Coupled feedback loops form dynamic motifs of cellular networks

The type of carbon source not the growth rate it supports can determine diauxie in Saccharomyces cerevisiae

How cells choose between carbon sources is a classic example of cellular decision-making. Microbes often prioritise glucose, but there has been little investigation of whether other sugars are also preferred. Here we study budding yeast growing on mixtures of sugars with palatinose, a sucrose isomer that cells catabolise with the MAL regulon. We find that the decision-making involves more than carbon flux-sensing: yeast prioritise galactose over palatinose, but sucrose and fructose weakly if at all despite each allowing faster growth than palatinose. With genetic perturbations and transcriptomics, we show that the regulation is active with repression of the MAL genes via Gal4, the GAL regulon's master regulator. We argue, using mathematical modelling, that cells enforce their preference for galactose through weakening the MAL regulon's positive feedback. They do so through decreasing intracellular palatinose by repressing MAL11, the palatinose transporter, and expressing the isomaltases IMA1 and IMA5. Supporting these predictions, we show that deleting IMA1 abolishes diauxie. Our results demonstrate that budding yeast actively prioritises carbon sources other than glucose and that such priorities need not reflect differences in growth rates. They imply that carbon-sensing strategies even in model organisms are more complex than previously thought.

Randomization based evaluation of distinct topological and cancer expression characteristics of mutually acting gene pairs

Small scale molecular network patterns and motifs are crucial for systems level understanding of cellular information transduction. Using randomizations, we statistically explored, previously overlooked basic patterns of mutually acting pairs, i.e. mutually positive (PP) or negative (NN) and positive-negative (PN) pairs, in two comprehensive and distinct large-scale molecular networks from literature; the human protein signaling network (PSN) and the human gene regulatory network (GRN). Only the positive and negative signs of all interacting pairs were randomized, while the gene pairs and the number of positive and negative signs in the original network were kept constant. While the numbers of NN and PN pairs were significantly higher, the number of PP pairs was significantly lower than randomly expected values. Genes participating in mutual pairs were more connected than other genes. NN genes were more connected than PP and PN in GRN for all types of degree values, including in, out, positive or negative connections, but less connected for in-degree and more connected for out-degree values in PSN. They also had significantly high number of intersections with each other and PN pairs than randomly expected values, indicating potential cooperative mechanisms. The three mutual interaction designs we examined had distinct RNA and protein expression correlation characteristics. NN protein pairs were uniquely over-represented across normal tissue samples, whose negative correlations were lost across cancer tissue samples. PP and PN pairs showed non-random positive RNA or protein expression correlation across normal or cancer tissue samples. Moreover, we developed an online tool, i.e. MGPNet, for further user specific analysis of mutual gene pairs. We identified SNCA with significantly enriched negatively correlated NN pairs. Unique non-random characteristics of mutual gene pairs identified in two different comprehensive molecular networks could provide valuable information for a better comparative understanding of molecular design principles between normal and cancer states. Insight Box/Paragraph Statement: This study provides a systems-level perspective on cellular information transduction by analyzing mutually acting pairs of genes. By examining mutually positive (PP), mutually negative (NN), and positive-negative (PN) pairs in the human protein signaling network (PSN) and the human gene regulatory network (GRN), we uncover significant variations in their connectivity and expression correlation. Our findings highlight the unique features of NN pairs across normal and cancer tissues and offer insights into molecular design principles. The development of the MGPNet tool further enhances user-specific analyses, enabling a deeper understanding of gene pair mechanisms and their potential cooperative roles in cellular processes.

Control of Cellular Differentiation Trajectories for Cancer Reversion

Cellular differentiation is controlled by intricate layers of gene regulation, involving the modulation of gene expression by various transcriptional regulators. Due to the complexity of gene regulation, identifying master regulators across the differentiation trajectory has been a longstanding challenge. To tackle this problem, a computational framework, single-cell Boolean network inference and control (BENEIN), is presented. Applying BENEIN to human large intestinal single-cell transcriptome data, MYB, HDAC2, and FOXA2 are identified as the master regulators whose inhibition induces enterocyte differentiation. It is found that simultaneous knockdown of these master regulators can revert colorectal cancer cells into normal-like enterocytes by synergistically inducing differentiation and suppressing malignancy, which is validated by in vitro and in vivo experiments.

Theoretical investigation of functional responses of bio-molecular assembly networks

Cooperative protein-protein and protein-DNA interactions form programmable complex assemblies, often performing non-linear gene regulatory operations involved in signal transductions and cell fate determination. The apparent structure of those complex assemblies is very similar, but their functional response strongly depends on the topology of the protein-DNA interaction networks. Here, we demonstrate how the coordinated self-assembly creates gene regulatory network motifs that corroborate the existence of a precise functional response at the molecular level using thermodynamic and dynamic analyses. Our theoretical and Monte Carlo simulations show that a complex network of interactions can form a decision-making loop, such as feedback and feed-forward circuits, only by a few molecular mechanisms. We characterize each possible network of interactions by systematic variations of free energy parameters associated with the binding among biomolecules and DNA looping. We also find that the higher-order networks exhibit alternative steady states from the stochastic dynamics of each network. We capture this signature by calculating stochastic potentials and attributing their multi-stability features. We validate our findings against the Gal promoter system in yeast cells. Overall, we show that the network topology is vital in phenotype diversity in regulatory circuits.

Critical transition and reversion of tumorigenesis

Cancer is caused by the accumulation of genetic alterations and therefore has been historically considered to be irreversible. Intriguingly, several studies have reported that cancer cells can be reversed to be normal cells under certain circumstances. Despite these experimental observations, conceptual and theoretical frameworks that explain these phenomena and enable their exploration in a systematic way are lacking. In this review, we provide an overview of cancer reversion studies and describe recent advancements in systems biological approaches based on attractor landscape analysis. We suggest that the critical transition in tumorigenesis is an important clue for achieving cancer reversion. During tumorigenesis, a critical transition may occur at a tipping point, where cells undergo abrupt changes and reach a new equilibrium state that is determined by complex intracellular regulatory events. We introduce a conceptual framework based on attractor landscapes through which we can investigate the critical transition in tumorigenesis and induce its reversion by combining intracellular molecular perturbation and extracellular signaling controls. Finally, we present a cancer reversion therapy approach that may be a paradigm-changing alternative to current cancer cell-killing therapies.

