Edge-based sensitivity analysis of signaling networks by using Boolean dynamics.

It has been a challenge in systems biology to unravel relationships between structural properties and dynamic behaviors of biological networks. A Cytoscape plugin named NetDS was recently proposed to analyze the robustness-related dynamics and feed-forward/feedback loop structures of biological networks. Despite such a useful function, limitations on the network size that can be analyzed exist due to high computational costs. In addition, the plugin cannot verify an intrinsic property which can be induced by an observed result because it has no function to simulate the observation on a large number of random networks. To overcome these limitations, we have developed a novel software tool, PANET. First, the time-consuming parts of NetDS were redesigned to be processed in parallel using the OpenCL library. This approach utilizes the full computing power of multi-core central processing units and graphics processing units. Eventually, this made it possible to investigate a large-scale network such as a human signaling network with 1,609 nodes and 5,063 links. We also developed a new function to perform a batch-mode simulation where it generates a lot of random networks and conducts robustness calculations and feed-forward/feedback loop examinations of them. This helps us to determine if the findings in real biological networks are valid in arbitrary random networks or not. We tested our plugin in two case studies based on two large-scale signaling networks and found interesting results regarding relationships between coherently coupled feed-forward/feedback loops and robustness. In addition, we verified whether or not those findings are consistently conserved in random networks through batch-mode simulations. Taken together, our plugin is expected to effectively investigate various relationships between dynamics and structural properties in large-scale networks. Our software tool, user manual and example datasets are freely available at http://panet-csc.sourceforge.net/.

The signaling system is a fundamental part of the cell, as it regulates essential functions including growth, differentiation, protein synthesis, and apoptosis. A malfunction in this subsystem can disrupt the cell significantly, and is believed to be involved in certain diseases, with cancer being a very important example. While the information available about intracellular signaling networks is constantly growing, and the network topology is actively being analyzed, the modeling of the dynamics of such a system faces difficulties due to the vast number of parameters, which can prove hard to estimate correctly. As the functioning of the signaling system depends on the parameters in a complex way, being able to make general statements based solely on the network topology could be especially appealing. We study a general kinetic model of the signaling system, giving results for the asymptotic behavior of the system in the case of a network with only activatory interactions. We also investigate the possible generalization of our results for the case of a more general model including inhibitory interactions too. We find that feedback cycles made up entirely of activatory interactions (which we call dynamically positive) are especially important, as their properties determine whether the system has a stable signal-off state, which is desirable in many situations to avoid autoactivation due to a noisy environment. To test our results, we investigate the network topology in the Signalink database, and find that the human signaling network indeed has only significantly few dynamically positive cycles, which agrees well with our theoretical arguments.

Objective To explore the pathogenesis of T-cells in the formation and development of atherosclerosis. Methods Significant differential permutation test based on the human signaling network and the data of gene expression profile containing normal and atherosclerosis samples with RNA expressions from T cells.Candidate Atherosclerosis-related Modules were identified using ClusterOne.Atherosclerosis-related Modules were identified using functional enrichment analysis. Results Nineteen potential atherosclerosis genes which played central roles and have consistent functions in modules(five atherosclerosis-related modules) were identified. Conclusion Based on a human signaling network, the atherosclerosis related module identification approach could not only identify modules and potential atherosclerosis genes closely related to disease, but also provide a new perspective for the pathogenesis of T cells in atherosclerosis. Key words: Atherosclerosis; T-cell; Human signal network; Module

MicroRNAs (miRNAs) are endogenous ∼22-nucleotide RNAs, which suppress gene expression by selectively binding to the 3′-noncoding region of specific messenger RNAs through base-pairing. Given the diversity and abundance of miRNA targets, miRNAs appear to functionally interact with various components of many cellular networks. By analyzing the interactions between miRNAs and a human cellular signaling network, we found that miRNAs predominantly target positive regulatory motifs, highly connected scaffolds and most downstream network components such as signaling transcription factors, but less frequently target negative regulatory motifs, common components of basic cellular machines and most upstream network components such as ligands. In addition, when an adaptor has potential to recruit more downstream components, these components are more frequently targeted by miRNAs. This work uncovers the principles of miRNA regulation of signal transduction networks and implies a potential function of miRNAs for facilitating robust transitions of cellular response to extracellular signals and maintaining cellular homeostasis.

