Bow ties, metabolism and disease

Dynamical Network Stability Analysis of Multiple Biological Ages Provides a Framework for Understanding the Aging Process

Widespread interest in nondestructive biomarkers of aging has led to a multitude of biological ages that each proffers a "true" health-adjusted individual age. Although each measure provides salient information on the aging process, they are each univariate, in contrast to the "hallmark" and "pillar" theories of aging, which are explicitly multidimensional, multicausal, and multiscale. Fortunately, multiple biological ages can be systematically combined into a multidimensional network representation. The interaction network between these biological ages permits analysis of the multidimensional effects of aging, as well as quantification of causal influences during both natural aging and, potentially, after anti-aging intervention. The behavior of the system as a whole can then be explored using dynamical network stability analysis, which identifies new, efficient biomarkers that quantify long-term resilience scores on the timescale between measurements (years). We demonstrate this approach using a set of 8 biological ages from the longitudinal Swedish Adoption/Twin Study of Aging (SATSA). After extracting an interaction network between these biological ages, we observed that physiological age, a proxy for cardiometabolic health, serves as a central node in the network, implicating it as a key vulnerability for slow, age-related decline. We furthermore show that while the system as a whole is stable, there is a weakly stable direction along which recovery is slow-on the timescale of a human lifespan. This slow direction provides an aging biomarker, which correlates strongly with chronological age and predicts longitudinal decline in health-suggesting that it estimates an important driver of age-related changes.

Versatile system cores as a conceptual basis for generality in cell and developmental biology

The discovery of general principles underlying the complexity and diversity of cellular and developmental systems is a central and long-standing aim of biology. While new technologies collect data at an ever-accelerating rate, there is growing concern that conceptual progress is not keeping pace. We contend that this is due to a paucity of conceptual frameworks that support meaningful generalizations. This led us to develop the core and periphery (C&P) hypothesis, which posits that many biological systems can be decomposed into a highly versatile core with a large behavioral repertoire and a specific periphery that configures said core to perform one particular function. Versatile cores tend to be widely reused across biology, which confers generality to theories describing them. Here, we introduce this concept and describe examples at multiple scales, including Turing patterning, actomyosin dynamics, multi-cellular morphogenesis, and vertebrate gastrulation. We also sketch its evolutionary basis and discuss key implications and open questions. We propose that the C&P hypothesis could unlock new avenues of conceptual progress in mesoscale biology.

Revisiting the evolution of bow-tie architecture in signaling networks

Bow-tie architecture is a layered network structure that has a narrow middle layer with multiple inputs and outputs. Such structures are widely seen in the molecular networks in cells, suggesting that a universal evolutionary mechanism underlies the emergence of bow-tie architecture. The previous theoretical studies have implemented evolutionary simulations of the feedforward network to satisfy a given input-output goal and proposed that the bow-tie architecture emerges when the ideal input-output relation is given as a rank-deficient matrix with mutations in network link intensities in a multiplicative manner. Here, we report that the bow-tie network inevitably appears when the link intensities representing molecular interactions are small at the initial condition of the evolutionary simulation, regardless of the rank of the goal matrix. Our dynamical system analysis clarifies the mechanisms underlying the emergence of the bow-tie structure. Further, we demonstrate that the increase in the input-output matrix reduces the width of the middle layer, resulting in the emergence of bow-tie architecture, even when evolution starts from large link intensities. Our data suggest that bow-tie architecture emerges as a side effect of evolution rather than as a result of evolutionary adaptation.