Computational analysis of synergism in small networks with different logic

Cell fate decision processes are regulated by networks which contain different molecules and interactions. Different network topologies may exhibit synergistic or antagonistic effects on cellular functions. Here, we analyze six most common small networks with regulatory logic AND or OR, trying to clarify the relationship between network topologies and synergism (or antagonism) related to cell fate decisions. We systematically examine the contribution of both network topologies and regulatory logic to the cell fate synergism by bifurcation and combinatorial perturbation analysis. Initially, under a single set of parameters, the synergism of three types of networks with AND and OR logic is compared. Furthermore, to consider whether these results depend on the choices of parameter values, statistics on the synergism of five hundred parameter sets is performed. It is shown that the results are not sensitive to parameter variations, indicating that the synergy or antagonism mainly depends on the network topologies rather than the choices of parameter values. The results indicate that the topology with "Dual Inhibition" shows good synergism, while the topology with "Dual Promotion" or "Hybrid" shows antagonism. The results presented here may help us to design synergistic networks based on network structure and regulation combinations, which has promising implications for cell fate decisions and drug combinations.

Encoding and Decoding of p53 Dynamics in Cellular Response to Stresses

In the cellular response to stresses, the tumor suppressor p53 is activated to maintain genomic integrity and fidelity. As a transcription factor, p53 exhibits rich dynamics to allow for discrimination of the type and intensity of stresses and to direct the selective activation of target genes involved in different processes including cell cycle arrest and apoptosis. In this review, we focused on how stresses are encoded into p53 dynamics and how the dynamics are decoded into cellular outcomes. Theoretical modeling may provide a global view of signaling in the p53 network by coupling the encoding and decoding processes. We discussed the significance of modeling in revealing the mechanisms of the transition between p53 dynamic modes. Moreover, we shed light on the crosstalk between the p53 network and other signaling networks. This review may advance the understanding of operating principles of the p53 signaling network comprehensively and provide insights into p53 dynamics-based cancer therapy.

Understanding noise in cell signalling in the prospect of drug-targets

The introduction of noise to signals can alter central regulatory switches of cellular processes leading to diseases. Noise is inherently present in the cellular signalling system and plays a decisive role in the input-output (I/O) relation. The current study aims to understand the noise tolerance of motif structures in the cell signalling processes. The vulnerability of a node to noise could be a significant factor in causing signalling error and need to be controlled. We developed stochastic differential equation (SDE) based mathematical models for different network motifs with two nodes and studied the association between motif structure and signal-noise relation. A two-dimensional parameter space analysis on motif sensitivity with noise and input signal variation was performed to classify and rank the motifs. Identifying sensitive motifs and their high druggability infers their significance in screening potential drug-target candidates. Finally, we proposed a theoretical framework to identify nodes from a network as potential drug targets. We applied this mathematical formalism to three cancer networks to identify drug-targets and validated them with existing databases.

Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Background

Feedback loops in gene regulatory networks play pivotal roles in governing functional dynamics of cells. Systems approaches demonstrated characteristic dynamical features, including multistability and oscillation, of positive and negative feedback loops. Recent experiments and theories have implicated highly interconnected feedback loops (high-feedback loops) in additional nonintuitive functions, such as controlling cell differentiation rate and multistep cell lineage progression. However, it remains challenging to identify and visualize high-feedback loops in complex gene regulatory networks due to the myriad of ways in which the loops can be combined. Furthermore, it is unclear whether the high-feedback loop structures with these potential functions are widespread in biological systems. Finally, it remains challenging to understand diverse dynamical features, such as high-order multistability and oscillation, generated by individual networks containing high-feedback loops. To address these problems, we developed HiLoop, a toolkit that enables discovery, visualization, and analysis of several types of high-feedback loops in large biological networks.

Results

HiLoop not only extracts high-feedback structures and visualize them in intuitive ways, but also quantifies the enrichment of overrepresented structures. Through random parameterization of mathematical models derived from target networks, HiLoop presents characteristic features of the underlying systems, including complex multistability and oscillations, in a unifying framework. Using HiLoop, we were able to analyze realistic gene regulatory networks containing dozens to hundreds of genes, and to identify many small high-feedback systems. We found more than a 100 human transcription factors involved in high-feedback loops that were not studied previously. In addition, HiLoop enabled the discovery of an enrichment of high feedback in pathways related to epithelial-mesenchymal transition.

Conclusions

HiLoop makes the study of complex networks accessible without significant computational demands. It can serve as a hypothesis generator through identification and modeling of high-feedback subnetworks, or as a quantification method for motif enrichment analysis. As an example of discovery, we found that multistep cell lineage progression may be driven by either specific instances of high-feedback loops with sparse appearances, or generally enriched topologies in gene regulatory networks. We expect HiLoop’s usefulness to increase as experimental data of regulatory networks accumulate. Code is freely available for use or extension at https://github.com/BenNordick/HiLoop.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04405-z.

Analysis of human mitochondrial genome co-occurrence networks of Asian population at varying altitudes

Networks have been established as an extremely powerful framework to understand and predict the behavior of many large-scale complex systems. We studied network motifs, the basic structural elements of networks, to describe the possible role of co-occurrence of genomic variations behind high altitude adaptation in the Asian human population. Mitochondrial DNA (mtDNA) variations have been acclaimed as one of the key players in understanding the biological mechanisms behind adaptation to extreme conditions. To explore the cumulative effects of variations in the mitochondrial genome with the variation in the altitude, we investigated human mt-DNA sequences from the NCBI database at different altitudes under the co-occurrence motifs framework. Analysis of the co-occurrence motifs using similarity clustering revealed a clear distinction between lower and higher altitude regions. In addition, the previously known high altitude markers 3394 and 7697 (which are definitive sites of haplogroup M9a1a1c1b) were found to co-occur within their own gene complexes indicating the impact of intra-genic constraint on co-evolution of nucleotides. Furthermore, an ancestral 'RSRS50' variant 10,398 was found to co-occur only at higher altitudes supporting the fact that a separate route of colonization at these altitudes might have taken place. Overall, our analysis revealed the presence of co-occurrence interactions specific to high altitude at a whole mitochondrial genome level. This study, combined with the classical haplogroups analysis is useful in understanding the role of co-occurrence of mitochondrial variations in high altitude adaptation.

