Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks

An atrial fibrillation-associated regulatory region modulates cardiac Tbx5 levels and arrhythmia susceptibility

Heart development and rhythm control are highly Tbx5 dosage-sensitive. TBX5 haploinsufficiency causes congenital conduction disorders, whereas increased expression levels of TBX5 in human heart samples has been associated with atrial fibrillation (AF). We deleted the conserved mouse orthologues of two independent AF-associated genomic regions in the Tbx5 locus, one intronic (RE(int)) and one downstream (RE(down)) of Tbx5. In both lines, we observed a modest (30%) increase of Tbx5 in the postnatal atria. To gain insight into the effects of slight dosage increase in vivo, we investigated the atrial transcriptional, epigenetic and electrophysiological properties of both lines. Increased atrial Tbx5 expression was associated with induction of genes involved in development, ion transport and conduction, with increased susceptibility to atrial arrhythmias, and increased action potential duration of atrial cardiomyocytes. We identified an AF-associated variant in the human RE(int) that increases its transcriptional activity. Expression of the AF-associated transcription factor Prrx1 was induced in Tbx5^RE(int)KO cardiomyocytes. We found that some of the transcriptional and functional changes in the atria caused by increased Tbx5 expression were normalized when reducing cardiac Prrx1 expression in Tbx5^RE(int)KO mice, indicating an interaction between these two AF genes. We conclude that modest increases in expression of dose-dependent transcription factors, caused by common regulatory variants, significantly impact on the cardiac gene regulatory network and disease susceptibility.

Functional Resilience of Mutually Repressing Motifs Embedded in Larger Networks

Elucidating the design principles of regulatory networks driving cellular decision-making has important implications for understanding cell differentiation and guiding the design of synthetic circuits. Mutually repressing feedback loops between 'master regulators' of cell fates can exhibit multistable dynamics enabling "single-positive" phenotypes: (high A, low B) and (low A, high B) for a toggle switch, and (high A, low B, low C), (low A, high B, low C) and (low A, low B, high C) for a toggle triad. However, the dynamics of these two motifs have been interrogated in isolation in silico, but in vitro and in vivo, they often operate while embedded in larger regulatory networks. Here, we embed these motifs in complex larger networks of varying sizes and connectivity to identify hallmarks under which these motifs maintain their canonical dynamical behavior. We show that an increased number of incoming edges onto a motif leads to a decay in their canonical stand-alone behaviors. We also show that this decay can be exacerbated by adding self-inhibition but not self-activation loops on the 'master regulators'. These observations offer insights into the design principles of biological networks containing these motifs and can help devise optimal strategies for the integration of these motifs into larger synthetic networks.

Idiosyncratic Purifying Selection on Metabolic Enzymes in the Long-Term Evolution Experiment with Escherichia coli

Bacteria, Archaea, and Eukarya all share a common set of metabolic reactions. This implies that the function and topology of central metabolism has been evolving under purifying selection over deep time. Central metabolism may similarly evolve under purifying selection during long-term evolution experiments, although it is unclear how long such experiments would have to run (decades, centuries, millennia) before signs of purifying selection on metabolism appear. I hypothesized that central and superessential metabolic enzymes would show evidence of purifying selection in the long-term evolution experiment with Escherichia coli (LTEE). I also hypothesized that enzymes that specialize on single substrates would show stronger evidence of purifying selection in the LTEE than generalist enzymes that catalyze multiple reactions. I tested these hypotheses by analyzing metagenomic time series covering 62,750 generations of the LTEE. I find mixed support for these hypotheses, because the observed patterns of purifying selection are idiosyncratic and population-specific. To explain this finding, I propose the Jenga hypothesis, named after a children's game in which blocks are removed from a tower until it falls. The Jenga hypothesis postulates that loss-of-function mutations degrade costly, redundant, and non-essential metabolic functions. Replicate populations can therefore follow idiosyncratic trajectories of lost redundancies, despite purifying selection on overall function. I tested the Jenga hypothesis by simulating the evolution of 1,000 minimal genomes under strong purifying selection. As predicted, the minimal genomes converge to different metabolic networks. Strikingly, the core genes common to all 1,000 minimal genomes show consistent signatures of purifying selection in the LTEE.