Self-Improvising Memory: A Perspective on Memories as Agential, Dynamically Reinterpreting Cognitive Glue

Many studies on memory emphasize the material substrate and mechanisms by which data can be stored and reliably read out. Here, I focus on complementary aspects: the need for agents to dynamically reinterpret and modify memories to suit their ever-changing selves and environment. Using examples from developmental biology, evolution, and synthetic bioengineering, in addition to neuroscience, I propose that a perspective on memory as preserving salience, not fidelity, is applicable to many phenomena on scales from cells to societies. Continuous commitment to creative, adaptive confabulation, from the molecular to the behavioral levels, is the answer to the persistence paradox as it applies to individuals and whole lineages. I also speculate that a substrate-independent, processual view of life and mind suggests that memories, as patterns in the excitable medium of cognitive systems, could be seen as active agents in the sense-making process. I explore a view of life as a diverse set of embodied perspectives-nested agents who interpret each other's and their own past messages and actions as best as they can (polycomputation). This synthesis suggests unifying symmetries across scales and disciplines, which is of relevance to research programs in Diverse Intelligence and the engineering of novel embodied minds.

Design patterns of biological cells

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

Robustness and complexity

When a system robustly corrects component-level errors, the direct pressure on component performance declines. Components become less reliable, maintain more genetic variability, or drift neutrally, creating new forms of complexity. Examples include the hourglass pattern of biological development and the hourglass architecture for robustly complex systems in engineering.

Biodiversity and Constrained Information Dynamics in Ecosystems: A Framework for Living Systems

The increase in ecosystem biodiversity can be perceived as one of the universal processes converting energy into information across a wide range of living systems. This study delves into the dynamics of living systems, highlighting the distinction between ex post adaptation, typically associated with natural selection, and its proactive counterpart, ex ante adaptability. Through coalescence experiments using synthetic ecosystems, we (i) quantified ecosystem stability, (ii) identified correlations between some biodiversity indexes and the stability, (iii) proposed a mechanism for increasing biodiversity through moderate inter-ecosystem interactions, and (iv) inferred that the information carrier of ecosystems is species composition, or merged genomic information. Additionally, it was suggested that (v) changes in ecosystems are constrained to a low-dimensional state space, with three distinct alteration trajectories-fluctuations, rapid environmental responses, and long-term changes-converging into this state space in common. These findings suggest that daily fluctuations may predict broader ecosystem changes. Our experimental insights, coupled with an exploration of living systems' information dynamics from an ecosystem perspective, enhance our predictive capabilities for natural ecosystem behavior, providing a universal framework for understanding a broad spectrum of living systems.

Drugging evolution of antibiotic resistance at a regulatory network hub

Evolution of antibiotic resistance is a world health crisis, fueled by new mutations. Drugs to slow mutagenesis could, as cotherapies, prolong the shelf-life of antibiotics, yet evolution-slowing drugs and drug targets have been underexplored and ineffective. Here, we used a network-based strategy to identify drugs that block hubs of fluoroquinolone antibiotic-induced mutagenesis. We identify a U.S. Food and Drug Administration- and European Medicines Agency-approved drug, dequalinium chloride (DEQ), that inhibits activation of the Escherichia coli general stress response, which promotes ciprofloxacin-induced (stress-induced) mutagenic DNA break repair. We uncover the step in the pathway inhibited: activation of the upstream "stringent" starvation stress response, and find that DEQ slows evolution without favoring proliferation of DEQ-resistant mutants. Furthermore, we demonstrate stress-induced mutagenesis during mouse infections and its inhibition by DEQ. Our work provides a proof-of-concept strategy for drugs to slow evolution in bacteria and generally.

Transcription factor localization dynamics and DNA binding drive distinct promoter interpretations

Environmental information may be encoded in the temporal dynamics of transcription factor (TF) activation and subsequently decoded by gene promoters to enact stimulus-specific gene expression programs. Previous studies of this behavior focused on the encoding and decoding of information in TF nuclear localization dynamics, yet cells control the activity of TFs in myriad ways, including by regulating their ability to bind DNA. Here, we use light-controlled mutants of the yeast TF Msn2 as a model system to investigate how promoter decoding of TF localization dynamics is affected by changes in the ability of the TF to bind DNA. We find that yeast promoters directly decode the light-controlled localization dynamics of Msn2 and that the effects of changing Msn2 affinity on that decoding behavior are highly promoter dependent, illustrating how cells could regulate TF localization dynamics and DNA binding in concert for improved control of gene expression.