Dissecting molecular network structures using a network subgraph approach

Biological processes are based on molecular networks, which exhibit biological functions through interactions of genetic elements or proteins. This study presents a graph-based method to characterize molecular networks by decomposing the networks into directed multigraphs: network subgraphs. Spectral graph theory, reciprocity and complexity measures were used to quantify the network subgraphs. Graph energy, reciprocity and cyclomatic complexity can optimally specify network subgraphs with some degree of degeneracy. Seventy-one molecular networks were analyzed from three network types: cancer networks, signal transduction networks, and cellular processes. Molecular networks are built from a finite number of subgraph patterns and subgraphs with large graph energies are not present, which implies a graph energy cutoff. In addition, certain subgraph patterns are absent from the three network types. Thus, the Shannon entropy of the subgraph frequency distribution is not maximal. Furthermore, frequently-observed subgraphs are irreducible graphs. These novel findings warrant further investigation and may lead to important applications. Finally, we observed that cancer-related cellular processes are enriched with subgraph-associated driver genes. Our study provides a systematic approach for dissecting biological networks and supports the conclusion that there are organizational principles underlying molecular networks.

Overcoming the Cost of Positive Autoregulation by Accelerating the Response with a Coupled Negative Feedback

A fundamental trade-off between rapid response and optimal expression of genes below cytotoxic levels exists for many signaling circuits, particularly for positively autoregulated systems with an inherent response delay. Here, we describe a regulatory scheme in the E. coli PhoB-PhoR two-component system, which overcomes the cost of positive feedback and achieves both fast and optimal steadystate response for maximal fitness across different environments. Quantitation of the cellular activities enables accurate modeling of the response dynamics to describe how requirements for optimal protein concentrations place limits on response speed. An observed fast response that exceeds the limit led to the prediction and discovery of a coupled negative autoregulation, which allows fast gene expression without increasing steady-state levels. We demonstrate the fitness advantages for the coupled feedbacks in both dynamic and stable environments. Such regulatory schemes offer great flexibility for accurate control of gene expression levels and dynamics upon environmental changes.

Positive autoregulation of transcription produces a delayed response. Gao and Stock describe the limit of response delay caused by requirements of optimal protein levels in the PhoBR twocomponent system. Coupled negative autoregulation is discovered to allow a strong promoter for fast response without incurring cost of increasing protein expression levels.

Agent-based modeling and bifurcation analysis reveal mechanisms of macrophage polarization and phenotype pattern distribution

Macrophages play a key role in tissue regeneration by polarizing to different destinies and generating various phenotypes. Recognizing the underlying mechanisms is critical in designing therapeutic procedures targeting macrophage fate determination. Here, to investigate the macrophage polarization, a nonlinear mathematical model is proposed in which the effect of IL4, IFNγ and LPS, as external stimuli, on STAT1, STAT6, and NFκB is studied using bifurcation analysis. The existence of saddle-node bifurcations in these internal key regulators allows different combinations of steady state levels which are attributable to different fates. Therefore, we propose dynamic bifurcation as a crucial built-in mechanism of macrophage polarization. Next, in order to investigate the polarization of a population of macrophages, bifurcation analysis is employed aligned with agent-based approach and a two-layer model is proposed in which the information from single cells is exploited to model the behavior in tissue level. Also, in this model, a partial differential equation describes the diffusion of secreted cytokines in the medium. Finally, the model was validated against a set of experimental data. Taken together, we have here developed a cell and tissue level model of macrophage polarization behavior which can be used for designing therapeutic interventions.

Interlinked GTPase cascades provide a motif for both robust switches and oscillators

GTPases regulate a wide range of cellular processes, such as intracellular vesicular transport, signal transduction and protein translation. These hydrolase enzymes operate as biochemical switches by toggling between an active guanosine triphosphate (GTP)-bound state and an inactive guanosine diphosphate (GDP)-bound state. We compare two network motifs, a single-species switch and an interlinked cascade that consists of two species coupled through positive and negative feedback loops. We find that interlinked cascades are closer to the ideal all-or-none switch and are more robust against fluctuating signals. While the single-species switch can only achieve bistability, interlinked cascades can be converted into oscillators by tuning the cofactor concentrations, which catalyse the activity of the cascade. These regimes can only be achieved with sufficient chemical driving provided by GTP hydrolysis. In this study, we present a thermodynamically consistent model that can achieve bistability and oscillations with the same feedback motif.

Dopamine modulates excitatory transmission to orexin neurons in a receptor subtype-specific manner

Dopamine (DA) can promote or inhibit consummatory and reward-related behaviors by activating different receptor subtypes in the lateral hypothalamus and perifornical area (LH/PF). Because orexin neurons are involved in reward and localized in the LH/PF, DA may modulate these neurons to influence reward-related behaviors. To determine the cellular mechanism underlying dopaminergic modulation of orexin neurons, the effect of DA on excitatory transmission to these neurons was investigated using in vitro electrophysiology on rat brain slices. We found that low concentrations (0.1-1 µM) of DA increased evoked excitatory postsynaptic current amplitude while decreasing paired-pulse ratio. In contrast, high concentrations (10-100 µM) of DA did the opposite. The excitatory effect of low DA was blocked by the D₁ receptor antagonist SCH-23390, whereas the inhibitory effect of high DA was blocked by the D₂ receptor antagonist sulpiride. These results indicate distinct roles of D₁ and D₂ receptors in bidirectional presynaptic modulation of excitatory transmission. DA had stronger effects on isolated synaptic activity than repetitive ones, suggesting that sensitivity to dopaminergic modulation depends on the level of network activity. In orexin neurons from high-fat diet-fed rats, a high concentration of DA was less effective in suppressing repetitive synaptic activity compared with chow controls. Therefore, in diet-induced obesity, intense synaptic inputs may preferentially reach orexin neurons while intermittent signals are inhibited by high DA levels. In summary, our study provides a cellular mechanism by which DA may exert opposite behavioral effects in the LH/PF through bidirectional modulation of orexin neurons via different DA receptors.

