Anti-correlations in the degree distribution increase stimulus detection performance in noisy spiking neural networks

Neuronal circuits in the rodent barrel cortex are characterized by stable low firing rates. However, recent experiments show that short spike trains elicited by electrical stimulation in single neurons can induce behavioral responses. Hence, the underlying neural networks provide stability against internal fluctuations in the firing rate, while simultaneously making the circuits sensitive to small external perturbations. Here we studied whether stability and sensitivity are affected by the connectivity structure in recurrently connected spiking networks. We found that anti-correlation between the number of afferent (in-degree) and efferent (out-degree) synaptic connections of neurons increases stability against pathological bursting, relative to networks where the degrees were either positively correlated or uncorrelated. In the stable network state, stimulation of a few cells could lead to a detectable change in the firing rate. To quantify the ability of networks to detect the stimulation, we used a receiver operating characteristic (ROC) analysis. For a given level of background noise, networks with anti-correlated degrees displayed the lowest false positive rates, and consequently had the highest stimulus detection performance. We propose that anti-correlation in the degree distribution may be a computational strategy employed by sensory cortices to increase the detectability of external stimuli. We show that networks with anti-correlated degrees can in principle be formed by applying learning rules comprised of a combination of spike-timing dependent plasticity, homeostatic plasticity and pruning to networks with uncorrelated degrees. To test our prediction we suggest a novel experimental method to estimate correlations in the degree distribution.     

Genealogical Trees of Scientific Papers

Many results have been obtained when studying scientific papers citations databases in a network perspective. Articles can be ranked according to their current in-degree and their future popularity or citation counts can even be predicted. The dynamical properties of such networks and the observation of the time evolution of their nodes started more recently. This work adopts an evolutionary perspective and proposes an original algorithm for the construction of genealogical trees of scientific papers on the basis of their citation count evolution in time. The fitness of a paper now amounts to its in-degree growing trend and a “dying” paper will suddenly see this trend declining in time. It will give birth and be taken over by some of its most prevalent citing “offspring”. Practically, this might be used to trace the successive published milestones of a research field.     

Degree Correlations in Directed Scale-Free Networks

Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which is a measure of the correlation between the degrees of the nodes at the end of the links. Degree correlations are known to affect both the structure of a network and the dynamics of the processes supported thereon, including the resilience to damage, the spread of information and epidemics, and the efficiency of defence mechanisms. Nonetheless, while many studies focus on undirected scale-free networks, the interactions in real-world systems often have a directionality. Here, we investigate the dependence of the degree correlations on the power-law exponents in directed scale-free networks. To perform our study, we consider the problem of building directed networks with a prescribed degree distribution, providing a method for proper generation of power-law-distributed directed degree sequences. Applying this new method, we perform extensive numerical simulations, generating ensembles of directed scale-free networks with exponents between 2 and 3, and measuring ensemble averages of the Pearson correlation coefficients. Our results show that scale-free networks are on average uncorrelated across directed links for three of the four possible degree-degree correlations, namely in-degree to in-degree, in-degree to out-degree, and out-degree to out-degree. However, they exhibit anticorrelation between the number of outgoing connections and the number of incoming ones. The findings are consistent with an entropic origin for the observed disassortativity in biological and technological networks.     

Network evolution: rewiring and signatures of conservation in signaling

The analysis of network evolution has been hampered by limited availability of protein interaction data for different organisms. In this study, we investigate evolutionary mechanisms in Src Homology 3 (SH3) domain and kinase interaction networks using high-resolution specificity profiles. We constructed and examined networks for 23 fungal species ranging from Saccharomyces cerevisiae to Schizosaccharomyces pombe. We quantify rates of different rewiring mechanisms and show that interaction change through binding site evolution is faster than through gene gain or loss. We found that SH3 interactions evolve swiftly, at rates similar to those found in phosphoregulation evolution. Importantly, we show that interaction changes are sufficiently rapid to exhibit saturation phenomena at the observed timescales. Finally, focusing on the SH3 interaction network, we observe extensive clustering of binding sites on target proteins by SH3 domains and a strong correlation between the number of domains that bind a target protein (target in-degree) and interaction conservation. The relationship between in-degree and interaction conservation is driven by two different effects, namely the number of clusters that correspond to interaction interfaces and the number of domains that bind to each cluster leads to sequence specific conservation, which in turn results in interaction conservation. In summary, we uncover several network evolution mechanisms likely to generalize across peptide recognition modules.     

Adaptive Cluster Synchronization of Directed Complex Networks with Time Delays

This paper studied the cluster synchronization of directed complex networks with time delays. It is different from undirected networks, the coupling configuration matrix of directed networks cannot be assumed as symmetric or irreducible. In order to achieve cluster synchronization, this paper uses an adaptive controller on each node and an adaptive feedback strategy on the nodes which in-degree is zero. Numerical example is provided to show the effectiveness of main theory. This method is also effective when the number of clusters is unknown. Thus, it can be used in the community recognizing of directed complex networks.     