Frank Beach Award Winner: The centrality of the hypothalamic-pituitary-adrenal axis in dealing with environmental change across temporal scales

Understanding if and how individuals and populations cope with environmental change is an enduring question in evolutionary ecology that has renewed importance given the pace of change in the Anthropocene. Two evolutionary strategies of coping with environmental change may be particularly important in rapidly changing environments: adaptive phenotypic plasticity and/or bet hedging. Adaptive plasticity could enable individuals to match their phenotypes to the expected environment if there is an accurate cue predicting the selective environment. Diversifying bet hedging involves the production of seemingly random phenotypes in an unpredictable environment, some of which may be adaptive. Here, I review the central role of the hypothalamic-pituitary-adrenal (HPA) axis and glucocorticoids (GCs) in enabling vertebrates to cope with environmental change through adaptive plasticity and bet hedging. I first describe how the HPA axis mediates three types of adaptive plasticity to cope with environmental change (evasion, tolerance, recovery) over short timescales (e.g., 1-3 generations) before discussing how the implications of GCs on phenotype integration may depend upon the timescale under consideration. GCs can promote adaptive phenotypic integration, but their effects on phenotypic co-variation could also limit the dimensions of phenotypic space explored by animals over longer timescales. Finally, I discuss how organismal responses to environmental stressors can act as a bet hedging mechanism and therefore enhance evolvability by increasing genetic or phenotypic variability or reducing patterns of genetic and phenotypic co-variance. Together, this emphasizes the crucial role of the HPA axis in understanding fundamental questions in evolutionary ecology.

FinO/ProQ-family proteins: an evolutionary perspective

RNA-binding proteins are key actors of post-transcriptional networks. Almost exclusively studied in the light of their interactions with RNA ligands and the associated functional events, they are still poorly understood as evolutionary units. In this review, we discuss the FinO/ProQ family of bacterial RNA chaperones, how they evolve and spread across bacterial populations and what properties and opportunities they provide to their host cells. We reflect on major conserved and divergent themes within the family, trying to understand how the same ancestral RNA-binding fold, augmented with additional structural elements, could yield either highly specialised proteins or, on the contrary, globally acting regulatory hubs with a pervasive impact on gene expression. We also consider dominant convergent evolutionary trends that shaped their RNA chaperone activity and recurrently implicated the FinO/ProQ-like proteins in bacterial DNA metabolism, translation and virulence. Finally, we offer a new perspective in which FinO/ProQ-family regulators emerge as active evolutionary players with both negative and positive roles, significantly impacting the evolutionary modes and trajectories of their bacterial hosts.

The protein corona from nanomedicine to environmental science

The protein corona spontaneously develops and evolves on the surface of nanoscale materials when they are exposed to biological environments, altering their physiochemical properties and affecting their subsequent interactions with biosystems. In this Review, we provide an overview of the current state of protein corona research in nanomedicine. We next discuss remaining challenges in the research methodology and characterization of the protein corona that slow the development of nanoparticle therapeutics and diagnostics, and we address how artificial intelligence can advance protein corona research as a complement to experimental research efforts. We then review emerging opportunities provided by the protein corona to address major issues in healthcare and environmental sciences. This Review details how mechanistic insights into nanoparticle protein corona formation can broadly address unmet clinical and environmental needs, as well as enhance the safety and efficacy of nanobiotechnology products.

Bow-tie architectures in biological and artificial neural networks: Implications for network evolution and assay design

Modern artificial neural networks (ANNs) have long been designed on foundations of mathematics as opposed to their original foundations of biomimicry. However, the structure and function of these modern ANNs are often analogous to real-life biological networks. We propose that the ubiquitous information-theoretic principles underlying the development of ANNs are similar to the principles guiding the macro-evolution of biological networks and that insights gained from one field can be applied to the other. We generate hypotheses on the bow-tie network structure of the Janus kinase - signal transducers and activators of transcription (JAK-STAT) pathway, additionally informed by the evolutionary considerations, and carry out ANN simulation experiments to demonstrate that an increase in the network's input and output complexity does not necessarily require a more complex intermediate layer. This observation should guide novel biomarker discovery-namely, to prioritize sections of the biological networks in which information is most compressed as opposed to biomarkers representing the periphery of the network.

Efficient representations of binarized health deficit data: the frailty index and beyond

We investigated efficient representations of binarized health deficit data using the 2001-2002 National Health and Nutrition Examination Survey (NHANES). We compared the abilities of features to compress health deficit data and to predict adverse outcomes. We used principal component analysis (PCA) and several other dimensionality reduction techniques, together with several varieties of the frailty index (FI). We observed that the FI approximates the first - primary - component obtained by PCA and other compression techniques. Most adverse outcomes were well predicted using only the FI. While the FI is therefore a useful technique for compressing binary deficits into a single variable, additional dimensions were needed for high-fidelity compression of health deficit data. Moreover, some outcomes - including inflammation and metabolic dysfunction - showed high-dimensional behaviour. We generally found that clinical data were easier to compress than lab data. Our results help to explain the success of the FI as a simple dimensionality reduction technique for binary health data. We demonstrate how PCA extends the FI, providing additional health information, and allows us to explore system dimensionality and complexity. PCA is a promising tool for determining and exploring collective health features from collections of binarized biomarkers.

Synthetic Biology Meets Machine Learning

This chapter outlines the myriad applications of machine learning (ML) in synthetic biology, specifically in engineering cell and protein activity, and metabolic pathways. Though by no means comprehensive, the chapter highlights several prominent computational tools applied in the field and their potential use cases. The examples detailed reinforce how ML algorithms can enhance synthetic biology research by providing data-driven insights into the behavior of living systems, even without detailed knowledge of their underlying mechanisms. By doing so, ML promises to increase the efficiency of research projects by modeling hypotheses in silico that can then be tested through experiments. While challenges related to training dataset generation and computational costs remain, ongoing improvements in ML tools are paving the way for smarter and more streamlined synthetic biology workflows that can be readily employed to address grand challenges across manufacturing, medicine, engineering, agriculture, and beyond.

Biomarkers of mitochondrial dysfunction and inflammaging in older adults and blood pressure variability

Most physiopathological mechanisms underlying blood pressure variability (BPV) are implicated in aging. Vascular aging is associated with chronic low-grade inflammation occurring in late life, known as "inflammaging" and the hallmark "mitochondrial dysfunction" due to age-related stress. We aimed to determine whether plasma levels of the pleiotropic stress-related mitokine growth/differentiation factor 15 (GDF-15) and two inflammatory biomarkers, interleukin 6 (IL-6) and tumor necrosis factor receptor 1 (TNFR-1), are associated with visit-to-visit BPV in a population of community-dwelling older adults. The study population consisted of 1096 community-dwelling participants [median age 75 (72-78) years; 699 females, 63.7%] aged ≥ 70 years from the MAPT study. Plasma blood sample was collected 12 months after enrolment and BP was assessed up to seven times over a 4-year period. Systolic (SBPV) and diastolic BPV (DBPV) were determined through several indicators taking into account BP change over time, the order of measurements and formulas independent of mean BP levels. Higher values of GDF-15 were significantly associated with increased SBPV (all indicators) after adjustment for relevant covariates [adjusted 1-SD increase in GDF-15: β (SE) = 0.07 (0.04), p < 0.044, for coefficient of variation%]. GDF-15 levels were not associated with DBPV. No significant associations were found between IL-6 and BPV, whereas TNFR1 was only partially related to DBPV. Unlike inflammation biomarkers, higher GDF-15 levels were associated with greater SBPV. Our findings support the age-related process of mitochondrial dysfunction underlying BP instability, suggesting that BPV might be a potential marker of aging.

