Quantitative analysis of robustness and fragility in biological networks based on feedback dynamics

Motivation: It has been widely reported that biological networksare robust against perturbations such as mutations. On the contrary,it has also been known that biological networks are often fragileagainst unexpected mutations. There is a growing interest inthese intriguing observations and the underlying design principlethat causes such robust but fragile characteristics of biologicalnetworks. For relatively small networks, a feedback loop hasbeen considered as an important motif for realizing the robustness.It is still, however, not clear how a number of coupled feedbackloops actually affect the robustness of large complex biologicalnetworks. In particular, the relationship between fragilityand feedback loops has not yet been investigated till now. Results: Through extensive computational experiments, we foundthat networks with a larger number of positive feedback loopsand a smaller number of negative feedback loops are likely tobe more robust against perturbations. Moreover, we found thatthe nodes of a robust network subject to perturbations are mostlyinvolved with a smaller number of feedback loops compared withthe other nodes not usually subject to perturbations. This topologicalcharacteristic eventually makes the robust network fragile againstunexpected mutations at the nodes not previously exposed toperturbations. Contact: ckh{at}kaist.ac.kr Supplementary information: Supplementary data are availableat Bioinformatics online. Associate Editor: Thomas Lengauer     

Robustness and Evolvability of the Human Signaling Network

Biological systems are known to be both robust and evolvable to internal and external perturbations, but what causes these apparently contradictory properties? We used Boolean network modeling and attractor landscape analysis to investigate the evolvability and robustness of the human signaling network. Our results show that the human signaling network can be divided into an evolvable core where perturbations change the attractor landscape in state space, and a robust neighbor where perturbations have no effect on the attractor landscape. Using chemical inhibition and overexpression of nodes, we validated that perturbations affect the evolvable core more strongly than the robust neighbor. We also found that the evolvable core has a distinct network structure, which is enriched in feedback loops, and features a higher degree of scale-freeness and longer path lengths connecting the nodes. In addition, the genes with high evolvability scores are associated with evolvability-related properties such as rapid evolvability, low species broadness, and immunity whereas the genes with high robustness scores are associated with robustness-related properties such as slow evolvability, high species broadness, and oncogenes. Intriguingly, US Food and Drug Administration-approved drug targets have high evolvability scores whereas experimental drug targets have high robustness scores.     

PANET: A GPU-Based Tool for Fast Parallel Analysis of Robustness Dynamics and Feed-Forward/Feedback Loop Structures in Large-Scale Biological Networks

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/.     

Robustness in phenotypic plasticity and heterogeneity patterns enabled by EMT networks

Epithelial-mesenchymal plasticity (EMP) is a key arm of cancer metastasis and is observed across many contexts. Cells undergoing EMP can reversibly switch between three classes of phenotypes: epithelial (E), mesenchymal (M), and hybrid E/M. While a large number of multistable regulatory networks have been identified to be driving EMP in various contexts, the exact mechanisms and design principles that enable robustness in driving EMP across contexts are not yet fully understood. Here, we investigated dynamic and structural robustness in EMP networks with regard to phenotypic heterogeneity and plasticity. We use two different approaches to simulate these networks: a computationally inexpensive, parameter-independent continuous state space Boolean model, and an ODE-based parameter-agnostic framework (RACIPE), both of which yielded similar phenotypic distributions. While the latter approach is useful for measurements of plasticity, the former model enabled us to extensively investigate robustness in phenotypic heterogeneity. Using perturbations to network topology and by varying network parameters, we show that multistable EMP networks are structurally and dynamically more robust compared with their randomized counterparts, thereby highlighting their topological hallmarks. These features of robustness are governed by a balance of positive and negative feedback loops embedded in these networks. Using a combination of the number of negative and positive feedback loops weighted by their lengths, we identified a metric that can explain the structural and dynamical robustness of these networks. This metric enabled us to compare networks across multiple sizes, and the network principles thus obtained can be used to identify fragilities in large networks without simulating their dynamics. Our analysis highlights a network topology-based approach to quantify robustness in the phenotypic heterogeneity and plasticity emergent from EMP networks.     