Reconstructing Boolean network ensembles from single-cell data for unraveling dynamics in the aging of human hematopoietic stem cells

Regulatory dependencies in molecular networks are the basis of dynamic behaviors affecting the phenotypical landscape. With the advance of high throughput technologies, the detail of omics data has arrived at the single-cell level. Nevertheless, new strategies are required to reconstruct regulatory networks based on populations of single-cell data. Here, we present a new approach to generate populations of gene regulatory networks from single-cell RNA-sequencing (scRNA-seq) data. Our approach exploits the heterogeneity of single-cell populations to generate pseudo-timepoints. This allows for the first time to uncouple network reconstruction from a direct dependency on time series measurements. The generated time series are then fed to a combined reconstruction algorithm. The latter allows a fast and efficient reconstruction of ensembles of gene regulatory networks. Since this approach does not require knowledge on time-related trajectories, it allows us to model heterogeneous processes such as aging. Applying the approach to the aging-associated NF-κB signaling pathway-based scRNA-seq data of human hematopoietic stem cells (HSCs), we were able to reconstruct eight ensembles, and evaluate their dynamic behavior. Moreover, we propose a strategy to evaluate the resulting attractor patterns. Interaction graph-based features and dynamic investigations of our model ensembles provide a new perspective on the heterogeneity and mechanisms related to human HSCs aging.

Capturing dynamic relevance in Boolean networks using graph theoretical measures

Motivation

Interaction graphs are able to describe regulatory dependencies between compounds without capturing dynamics. In contrast, mathematical models that are based on interaction graphs allow to investigate the dynamics of biological systems. However, since dynamic complexity of these models grows exponentially with their size, exhaustive analyses of the dynamics and consequently screening all possible interventions eventually becomes infeasible. Thus, we designed an approach to identify dynamically relevant compounds based on the static network topology.

Results

Here, we present a method only based on static properties to identify dynamically influencing nodes. Coupling vertex betweenness and determinative power, we could capture relevant nodes for changing dynamics with an accuracy of 75% in a set of 35 published logical models. Further analyses of the selected compounds’ connectivity unravelled a new class of not highly connected nodes with high impact on the networks’ dynamics, which we call gatekeepers. We validated our method’s working concept on logical models, which can be readily scaled up to complex interaction networks, where dynamic analyses are not even feasible.

Availability and implementation

Code is freely available at https://github.com/sysbio-bioinf/BNStatic.

Supplementary information

Supplementary data are available at Bioinformatics online.

The Branched Nature of the Nonsense-Mediated mRNA Decay Pathway

Nonsense-mediated mRNA decay (NMD) is a conserved translation-coupled quality control mechanism in all eukaryotes that regulates the expression of a significant fraction of both the aberrant and normal transcriptomes. In vertebrates, NMD has become an essential process owing to expansion of the diversity of NMD-regulated transcripts, particularly during various developmental processes. Surprisingly, however, some core NMD factors that are essential for NMD in simpler organisms appear to be dispensable for vertebrate NMD. At the same time, numerous NMD enhancers and suppressors have been identified in multicellular organisms including vertebrates. Collectively, the available data suggest that vertebrate NMD is a complex, branched pathway wherein individual branches regulate specific mRNA subsets to fulfill distinct physiological functions.

Genomic and phenotypic evolution of Escherichia coli in a novel citrate-only resource environment

Evolutionary innovations allow populations to colonize new ecological niches. We previously reported that aerobic growth on citrate (Cit⁺) evolved in an Escherichia coli population during adaptation to a minimal glucose medium containing citrate (DM25). Cit⁺ variants can also grow in citrate-only medium (DM0), a novel environment for E. coli. To study adaptation to this niche, we founded two sets of Cit⁺ populations and evolved them for 2500 generations in DM0 or DM25. The evolved lineages acquired numerous parallel mutations, many mediated by transposable elements. Several also evolved amplifications of regions containing the maeA gene. Unexpectedly, some evolved populations and clones show apparent declines in fitness. We also found evidence of substantial cell death in Cit⁺ clones. Our results thus demonstrate rapid trait refinement and adaptation to the new citrate niche, while also suggesting a recalcitrant mismatch between E. coli physiology and growth on citrate.