Importance of Feedback and Feedforward Loops to Adaptive Immune Response Modeling

The human adaptive immune system is a very complex network of different types of cells, cytokines, and signaling molecules. This complex network makes it difficult to understand the system level regulations. To properly explain the immune system, it is necessary to explicitly investigate the presence of different feedback and feedforward loops (FFLs) and their crosstalks. Considering that these loops increase the complexity of the system, the mathematical modeling has been proved to be an important tool to explain such complex biological systems. This review focuses on these regulatory loops and discusses their importance on systems modeling of the immune system.

Investigation on changes of modularity and robustness by edge-removal mutations in signaling networks

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.

Electronic supplementary material

The online version of this article (10.1186/s12918-017-0505-2) contains supplementary material, which is available to authorized users.

Parallel arrangements of positive feedback loops limit cell-to-cell variability in differentiation

Cellular differentiations are often regulated by bistable switches resulting from specific arrangements of multiple positive feedback loops (PFL) fused to one another. Although bistability generates digital responses at the cellular level, stochasticity in chemical reactions causes population heterogeneity in terms of its differentiated states. We hypothesized that the specific arrangements of PFLs may have evolved to minimize the cellular heterogeneity in differentiation. In order to test this we investigated variability in cellular differentiation controlled either by parallel or serial arrangements of multiple PFLs having similar average properties under extrinsic and intrinsic noises. We find that motifs with PFLs fused in parallel to one another around a central regulator are less susceptible to noise as compared to the motifs with PFLs arranged serially. Our calculations suggest that the increased resistance to noise in parallel motifs originate from the less sensitivity of bifurcation points to the extrinsic noise. Whereas estimation of mean residence times indicate that stable branches of bifurcations are robust to intrinsic noise in parallel motifs as compared to serial motifs. Model conclusions are consistent both in AND- and OR-gate input signal configurations and also with two different modeling strategies. Our investigations provide some insight into recent findings that differentiation of preadipocyte to mature adipocyte is controlled by network of parallel PFLs.

Operating principles of tristable circuits regulating cellular differentiation

Many cell-fate decisions during embryonic development are governed by a motif comprised of two transcription factors (TFs) A and B that mutually inhibit each other and may self-activate. This motif, called as a self-activating toggle switch (SATS), can typically have three stable states (phenotypes)-two corresponding to differentiated cell fates, each of which has a much higher level of one TF than the other-[Formula: see text] or [Formula: see text]-and the third state corresponding to an 'undecided' stem-like state with similar levels of both A and B-[Formula: see text]. Furthermore, two or more SATSes can be coupled together in various topologies in different contexts, thereby affecting the coordination between multiple cellular decisions. However, two questions remain largely unanswered: (a) what governs the co-existence and relative stability of these three stable states? (b) What orchestrates the decision-making of coupled SATSes? Here, we first demonstrate that the co-existence and relative stability of the three stable states in an individual SATS can be governed by the relative strength of self-activation, external signals activating and/or inhibiting A and B, and mutual degradation between A and B. Simultaneously, we investigate the effects of these factors on the decision-making of two coupled SATSes. Our results offer novel understanding into the operating principles of individual and coupled tristable self-activating toggle switches (SATSes) regulating cellular differentiation and can yield insights into synthesizing three-way genetic circuits and understanding of cellular reprogramming.

Design Principles of Biological Oscillators through Optimization: Forward and Reverse Analysis

From cyanobacteria to human, sustained oscillations coordinate important biological functions. Although much has been learned concerning the sophisticated molecular mechanisms underlying biological oscillators, design principles linking structure and functional behavior are not yet fully understood. Here we explore design principles of biological oscillators from a multiobjective optimization perspective, taking into account the trade-offs between conflicting performance goals or demands. We develop a comprehensive tool for automated design of oscillators, based on multicriteria global optimization that allows two modes: (i) the automatic design (forward problem) and (ii) the inference of design principles (reverse analysis problem). From the perspective of synthetic biology, the forward mode allows the solution of design problems that mimic some of the desirable properties appearing in natural oscillators. The reverse analysis mode facilitates a systematic exploration of the design space based on Pareto optimality concepts. The method is illustrated with two case studies: the automatic design of synthetic oscillators from a library of biological parts, and the exploration of design principles in 3-gene oscillatory systems.

Obg-like ATPase 1 regulates global protein serine/threonine phosphorylation in cancer cells by suppressing the GSK3β-inhibitor 2-PP1 positive feedback loop

OLA1 is an Obg family P-loop NTPase that possesses both GTP- and ATP-hydrolyzing activities. Here we report that OLA1 is a GSK3β interacting protein, and through its ATPase activity, inhibits the GSK3β-mediated activation of protein serine/threonine phosphatase 1 (PP1). It is hypothesized that GSK3β phosphorylates inhibitor 2 (I-2) of PP1 at Thr-72 and activates the PP1 · I-2 complex, which in turn dephosphorylates and stimulates GSK3β, thus forming a positive feedback loop. We revealed that the positive feedback loop is normally suppressed by OLA1, and becomes over-activated under OLA1 deficiency, resulting in increased cellular PP1 activity and dephosphorylation of multiple Ser/Thr phosphoproteins, and more strikingly, decreased global protein threonine phosphorylation. Furthermore, using xenograft models of colon cancer (H116) and ovarian cancer (SKOV3), we established a correlation among downregulation of OLA1, over-activation of the positive feedback loop as indicated by under-phosphorylation of I-2, and more aggressive tumor growth. This study provides the first evidence for the existence of a GSK3β-I-2-PP1 positive feedback loop in human cancer cells, and identifies OLA1 as an endogenous suppressor of this signaling motif.

