Not all scale-free networks are born equal: the role of the seed graph in PPI network evolution

The (asymptotic) degree distributions of the best-known “scale-free” network models are all similar and are independent of the seed graph used; hence, it has been tempting to assume that networks generated by these models are generally similar. In this paper, we observe that several key topological features of such networks depend heavily on the specific model and the seed graph used. Furthermore, we show that starting with the “right” seed graph (typically a dense subgraph of the protein–protein interaction network analyzed), the duplication model captures many topological features of publicly available protein–protein interaction networks very well.     

An Evaluation of Methods for Inferring Boolean Networks from Time-Series Data

Regulatory networks play a central role in cellular behavior and decision making. Learning these regulatory networks is a major task in biology, and devising computational methods and mathematical models for this task is a major endeavor in bioinformatics. Boolean networks have been used extensively for modeling regulatory networks. In this model, the state of each gene can be either ‘on’ or ‘off’ and that next-state of a gene is updated, synchronously or asynchronously, according to a Boolean rule that is applied to the current-state of the entire system. Inferring a Boolean network from a set of experimental data entails two main steps: first, the experimental time-series data are discretized into Boolean trajectories, and then, a Boolean network is learned from these Boolean trajectories. In this paper, we consider three methods for data discretization, including a new one we propose, and three methods for learning Boolean networks, and study the performance of all possible nine combinations on four regulatory systems of varying dynamics complexities. We find that employing the right combination of methods for data discretization and network learning results in Boolean networks that capture the dynamics well and provide predictive power. Our findings are in contrast to a recent survey that placed Boolean networks on the low end of the “faithfulness to biological reality” and “ability to model dynamics” spectra. Further, contrary to the common argument in favor of Boolean networks, we find that a relatively large number of time points in the time-series data is required to learn good Boolean networks for certain data sets. Last but not least, while methods have been proposed for inferring Boolean networks, as discussed above, missing still are publicly available implementations thereof. Here, we make our implementation of the methods available publicly in open source at http://bioinfo.cs.rice.edu/.     

Data-dependent visualization of biological networks in the web-browser with NDExEdit

Networks are a common methodology used to capture increasingly complex associations between biological entities. They serve as a resource of biological knowledge for bioinformatics analyses, and also comprise the subsequent results. However, the interpretation of biological networks is challenging and requires suitable visualizations dependent on the contained information. The most prominent software in the field for the visualization of biological networks is Cytoscape, a desktop modeling environment also including many features for analysis.A further challenge when working with networks is their distribution. Within a typical collaborative workflow, even slight changes of the network data force one to repeat the visualization step as well. Also, just minor adjustments to the visual representation not only need the networks to be transferred back and forth. Collaboration on the same resources requires specific infrastructure to avoid redundancies, or worse, the corruption of the data. A well-established solution is provided by the NDEx platform where users can upload a network, share it with selected colleagues or make it publicly available.NDExEdit is a web-based application where simple changes can be made to biological networks within the browser, and which does not require installation. With our tool, plain networks can be enhanced easily for further usage in presentations and publications. Since the network data is only stored locally within the web browser, users can edit their private networks without concerns of unintentional publication. The web tool is designed to conform to the Cytoscape Exchange (CX) format as a data model, which is used for the data transmission by both tools, Cytoscape and NDEx. Therefore the modified network can be directly exported to the NDEx platform or saved as a compatible CX file, additionally to standard image formats like PNG and JPEG.     

A graphic editor for analyzing signal-transduction pathways

We describe a graphical editor designed specifically to facilitate analysis and visualization of complex signal-transduction pathways. The editor provides automatic layout of complex regulatory graphs and enables users easily to maintain, edit, and exchange publication-quality images of regulatory networks.     

