Hierarchical Feedback Modules and Reaction Hubs in Cell Signaling Networks

Despite much effort, identification of modular structures and study of their organizing and functional roles remain a formidable challenge in molecular systems biology, which, however, is essential in reaching a systematic understanding of large-scale cell regulation networks and hence gaining capacity of exerting effective interference to cell activity. Combining graph theoretic methods with available dynamics information, we successfully retrieved multiple feedback modules of three important signaling networks. These feedbacks are structurally arranged in a hierarchical way and dynamically produce layered temporal profiles of output signals. We found that global and local feedbacks act in very different ways and on distinct features of the information flow conveyed by signal transduction but work highly coordinately to implement specific biological functions. The redundancy embodied with multiple signal-relaying channels and feedback controls bestow great robustness and the reaction hubs seated at junctions of different paths announce their paramount importance through exquisite parameter management. The current investigation reveals intriguing general features of the organization of cell signaling networks and their relevance to biological function, which may find interesting applications in analysis, design and control of bio-networks.     

Modeling cell signaling networks

Cell signaling pathways interact with one another to form networks in mammalian systems. Such networks are complex in their organization and exhibit emergent properties such as bistability and ultrasensitivity. Analysis of signaling networks requires a combination of experimental and theoretical approaches including the development and analysis of models. This review focuses on theoretical approaches to understanding cell signaling networks. Using heterotrimeric G protein pathways an example, we demonstrate how interactions between two pathways can result in a network that contains a positive feedback loop and function as a switch. Different mathematical approaches that are currently used to model signaling networks are described, and future challenges including the need for databases as well as enhanced computing environments are discussed.     

Disordered domains and high surface charge confer hubs with the ability to interact with multiple proteins in interaction networks

We investigate the structural properties of hubs that enable them to interact with several partners in protein-protein interaction networks. We find that hubs have more observed and predicted disordered residues with fewer loops/coils, and more charged residues on the surface as compared to non-hubs. Smaller hubs have fewer disordered residues and more charged residues on the surface than larger hubs. We conclude that the global flexibility provided by disordered domains, and high surface charge are complementary factors that play a significant role in the binding ability of hubs.     

Recurrent fractal neural networks: a strategy for the exchange of local and global information processing in the brain

The regulation of biological networks relies significantly on convergent feedback signaling loops that render a global output locally accessible. Ideally, the recurrent connectivity within these systems is self-organized by a time-dependent phase-locking mechanism. This study analyzes recurrent fractal neural networks (RFNNs), which utilize a self-similar or fractal branching structure of dendrites and downstream networks for phase-locking of reciprocal feedback loops: output from outer branch nodes of the network tree enters inner branch nodes of the dendritic tree in single neurons. This structural organization enables RFNNs to amplify re-entrant input by over-the-threshold signal summation from feedback loops with equivalent signal traveling times. The columnar organization of pyramidal neurons in the neocortical layers V and III is discussed as the structural substrate for this network architecture. RFNNs self-organize spike trains and render the entire neural network output accessible to the dendritic tree of each neuron within this network. As the result of a contraction mapping operation, the local dendritic input pattern contains a downscaled version of the network output coding structure. RFNNs perform robust, fractal data compression, thus coping with a limited number of feedback loops for signal transport in convergent neural networks. This property is discussed as a significant step toward the solution of a fundamental problem in neuroscience: how is neuronal computation in separate neurons and remote brain areas unified as an instance of experience in consciousness? RFNNs are promising candidates for engaging neural networks into a coherent activity and provide a strategy for the exchange of global and local information processing in the human brain, thereby ensuring the completeness of a transformation from neuronal computation into conscious experience.     

Protein interaction networks in medicine and disease

The physical interaction of proteins is subject to intense investigation that has revealed that proteins are assembled into large densely connected networks. In this review, we will examine how signaling pathways can be combined to form higher order protein interaction networks. By using network graph theory, these interaction networks can be further analyzed for global organization, which has revealed unique aspects of the relationships between protein networks and complex biological phenotypes. Moreover, several studies have shown that the structure and dynamics of protein networks are disturbed in complex diseases such as cancer progression. These relationships suggest a novel paradigm for treatment of complex multigenic disease where the protein interaction network is the target of therapy more so than individual molecules within the network.     

