Modularized study of human calcium signalling pathway

Signalling pathways are complex biochemical networks responsible for regulation of numerous cellular functions. These networks function by serial and successive interactions among a large number of vital biomolecules and chemical compounds. For deciphering and analysing the underlying mechanism of such networks, a modularized study is quite helpful. Here we propose an algorithm for modularization of calcium signalling pathway of H. sapiens. The idea that “a node whose function is dependant on maximum number of other nodes tends to be the center of a subnetwork” is used to divide a large signalling network into smaller subnetworks. Inclusion of node(s) into subnetworks(s) is dependant on the outdegree of the node(s). Here outdegree of a node refers to the number of relations of the considered node lying outside the constructed subnetwork. Node(s) having more than c relations lying outside the expanding subnetwork have to be excluded from it. Here c is a specified variable based on user preference, which is finally fixed during adjustments of created subnetworks, so that certain biological significance can be conferred on them.     

Emergence of Scale-Free Close-Knit Friendship Structure in Online Social Networks

Although the structural properties of online social networks have attracted much attention, the properties of the close-knit friendship structures remain an important question. Here, we mainly focus on how these mesoscale structures are affected by the local and global structural properties. Analyzing the data of four large-scale online social networks reveals several common structural properties. It is found that not only the local structures given by the indegree, outdegree, and reciprocal degree distributions follow a similar scaling behavior, the mesoscale structures represented by the distributions of close-knit friendship structures also exhibit a similar scaling law. The degree correlation is very weak over a wide range of the degrees. We propose a simple directed network model that captures the observed properties. The model incorporates two mechanisms: reciprocation and preferential attachment. Through rate equation analysis of our model, the local-scale and mesoscale structural properties are derived. In the local-scale, the same scaling behavior of indegree and outdegree distributions stems from indegree and outdegree of nodes both growing as the same function of the introduction time, and the reciprocal degree distribution also shows the same power-law due to the linear relationship between the reciprocal degree and in/outdegree of nodes. In the mesoscale, the distributions of four closed triples representing close-knit friendship structures are found to exhibit identical power-laws, a behavior attributed to the negligible degree correlations. Intriguingly, all the power-law exponents of the distributions in the local-scale and mesoscale depend only on one global parameter, the mean in/outdegree, while both the mean in/outdegree and the reciprocity together determine the ratio of the reciprocal degree of a node to its in/outdegree. Structural properties of numerical simulated networks are analyzed and compared with each of the four real networks. This work helps understand the interplay between structures on different scales in online social networks.     

A thermodynamic view of networks

Networks can be described by the frequency distribution of the number of links associated with each node (the degree of the node). Of particular interest are the power law distributions, which give rise to the so-called scale-free networks, and the distributions of the form of the simplified canonical law (SCL) introduced by Mandelbrot, which give what we shall call the Mandelbrot networks. Many dynamical methods have been obtained for the construction of scale-free networks, but no dynamical construction of Mandelbrot networks has been demonstrated. Here we develop a systematic technique to obtain networks with any given distribution of the degrees of the nodes. This is done using a thermodynamic approach in which we maximise the entropy associated with degree distribution of the nodes of the network subject to certain constraints. These constraints can be chosen systematically to produce the desired network architecture. For large networks we therefore replace a dynamical approach to the stationary state by a thermodynamical viewpoint. We use the method to generate scale-free and Mandelbrot networks with arbitrarily chosen parameters. We emphasise that this approach opens the possibility of insights into a thermodynamics of networks by suggesting thermodynamic relations between macroscopic variables for networks.     