Multiplexed Gene Expression Tuning with Orthogonal Synthetic Gene Circuits

Understanding the individual and joint contribution of multiple protein levels toward a phenotype requires precise and tunable multigene expression control. Here we introduce a pair of mammalian synthetic gene circuits that linearly and orthogonally control the expression of two reporter genes in mammalian cells with low variability in response to chemical inducers introduced into the growth medium. These gene expression systems can be used to simultaneously probe the individual and joint effects of two gene product concentrations on a cellular phenotype in basic research or biomedical applications.

Evolution in the Debian GNU/Linux software network: analogies and differences with gene regulatory networks

Biological networks exhibit intricate architectures deemed to be crucial for their functionality. In particular, gene regulatory networks, which play a key role in information processing in the cell, display non-trivial architectural features such as scale-free degree distributions, high modularity and low average distance between connected genes. Such networks result from complex evolutionary and adaptive processes difficult to track down empirically. On the other hand, there exists detailed information on the developmental (or evolutionary) stages of open-software networks that result from self-organized growth across versions. Here, we study the evolution of the Debian GNU/Linux software network, focusing on the changes of key structural and statistical features over time. Our results show that evolution has led to a network structure in which the out-degree distribution is scale-free and the in-degree distribution is a stretched exponential. In addition, while modularity, directionality of information flow, and average distance between elements grew, vulnerability decreased over time. These features resemble closely those currently shown by gene regulatory networks, suggesting the existence of common adaptive pathways for the architectural design of information-processing networks. Differences in other hierarchical aspects point to system-specific solutions to similar evolutionary challenges.

Roadmap to Local Tumour Growth: Insights from Cervical Cancer

Wide tumour excision is currently the standard approach to surgical treatment of solid cancers including carcinomas of the lower genital tract. This strategy is based on the premise that tumours exhibit isotropic growth potential. We reviewed and analysed local tumour spreading patterns in 518 patients with cancer of the uterine cervix who underwent surgical tumour resection. Based on data obtained from pathological examination of the surgical specimen, we applied computational modelling techniques to simulate local tumour spread in order to identify parameters influencing preferred infiltration patterns and used area-proportional Euler diagrams to detect and confirm ordered patterns of tumour spread. Some anatomical structures, e.g. tissues of the urinary bladder, were significantly more likely to be infiltrated than other structures, e.g. the ureter and the rectum. Computational models assuming isotropic growth could not explain these infiltration patterns. Introducing ontogenetic distance of a tissue relative to the uterine cervix as a parameter led to accurate predictions of the clinically observed infiltration likelihoods. The clinical data indicates that successive infiltration likelihoods of ontogenetically distant tissues are nearly perfect subsets of ontogenetically closer tissues. The prevailing assumption of isotropic tumour extension has significant shortcomings in the case of cervical cancer. Rather, cervical cancer spread seems to follow ontogenetically defined trajectories.

Inferring hidden causal relations between pathway members using reduced Google matrix of directed biological networks

Signaling pathways represent parts of the global biological molecular network which connects them into a seamless whole through complex direct and indirect (hidden) crosstalk whose structure can change during development or in pathological conditions. We suggest a novel methodology, called Googlomics, for the structural analysis of directed biological networks using spectral analysis of their Google matrices, using parallels with quantum scattering theory, developed for nuclear and mesoscopic physics and quantum chaos. We introduce analytical "reduced Google matrix" method for the analysis of biological network structure. The method allows inferring hidden causal relations between the members of a signaling pathway or a functionally related group of genes. We investigate how the structure of hidden causal relations can be reprogrammed as a result of changes in the transcriptional network layer during cancerogenesis. The suggested Googlomics approach rigorously characterizes complex systemic changes in the wiring of large causal biological networks in a computationally efficient way.