Dynamic-module redundancy confers robustness to the gene regulatory network involved in hair patterning of Arabidopsis epidermis

Redundancy among dynamic modules is emerging as a potentially generic trait in gene regulatory networks. Moreover, module redundancy could play an important role in network robustness to perturbations. We explored the effect of dynamic-module redundancy in the networks associated to hair patterning in Arabidopsis root and leaf epidermis. Recent studies have put forward several dynamic modules belonging to these networks. We defined these modules in a discrete dynamical framework that was previously reported. Then, we addressed whether these modules are sufficient or necessary for recovering epidermal cell types and patterning. After defining two quantitative estimates of the system's robustness, we also compared the robustness of each separate module with that of a network coupling all the leaf or root modules. We found that, considering certain assumptions, all the dynamic modules proposed so far are sufficient on their own for pattern formation, but reinforce each other during epidermal development. Furthermore, we found that networks of coupled modules are more robust to perturbations than single modules. These results suggest that dynamic-module redundancy might be an important trait in gene regulatory networks and point at central questions regarding network evolution, module coupling, pattern robustness and the evolution of development.     

Boolean dynamics of biological networks with multiple coupled feedback loops

Boolean networks have been frequently used to study the dynamics of biological networks. In particular, there have been various studies showing that the network connectivity and the update rule of logical functions affect the dynamics of Boolean networks. There has been, however, relatively little attention paid to the dynamical role of a feedback loop, which is a circular chain of interactions between Boolean variables. We note that such feedback loops are ubiquitously found in various biological systems as multiple coupled structures and they are often the primary cause of complex dynamics. In this article, we investigate the relationship between the multiple coupled feedback loops and the dynamics of Boolean networks. We show that networks have a larger proportion of basins corresponding to fixed-point attractors as they have more coupled positive feedback loops, and a larger proportion of basins for limit-cycle attractors as they have more coupled negative feedback loops.     

The regulatory circuits for hysteretic switching in cellular signal transduction pathways

Hysteresis can be found in many physical systems, and a hysteretic switch has been used for various mechanical and electrical systems. Such a hysteretic switch can be created by using a single positive feedback loop, as often used in engineering systems. It is, however, intriguing that various cellular signaling systems use coupled positive feedback loops to implement the hysteretic switch. A question then arises about the advantage of using coupled positive feedback loops instead of simple isolated positive feedback for an apparently equivalent hysteretic switch. Through mathematical simulations, we determined that cellular systems with coupled positive feedback loops show enhanced hysteretic switching, and can thereby make a more reliable decision under conditions of noisy signaling. As most intracellular processes are accompanied by intrinsic noise, important cellular decisions such as differentiation and apoptosis need to be highly robust to such noises. The coupled positive feedback loops might have been evolutionarily acquired to enable correct cell fate decisions to be made through enhanced hysteretic switching in noisy cellular environments.     

Ground State Robustness as an Evolutionary Design Principle in Signaling Networks

The ability of an organism to survive depends on its capability to adapt to external conditions. In addition to metabolic versatility and efficient replication, reliable signal transduction is essential. As signaling systems are under permanent evolutionary pressure one may assume that their structure reflects certain functional properties. However, despite promising theoretical studies in recent years, the selective forces which shape signaling network topologies in general remain unclear. Here, we propose prevention of autoactivation as one possible evolutionary design principle. A generic framework for continuous kinetic models is used to derive topological implications of demanding a dynamically stable ground state in signaling systems. To this end graph theoretical methods are applied. The index of the underlying digraph is shown to be a key topological property which determines the so-called kinetic ground state (or off-state) robustness. The kinetic robustness depends solely on the composition of the subdigraph with the strongly connected components, which comprise all positive feedbacks in the network. The component with the highest index in the feedback family is shown to dominate the kinetic robustness of the whole network, whereas relative size and girth of these motifs are emphasized as important determinants of the component index. Moreover, depending on topological features, the maintenance of robustness differs when networks are faced with structural perturbations. This structural off-state robustness, defined as the average kinetic robustness of a network''s neighborhood, turns out to be useful since some structural features are neutral towards kinetic robustness, but show up to be supporting against structural perturbations. Among these are a low connectivity, a high divergence and a low path sum. All results are tested against real signaling networks obtained from databases. The analysis suggests that ground state robustness may serve as a rationale for some structural peculiarities found in intracellular signaling networks.     