Socio-Spatial Relationships in Dairy Cows

Farm animals may serve as models for evaluating social networks in a controlled environment. We used an automated system to track, at fine temporal and spatial resolution (once per minute, ±50 cm) every individual in six herds of dairy cows ( Bos taurus ). We then analysed the data using social network analyses. Relationships were based on non-random attachment and avoidance relationships in respect to synchronous use and distances observed in three different functional areas (activity, feeding and lying). We found that neither synchrony nor distance between cows was strongly predictable among the three functional areas. The emerging social networks were tightly knit for attachment relationships and less dense for avoidance relationships. These networks loosened up from the feeding and lying area to the activity area, and were less dense for relationships based on synchronicity than on median distance with respect to node degree, relative size of the largest cluster, density and diameter of the network. In addition, synchronicity was higher in dyads of dairy cows that had grown up together and shared their last dry period. This last effect disappeared with increasing herd size. Dairy herds can be characterized by one strongly clustered network including most of the herd members with many non-random attachment and avoidance relationships. Closely synchronous dyads were composed of cows with more intense previous contact. The automatic tracking of a large number of individuals proved promising in acquiring the data necessary for tackling social network analyses.     

Improving plant drought tolerance and growth under water limitation through combinatorial engineering of signalling networks

Agriculture is by far the biggest water consumer on our planet, accounting for 70 per cent of all freshwater withdrawals. Climate change and a growing world population increase pressure on agriculture to use water more efficiently (‘more crop per drop’). Water‐use efficiency (WUE) and drought tolerance of crops are complex traits that are determined by many physiological processes whose interplay is not well understood. Here, we describe a combinatorial engineering approach to optimize signalling networks involved in the control of stress tolerance. Screening a large population of combinatorially transformed plant lines, we identified a combination of calcium‐dependent protein kinase genes that confers enhanced drought stress tolerance and improved growth under water‐limiting conditions. Targeted introduction of this gene combination into plants increased plant survival under drought and enhanced growth under water‐limited conditions. Our work provides an efficient strategy for engineering complex signalling networks to improve plant performance under adverse environmental conditions, which does not depend on prior understanding of network function.     

Stoichiometric design of metabolic networks: multifunctionality,clusters, optimization,weak and strong robustness

Starting from a limited set of reactions describing changes in the carbon skeleton of biochemical compounds complete sets of metabolic networks are constructed. The networks are characterized by the number and types of participating reactions. Elementary networks are defined by the condition that a specific chemical conversion can be performed by a set of given reactions and that this ability will be lost by elimination of any of these reactions. Groups of networks are identified with respect to their ability to perform a certain number of metabolic conversions in an elementary way which are called the network’s functions. The number of the network functions defines the degree of multifunctionality. Transitions between networks and mutations of networks are defined by exchanges of single reactions. Different mutations exist such as gain or loss of function mutations and neutral mutations. Based on these mutations neighbourhood relations between networks are established which are described in a graph theoretical way. Basic properties of these graphs are determined such as diameter, connectedness, distance distribution of pairs of vertices. A concept is developed to quantify the robustness of networks against changes in their stoichiometry where we distinguish between strong and weak robustness. Evolutionary algorithms are applied to study the development of network populations under constant and time dependent environmental conditions. It is shown that the populations evolve toward clusters of networks performing a common function and which are closely neighboured. Under changing environmental conditions multifunctional networks prove to be optimal and will be selected.     

Colored motifs reveal computational building blocks in the C. elegans brain

Background

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.

Methodology/Principal Findings

Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm''s locomotion.

Conclusions/Significance

The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available.     

Labeling Nodes Using Three Degrees of Propagation

The properties (or labels) of nodes in networks can often be predicted based on their proximity and their connections to other labeled nodes. So-called “label propagation algorithms” predict the labels of unlabeled nodes by propagating information about local label density iteratively through the network. These algorithms are fast, simple and scale to large networks but nonetheless regularly perform better than slower and much more complex algorithms on benchmark problems. We show here, however, that these algorithms have an intrinsic limitation that prevents them from adapting to some common patterns of network node labeling; we introduce a new algorithm, 3Prop, that retains all their advantages but is much more adaptive. As we show, 3Prop performs very well on node labeling problems ill-suited to label propagation, including predicting gene function in protein and genetic interaction networks and gender in friendship networks, and also performs slightly better on problems already well-suited to label propagation such as labeling blogs and patents based on their citation networks. 3Prop gains its adaptability by assigning separate weights to label information from different steps of the propagation. Surprisingly, we found that for many networks, the third iteration of label propagation receives a negative weight.

Availability

The code is available from the authors by request.     

How structure determines correlations in neuronal networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.     