Control of MarRAB Operon in Escherichia coli via Autoactivation and Autorepression

Choice of network topology for gene regulation has been a question of interest for a long time. How do simple and more complex topologies arise? In this work, we analyze the topology of the marRAB operon in Escherichia coli, which is associated with control of expression of genes associated with conferring resistance to low-level antibiotics to the bacterium. Among the 2102 promoters in E. coli, the marRAB promoter is the only one that encodes for an autoactivator and an autorepressor. What advantages does this topology confer to the bacterium? In this work, we demonstrate that, compared to control by a single regulator, the marRAB regulatory arrangement has the least control cost associated with modulating gene expression in response to environmental stimuli. In addition, the presence of dual regulators allows the regulon to exhibit a diverse range of dynamics, a feature that is not observed in genes controlled by a single regulator.

Realization of tristability in a multiplicatively coupled dual-loop genetic network

Multistability is a crucial recurring theme in cell signaling. Multistability is attributed to the presence of positive feedback loops, but the general condition and essential mechanism for realizing multistability remain unclear. Here, we build a generic circuit model comprising two transcription factors and a microRNA, representing a kind of core architecture in gene regulatory networks. The circuit can be decomposed into two positive feedback loops (PFLs) or one PFL and one negative feedback loop (NFL), which are multiplicatively coupled. Bifurcation analyses of the model reveal that the circuit can achieve tristability through four kinds of bifurcation scenarios when parameter values are varied in a wide range. We formulate the general requirement for tristability in terms of logarithmic gain of the circuit. The parameter ranges for tristability and possible transition routes among steady states are determined by the combination of gain features of individual feedback loops. Coupling two PFLs with bistability or one NFL with a bistable PFL is most likely to generate tristability, but the underlying mechanisms are largely different. We also interpret published results and make testable predictions. This work sheds new light on interlinking feedback loops to realize tristability. The proposed theoretical framework can be of wide applicability.

Modular genetic regulatory networks increase organization during pattern formation

Studies have shown that genetic regulatory networks (GRNs) consist of modules that are densely connected subnetworks that function quasi-autonomously. Modules may be recognized motifs that comprise of two or three genes with particular regulatory functions and connectivity or be purely structural and identified through connection density. It is unclear what evolutionary and developmental advantages modular structure and in particular motifs provide that have led to this enrichment. This study seeks to understand how modules within developmental GRNs influence the complexity of multicellular patterns that emerge from the dynamics of the regulatory networks. We apply an algorithmic complexity to measure the organization of the patterns. A computational study was performed by creating Boolean intracellular networks within a simulated epithelial field of embryonic cells, where each cell contains the same network and communicates with adjacent cells using contact-mediated signaling. Intracellular networks with random connectivity were compared to those with modular connectivity and with motifs. Results show that modularity effects network dynamics and pattern organization significantly. In particular: (1) modular connectivity alone increases complexity in network dynamics and patterns; (2) bistable switch motifs simplify both the pattern and network dynamics; (3) all other motifs with feedback loops increase multicellular pattern complexity while simplifying the network dynamics; (4) negative feedback loops affect the dynamics complexity more significantly than positive feedback loops.

Transient amplification limits noise suppression in biochemical networks

Cell physiology is orchestrated, on a molecular level, through complex networks of biochemical reactions. The propagation of random fluctuations through these networks can significantly impact cell behavior, raising challenging questions about how network design shapes the cell's ability to suppress or exploit these fluctuations. Here, drawing on insights from statistical physics, fluid dynamics, and systems biology, we explore how transient amplification phenomena arising from network connectivity naturally limit a biochemical system's ability to suppress small fluctuations around steady-state behaviors. We find that even a simple system consisting of two variables linked by a single interaction is capable of amplifying small fluctuations orders of magnitude beyond the levels predicted by linear stability theory. We also find that adding additional interactions can promote further amplification, even when these interactions implement classic design strategies known to suppress fluctuations. These results establish that transient amplification is an essential factor determining baseline noise levels in stable intracellular networks. Significantly, our analysis is not bound to specific systems or interaction mechanisms: we find that noise amplification is an emergent phenomenon found near steady states in any network containing sufficiently strong interactions, regardless of its form or function.

Evolving modular genetic regulatory networks with a recursive, top-down approach

Being able to design genetic regulatory networks (GRNs) to achieve a desired cellular function is one of the main goals of synthetic biology. However, determining minimal GRNs that produce desired time-series behaviors is non-trivial. In this paper, we propose a 'top-down' approach to evolving small GRNs and then use these to recursively boot-strap the identification of larger, more complex, modular GRNs. We start with relatively dense GRNs and then use differential evolution (DE) to evolve interaction coefficients. When the target dynamical behavior is found embedded in a dense GRN, we narrow the focus of the search and begin aggressively pruning out excess interactions at the end of each generation. We first show that the method can quickly rediscover known small GRNs for a toggle switch and an oscillatory circuit. Next we include these GRNs as non-evolvable subnetworks in the subsequent evolution of more complex, modular GRNs. Successful solutions found in canonical DE where we truncated small interactions to zero, with or without an interaction penalty term, invariably contained many excess interactions. In contrast, by incorporating aggressive pruning and the penalty term, the DE was able to find minimal or nearly minimal GRNs in all test problems.