B-cell ligand processing pathways detected by large-scale comparative analysis

The initiation of B-cell ligand recognition is a critical step for the generation of an immune response against foreign bodies.We sought to identify the biochemical pathways involved in the B-cell ligand recognition cascade and sets of ligands that trigger similar immunological responses.We utilized several comparative approaches to analyze the gene coexpression networks generated from a set of microarray experiments spanning 33 different ligands.First,we compared the degree distributions of the generated networks.Second,we utilized a pairwise network alignment algorithm,BiNA,to align the networks based on the hubs in the networks.Third,we aligned the networks based on a set of K_EGG pathways.We summarized our results by constructing a consensus hierarchy of pathways that are involved in B cell ligand recognition.The resulting pathways were further validated through literature for their common physiological responses.Collectively,the results based on our comparative analyses of degree distributions,alignment of hubs,and alignment based on KEGG pathways provide a basis for molecular characterization of the immune response states of B-cells and demonstrate the power of comparative approaches(e.g.,gene coexpression network alignment algorithms) in elucidating biochemical pathways involved in complex signaling events in cells.     

Shuffling the cards in signal transduction: Calcium, arachidonic acid and mechanosensitivity

Cell signaling is a very complex network of biochemical reactions triggered by a huge number of stimuli coming from the external medium. The function of any single signaling component depends not only on its own structure but also on its connections with other biomolecules. During prokaryotic-eukaryotic transition, the rearrangement of cell organization in terms of diffusional compartmentalization exerts a deep change in cell signaling functional potentiality. In this review I briefly introduce an intriguing ancient relationship between pathways involved in cell responses to chemical agonists (growth factors, nutrients, hormones) as well as to mechanical forces (stretch, osmotic changes). Some biomolecules (ion channels and enzymes) act as "hubs", thanks to their ability to be directly or indirectly chemically/mechanically co-regulated. In particular calcium signaling machinery and arachidonic acid metabolism are very ancient networks, already present before eukaryotic appearance. A number of molecular "hubs", including phospholipase A2 and some calcium channels, appear tightly interconnected in a cross regulation leading to the cellular response to chemical and mechanical stimulations.     

AKT as locus of cancer positive feedback loops and extreme robustness

A positive feedback loops induce extreme robustness in metastatic cancer, relapsed leukemia, myeloma or lymphoma. The loops are generated by the signaling interactome networks of autocrine and paracrine elements from cancer hypoxic microenvironment. The elements of the networks are signaling proteins synthesized in hypoxic microenvironment such as the vascular endothelial growth factor, HIF‐1α, hepatocyte growth factor, and molecules nitric oxide and H₂O₂. The signals from upstream or rebound downstream pathways are amplified by the short or wide positive feedback loops, hyperstimulating AKT‐inducing cancer extreme robustness. Targeting the phosphorylated AKT locus by an oxidant/antioxidant modulation induces collapse of positive feedback loops and establishment of negative feedback loops leading to stability of the system and disappearance of cancer extreme robustness. This is a new principle for the conversion of cancer positive loops into negative feedback loops by the locus chemotherapy. J. Cell. Physiol. 228: 522–524, 2013. © 2012 Wiley Periodicals, Inc.     

Network Reconstruction Based on Proteomic Data and Prior Knowledge of Protein Connectivity Using Graph Theory

Modeling of signal transduction pathways is instrumental for understanding cells’ function. People have been tackling modeling of signaling pathways in order to accurately represent the signaling events inside cells’ biochemical microenvironment in a way meaningful for scientists in a biological field. In this article, we propose a method to interrogate such pathways in order to produce cell-specific signaling models. We integrate available prior knowledge of protein connectivity, in a form of a Prior Knowledge Network (PKN) with phosphoproteomic data to construct predictive models of the protein connectivity of the interrogated cell type. Several computational methodologies focusing on pathways’ logic modeling using optimization formulations or machine learning algorithms have been published on this front over the past few years. Here, we introduce a light and fast approach that uses a breadth-first traversal of the graph to identify the shortest pathways and score proteins in the PKN, fitting the dependencies extracted from the experimental design. The pathways are then combined through a heuristic formulation to produce a final topology handling inconsistencies between the PKN and the experimental scenarios. Our results show that the algorithm we developed is efficient and accurate for the construction of medium and large scale signaling networks. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGF/TNFA stimulation against made up experimental data. To avoid the possibility of erroneous predictions, we performed a cross-validation analysis. Finally, we validate that the introduced approach generates predictive topologies, comparable to the ILP formulation. Overall, an efficient approach based on graph theory is presented herein to interrogate protein–protein interaction networks and to provide meaningful biological insights.     