Rare symbionts may contribute to the resilience of coral-algal assemblages

The association between corals and photosynthetic dinoflagellates (Symbiodinium spp.) is the key to the success of reef ecosystems in highly oligotrophic environments, but it is also their Achilles‘ heel due to its vulnerability to local stressors and the effects of climate change. Research during the last two decades has shaped a view that coral host–Symbiodinium pairings are diverse, but largely exclusive. Deep sequencing has now revealed the existence of a rare diversity of cryptic Symbiodinium assemblages within the coral holobiont, in addition to one or a few abundant algal members. While the contribution of the most abundant resident Symbiodinium species to coral physiology is widely recognized, the significance of the rare and low abundant background Symbiodinium remains a matter of debate. In this study, we assessed how coral–Symbiodinium communities assemble and how rare and abundant components together constitute the Symbiodinium community by analyzing 892 coral samples comprising >110 000 unique Symbiodinium ITS2 marker gene sequences. Using network modeling, we show that host–Symbiodinium communities assemble in non-random ‘clusters‘ of abundant and rare symbionts. Symbiodinium community structure follows the same principles as bacterial communities, for which the functional significance of rare members (the ‘rare bacterial biosphere’) has long been recognized. Importantly, the inclusion of rare Symbiodinium taxa in robustness analyses revealed a significant contribution to the stability of the host–symbiont community overall. As such, it highlights the potential functions rare symbionts may provide to environmental resilience of the coral holobiont.

The Wisdom of Networks: A General Adaptation and Learning Mechanism of Complex Systems: The Network Core Triggers Fast Responses to Known Stimuli; Innovations Require the Slow Network Periphery and Are Encoded by Core-Remodeling

I hypothesize that re-occurring prior experience of complex systems mobilizes a fast response, whose attractor is encoded by their strongly connected network core. In contrast, responses to novel stimuli are often slow and require the weakly connected network periphery. Upon repeated stimulus, peripheral network nodes remodel the network core that encodes the attractor of the new response. This "core-periphery learning" theory reviews and generalizes the heretofore fragmented knowledge on attractor formation by neural networks, periphery-driven innovation, and a number of recent reports on the adaptation of protein, neuronal, and social networks. The core-periphery learning theory may increase our understanding of signaling, memory formation, information encoding and decision-making processes. Moreover, the power of network periphery-related "wisdom of crowds" inventing creative, novel responses indicates that deliberative democracy is a slow yet efficient learning strategy developed as the success of a billion-year evolution. Also see the video abstract here: https://youtu.be/IIjP7zWGjVE.

Universal attenuators and their interactions with feedback loops in gene regulatory networks

Using a combination of mathematical modelling, statistical simulation and large-scale data analysis we study the properties of linear regulatory chains (LRCs) within gene regulatory networks (GRNs). Our modelling indicates that downstream genes embedded within LRCs are highly insulated from the variation in expression of upstream genes, and thus LRCs act as attenuators. This observation implies a progressively weaker functionality of LRCs as their length increases. When analyzing the preponderance of LRCs in the GRNs of Escherichia coli K12 and several other organisms, we find that very long LRCs are essentially absent. In both E. coli and M. tuberculosis we find that four-gene LRCs are intimately linked to identical feedback loops that are involved in potentially chaotic stress response, indicating that the dynamics of these potentially destabilising motifs are strongly restrained under homeostatic conditions. The same relationship is observed in a human cancer cell line (K562), and we postulate that four-gene LRCs act as ‘universal attenuators’. These findings suggest a role for long LRCs in dampening variation in gene expression, thereby protecting cell identity, and in controlling dramatic shifts in cell-wide gene expression through inhibiting chaos-generating motifs.