A Simulation Study Comparing Epidemic Dynamics on Exponential Random Graph and Edge-Triangle Configuration Type Contact Network Models

We compare two broad types of empirically grounded random network models in terms of their abilities to capture both network features and simulated Susceptible-Infected-Recovered (SIR) epidemic dynamics. The types of network models are exponential random graph models (ERGMs) and extensions of the configuration model. We use three kinds of empirical contact networks, chosen to provide both variety and realistic patterns of human contact: a highly clustered network, a bipartite network and a snowball sampled network of a “hidden population”. In the case of the snowball sampled network we present a novel method for fitting an edge-triangle model. In our results, ERGMs consistently capture clustering as well or better than configuration-type models, but the latter models better capture the node degree distribution. Despite the additional computational requirements to fit ERGMs to empirical networks, the use of ERGMs provides only a slight improvement in the ability of the models to recreate epidemic features of the empirical network in simulated SIR epidemics. Generally, SIR epidemic results from using configuration-type models fall between those from a random network model (i.e., an Erdős-Rényi model) and an ERGM. The addition of subgraphs of size four to edge-triangle type models does improve agreement with the empirical network for smaller densities in clustered networks. Additional subgraphs do not make a noticeable difference in our example, although we would expect the ability to model cliques to be helpful for contact networks exhibiting household structure.     

Training Excitatory-Inhibitory Recurrent Neural Networks for Cognitive Tasks: A Simple and Flexible Framework

The ability to simultaneously record from large numbers of neurons in behaving animals has ushered in a new era for the study of the neural circuit mechanisms underlying cognitive functions. One promising approach to uncovering the dynamical and computational principles governing population responses is to analyze model recurrent neural networks (RNNs) that have been optimized to perform the same tasks as behaving animals. Because the optimization of network parameters specifies the desired output but not the manner in which to achieve this output, “trained” networks serve as a source of mechanistic hypotheses and a testing ground for data analyses that link neural computation to behavior. Complete access to the activity and connectivity of the circuit, and the ability to manipulate them arbitrarily, make trained networks a convenient proxy for biological circuits and a valuable platform for theoretical investigation. However, existing RNNs lack basic biological features such as the distinction between excitatory and inhibitory units (Dale’s principle), which are essential if RNNs are to provide insights into the operation of biological circuits. Moreover, trained networks can achieve the same behavioral performance but differ substantially in their structure and dynamics, highlighting the need for a simple and flexible framework for the exploratory training of RNNs. Here, we describe a framework for gradient descent-based training of excitatory-inhibitory RNNs that can incorporate a variety of biological knowledge. We provide an implementation based on the machine learning library Theano, whose automatic differentiation capabilities facilitate modifications and extensions. We validate this framework by applying it to well-known experimental paradigms such as perceptual decision-making, context-dependent integration, multisensory integration, parametric working memory, and motor sequence generation. Our results demonstrate the wide range of neural activity patterns and behavior that can be modeled, and suggest a unified setting in which diverse cognitive computations and mechanisms can be studied.     

Bio-Logic Builder: A Non-Technical Tool for Building Dynamical,Qualitative Models

Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized “bio-logic” modules have been defined to provide users with the building blocks for many biological processes. To build/modify computational models, experimentalists provide purely qualitative information about a particular regulatory mechanisms as is generally found in the laboratory. The Bio-Logic Builder subsequently converts the provided information into a mathematical representation described with Boolean expressions/rules. We used this tool to build a number of dynamical models, including a 130-protein large-scale model of signal transduction with over 800 interactions, influenza A replication cycle with 127 species and 200+ interactions, and mammalian and budding yeast cell cycles. We also show that any and all qualitative regulatory mechanisms can be built using this tool.     

Analyzing Self-Similar and Fractal Properties of the C. elegans Neural Network

The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron “giant component” of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been “rewired” to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.     

PATIKAmad: putting microarray data into pathway context

High-throughput experiments, most significantly DNA microarrays, provide us with system-scale profiles. Connecting these data with existing biological networks poses a formidable challenge to uncover facts about a cell's proteome. Studies and tools with this purpose are limited to networks with simple structure, such as protein-protein interaction graphs, or do not go much beyond than simply displaying values on the network. We have built a microarray data analysis tool, named PATIKAmad, which can be used to associate microarray data with the pathway models in mechanistic detail, and provides facilities for visualization, clustering, querying, and navigation of biological graphs related with loaded microarray experiments. PATIKAmad is freely available to noncommercial users as a new module of PATIKAweb at http://web.patika.org.     