Biology using engineering tools

Negative feedback is an ubiquitous feature of biological networks. Recent work from Sturm and colleaguespresents experimental evidence that biological negative feedback can serve the same function as it does for engineered systems: robustness to perturbations within the feedback loop. Such behavior has important implications for how to attack deregulated signaling networks containing negative feedback in diseases such as cancer.     

Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways

Cellular circuits have positive and negative feedback loops that allow them to respond properly to noisy external stimuli. It is intriguing that such feedback loops exist in many cases in a particular form of coupled positive and negative feedback loops with different time delays. As a result of our mathematical simulations and investigations into various experimental evidences, we found that such coupled feedback circuits can rapidly turn on a reaction to a proper stimulus, robustly maintain its status, and immediately turn off the reaction when the stimulus disappears. In other words, coupled feedback loops enable cellular systems to produce perfect responses to noisy stimuli with respect to signal duration and amplitude. This suggests that coupled positive and negative feedback loops form essential signal transduction motifs in cellular signaling systems.     

Coupled feedback loops form dynamic motifs of cellular networks

Cellular networks are composed of complicated interconnections among components, and some subnetworks of particular functioning are often identified as network motifs. Among such network motifs, feedback loops are thought to play important dynamical roles. Intriguingly, such feedback loops are very often found as a coupled structure in cellular circuits. Therefore, we integrated all the scattered information regarding the coupled feedbacks in various cellular circuits and investigated the dynamical role of each coupled structure. Finally, we discovered that coupled positive feedbacks enhance signal amplification and bistable characteristics; coupled negative feedbacks realize enhanced homeostasis; coupled positive and negative feedbacks enable reliable decision-making by properly modulating signal responses and effectively dealing with noise.     

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.     

Architecture-Dependent Robustness and Bistability in a Class of Genetic Circuits

Understanding the relationship between genotype and phenotype is a challenge in systems biology. An interesting yet related issue is why a particular circuit topology is present in a cell when the same function can supposedly be obtained from an alternative architecture. Here we analyzed two topologically equivalent genetic circuits of coupled positive and negative feedback loops, named NAT and ALT circuits, respectively. The computational search for the oscillation volume of the entire biologically reasonable parameter region through large-scale random samplings shows that the NAT circuit exhibits a distinctly larger fraction of the oscillatory region than the ALT circuit. Such a global robustness difference between two circuits is supplemented by analyzing local robustness, including robustness to parameter perturbations and to molecular noise. In addition, detailed dynamical analysis shows that the molecular noise of both circuits can induce transient switching of the different mechanism between a stable steady state and a stable limit cycle. Our investigation on robustness and dynamics through examples provides insights into the relationship between network architecture and its function.     

<Emphasis FontCategory="SansSerif">Investigation on changes of modularity and robustness by edge-removal mutations in signaling networks</Emphasis>

Background

Biological networks consisting of molecular components and interactions are represented by a graph model. There have been some studies based on that model to analyze a relationship between structural characteristics and dynamical behaviors in signaling network. However, little attention has been paid to changes of modularity and robustness in mutant networks.

Results

In this paper, we investigated the changes of modularity and robustness by edge-removal mutations in three signaling networks. We first observed that both the modularity and robustness increased on average in the mutant network by the edge-removal mutations. However, the modularity change was negatively correlated with the robustness change. This implies that it is unlikely that both the modularity and the robustness values simultaneously increase by the edge-removal mutations. Another interesting finding is that the modularity change was positively correlated with the degree, the number of feedback loops, and the edge betweenness of the removed edges whereas the robustness change was negatively correlated with them. We note that these results were consistently observed in randomly structure networks. Additionally, we identified two groups of genes which are incident to the highly-modularity-increasing and the highly-robustness-decreasing edges with respect to the edge-removal mutations, respectively, and observed that they are likely to be central by forming a connected component of a considerably large size. The gene-ontology enrichment of each of these gene groups was significantly different from the rest of genes. Finally, we showed that the highly-robustness-decreasing edges can be promising edgetic drug-targets, which validates the usefulness of our analysis.

Conclusions

Taken together, the analysis of changes of robustness and modularity against edge-removal mutations can be useful to unravel novel dynamical characteristics underlying in signaling networks.

     

Robust signal processing in living cells

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations.