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Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve over time, spontaneously or under stimulation. It requires a method for inferring the structure and composition of a network from neuronal activities. Tracking the evolution of networks and their changing functionality will provide invaluable insight into the occurrence of plasticity and the underlying learning process. We devise a probabilistic method for inferring the effective network structure by integrating techniques from Bayesian statistics, statistical physics and principled machine learning. The method and resulting algorithm allow one to infer the effective network structure, identify the excitatory and inhibitory nature of its constituents, and predict neuronal spiking activities by employing the inferred structure. We validate the method and algorithm's performance using synthetic data, spontaneous activity of an in silico emulator and realistic in vitro neuronal networks of modular and homogeneous connectivity, demonstrating excellent structure inference and activity prediction. We also show that our method outperforms commonly used existing methods for inferring neuronal network structure. Inferring the evolving effective structure of neuronal networks will provide new insight into the learning process due to stimulation in general and will facilitate the development of neuron-based circuits with computing capabilities.

The properties of complex networked systems arise from the interplay between the dynamics of their elements and the underlying topology. Thus, to understand their behaviour, it is crucial to convene as much information as possible about their topological organization. However, in a large systems such as neuronal networks, the reconstruction of such topology is usually carried out from the information encoded in the dynamics on the network, such as spike train time series, and by measuring the Transfer Entropy between system elements. The topological information recovered by these methods does not necessarily capture the connectivity layout, but rather the causal flow of information between elements. New theoretical frameworks, such as Integrated Information Decomposition ($\Phi$-ID), allow to explore the modes in which information can flow between parts of a system, opening a rich landscape of interactions between network topology, dynamics and information. Here, we apply $\Phi$-ID on $in$ $silico$ and $in$ $vitro$ data to decompose the usual Transfer Entropy measure into different modes of information transfer, namely synergistic, redundant or unique. We demonstrate that the unique information transfer is the most relevant measure to uncover structural topological details from network activity data, while redundant information only introduces residual information for this application. Although the retrieved network connectivity is still functional, it captures more details of the underlying structural topology by avoiding to take into account emergent high-order interactions and information redundancy between elements, which are important for the functional behavior, but mask the detection of direct simple interactions between elements constituted by the structural network topology., Comment: 13 pages, 5 figures

The architecture of the human connectome supports efficient communication protocols relying either on distances between brain regions or on the intensities of connections. However, none of these protocols combines information about the two or reaches full efficiency. Here, we introduce a continuous spectrum of decentralized routing strategies that combine link weights and the spatial embedding of connectomes to transmit signals. We applied the protocols to individual connectomes in two cohorts, and to cohort archetypes designed to capture weighted connectivity properties. We found that there is an intermediate region, a sweet spot, in which navigation achieves maximum communication efficiency at low transmission cost. Interestingly, this phenomenon is robust and independent of the particular configuration of weights.Our results indicate that the intensity and topology of neural connections and brain geometry interplay to boost communicability, fundamental to support effective responses to external and internal stimuli and the diversity of brain functions., Comment: 49 pages (10 main text, 39 Supplementary Material)

Brain functions require both segregated processing of information in specialized circuits, as well as integration across circuits to perform high-level information processing. One possible way to implement these seemingly opposing demands is by flexibly switching between synchronous and less synchronous states. Understanding how complex synchronization patterns are controlled by the interaction of network architecture and external perturbations is thus a central challenge in neuroscience, but the mechanisms behind such interactions remain elusive. Here, we utilise precision neuroengineering to manipulate cultured neuronal networks and show that a modular architecture facilitates desynchronization upon asynchronous stimulation, making external noise a control parameter of synchrony. Using spiking neuron models, we then demonstrate that external noise can reduce the level of available synaptic resources, which make intermodular interactions more stochastic and thereby facilitates the breakdown of synchrony. Finally, the phenomenology of stochastic intermodular interactions is formulated into a mesoscopic model that incorporates a state-dependent gating mechanism for signal propagation. Taken together, our results demonstrate a network mechanism by which asynchronous inputs tune the inherent dynamical state in structured networks of excitable units., Comment: 23 pages, 5 figures