Transcriptional Network Growing Models Using Motif-Based Preferential Attachment

Understanding relationships between architectural properties of gene-regulatory networks (GRNs) has been one of the major goals in systems biology and bioinformatics, as it can provide insights into, e.g., disease dynamics and drug development. Such GRNs are characterized by their scale-free degree distributions and existence of network motifs – i.e., small-node subgraphs that occur more abundantly in GRNs than expected from chance alone. Because these transcriptional modules represent “building blocks” of complex networks and exhibit a wide range of functional and dynamical properties, they may contribute to the remarkable robustness and dynamical stability associated with the whole of GRNs. Here, we developed network-construction models to better understand this relationship, which produce randomized GRNs by using transcriptional motifs as the fundamental growth unit in contrast to other methods that construct similar networks on a node-by-node basis. Because this model produces networks with a prescribed lower bound on the number of choice transcriptional motifs (e.g., downlinks, feed-forward loops), its fidelity to the motif distributions observed in model organisms represents an improvement over existing methods, which we validated by contrasting their resultant motif and degree distributions against existing network-growth models and data from the model organism of the bacterium Escherichia coli. These models may therefore serve as novel testbeds for further elucidating relationships between the topology of transcriptional motifs and network-wide dynamical properties.

Damped oscillations in a multiple delayed feedback NF-κB signaling module

The NF-[Formula: see text]B signaling system regulates a number of cellular processes. Recent studies with simplified models found a damped function of the dual delayed feedback NF-κB signaling module. We use a computational model to investigate how multiple delayed feedback aids achieving damping oscillation in the system and how internal noise can influence the damping function. A curve-fitting method (CFM) is introduced to quantify the damped oscillation. Our results show that (1) the structure of multiple delayed feedback, containing double or triple significantly delayed feedback, determines achieving damped oscillation. (2) Internal noise could aid the system to achieve damped oscillation under almost all circumstances.

Coupled positive and negative feedbacks produce diverse gene expression patterns in colonies

Formation of patterns is a common feature in the development of multicellular organism as well as of microbial communities. To investigate the formation of gene expression patterns in colonies, we build a mathematical model of two-dimensional colony growth, where cells carry a coupled positive-and-negative-feedback circuit. We demonstrate that the model can produce sectored, target (concentric), uniform, and scattered expression patterns of regulators, depending on gene expression dynamics and nutrient diffusion. We reconstructed the same regulatory structure in Escherichia coli cells and found gene expression patterns on the surface of colonies similar to the ones produced by the computer simulations. By comparing computer simulations and experimental results, we observed that very simple rules of gene expression can yield a spectrum of well-defined patterns in a growing colony. Our results suggest that variations of the protein content among cells lead to a high level of heterogeneity in colonies.

Importance Formation of patterns is a common feature in the development of microbial communities. In this work, we show that a simple genetic circuit composed of a positive-feedback loop and a negative-feedback loop can produce diverse expression patterns in colonies. We obtained similar sets of gene expression patterns in the simulations and in the experiments. Because the combination of positive feedback and negative feedback is common in intracellular molecular networks, our results suggest that the protein content of cells is highly diversified in colonies.

Formation of patterns is a common feature in the development of microbial communities. In this work, we show that a simple genetic circuit composed of a positive-feedback loop and a negative-feedback loop can produce diverse expression patterns in colonies. We obtained similar sets of gene expression patterns in the simulations and in the experiments. Because the combination of positive feedback and negative feedback is common in intracellular molecular networks, our results suggest that the protein content of cells is highly diversified in colonies.

A novel TGFβ modulator that uncouples R-Smad/I-Smad-mediated negative feedback from R-Smad/ligand-driven positive feedback

As some of the most widely utilised intercellular signalling molecules, transforming growth factor β (TGFβ) superfamily members play critical roles in normal development and become disrupted in human disease. Establishing appropriate levels of TGFβ signalling involves positive and negative feedback, which are coupled and driven by the same signal transduction components (R-Smad transcription factor complexes), but whether and how the regulation of the two can be distinguished are unknown. Genome-wide comparison of published ChIP-seq datasets suggests that LIM domain binding proteins (Ldbs) co-localise with R-Smads at a substantial subset of R-Smad target genes including the locus of inhibitory Smad7 (I-Smad7), which mediates negative feedback for TGFβ signalling. We present evidence suggesting that zebrafish Ldb2a binds and directly activates the I-Smad7 gene, whereas it binds and represses the ligand gene, Squint (Sqt), which drives positive feedback. Thus, the fine tuning of TGFβ signalling derives from positive and negative control by Ldb2a. Expression of ldb2a is itself activated by TGFβ signals, suggesting potential feed-forward loops that might delay the negative input of Ldb2a to the positive feedback, as well as the positive input of Ldb2a to the negative feedback. In this way, precise gene expression control by Ldb2a enables an initial build-up of signalling via a fully active positive feedback in the absence of buffering by the negative feedback. In Ldb2a-deficient zebrafish embryos, homeostasis of TGFβ signalling is perturbed and signalling is stably enhanced, giving rise to excess mesoderm and endoderm, an effect that can be rescued by reducing signalling by the TGFβ family members, Nodal and BMP. Thus, Ldb2a is critical to the homeostatic control of TGFβ signalling and thereby embryonic patterning.

Mathematical modelling suggests a differential impact of β-transducin repeat-containing protein paralogues on Wnt/β-catenin signalling dynamics

The Wnt/β-catenin signalling pathway is involved in the regulation of a multitude of cellular processes by controlling the concentration of the transcriptional regulator β-catenin. Proteasomal degradation of β-catenin is mediated by two β-transducin repeat-containing protein paralogues, homologous to Slimb protein (HOS) and F-box/WD repeat-containing protein 1A (FWD1), which are functionally interchangeable and thereby considered to function redundantly in the pathway. HOS and FWD1 are both regulated by Wnt/β-catenin signalling, albeit in opposite directions, thus establishing interlocked negative and positive feedback loops. The functional relevance of the opposite regulation of HOS and FWD1 by Wnt/β-catenin signalling in conjunction with their redundant activities in proteasomal degradation of β-catenin remains unresolved. Using a detailed ordinary differential equation model, we investigated the specific influence of each individual feedback mechanism and their combination on Wnt/β-catenin signal transduction under wild-type and cancerous conditions. We found that, under wild-type conditions, the signalling dynamics are predominantly affected by the HOS feedback as a result of a higher concentration of HOS than FWD1. Transcriptional up-regulation of FWD1 by other signalling pathways reduced the impact of the HOS feedback. The opposite regulation of HOS and FWD1 expression by Wnt/β-catenin signalling allows the FWD1 feedback to be employed as a compensation mechanism against aberrant pathway activation as a result of a reduced HOS concentration. By contrast, the FWD1 feedback provides no protection against aberrant activation in adenomatous polyposis coli protein mutant cancer cells.