Looplessness in networks is linked to trophic coherence

Many natural, complex systems are remarkably stable thanks to an absence of feedback acting on their elements. When described as networks these exhibit few or no cycles, and associated matrices have small leading eigenvalues. It has been suggested that this architecture can confer advantages to the system as a whole, such as "qualitative stability," but this observation does not in itself explain how a loopless structure might arise. We show here that the number of feedback loops in a network, as well as the eigenvalues of associated matrices, is determined by a structural property called trophic coherence, a measure of how neatly nodes fall into distinct levels. Our theory correctly classifies a variety of networks-including those derived from genes, metabolites, species, neurons, words, computers, and trading nations-into two distinct regimes of high and low feedback and provides a null model to gauge the significance of related magnitudes. Because trophic coherence suppresses feedback, whereas an absence of feedback alone does not lead to coherence, our work suggests that the reasons for "looplessness" in nature should be sought in coherence-inducing mechanisms.

Modular bond-graph modelling and analysis of biomolecular systems

Bond graphs can be used to build thermodynamically-compliant hierarchical models of biomolecular systems. As bond graphs have been widely used to model, analyse and synthesise engineering systems, this study suggests that they can play the same rôle in the modelling, analysis and synthesis of biomolecular systems. The particular structure of bond graphs arising from biomolecular systems is established and used to elucidate the relation between thermodynamically closed and open systems. Block diagram representations of the dynamics implied by these bond graphs are used to reveal implicit feedback structures and are linearised to allow the application of control-theoretical methods. Two concepts of modularity are examined: computational modularity where physical correctness is retained and behavioural modularity where module behaviour (such as ultrasensitivity) is retained. As well as providing computational modularity, bond graphs provide a natural formulation of behavioural modularity and reveal the sources of retroactivity. A bond graph approach to reducing retroactivity, and thus inter-module interaction, is shown to require a power supply such as that provided by the ATP ⇌ ADP + Pi reaction. The mitogen-activated protein kinase cascade (Raf-MEK-ERK pathway) is used as an illustrative example.

Insights into Biological Complexity from Simple Foundations

We discuss an overtly "simple approach" to complex biological systems borrowing selectively from theoretical physics. The approach is framed by three maxims, and we show examples of its success in two different applications: investigating cellular robustness at the level of gene regulatory networks and quantifying rare events of DNA replication errors.

Buffering of Genetic Regulatory Networks in Drosophila melanogaster

Regulatory variation in gene expression can be described by cis- and trans-genetic components. Here we used RNA-seq data from a population panel of Drosophila melanogaster test crosses to compare allelic imbalance (AI) in female head tissue between mated and virgin flies, an environmental change known to affect transcription. Indeed, 3048 exons (1610 genes) are differentially expressed in this study. A Bayesian model for AI, with an intersection test, controls type I error. There are ∼200 genes with AI exclusively in mated or virgin flies, indicating an environmental component of expression regulation. On average 34% of genes within a cross and 54% of all genes show evidence for genetic regulation of transcription. Nearly all differentially regulated genes are affected in cis, with an average of 63% of expression variation explained by the cis-effects. Trans-effects explain 8% of the variance in AI on average and the interaction between cis and trans explains an average of 11% of the total variance in AI. In both environments cis- and trans-effects are compensatory in their overall effect, with a negative association between cis- and trans-effects in 85% of the exons examined. We hypothesize that the gene expression level perturbed by cis-regulatory mutations is compensated through trans-regulatory mechanisms, e.g., trans and cis by trans-factors buffering cis-mutations. In addition, when AI is detected in both environments, cis-mated, cis-virgin, and trans-mated-trans-virgin estimates are highly concordant with 99% of all exons positively correlated with a median correlation of 0.83 for cis and 0.95 for trans We conclude that the gene regulatory networks (GRNs) are robust and that trans-buffering explains robustness.

Large molecular systems landscape uncovers T cell trapping in human skin cancer

Immune surveillance of tumour cells is an important function of CD8 T lymphocytes, which has failed in cancer for reasons still unknown in many respect but mainly related to cellular processes in the tumour microenvironment. Applying imaging cycler microscopy to analyse the immune contexture in a human skin cancer we could identify and map 7,000 distinct cell surface-associated multi-protein assemblies. The resulting combinatorial geometry-based high-functional resolution led to discovery of a mechanism of T cell trapping in the epidermis, which involves SPIKE, a network of suprabasal keratinocyte projections piercing and interconnecting CD8 T cells. It appears initiated by clusters of infrabasal T and dendritic cells connected via cell projections across a fractured basal lamina to suprabasal keratinocytes and T lymphocytes.

Biology is simple

This paper explores the potential for simplicity to reveal new biological understanding. Borrowing selectively from physics thinking, and contrasting with Crick's reductionist philosophy, the author argues that greater emphasis on simplicity is necessary to advance biology and its applications.

Comparative Study of Regulatory Circuits in Two Sea Urchin Species Reveals Tight Control of Timing and High Conservation of Expression Dynamics

Accurate temporal control of gene expression is essential for normal development and must be robust to natural genetic and environmental variation. Studying gene expression variation within and between related species can delineate the level of expression variability that development can tolerate. Here we exploit the comprehensive model of sea urchin gene regulatory networks and generate high-density expression profiles of key regulatory genes of the Mediterranean sea urchin, Paracentrotus lividus (Pl). The high resolution of our studies reveals highly reproducible gene initiation times that have lower variation than those of maximal mRNA levels between different individuals of the same species. This observation supports a threshold behavior of gene activation that is less sensitive to input concentrations. We then compare Mediterranean sea urchin gene expression profiles to those of its Pacific Ocean relative, Strongylocentrotus purpuratus (Sp). These species shared a common ancestor about 40 million years ago and show highly similar embryonic morphologies. Our comparative analyses of five regulatory circuits operating in different embryonic territories reveal a high conservation of the temporal order of gene activation but also some cases of divergence. A linear ratio of 1.3-fold between gene initiation times in Pl and Sp is partially explained by scaling of the developmental rates with temperature. Scaling the developmental rates according to the estimated Sp-Pl ratio and normalizing the expression levels reveals a striking conservation of relative dynamics of gene expression between the species. Overall, our findings demonstrate the ability of biological developmental systems to tightly control the timing of gene activation and relative dynamics and overcome expression noise induced by genetic variation and growth conditions.

Connecting growth with gene expression: of noise and numbers

Growth is a dynamic process whereby cells accumulate mass. Growth rates of single cells are connected to RNA and protein synthesis rates, and therefore with biomolecule numbers. Noise in gene expression depends on these numbers, and is thus linked with cellular growth. Whether these global attributes of the cell participate in gene regulation is still largely unexplored. New experimental and modelling studies suggest that systemic variations in biomolecule numbers can coordinate cellular processes, including growth itself, through global regulatory feedback that acts in addition to genetic regulatory networks. Here, we review these findings and speculate on possible implications of this less appreciated layer of gene regulation for cellular physiology and adaptation to changing environments.

Rethinking gene regulatory networks in light of alternative splicing, intrinsically disordered protein domains, and post-translational modifications

Models for genetic regulation and cell fate specification characteristically assume that gene regulatory networks (GRNs) are essentially deterministic and exhibit multiple stable states specifying alternative, but pre-figured cell fates. Mounting evidence shows, however, that most eukaryotic precursor RNAs undergo alternative splicing (AS) and that the majority of transcription factors contain intrinsically disordered protein (IDP) domains whose functionalities are context dependent as well as subject to post-translational modification (PTM). Consequently, many transcription factors do not have fixed cis-acting regulatory targets, and developmental determination by GRNs alone is untenable. Modeling these phenomena requires a multi-scale approach to explain how GRNs operationally interact with the intra- and intercellular environments. Evidence shows that AS, IDP, and PTM complicate gene expression and act synergistically to facilitate and promote time- and cell-specific protein modifications involved in cell signaling and cell fate specification and thereby disrupt a strict deterministic GRN-phenotype mapping. The combined effects of AS, IDP, and PTM give proteomes physiological plasticity, adaptive responsiveness, and developmental versatility without inefficiently expanding genome size. They also help us understand how protein functionalities can undergo major evolutionary changes by buffering mutational consequences.