The analysis of the activity of neuronal cultures is considered to be a good proxy of the functional connectivity of in vivo neuronal tissues. Thus, the functional complex network inferred from activity patterns is a promising way to unravel the interplay between structure and functionality of neuronal systems. Here, we monitor the spontaneous self-sustained dynamics in neuronal cultures formed by interconnected aggregates of neurons (clusters). Dynamics is characterized by the fast activation of groups of clusters in sequences termed bursts. The analysis of the time delays between clusters' activations within the bursts allows the reconstruction of the directed functional connectivity of the network. We propose a method to statistically infer this connectivity and analyze the resulting properties of the associated complex networks. Surprisingly enough, in contrast to what has been reported for many biological networks, the clustered neuronal cultures present assortative mixing connectivity values, as well as a rich--club core, meaning that there is a preference for clusters to link to other clusters that share similar functional connectivity, which shapes a `connectivity backbone' in the network. These results point out that the grouping of neurons and the assortative connectivity between clusters are intrinsic survival mechanisms of the culture., Comment: 33 pages, 10 figures

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter- burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron., Comment: 24 pages, 4 figures

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 publication

We introduce a novel approach for the quantitative assessment of the connectivity in neuronal cultures, based on the statistical mechanics of percolation on a graph. This allows us to follow the development of the culture and see the emergence of connectivity in the network. The culture becomes fully connected at a time equivalent to full term. The spontaneous bursting activity that characterizes cultures develops in parallel with the connectivity. The average number of inputs per neuron can be quantitatively determined in units of $m_0$, the number of activated inputs needed to excite the neuron. For $m_0\sim 10$ we find that hippocampal neurons have on average $\sim 40-80$ inputs while cortical neurons have $\sim 50-100$, depending on neuronal density. The ratio of excitatory to inhibitory neurons is determined using the GABA$_\text{A}$ antagonist bicuculine. This ratio changes during development and reaches the final value at day $7-8$, coinciding with the expected time of the GABA switch. For hippocampal cultures the inhibitory cells comprise about $30\%$ of the neurons in the culture while for cortical cultures they are about $20\%$. Such detailed global information on the connectivity of networks in neuronal cultures is at present inaccessible by any electrophysiological or other technique., Comment: Neural cultures | Percolation | Development | Network connectivity http://www.weizmann.ac.il/complex/tlusty/papers/PNAS2008c.pdf

Improvements in technique in conjunction with an evolution of the theoretical and conceptual approach to neuronal networks provide a new perspective on living neurons in culture. Organization and connectivity are being measured quantitatively along with other physical quantities such as information, and are being related to function. In this review we first discuss some of these advances, which enable elucidation of structural aspects. We then discuss two recent experimental models that yield some conceptual simplicity. A one-dimensional network enables precise quantitative comparison to analytic models, for example of propagation and information transport. A two-dimensional percolating network gives quantitative information on connectivity of cultured neurons. The physical quantities that emerge as essential characteristics of the network in vitro are propagation speeds, synaptic transmission, information creation and capacity. Potential application to neuronal devices is discussed., Comment: PACS: 87.18.Sn, 87.19.La, 87.80.-y, 87.80.Xa, 64.60.Ak Keywords: complex systems, neuroscience, neural networks, transport of information, neural connectivity, percolation http://www.weizmann.ac.il/complex/tlusty/papers/PhysRep2007.pdf http://www.weizmann.ac.il/complex/EMoses/pdf/PhysRep-448-56.pdf

Cooperative effects in neural networks appear because a neuron fires only if a minimal number $m$ of its inputs are excited. The multiple inputs requirement leads to a percolation model termed {\it quorum percolation}. The connectivity undergoes a phase transition as $m$ grows, from a network--spanning cluster at low $m$ to a set of disconnected clusters above a critical $m$. Both numerical simulations and the model reproduce the experimental results well. This allows a robust quantification of biologically relevant quantities such as the average connectivity $\kbar$ and the distribution of connections $p_k$, Comment: 87.19.L-: Neuroscience 87.19.ll: Models of single neurons and networks 64.60.ah: Percolation http://iopscience.iop.org/0295-5075/89/1/18008 http://www.weizmann.ac.il/complex/tlusty/papers/EuroPhysLett2010.pdf