Transcription factor and microRNA-regulated network motifs for cancer and signal transduction networks

Abstract

Conclusions

To validate the role of network motifs in cancer formation, several examples are presented which demonstrated the effectiveness of the present approach. A web-based platform has been set up which can be accessed at: http://ppi.bioinfo.asia.edu.tw/pathway/. It is very likely that our results can supply very specific CMS missing information for certain cancer types, it is an indispensable tool for cancer biology research.

Identification of important nodes in directed biological networks: a network motif approach

Identification of important nodes in complex networks has attracted an increasing attention over the last decade. Various measures have been proposed to characterize the importance of nodes in complex networks, such as the degree, betweenness and PageRank. Different measures consider different aspects of complex networks. Although there are numerous results reported on undirected complex networks, few results have been reported on directed biological networks. Based on network motifs and principal component analysis (PCA), this paper aims at introducing a new measure to characterize node importance in directed biological networks. Investigations on five real-world biological networks indicate that the proposed method can robustly identify actually important nodes in different networks, such as finding command interneurons, global regulators and non-hub but evolutionary conserved actually important nodes in biological networks. Receiver Operating Characteristic (ROC) curves for the five networks indicate remarkable prediction accuracy of the proposed measure. The proposed index provides an alternative complex network metric. Potential implications of the related investigations include identifying network control and regulation targets, biological networks modeling and analysis, as well as networked medicine.

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/.

A design principle underlying the paradoxical roles of E3 ubiquitin ligases

E3 ubiquitin ligases are important cellular components that determine the specificity of proteolysis in the ubiquitin-proteasome system. However, an increasing number of studies have indicated that E3 ubiquitin ligases also participate in transcription. Intrigued by the apparently paradoxical functions of E3 ubiquitin ligases in both proteolysis and transcriptional activation, we investigated the underlying design principles using mathematical modeling. We found that the antagonistic functions integrated in E3 ubiquitin ligases can prevent any undesirable sustained activation of downstream genes when E3 ubiquitin ligases are destabilized by unexpected perturbations. Interestingly, this design principle of the system is similar to the operational principle of a safety interlock device in engineering systems, which prevents a system from abnormal operation unless stability is guaranteed.

Multistable switches and their role in cellular differentiation networks

Background

Cellular differentiation during development is controlled by gene regulatory networks (GRNs). This complex process is always subject to gene expression noise. There is evidence suggesting that commonly seen patterns in GRNs, referred to as biological multistable switches, play an important role in creating the structure of lineage trees by providing stability to cell types.

Results

To explore this question a new methodology is developed and applied to study (a) the multistable switch-containing GRN for hematopoiesis and (b) a large set of random boolean networks (RBNs) in which multistable switches were embedded systematically. In this work, each network attractor is taken to represent a distinct cell type. The GRNs were seeded with one or two identical copies of each multistable switch and the effect of these additions on two key aspects of network dynamics was assessed. These properties are the barrier to movement between pairs of attractors (separation) and the degree to which one direction of movement between attractor pairs is favored over another (directionality). Both of these properties are instrumental in shaping the structure of lineage trees. We found that adding one multistable switch of any type had a modest effect on increasing the proportion of well-separated attractor pairs. Adding two identical switches of any type had a much stronger effect in increasing the proportion of well-separated attractors. Similarly, there was an increase in the frequency of directional transitions between attractor pairs when two identical multistable switches were added to GRNs. This effect on directionality was not observed when only one multistable switch was added.

Conclusions

This work provides evidence that the occurrence of multistable switches in networks that control cellular differentiation contributes to the structure of lineage trees and to the stabilization of cell types.

Control of the G-protein cascade dynamics by GDP dissociation inhibitors

A network of the Rho family GTPases, which cycle between inactive GDP-bound and active GTP-bound states, controls key cellular processes, including proliferation and migration. Activating and deactivating GTPase transitions are controlled by guanine nucleotide exchange factors (GEFs), GTPase activating proteins (GAPs) and GDP dissociation inhibitors (GDIs) that sequester GTPases from the membrane to the cytoplasm. Here we show that a cascade of two Rho family GTPases, RhoA and Rac1, regulated by RhoGDI1, exhibits distinct modes of the dynamic behavior, including abrupt, bistable switches, excitable overshoot transitions and oscillations. The RhoGDI1 abundance and signal-induced changes in the RhoGDI1 affinity for GTPases control these different dynamics, enabling transitions from a single stable steady state to bistability, to excitable pulses and to sustained oscillations of GTPase activities. These RhoGDI1-controlled dynamic modes of RhoA and Rac1 activities form the basis of cell migration behaviors, including protrusion-retraction cycles at the leading edge of migrating cells.

Regulatory networks and complex interactions between the insulin and angiotensin II signalling systems: models and implications for hypertension and diabetes

The cross-talk between insulin and angiotensin II signalling pathways plays a significant role in the co-occurrence of diabetes and hypertension. We developed a mathematical model of the system of interactions among the biomolecules that are involved in the cross-talk between the insulin and angiotensin II signalling pathways. We have identified several feedback structures that regulate the dynamic behavior of the individual signalling pathways and their interactions. Different scenarios are simulated and dominant steady-state, dynamic and stability characteristics are revealed. The proposed mechanistic model describes how angiotensin II inhibits the actions of insulin and impairs the insulin-mediated vasodilation. The model also predicts that poor glycaemic control induced by diabetes contributes to hypertension by activating the renin angiotensin aystem.