Inflammaging: Implications in Sarcopenia

In a world in which life expectancy is increasing, understanding and promoting healthy aging becomes a contemporary demand. In the elderly, a sterile, chronic and low-grade systemic inflammation known as "inflammaging" is linked with many age-associated diseases. Considering sarcopenia as a loss of strength and mass of skeletal muscle related to aging, correlations between these two terms have been proposed. Better knowledge of the immune system players in skeletal muscle would help to elucidate their implications in sarcopenia. Characterizing the activators of damage sensors and the downstream effectors explains the inference with skeletal muscle performance. Sarcopenia has also been linked to chronic diseases such as diabetes, metabolic syndrome and obesity. Implications of inflammatory signals from these diseases negatively affect skeletal muscle. Autophagic mechanisms are closely related with the inflammasome, as autophagy eliminates stress signaling sent by damage organelles, but also acts with an immunomodulatory function affecting immune cells and cytokine release. The use of melatonin, an antioxidant, ROS scavenger and immune and autophagy modulator, or senotherapeutic compounds targeting senescent cells could represent strategies to counteract inflammation. This review aims to present the many factors regulating skeletal muscle inflammaging and their major implications in order to understand the molecular mechanisms involved in sarcopenia.

Layered feedback control overcomes performance trade-off in synthetic biomolecular networks

Layered feedback is an optimization strategy in feedback control designs widely used in engineering. Control theory suggests that layering multiple feedbacks could overcome the robustness-speed performance trade-off limit. In natural biological networks, genes are often regulated in layers to adapt to environmental perturbations. It is hypothesized layering architecture could also overcome the robustness-speed performance trade-off in genetic networks. In this work, we validate this hypothesis with a synthetic biomolecular network in living E. coli cells. We start with system dynamics analysis using models of various complexities to guide the design of a layered control architecture in living cells. Experimentally, we interrogate system dynamics under three groups of perturbations. We consistently observe that the layered control improves system performance in the robustness-speed domain. This work confirms that layered control could be adopted in synthetic biomolecular networks for performance optimization. It also provides insights into understanding genetic feedback control architectures in nature.

Localization of signaling receptors maximizes cellular information acquisition in spatially structured natural environments

Cells in natural environments, such as tissue or soil, sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions, sculpted by processes such as fluid flow and substrate adhesion. In this work, we show that spatial sensing and navigation can be optimized by adapting the spatial organization of signaling pathways to the spatial structure of the environment. We develop an information-theoretic framework for computing the optimal spatial organization of a sensing system for a given signaling environment. We find that receptor localization previously observed in cells maximizes information acquisition in simulated natural contexts, including tissue and soil. Specifically, information acquisition is maximized when receptors form localized patches at regions of maximal ligand concentration. Receptor localization extends naturally to produce a dynamic protocol for continuously redistributing signaling receptors, which when implemented using simple feedback, boosts cell navigation efficiency by 30-fold.

A complex systems approach to aging biology

Having made substantial progress understanding molecules, cells, genes and pathways, aging biology research is now moving toward integration of these parts, attempting to understand how their joint dynamics may contribute to aging. Such a shift of perspective requires the adoption of a formal complex systems framework, a transition being facilitated by large-scale data collection and new analytical tools. Here, we provide a theoretical framework to orient researchers around key concepts for this transition, notably emergence, interaction networks and resilience. Drawing on evolutionary theory, network theory and principles of homeostasis, we propose that organismal function is accomplished by the integration of regulatory mechanisms at multiple hierarchical scales, and that the disruption of this ensemble causes the phenotypic and functional manifestations of aging. We present key examples at scales ranging from sub-organismal biology to clinical geriatrics, outlining how this approach can potentially enrich our understanding of aging.