Using the topology of metabolic networks to predict viability of mutant strains

Understanding the relationships between the structure (topology) and function of biological networks is a central question of systems biology. The idea that topology is a major determinant of systems function has become an attractive and highly disputed hypothesis. Although structural analysis of interaction networks demonstrates a correlation between the topological properties of a node (protein, gene) in the network and its functional essentiality, the analysis of metabolic networks fails to find such correlations. In contrast, approaches utilizing both the topology and biochemical parameters of metabolic networks, e.g., flux balance analysis, are more successful in predicting phenotypes of knockout strains. We reconcile these seemingly conflicting results by showing that the topology of the metabolic networks of both Escherichia coli and Saccharomyces cerevisiae are, in fact, sufficient to predict the viability of knockout strains with accuracy comparable to flux balance analysis on large, unbiased mutant data sets. This surprising result is obtained by introducing a novel topology-based measure of network transport: synthetic accessibility. We also show that other popular topology-based characteristics such as node degree, graph diameter, and node usage (betweenness) fail to predict the viability of E. coli mutant strains. The success of synthetic accessibility demonstrates its ability to capture the essential properties of the metabolic network, such as the branching of chemical reactions and the directed transport of material from inputs to outputs. Our results strongly support a link between the topology and function of biological networks and, in agreement with recent genetic studies, emphasize the minimal role of flux rerouting in providing robustness of mutant strains.     

Intracellular signalling as a parallel distributed process

Living cells respond to their environment by means of an interconnected network of receptors, second messengers, protein kinases and other signalling molecules. This article suggests that the performance of cell signalling pathways taken as a whole has similarities to that of the parallel distributed process networks (PDP networks) used in computer-based pattern recognition. Using the response of hepatocytes to glucagon as an example, a procedure is described by which a PDP network could simulate a cell signalling pathway. This procedure involves the following steps: (a) a bounded set of molecules is defined that carry the signals of interest; (b) each of these molecules is represented by a PDP-type of unit, with input and output functions and connection weights corresponding to specific biochemical parameters; (c) a "learning algorithm" is applied in which small random changes are made in the parameters of the cell signalling units and the new network is then tested by a selection procedure in favour of a specific input-output relationship. The analogy with PDP networks shows how living cells can recognize combinations of environmental influences, how cell responses can be stabilized and made resistant to damage, and how novel cell signalling pathways might appear during evolution.     

Cliques and cavities in the human connectome

Encoding brain regions and their connections as a network of nodes and edges captures many of the possible paths along which information can be transmitted as humans process and perform complex behaviors. Because cognitive processes involve large, distributed networks of brain areas, principled examinations of multi-node routes within larger connection patterns can offer fundamental insights into the complexities of brain function. Here, we investigate both densely connected groups of nodes that could perform local computations as well as larger patterns of interactions that would allow for parallel processing. Finding such structures necessitates that we move from considering exclusively pairwise interactions to capturing higher order relations, concepts naturally expressed in the language of algebraic topology. These tools can be used to study mesoscale network structures that arise from the arrangement of densely connected substructures called cliques in otherwise sparsely connected brain networks. We detect cliques (all-to-all connected sets of brain regions) in the average structural connectomes of 8 healthy adults scanned in triplicate and discover the presence of more large cliques than expected in null networks constructed via wiring minimization, providing architecture through which brain network can perform rapid, local processing. We then locate topological cavities of different dimensions, around which information may flow in either diverging or converging patterns. These cavities exist consistently across subjects, differ from those observed in null model networks, and – importantly – link regions of early and late evolutionary origin in long loops, underscoring their unique role in controlling brain function. These results offer a first demonstration that techniques from algebraic topology offer a novel perspective on structural connectomics, highlighting loop-like paths as crucial features in the human brain’s structural architecture.     