We study neural connectivity in cultures of rat hippocampal neurons. We measure the neurons' response to an electric stimulation for gradual lower connectivity, and characterize the size of the giant cluster in the network. The connectivity undergoes a percolation transition described by the critical exponent $\beta \simeq 0.65$. We use a theoretic approach based on bond.percolation on a graph to describe the process of disintegration of the network and extract its statistical properties. Together with numerical simulations we show that the connectivity in the neural culture is local, characterized by a gaussian degree distribution and not a power law on, Comment: Keywords: neural networks, graphs, connectivity, percolation, giant component PACS: 87.18.Sn, 87.19.La, 64.60.Ak http://www.weizmann.ac.il/complex/tlusty/papers/AIP2006.pdf

We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a graph-theoretic approach to show that the connectivity undergoes a percolation transition. This occurs as the giant component disintegrates, characterized by a power law with critical exponent $\beta \simeq 0.65$ is independent of the balance between excitatory and inhibitory neurons and indicates that the degree distribution is gaussian rather than scale free, Comment: PACS numbers: 87.18.Sn, 87.19.La, 64.60.Ak http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevLett2006.pdf

Single cell experiments of simple regulatory networks can markedly differ from cell population experiments. Such differences arise from stochastic events in individual cells that are averaged out in cell populations. For instance, while individual cells may show sustained oscillations in the concentrations of some proteins, such oscillations may appear damped in the population average. In this paper we investigate the role of RNA stochastic fluctuations as a leading force to produce a sustained excitatory behavior at the single cell level. Opposed to some previous models, we build a fully stochastic model of a negative feedback loop that explicitly takes into account the RNA stochastic dynamics. We find that messenger RNA random fluctuations can be amplified during translation and produce sustained pulses of protein expression. Motivated by the recent appreciation of the importance of non--coding regulatory RNAs in post--transcription regulation, we also consider the possibility that a regulatory RNA transcript could bind to the messenger RNA and repress translation. Our findings show that the regulatory transcript helps reduce gene expression variability both at the single cell level and at the cell population level., Comment: 87.18.Vf --> Systems biology 87.10.Mn --> Stochastic models in biological systems 87.18.Tt --> Noise in biological systems http://www.ncbi.nlm.nih.gov/pubmed/20365787 http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevE2010.pdf

We report experimental evidences of anomalous kinetic roughening in the stable displacement of an oil-air interface in a Hele-Shaw cell with strong quenched disorder. The disorder consists on a random modulation of the gap spacing transverse to the growth direction (tracks). We have performed experiments varying average interface velocity and gap spacing, and measured the scaling exponents. We have obtained beta=0.50, beta*=0.25, alpha=1.0, alpha_l=0.5, and z=2. When there is no fluid injection, the interface is driven solely by capillary forces, and a higher value of beta around beta=0.65 is measured. The presence of multiscaling and the particular morphology of the interfaces, characterized by high slopes that follow a L\'evy distribution, confirms the existence of anomalous scaling. From a detailed study of the motion of the oil--air interface we show that the anomaly is a consequence of different local velocities over tracks plus the coupling in the motion between neighboring tracks. The anomaly disappears at high interface velocities, weak capillary forces, or when the disorder is not sufficiently persistent in the growth direction. We have also observed the absence of scaling when the disorder is very strong or when a regular modulation of the gap spacing is introduced., Comment: 14 pages, 17 figures

We have studied the kinetic roughening of an oil--air interface in a forced imbibition experiment in a horizontal Hele--Shaw cell with quenched disorder. Different disorder configurations, characterized by their persistence length in the direction of growth, have been explored by varying the average interface velocity v and the gap spacing b. Through the analysis of the rms width as a function of time, we have measured a growth exponent beta ~= 0.5 that is almost independent of the experimental parameters. The analysis of the roughness exponent alpha through the power spectrum have shown different behaviors at short (alpha_1) and long (alpha_2) length scales, separated by a crossover wavenumber q_c. The values of the measured roughness exponents depend on experimental parameters, but at large velocities we obtain alpha_1 ~= 1.3 independently of the disorder configuration. The dependence of the crossover wavenumber with the experimental parameters has also been investigated, measuring q_c ~ v^{0.47} for the shortest persistence length, in agreement with theoretical predictions., Comment: 20 pages, 22 figures