GDF15, an emerging key player in human aging

Growth differentiation factor 15 (GDF15) is recently emerging not only as a stress-related mitokine, but also as a key player in the aging process, being one of the most up-regulated protein with age and associated with a variety of age-related diseases (ARDs). Many data indicate that GDF15 has protective roles in several tissues during different stress and aging, thus playing a beneficial role in apparent contrast with the observed association with many ARDs. A possible detrimental role for this protein is then hypothesized to emerge with age. Therefore, GDF15 can be considered as a pleiotropic factor with beneficial activities that can turn detrimental in old age possibly when it is chronically elevated. In this review, we summarize the current knowledge on the biology of GDF15 during aging. We also propose GDF15 as a part of a dormancy program, where it may play a role as a mediator of defense processes aimed to protect from inflammatory damage and other stresses, according to the life history theory.

Gene regulatory network inference in long-lived C. elegans reveals modular properties that are predictive of novel aging genes

We design a “wisdom-of-the-crowds” GRN inference pipeline and couple it to complex network analysis to understand the organizational principles governing gene regulation in long-lived glp-1/Notch Caenorhabditis elegans. The GRN has three layers (input, core, and output) and is topologically equivalent to bow-tie/hourglass structures prevalent among metabolic networks. To assess the functional importance of structural layers, we screened 80% of regulators and discovered 50 new aging genes, 86% with human orthologues. Genes essential for longevity—including ones involved in insulin-like signaling (ILS)—are at the core, indicating that GRN's structure is predictive of functionality. We used in vivo reporters and a novel functional network covering 5,497 genetic interactions to make mechanistic predictions. We used genetic epistasis to test some of these predictions, uncovering a novel transcriptional regulator, sup-37, that works alongside DAF-16/FOXO. We present a framework with predictive power that can accelerate discovery in C. elegans and potentially humans.

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Gene-regulatory inference provides global network of long-lived animals

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The large-scale topology of the network has an hourglass structure

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Membership to the core of the hourglass is a good predictor of functionality

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Discovered 50 novel aging genes, including sup-37, a DAF-16 dependent gene

The Danaid Theory of Aging

The classical evolutionary theories of aging suggest that aging evolves due to insufficient selective pressure against it. In these theories, declining selection pressure with age leads to aging through genes or resource allocations, implying that aging could potentially be stalled were genes, resource allocation, or selection pressure somewhat different. While these classical evolutionary theories are undeniably part of a description of the evolution of aging, they do not explain the diversity of aging patterns, and they do not constitute the only possible evolutionary explanation. Without denying selection pressure a role in the evolution of aging, we argue that the origin and diversity of aging should also be sought in the nature and evolution of organisms that are, from their very physiological make up, unmaintainable. Drawing on advances in developmental biology, genetics, biochemistry, and complex systems theory since the classical theories emerged, we propose a fresh evolutionary-mechanistic theory of aging, the Danaid theory. We argue that, in complex forms of life like humans, various restrictions on maintenance and repair may be inherent, and we show how such restrictions are laid out during development. We further argue that there is systematic variation in these constraints across taxa, and that this is a crucial factor determining variation in aging and lifespan across the tree of life. Accordingly, the core challenge for the field going forward is to map and understand the mosaic of constraints, trade-offs, chance events, and selective pressures that shape aging in diverse ways across diverse taxa.

Feedback regulation and coordination of the main metabolism for bacterial growth and metabolic engineering for amino acid fermentation

Living organisms such as bacteria are often exposed to continuous changes in the nutrient availability in nature. Therefore, bacteria must constantly monitor the environmental condition, and adjust the metabolism quickly adapting to the change in the growth condition. For this, bacteria must orchestrate (coordinate and integrate) the complex and dynamically changing information on the environmental condition. In particular, the central carbon metabolism (CCM), monomer synthesis, and macromolecular synthesis must be coordinately regulated for the efficient growth. It is a grand challenge in bioscience, biotechnology, and synthetic biology to understand how living organisms coordinate the metabolic regulation systems. Here, we consider the integrated sensing of carbon sources by the phosphotransferase system (PTS), and the feed-forward/feedback regulation systems incorporated in the CCM in relation to the pool sizes of flux-sensing metabolites and αketoacids. We also consider the metabolic regulation of amino acid biosynthesis (as well as purine and pyrimidine biosyntheses) paying attention to the feedback control systems consisting of (fast) enzyme level regulation with (slow) transcriptional regulation. The metabolic engineering for the efficient amino acid production by bacteria such as Escherichia coli and Corynebacterium glutamicum is also discussed (in relation to the regulation mechanisms). The amino acid synthesis is important for determining the rate of ribosome biosynthesis. Thus, the growth rate control (growth law) is further discussed on the relationship between (p)ppGpp level and the ribosomal protein synthesis.