Cellular and population plasticity of helper CD4(+) T cell responses

Vertebrates are constantly exposed to pathogens, and the adaptive immunity has most likely evolved to control and clear such infectious agents. CD4⁺ T cells are the major players in the adaptive immune response to pathogens. Following recognition of pathogen-derived antigens naïve CD4⁺ T cells differentiate into effectors which then control pathogen replication either directly by killing pathogen-infected cells or by assisting with generation of cytotoxic T lymphocytes (CTLs) or pathogen-specific antibodies. Pathogen-specific effector CD4⁺ T cells are highly heterogeneous in terms of cytokines they produce. Three major subtypes of effector CD4⁺ T cells have been identified: T-helper 1 (Th1) cells producing IFN-γ and TNF-α, Th2 cells producing IL-4 and IL-10, and Th17 cells producing IL-17. How this heterogeneity is maintained and what regulates changes in effector T cell composition during chronic infections remains poorly understood. In this review we discuss recent advances in our understanding of CD4⁺ T cell differentiation in response to microbial infections. We propose that a change in the phenotype of pathogen-specific effector CD4⁺ T cells during chronic infections, for example, from Th1 to Th2 response as observed in Mycobactrium avium ssp. paratuberculosis (MAP) infection of ruminants, can be achieved by conversion of T cells from one effector subset to another (cellular plasticity) or due to differences in kinetics (differentiation, proliferation, death) of different effector T cell subsets (population plasticity). We also shortly review mathematical models aimed at describing CD4⁺ T cell differentiation and outline areas for future experimental and theoretical research.

Dual delayed feedback provides sensitivity and robustness to the NF-κB signaling module

Many cellular stress-responsive signaling systems exhibit highly dynamic behavior with oscillatory features mediated by delayed negative feedback loops. What remains unclear is whether oscillatory behavior is the basis for a signaling code based on frequency modulation (FM) or whether the negative feedback control modules have evolved to fulfill other functional requirements. Here, we use experimentally calibrated computational models to interrogate the negative feedback loops that regulate the dynamic activity of the transcription factor NF-κB. Linear stability analysis of the model shows that oscillatory frequency is a hard-wired feature of the primary negative feedback loop and not a function of the stimulus, thus arguing against an FM signaling code. Instead, our modeling studies suggest that the two feedback loops may be tuned to provide for rapid activation and inactivation capabilities for transient input signals of a wide range of durations; by minimizing late phase oscillations response durations may be fine-tuned in a graded rather than quantized manner. Further, in the presence of molecular noise the dual delayed negative feedback system minimizes stochastic excursions of the output to produce a robust NF-κB response.

Impaired coupling of local and global functional feedbacks underlies abnormal synchronization and negative symptoms of schizophrenia

Background

Abnormal synchronization of brain oscillations is found to be associated with various core symptoms of schizophrenia. However, the underlying mechanism of this association remains yet to be elucidated.

Results

In this study, we found that coupled local and global feedback (CLGF) circuits in the cortical functional network are related to the abnormal synchronization and also correlated to the negative symptom of schizophrenia. Analysis of the magnetoencephalography data obtained from patients with chronic schizophrenia during rest revealed an increase in beta band synchronization and a reduction in gamma band power compared to healthy controls. Using a feedback identification method based on non-causal impulse responses, we constructed functional feedback networks and found that CLGF circuits were significantly reduced in schizophrenia. From computational analysis on the basis of the Wilson-Cowan model, we unraveled that the CLGF circuits are critically involved in the abnormal synchronization and the dynamical switching between beta and gamma bands power in schizophrenia. Moreover, we found that the abundance of CLGF circuits was negatively correlated with the development of negative symptoms of schizophrenia, suggesting that the negative symptom is closely related to the impairment of this circuit.

Conclusions

Our study implicates that patients with schizophrenia might have the impaired coupling of inter- and intra-regional functional feedbacks and that the CLGF circuit might serve as a critical bridge between abnormal synchronization and the negative symptoms of schizophrenia.

Architecture-dependent robustness in a class of multiple positive feedback loops

Many types of multiple positive feedbacks with each having potentials to generate bistability exist extensively in natural, raising the question of why a particular architecture is present in a cell. In this study, the authors investigate multiple positive feedback loops across three classes: one-loop class, two-loop class and three-loop class, where each class is composed of double positive feedback loop (DPFL) or double negative feedback loop (DNFL) or both. Through large-scale sampling and robustness analysis, the authors find that for a given class, the homogeneous DPFL circuit (i.e. the coupled circuit that is composed of only DPFLs) is more robust than all the other circuits in generating bistable behaviour. In addition, stochastic simulation shows that the low stable state is more robust than the high stable state in homogeneous DPFL whereas the high-stable state is more robust than the low-stable state in homogeneous DNFL circuits. It was argued that this investigation provides insight into the relationship between robustness and network architecture.

Noise propagation in gene regulation networks involving interlinked positive and negative feedback loops

It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.

Motif Participation by Genes in E. coli Transcriptional Networks

Motifs are patterns of recurring connections among the genes of genetic networks that occur more frequently than would be expected from randomized networks with the same degree sequence. Although the abundance of certain three-node motifs, such as the feed-forward loop, is positively correlated with a networks’ ability to tolerate moderate disruptions to gene expression, little is known regarding the connectivity of individual genes participating in multiple motifs. Using the transcriptional network of the bacterium Escherichia coli, we investigate this feature by reconstructing the distribution of genes participating in feed-forward loop motifs from its largest connected network component. We contrast these motif participation distributions with those obtained from model networks built using the preferential attachment mechanism employed by many biological and man-made networks. We report that, although some of these model networks support a motif participation distribution that appears qualitatively similar to that obtained from the bacterium E. coli, the probability for a node to support a feed-forward loop motif may instead be strongly influenced by only a few master transcriptional regulators within the network. From these analyses we conclude that such master regulators may be a crucial ingredient to describe coupling among feed-forward loop motifs in transcriptional regulatory networks.

Boolean versus continuous dynamics in modules with two feedback loops

We investigate the dynamical behavior of simple networks, namely loops with an additional internal regulating connection. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method and within a single framework, we study different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations or stable fixed points. These conditions depend only on general features such as the degree of cooperativity of the regulating interactions and the logical structure of the interactions. There are no simple rules for deciding when Boolean and continuous dynamics agree with each other, but we identify several relevant criteria.