BackgroundUnderstanding how signals propagate through signaling pathways and networks is a central goal in systems biology. Quantitative dynamic models help to achieve this understanding, but are difficult to construct and validate because of the scarcity of known mechanistic details and kinetic parameters. Structural and qualitative analysis is emerging as a feasible and useful alternative for interpreting signal transduction.ResultsIn this work, we present an integrative computational method for evaluating the essentiality of components in signaling networks. This approach expands an existing signaling network to a richer representation that incorporates the positive or negative nature of interactions and the synergistic behaviors among multiple components. Our method simulates both knockout and constitutive activation of components as node disruptions, and takes into account the possible cascading effects of a node's disruption. We introduce the concept of elementary signaling mode (ESM), as the minimal set of nodes that can perform signal transduction independently. Our method ranks the importance of signaling components by the effects of their perturbation on the ESMs of the network. Validation on several signaling networks describing the immune response of mammals to bacteria, guard cell abscisic acid signaling in plants, and T cell receptor signaling shows that this method can effectively uncover the essentiality of components mediating a signal transduction process and results in strong agreement with the results of Boolean (logical) dynamic models and experimental observations.ConclusionsThis integrative method is an efficient procedure for exploratory analysis of large signaling and regulatory networks where dynamic modeling or experimental tests are impractical. Its results serve as testable predictions, provide insights into signal transduction and regulatory mechanisms and can guide targeted computational or experimental follow-up studies. The source codes for the algorithms developed in this study can be found at http://www.phys.psu.edu/~ralbert/ESM.

The molecular regulatory network (MRN) within a cell determines cellular states and transitions between them. Thus, modeling of MRNs is crucial, but this usually requires extensive analysis of time-series measurements, which is extremely difficult to obtain from biological experiments. However, single-cell measurement data such as single-cell RNA-sequencing databases have recently provided a new insight into resolving this problem by ordering thousands of cells in pseudo-time according to their differential gene expressions. Neural network modeling can be employed by using temporal data as learning data. In contrast, Boolean network modeling of MRNs has a growing interest, as it is a parameter-free logical modeling and thereby robust to noisy data while still capturing essential dynamics of biological networks. In this study, we propose a Boolean feedforward neural network (FFN) modeling by combining neural network and Boolean network modeling approach to reconstruct a practical and useful MRN model from large temporal data. Furthermore, analyzing the reconstructed MRN model can enable us to identify control targets for potential cellular state conversion. Here, we show the usefulness of Boolean FFN modeling by demonstrating its applicability through a toy model and biological networks.

Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within computer science, probability and statistics. A fundamental initial question regarding these models is: when are these random graphs affected by their latent geometry and when are they indistinguishable from simpler models without latent structure, such as the Erdős–Rényi graph $${\mathcal {G}}(n, p)$$ ? We address this question for two of the most well-studied models of random graphs with latent geometry—the random intersection and random geometric graph. Our results are as follows: (a) The random intersection graph is defined by sampling n random sets $$S_1, S_2, \ldots , S_n$$ by including each element of a set of size d in each $$S_i$$ independently with probability $$\delta $$ , and including the edge $$\{i, j\}$$ if $$S_i \cap S_j \ne \emptyset $$ . We prove that the random intersection graph converges in total variation to an Erdős–Rényi graph if $$d = {\tilde{\omega }}(n^3)$$ , and does not if $$d = o(n^3)$$ , for both dense and sparse edge densities p. This resolves an open problem in Fill et al. (Random Struct Algorithms 16(2):156–176, 2000), Rybarczyk (Random Struct Algorithms 38(1–2):205–234, 2011) and Kim et al. (Random Struct Algorithms 52(4):662–679, 2018). The same result was obtained simultaneously and independently by Bubeck et al. (When random intersection graphs lose geometry. Manuscript, 2019). (b) We strengthen the preceding argument to show that the matrix of random intersection sizes $$|S_i \cap S_j|$$ converges in total variation to a symmetric matrix with independent Poisson entries. This yields the first total variation convergence result for $$\tau $$ -random intersection graphs, where the edge $$\{i, j\}$$ is included if $$|S_i \cap S_j| \ge \tau $$ . More precisely, our results imply that, if p is bounded away from 1, then the $$\tau $$ -random intersection graph with edge density p converges to $${\mathcal {G}}(n, p)$$ if $$d = \omega (\tau ^3 n^3)$$ . (c) The random geometric graph on $${\mathbb {S}}^{d - 1}$$ is defined by sampling $$X_1, X_2, \dots , X_n$$ uniformly at random from $${\mathbb {S}}^{d - 1}$$ and including the edge $$\{i, j\}$$ if $$\Vert X_i - X_j \Vert _2 \le \tau $$ . A result of Bubeck et al. (Random Struct Algorithms 49:503–532, 2016) showed that this model converges to $${\mathcal {G}}(n, p)$$ in total variation, where p is chosen so that the models have matching edge densities, as long as $$d = \omega (n^3)$$ . It was conjectured in Bubeck et al. (2016) that this threshold decreases drastically for p small. We make the first progress towards this conjecture by showing convergence if $$d = {\tilde{\omega }}\left( \min \{ pn^3, p^2 n^{7/2} \} \right) $$ . Our proofs are a hybrid of combinatorial arguments, direct couplings and applications of information inequalities. Previous upper bounds on the total variation distance between random graphs with latent geometry and $${\mathcal {G}}(n, p)$$ have typically not been both combinatorial and information-theoretic, while this interplay is essential to the sharpness of our bounds.

