompNeuro2010.pd
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
Noise, coherent activity and network structure in neuronal cultures
In this thesis we apply a multidisciplinary approach, based on statistical physics and complex systems, to the study of neuronal dynamics. We focus on understanding, using theoretical and computational tools, how collective neuronal activity emerges in a controlled system, a neuronal culture. We show how the interplay between noise and network structure defines the emergent collective behavior of the system. We build, using theory and simulation, a framework that takes carefully describes spontaneous activity in neuronal cultures by taking into account the underlying network structure of neuronal cultures and use an accurate, yet simple, model for the individual neuronal dynamics. We show that the collective behavior of young cultures is dominated by the nucleation and propagations of activity fronts (bursts) throughout the system. These bursts nucleate at specific sites of the culture, called nucleation points, which result in a highly heterogeneous probability distribution of nucleation. We are able to explain the nucleation mechanism theoretically as a mechanism of noise propagation and amplification called noise focusing. We also explore the internal structure of activity avalanches by using well--defined regular networks, in which all the neurons have the same connectivity rules (motifs). Within these networks, we are able to associate to the avalanches an effective velocity and topological size and relate it to specific motifs. We also devise a continuum description of a neuronal culture at the mesoscale, i.e., we move away from the single neuron dynamics into a coarse--grained description that is able to capture most of the characteristic observables presented in previous chapters. This thesis also studies the spontaneous activity of neuronal cultures within the framework of quorum percolation. We study the effect of network structure within quorum percolation and propose a new model, called stochastic quorum percolation, that includes dynamics and the effect of internal noise. Finally, we use tools from information theory, namely transfer entropy, to show how to reliably infer the connectivity of a neuronal network from its activity, and how to distinguish between different excitatory and inhibitory connections purely from the activity, with no prior knowledge of the different neuronal types. The technique works directly on the fluorescence traces obtained in calcium imaging experiments, without the need to infer the underlying spike trains