Performance of Social Network Sensors during Hurricane Sandy

Information flow during catastrophic events is a critical aspect of disaster management. Modern communication platforms, in particular online social networks, provide an opportunity to study such flow and derive early-warning sensors, thus improving emergency preparedness and response. Performance of the social networks sensor method, based on topological and behavioral properties derived from the “friendship paradox”, is studied here for over 50 million Twitter messages posted before, during, and after Hurricane Sandy. We find that differences in users’ network centrality effectively translate into moderate awareness advantage (up to 26 hours); and that geo-location of users within or outside of the hurricane-affected area plays a significant role in determining the scale of such an advantage. Emotional response appears to be universal regardless of the position in the network topology, and displays characteristic, easily detectable patterns, opening a possibility to implement a simple “sentiment sensing” technique that can detect and locate disasters.     

Evaluation of the Performance of Information Theory-Based Methods and Cross-Correlation to Estimate the Functional Connectivity in Cortical Networks

Functional connectivity of in vitro neuronal networks was estimated by applying different statistical algorithms on data collected by Micro-Electrode Arrays (MEAs). First we tested these “connectivity methods” on neuronal network models at an increasing level of complexity and evaluated the performance in terms of ROC (Receiver Operating Characteristic) and PPC (Positive Precision Curve), a new defined complementary method specifically developed for functional links identification. Then, the algorithms better estimated the actual connectivity of the network models, were used to extract functional connectivity from cultured cortical networks coupled to MEAs. Among the proposed approaches, Transfer Entropy and Joint-Entropy showed the best results suggesting those methods as good candidates to extract functional links in actual neuronal networks from multi-site recordings.     

Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models

Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best “LFP proxy”, we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with “ground-truth” LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.     

A network approach to elucidate and prioritize microbial dark matter in microbial communities

Microbes compose most of the biomass on the planet, yet the majority of taxa remain uncharacterized. These unknown microbes, often referred to as “microbial dark matter,” represent a major challenge for biology. To understand the ecological contributions of these Unknown taxa, it is essential to first understand the relationship between unknown species, neighboring microbes, and their respective environment. Here, we establish a method to study the ecological significance of “microbial dark matter” by building microbial co-occurrence networks from publicly available 16S rRNA gene sequencing data of four extreme aquatic habitats. For each environment, we constructed networks including and excluding unknown organisms at multiple taxonomic levels and used network centrality measures to quantitatively compare networks. When the Unknown taxa were excluded from the networks, a significant reduction in degree and betweenness was observed for all environments. Strikingly, Unknown taxa occurred as top hubs in all environments, suggesting that “microbial dark matter” play necessary ecological roles within their respective communities. In addition, novel adaptation-related genes were detected after using 16S rRNA gene sequences from top-scoring hub taxa as probes to blast metagenome databases. This work demonstrates the broad applicability of network metrics to identify and prioritize key Unknown taxa and improve understanding of ecosystem structure across diverse habitats.Subject terms: Microbial ecology, Metagenomics     

Integrating Interactive Computational Modeling in Biology Curricula

While the use of computer tools to simulate complex processes such as computer circuits is normal practice in fields like engineering, the majority of life sciences/biological sciences courses continue to rely on the traditional textbook and memorization approach. To address this issue, we explored the use of the Cell Collective platform as a novel, interactive, and evolving pedagogical tool to foster student engagement, creativity, and higher-level thinking. Cell Collective is a Web-based platform used to create and simulate dynamical models of various biological processes. Students can create models of cells, diseases, or pathways themselves or explore existing models. This technology was implemented in both undergraduate and graduate courses as a pilot study to determine the feasibility of such software at the university level. First, a new (In Silico Biology) class was developed to enable students to learn biology by “building and breaking it” via computer models and their simulations. This class and technology also provide a non-intimidating way to incorporate mathematical and computational concepts into a class with students who have a limited mathematical background. Second, we used the technology to mediate the use of simulations and modeling modules as a learning tool for traditional biological concepts, such as T cell differentiation or cell cycle regulation, in existing biology courses. Results of this pilot application suggest that there is promise in the use of computational modeling and software tools such as Cell Collective to provide new teaching methods in biology and contribute to the implementation of the “Vision and Change” call to action in undergraduate biology education by providing a hands-on approach to biology.     

Geographies of an Online Social Network

How is online social media activity structured in the geographical space? Recent studies have shown that in spite of earlier visions about the “death of distance”, physical proximity is still a major factor in social tie formation and maintenance in virtual social networks. Yet, it is unclear, what are the characteristics of the distance dependence in online social networks. In order to explore this issue the complete network of the former major Hungarian online social network is analyzed. We find that the distance dependence is weaker for the online social network ties than what was found earlier for phone communication networks. For a further analysis we introduced a coarser granularity: We identified the settlements with the nodes of a network and assigned two kinds of weights to the links between them. When the weights are proportional to the number of contacts we observed weakly formed, but spatially based modules resemble to the borders of macro-regions, the highest level of regional administration in the country. If the weights are defined relative to an uncorrelated null model, the next level of administrative regions, counties are reflected.     