Effective Connectivity Extracted from Resting-State fMRI Images Using Transfer Entropy

Background and objectiveBased on magnetic resonance imaging (MRI), macroscopic structural and functional connectivity of human brain has been widely explored in the last decade. However, little work has been done on effective connectivity between individual brain parcels. In this preliminary study, we aim to investigate whole-brain effective connectivity networks from resting-state functional MRI (rs-fMRI) images.Material and methodsAfter the functional connectivity networks of 26 healthy subjects (aged from 25 to 35 years old) from Human Connectome Project database were derived from rs-fMRI images with dynamic time warping, proportional thresholding (PT) was performed on the functional connectivity matrices by retaining the PT% strongest functional connections. PT% ranges from 40% to 10% in steps of 5%. Then, effective connections corresponding to the PT% strongest functional connections, both bi-directional and unidirectional, were estimated with Renyi's 2-order transfer entropy (TE) method. Topological metrics of the built functional and effective connectivity networks were further characterized, including clustering coefficient, transitivity, and modularity.ResultsIt is found that the effective connectivity networks exhibit small world attributes, and that the networks contain a subset of highly interactive regions, including right frontal pole (in-degree 6), left middle frontal gyrus (in-degree 8, out-degree 1), right precentral gyrus (out-degree 9), left precentral gyrus (out-degree 7), right posterior division of supramarginal gyrus (in-degree 2, out-degree 3), left angular gyrus (out-degree 6), left inferior division of lateral occipital cortex (out-degree 6), right occipital pole (in-degree 5), right cerebellum 7b parcel (in-degree 15), and right cerebellum 8 parcel (in-degree 7, out-degree 1).ConclusionsThe observations in this study provide information about the casual interactions among brain parcels in resting state, helping reveal how different subregions of large-scale distributed neural networks are coupled together in performing cognitive functions.     

Fast digital simulation of spiking neural networks and neuromorphic integration with SPIKELAB

We present a simulation environment called SPIKELAB which incorporates a simulator that is able to simulate large networks of spiking neurons using a distributed event driven simulation. Contrary to a time driven simulation, which is usually used to simulate spiking neural networks, our simulation needs less computational resources because of the low average activity of typical networks. The paper addresses the speed up using an event driven versus a time driven simulation and how large networks can be simulated by a distribution of the simulation using already available computing resources. It also presents a solution for the integration of digital or analogue neuromorphic circuits into the simulation process.     

New bioreactor-coupled rapid stopped-flow sampling technique for measurements of metabolite dynamics on a subsecond time scale

Knowledge of concentrations of intracellular metabolites is important for quantitative analysis of metabolic networks. As far as the very fast response of intracellular metabolites in the millisecond range is concerned, the frequently used pulse technique shows an inherent limitation. The time span between the disturbance and the first sample is constrained by the time necessary to obtain a homogeneous distribution of the pertubation within the bioreactor. For determination of rapid changes, a novel sampling technique based on the stopped-flow method has been developed. A continuous stream of biosuspension leaving the bioreactor is being mixed with a glucose solution in a turbulent mixing chamber. Through computer-aided activation of sequentially positioned three-way valves, different residence times and thus reaction times can be verified. The application of this new sampling method is illustrated with examples including measurements of adenine nucleotides and glucose-6-phosphate in Saccharomyces cerevisiae as well as measurements related to the PTS system in Escherichia coli.     

Structure-Dynamics Relationships in Bursting Neuronal Networks Revealed Using a Prediction Framework

The question of how the structure of a neuronal network affects its functionality has gained a lot of attention in neuroscience. However, the vast majority of the studies on structure-dynamics relationships consider few types of network structures and assess limited numbers of structural measures. In this in silico study, we employ a wide diversity of network topologies and search among many possibilities the aspects of structure that have the greatest effect on the network excitability. The network activity is simulated using two point-neuron models, where the neurons are activated by noisy fluctuation of the membrane potential and their connections are described by chemical synapse models, and statistics on the number and quality of the emergent network bursts are collected for each network type. We apply a prediction framework to the obtained data in order to find out the most relevant aspects of network structure. In this framework, predictors that use different sets of graph-theoretic measures are trained to estimate the activity properties, such as burst count or burst length, of the networks. The performances of these predictors are compared with each other. We show that the best performance in prediction of activity properties for networks with sharp in-degree distribution is obtained when the prediction is based on clustering coefficient. By contrast, for networks with broad in-degree distribution, the maximum eigenvalue of the connectivity graph gives the most accurate prediction. The results shown for small () networks hold with few exceptions when different neuron models, different choices of neuron population and different average degrees are applied. We confirm our conclusions using larger () networks as well. Our findings reveal the relevance of different aspects of network structure from the viewpoint of network excitability, and our integrative method could serve as a general framework for structure-dynamics studies in biosciences.     