An Efficient Steady-State Analysis Method for Large Boolean Networks with High Maximum Node Connectivity

Boolean networks have been widely used to model biological processes lacking detailed kinetic information. Despite their simplicity, Boolean network dynamics can still capture some important features of biological systems such as stable cell phenotypes represented by steady states. For small models, steady states can be determined through exhaustive enumeration of all state transitions. As the number of nodes increases, however, the state space grows exponentially thus making it difficult to find steady states. Over the last several decades, many studies have addressed how to handle such a state space explosion. Recently, increasing attention has been paid to a satisfiability solving algorithm due to its potential scalability to handle large networks. Meanwhile, there still lies a problem in the case of large models with high maximum node connectivity where the satisfiability solving algorithm is known to be computationally intractable. To address the problem, this paper presents a new partitioning-based method that breaks down a given network into smaller subnetworks. Steady states of each subnetworks are identified by independently applying the satisfiability solving algorithm. Then, they are combined to construct the steady states of the overall network. To efficiently apply the satisfiability solving algorithm to each subnetwork, it is crucial to find the best partition of the network. In this paper, we propose a method that divides each subnetwork to be smallest in size and lowest in maximum node connectivity. This minimizes the total cost of finding all steady states in entire subnetworks. The proposed algorithm is compared with others for steady states identification through a number of simulations on both published small models and randomly generated large models with differing maximum node connectivities. The simulation results show that our method can scale up to several hundreds of nodes even for Boolean networks with high maximum node connectivity. The algorithm is implemented and available at http://cps.kaist.ac.kr/∼ckhong/tools/download/PAD.tar.gz.     

Evaluation of energetic and dynamic coupling networks in a PDZ domain protein

A number of computational and experimental studies have identified intramolecular communication "pathways" or "networks" important for transmitting allostery. Here, we have used mutagenesis and NMR relaxation methods to investigate the scope and nature of the communication networks found in the second post-synaptic density-95/discs large/zonula occludens-1 (PDZ) domain of the human protein tyrosine phosphatase 1E protein (hPTP1E) (PDZ2). It was found that most mutations do not have a significant energetic contribution to peptide ligand binding. Three mutants that showed significant changes in binding also displayed context-dependent dynamic effects. Both a mutation at a partially exposed site (H71Y) and a buried core position (I35V) had a limited response in side-chain (2)H-based dynamics when compared to wild-type PDZ2. In contrast, a change at a second core position (I20F) that had previously been shown to be part of an energetic and dynamic network, resulted in extensive changes in side-chain dynamics. This response is reminiscent to that seen previously upon peptide ligand binding. These results shed light on the nature of the PDZ2 dynamic network and suggest that position 20 in PDZ2 acts as a "hub" that is energetically and dynamically critical for transmitting changes in dynamics throughout the PDZ domain.     

Multiplex Networks of Cortical and Hippocampal Neurons Revealed at Different Timescales

Recent studies have emphasized the importance of multiplex networks – interdependent networks with shared nodes and different types of connections – in systems primarily outside of neuroscience. Though the multiplex properties of networks are frequently not considered, most networks are actually multiplex networks and the multiplex specific features of networks can greatly affect network behavior (e.g. fault tolerance). Thus, the study of networks of neurons could potentially be greatly enhanced using a multiplex perspective. Given the wide range of temporally dependent rhythms and phenomena present in neural systems, we chose to examine multiplex networks of individual neurons with time scale dependent connections. To study these networks, we used transfer entropy – an information theoretic quantity that can be used to measure linear and nonlinear interactions – to systematically measure the connectivity between individual neurons at different time scales in cortical and hippocampal slice cultures. We recorded the spiking activity of almost 12,000 neurons across 60 tissue samples using a 512-electrode array with 60 micrometer inter-electrode spacing and 50 microsecond temporal resolution. To the best of our knowledge, this preparation and recording method represents a superior combination of number of recorded neurons and temporal and spatial recording resolutions to any currently available in vivo system. We found that highly connected neurons (“hubs”) were localized to certain time scales, which, we hypothesize, increases the fault tolerance of the network. Conversely, a large proportion of non-hub neurons were not localized to certain time scales. In addition, we found that long and short time scale connectivity was uncorrelated. Finally, we found that long time scale networks were significantly less modular and more disassortative than short time scale networks in both tissue types. As far as we are aware, this analysis represents the first systematic study of temporally dependent multiplex networks among individual neurons.