Intrinsic properties of Boolean dynamics in complex networks

Noisy attractors and ergodic sets in models of gene regulatory networks

A multi-scale model of the interplay between cell signalling and hormone transport in specifying the root meristem of Arabidopsis thaliana

BackgroundMany biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.ResultsIn this paper, we focus on the robustness of a network that is acquired during its evolutionary process. Through simulations using Boolean network models, we found that preferential attachment increases the number of coupled feedback loops in the course of network evolution. Whereas, if networks evolve to have more coupled feedback loops rather than following preferential attachment, the resulting networks are more robust than those obtained through preferential attachment, although both of them have similar degree distributions.ConclusionThe presented analysis demonstrates that coupled feedback loops may play an important role in network evolution to acquire robustness. The result also provides a hint as to why various biological networks have evolved to contain a number of coupled feedback loops.

We provide a lightweight decentralized publish-subscribe framework for supporting large-scale actor communication on edge networks. Our framework, called Loquat, does not depend on any reliable central nodes (e.g., data centers), provides reliability in the face of massive node failures and network partitioning, and provides scalability as the number of nodes increases. We consider that high reliability, i.e., that send operations reach close to 100% of live destination nodes, is a critical property for communication frameworks on edge networks. But reliability is difficult to achieve in a scalable way on edge networks because of the network's dynamicity, i.e., frequent node failures and partitioning. For example, both Internet of Things networks and mobile phone networks consist of devices that are often offline. To achieve reliability, our framework is based on two hybrid gossip algorithms, namely HyParView and Plumtree. Hybrid gossip algorithms combine gossip with other distributed algorithms to achieve both efficiency and high resilience. Our current implementation is written in Erlang and has demonstrated scalability up to 1024 nodes in Amazon's cloud computing environment.

Entropy of the ensemble of acyclic graphs

BackgroundDefective tumor suppressor genes (TSGs) and hyperactive oncogenes (OCGs) heavily contribute to cell proliferation and apoptosis during cancer development through genetic variations such as somatic mutations and deletions. Moreover, they usually do not perform their cellular functions individually but rather execute jointly. Therefore, a comprehensive comparison of their mutation patterns and network properties may provide a deeper understanding of their roles in the cancer development and provide some clues for identification of novel targets.ResultsIn this study, we performed a comprehensive survey of TSGs and OCGs from the perspectives of somatic mutations and network properties. For comparative purposes, we choose five gene sets: TSGs, OCGs, cancer drug target genes, essential genes, and other genes. Based on the data from Pan-Cancer project, we found that TSGs had the highest mutation frequency in most tumor types and the OCGs second. The essential genes had the lowest mutation frequency in all tumor types. For the network properties in the human protein-protein interaction (PPI) network, we found that, relative to target proteins, essential proteins, and other proteins, the TSG proteins and OCG proteins both tended to have higher degrees, higher betweenness, lower clustering coefficients, and shorter shortest-path distances. Moreover, the TSG proteins and OCG proteins tended to have direct interactions with cancer drug target proteins. To further explore their relationship, we generated a TSG-OCG network and found that TSGs and OCGs connected strongly with each other. The integration of the mutation frequency with the TSG-OCG network offered a network view of TSGs, OCGs, and their interactions, which may provide new insights into how the TSGs and OCGs jointly contribute to the cancer development.ConclusionsOur study first discovered that the OCGs and TSGs had different mutation patterns, but had similar and stronger protein-protein characteristics relative to the essential proteins or control proteins in the whole human interactome. We also found that the TSGs and OCGs had the most direct interactions with cancer drug targets. The results will be helpful for cancer drug target identification, and ultimately, understanding the etiology of cancer and treatment at the network level.

BackgroundIn the post-genomic era, a central and overarching question in the analysis of protein-protein interaction networks continues to be whether biological characteristics and functions of proteins such as lethality, physiological malfunctions and malignancy are intimately linked to the topological role proteins play in the network as a mathematical structure. One of the key features that have implicitly been presumed is the existence of hubs, highly connected proteins considered to play a crucial role in biological networks. We explore the structure of protein interaction networks of a number of organisms as metric spaces and show that hubs are non randomly positioned and, from a distance point of view, centrally located.ResultsBy analysing how the human functional protein interaction network, the human signalling network, Saccharomyces cerevisiae, Arabidopsis thaliana and Escherichia coli protein-protein interaction networks from various databases are distributed as metric spaces, we found that proteins interact radially through a central node, high degree proteins coagulate in the centre of the network, and those far away from the centre have low degree. We further found that the distribution of proteins from the centre is in some hierarchy of importance and has biological significance.ConclusionsWe conclude that structurally, protein interaction networks are mathematical entities that share properties between organisms but not necessarily with other networks that follow power-law. We therefore conclude that (i) if there are hubs defined by degree, they are not distributed randomly; (ii) zones closest to the centre of the network are enriched for critically important proteins and are also functionally very specialised for specific 'house keeping’ functions; (iii) proteins closest to the network centre are functionally less dispensable and may present good targets for therapy development; and (iv) network biology requires its own network theory modelled on actual biological evidence and that simply adopting theories from the social sciences may be misleading.