Quantifying and analyzing the network basis of genetic complexity

Genotype-to-phenotype maps exhibit complexity. This genetic complexity is mentioned frequently in the literature, but a consistent and quantitative definition is lacking. Here, we derive such a definition and investigate its consequences for model genetic systems. The definition equates genetic complexity with a surplus of genotypic diversity over phenotypic diversity. Applying this definition to ensembles of Boolean network models, we found that the in-degree distribution and the number of periodic attractors produced determine the relative complexity of different topology classes. We found evidence that networks that are difficult to control, or that exhibit a hierarchical structure, are genetically complex. We analyzed the complexity of the cell cycle network of Sacchoromyces cerevisiae and pinpointed genes and interactions that are most important for its high genetic complexity. The rigorous definition of genetic complexity is a tool for unraveling the structure and properties of genotype-to-phenotype maps by enabling the quantitative comparison of the relative complexities of different genetic systems. The definition also allows the identification of specific network elements and subnetworks that have the greatest effects on genetic complexity. Moreover, it suggests ways to engineer biological systems with desired genetic properties.     

A publish-subscribe model of genetic networks

We present a simple model of genetic regulatory networks in which regulatory connections among genes are mediated by a limited number of signaling molecules. Each gene in our model produces (publishes) a single gene product, which regulates the expression of other genes by binding to regulatory regions that correspond (subscribe) to that product. We explore the consequences of this publish-subscribe model of regulation for the properties of single networks and for the evolution of populations of networks. Degree distributions of randomly constructed networks, particularly multimodal in-degree distributions, which depend on the length of the regulatory sequences and the number of possible gene products, differed from simpler Boolean NK models. In simulated evolution of populations of networks, single mutations in regulatory or coding regions resulted in multiple changes in regulatory connections among genes, or alternatively in neutral change that had no effect on phenotype. This resulted in remarkable evolvability in both number and length of attractors, leading to evolved networks far beyond the expectation of these measures based on random distributions. Surprisingly, this rapid evolution was not accompanied by changes in degree distribution; degree distribution in the evolved networks was not substantially different from that of randomly generated networks. The publish-subscribe model also allows exogenous gene products to create an environment, which may be noisy or stable, in which dynamic behavior occurs. In simulations, networks were able to evolve moderate levels of both mutational and environmental robustness.     

Biomolecular network motif counting and discovery by color coding

Protein-protein interaction (PPI) networks of many organisms share global topological features such as degree distribution, k-hop reachability, betweenness and closeness. Yet, some of these networks can differ significantly from the others in terms of local structures: e.g. the number of specific network motifs can vary significantly among PPI networks. Counting the number of network motifs provides a major challenge to compare biomolecular networks. Recently developed algorithms have been able to count the number of induced occurrences of subgraphs with k < or = 7 vertices. Yet no practical algorithm exists for counting non-induced occurrences, or counting subgraphs with k > or = 8 vertices. Counting non-induced occurrences of network motifs is not only challenging but also quite desirable as available PPI networks include several false interactions and miss many others. In this article, we show how to apply the 'color coding' technique for counting non-induced occurrences of subgraph topologies in the form of trees and bounded treewidth subgraphs. Our algorithm can count all occurrences of motif G' with k vertices in a network G with n vertices in time polynomial with n, provided k = O(log n). We use our algorithm to obtain 'treelet' distributions for k < or = 10 of available PPI networks of unicellular organisms (Saccharomyces cerevisiae Escherichia coli and Helicobacter Pyloris), which are all quite similar, and a multicellular organism (Caenorhabditis elegans) which is significantly different. Furthermore, the treelet distribution of the unicellular organisms are similar to that obtained by the 'duplication model' but are quite different from that of the 'preferential attachment model'. The treelet distribution is robust w.r.t. sparsification with bait/edge coverage of 70% but differences can be observed when bait/edge coverage drops to 50%.     

Construction of synthetic regulatory networks in yeast

Yeast species such as Saccharomyces cerevisiae have been exploited by humans for millennia and so it is therefore unsurprising that they are attractive cells to re-engineer for industrial use. Despite many beneficial traits yeast has for synthetic biology, it currently lags behind Escherichia coli in the number of synthetic networks that have been described. While the eukaryotic nature of yeast means that its regulation is not as simple to predict as it is for E. coli, once initial considerations have been made yeast is pleasingly tractable. In this review we provide a loose guide for constructing and implementing synthetic regulatory networks in S. cerevisiae using examples from previous research to highlight available resources, specific considerations and potential future advances.     

Discrete time piecewise affine models of genetic regulatory networks

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. These models reduce to boolean networks in one limiting case of a parameter, and their asymptotic dynamics approaches that of a differential equation in another limiting case of this parameter. For intermediate values, the model present an original phenomenology which is argued to be due to delay effects. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle – with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with non-negligible delay effects.