Using plasma membrane nanoclusters to build better signaling circuits

Cellular signaling pathways do not simply transmit data; they integrate and process signals to operate as switches, oscillators, logic gates, memory modules and many other types of control system. These complex processing capabilities enable cells to respond appropriately to the myriad of external cues that direct growth and development. The idea that crosstalk and feedback loops are used as control systems in biological signaling networks is well established. Signaling networks are also subject to exquisite spatial regulation, yet how spatial control modulates signal outputs is less well understood. Here, we explore the spatial organization of two different signal transduction circuits: receptor tyrosine kinase activation of the mitogen-activated protein kinase module; and glycosylphosphatidylinositol-anchored receptor activation of phospholipase C. With regards to these pathways, recent results have refocused attention on the crucial role of lipid rafts and plasma membrane nanodomains in signal transmission. We identify common design principals that highlight how the spatial organization of signal transduction circuits can be used as a fundamental control mechanism to modulate system outputs in vivo.     

Identification of biochemical network modules based on shortest retroactive distances

Modularity analysis offers a route to better understand the organization of cellular biochemical networks as well as to derive practically useful, simplified models of these complex systems. While there is general agreement regarding the qualitative properties of a biochemical module, there is no clear consensus on the quantitative criteria that may be used to systematically derive these modules. In this work, we investigate cyclical interactions as the defining characteristic of a biochemical module. We utilize a round trip distance metric, termed Shortest Retroactive Distance (ShReD), to characterize the retroactive connectivity between any two reactions in a biochemical network and to group together network components that mutually influence each other. We evaluate the metric on two types of networks that feature feedback interactions: (i) epidermal growth factor receptor (EGFR) signaling and (ii) liver metabolism supporting drug transformation. For both networks, the ShReD partitions found hierarchically arranged modules that confirm biological intuition. In addition, the partitions also revealed modules that are less intuitive. In particular, ShReD-based partition of the metabolic network identified a 'redox' module that couples reactions of glucose, pyruvate, lipid and drug metabolism through shared production and consumption of NADPH. Our results suggest that retroactive interactions arising from feedback loops and metabolic cycles significantly contribute to the modularity of biochemical networks. For metabolic networks, cofactors play an important role as allosteric effectors that mediate the retroactive interactions.     

Flexible and robust networks

We consider networks with two types of nodes. The v-nodes, called centers, are hyperconnected and interact with one another via many u-nodes, called satellites. This centralized architecture, widespread in gene networks, possesses two fundamental properties. Namely, this organization creates feedback loops that are capable of generating practically any prescribed patterning dynamics, chaotic or periodic, or having a number of equilibrium states. Moreover, this organization is robust with respect to random perturbations of the system.     

Coherent coupling of feedback loops: a design principle of cell signaling networks

MOTIVATION: It is widely accepted that cell signaling networks have been evolved to be robust against perturbations. To investigate the topological characteristics resulting in such robustness, we have examined large-scale signaling networks and found that a number of feedback loops are present mostly in coupled structures. In particular, the coupling was made in a coherent way implying that same types of feedback loops are interlinked together. RESULTS: We have investigated the role of such coherently coupled feedback loops through extensive Boolean network simulations and found that a high proportion of coherent couplings can enhance the robustness of a network against its state perturbations. Moreover, we found that the robustness achieved by coherently coupled feedback loops can be kept evolutionarily stable. All these results imply that the coherent coupling of feedback loops might be a design principle of cell signaling networks devised to achieve the robustness.     

Graph models of habitat mosaics

Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights.     

Detecting conserved interaction patterns in biological networks.

Molecular interaction data plays an important role in understanding biological processes at a modular level by providing a framework for understanding cellular organization, functional hierarchy, and evolutionary conservation. As the quality and quantity of network and interaction data increases rapidly, the problem of effectively analyzing this data becomes significant. Graph theoretic formalisms, commonly used for these analysis tasks, often lead to computationally hard problems due to their relation to subgraph isomorphism. This paper presents an innovative new algorithm, MULE, for detecting frequently occurring patterns and modules in biological networks. Using an innovative graph simplification technique based on ortholog contraction, which is ideally suited to biological networks, our algorithm renders these problems computationally tractable and scalable to large numbers of networks. We show, experimentally, that our algorithm can extract frequently occurring patterns in metabolic pathways and protein interaction networks from the KEGG, DIP, and BIND databases within seconds. When compared to existing approaches, our graph simplification technique can be viewed either as a pruning heuristic, or a closely related, but computationally simpler task. When used as a pruning heuristic, we show that our technique reduces effective graph sizes significantly, accelerating existing techniques by several orders of magnitude! Indeed, for most of the test cases, existing techniques could not even be applied without our pruning step. When used as a stand-alone analysis technique, MULE is shown to convey significant biological insights at near-interactive rates. The software, sample input graphs, and detailed results for comprehensive analysis of nine eukaryotic PPI networks are available at www.cs.purdue.edu/homes/koyuturk/mule.     

Comparing brain networks of different size and connectivity density using graph theory

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.