Structural Properties and Complexity of a New Network Class: Collatz Step Graphs

In this paper, we introduce a biologically inspired model to generate complex networks. In contrast to many other construction procedures for growing networks introduced so far, our method generates networks from one-dimensional symbol sequences that are related to the so called Collatz problem from number theory. The major purpose of the present paper is, first, to derive a symbol sequence from the Collatz problem, we call the step sequence, and investigate its structural properties. Second, we introduce a construction procedure for growing networks that is based on these step sequences. Third, we investigate the structural properties of this new network class including their finite scaling and asymptotic behavior of their complexity, average shortest path lengths and clustering coefficients. Interestingly, in contrast to many other network models including the small-world network from Watts & Strogatz, we find that CS graphs become ‘smaller’ with an increasing size.     

Bayesian Network Reconstruction Using Systems Genetics Data: Comparison of MCMC Methods

Reconstructing biological networks using high-throughput technologies has the potential to produce condition-specific interactomes. But are these reconstructed networks a reliable source of biological interactions? Do some network inference methods offer dramatically improved performance on certain types of networks? To facilitate the use of network inference methods in systems biology, we report a large-scale simulation study comparing the ability of Markov chain Monte Carlo (MCMC) samplers to reverse engineer Bayesian networks. The MCMC samplers we investigated included foundational and state-of-the-art Metropolis–Hastings and Gibbs sampling approaches, as well as novel samplers we have designed. To enable a comprehensive comparison, we simulated gene expression and genetics data from known network structures under a range of biologically plausible scenarios. We examine the overall quality of network inference via different methods, as well as how their performance is affected by network characteristics. Our simulations reveal that network size, edge density, and strength of gene-to-gene signaling are major parameters that differentiate the performance of various samplers. Specifically, more recent samplers including our novel methods outperform traditional samplers for highly interconnected large networks with strong gene-to-gene signaling. Our newly developed samplers show comparable or superior performance to the top existing methods. Moreover, this performance gain is strongest in networks with biologically oriented topology, which indicates that our novel samplers are suitable for inferring biological networks. The performance of MCMC samplers in this simulation framework can guide the choice of methods for network reconstruction using systems genetics data.     

A web platform for the network analysis of high-throughput data in melanoma and its use to investigate mechanisms of resistance to anti-PD1 immunotherapy

Cellular phenotypes are established and controlled by complex and precisely orchestrated molecular networks. In cancer, mutations and dysregulations of multiple molecular factors perturb the regulation of these networks and lead to malignant transformation. High-throughput technologies are a valuable source of information to establish the complex molecular relationships behind the emergence of malignancy, but full exploitation of this massive amount of data requires bioinformatics tools that rely on network-based analyses.In this report we present the Virtual Melanoma Cell, an online tool developed to facilitate the mining and interpretation of high-throughput data on melanoma by biomedical researches. The platform is based on a comprehensive, manually generated and expert-validated regulatory map composed of signaling pathways important in malignant melanoma. The Virtual Melanoma Cell is a tool designed to accept, visualize and analyze user-generated datasets. It is available at: https://www.vcells.net/melanoma. To illustrate the utilization of the web platform and the regulatory map, we have analyzed a large publicly available dataset accounting for anti-PD1 immunotherapy treatment of malignant melanoma patients.     

BNArray: an R package for constructing gene regulatory networks from microarray data by using Bayesian network

BNArray is a systemized tool developed in R. It facilitates the construction of gene regulatory networks from DNA microarray data by using Bayesian network. Significant sub-modules of regulatory networks with high confidence are reconstructed by using our extended sub-network mining algorithm of directed graphs. BNArray can handle microarray datasets with missing data. To evaluate the statistical features of generated Bayesian networks, re-sampling procedures are utilized to yield collections of candidate 1st-order network sets for mining dense coherent sub-networks. AVAILABILITY: The R package and the supplementary documentation are available at http://www.cls.zju.edu.cn/binfo/BNArray/.