Identification of metabolomic profile related to adult Fontan pathophysiology

Background

Metabolic disorders are important pathophysiologies that can cause multiple organ dysfunction and worsen prognosis in Fontan patients. This study aimed to comprehensively evaluate the metabolomic profile of adult Fontan patients and characterize its pathophysiology in relation to 2 control groups.

Methods and Results

We performed metabolomic analysis of 31 plasma samples using capillary electrophoresis time-of-flight mass spectrometry. This observational cross-sectional study compared plasma metabolites of 14 heterogeneous adult Fontan patients with those of control groups, including 9 patients with congenital heart disease after biventricular repair and 8 normal healthy controls. Fontan patients exhibited significant differences in intermediate metabolite concentrations related to glycolysis, the tricarboxylic acid (TCA) cycle, and the urea cycle. The plasma concentrations of lactic acid, 2-oxoglutarate, isocitric acid, malic acid, cis-aconitic acid, arginine, citrulline, and the ratio of ornithine/citrulline showed significantly differences among the groups. Multiple logistic regression analysis with a stepwise selection-elimination method identified 2-oxoglutaric acid (odds ratio [OR] 1.98, 95% confidence interval [CI] 1.05–3.76) and cis-aconitic acid (OR 2.69, 95% CI 1.04–6.99) as independently associated with Fontan patients. After adjustment for the covariates of age and gender, 2-oxoglutaric acid (OR 1.97, 95% CI 0.98–3.93) and cis-aconitic acid (OR 3.88, 95% CI 0.99–15.2) showed remarkable relationships with Fontan patients.

Conclusions

The present findings suggest that abnormalities in the TCA cycle and amino acid metabolism are distinguishing features in the pathophysiology of Fontan patients. Future metabolomic studies will assist in developing biomarkers for the early prediction of “silent” Fontan pathophysiologies.

Global connectivity in genome-scale metabolic networks revealed by comprehensive FBA-based pathway analysis

Background

Graph-based analysis (GBA) of genome-scale metabolic networks has revealed system-level structures such as the bow-tie connectivity that describes the overall mass flow in a network. However, many pathways obtained by GBA are biologically impossible, making it difficult to study how the global structures affect the biological functions of a network. New method that can calculate the biologically relevant pathways is desirable for structural analysis of metabolic networks.

Results

Here, we present a new method to determine the bow-tie connectivity structure by calculating possible pathways between any pairs of metabolites in the metabolic network using a flux balance analysis (FBA) approach to ensure that the obtained pathways are biologically relevant. We tested this method with 15 selected high-quality genome-scale metabolic models from BiGG database. The results confirmed the key roles of central metabolites in network connectivity, locating in the core part of the bow-tie structure, the giant strongly connected component (GSC). However, the sizes of GSCs revealed by GBA are significantly larger than those by FBA approach. A great number of metabolites in the GSC from GBA actually cannot be produced from or converted to other metabolites through a mass balanced pathway and thus should not be in GSC but in other subsets of the bow-tie structure. In contrast, the bow-tie structural classification of metabolites obtained by FBA is more biologically relevant and suitable for the study of the structure-function relationships of genome scale metabolic networks.

Conclusions

The FBA based pathway calculation improve the biologically relevant classification of metabolites in the bow-tie connectivity structure of the metabolic network, taking us one step further toward understanding how such system-level structures impact the biological functions of an organism.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12866-021-02357-1.

An orthogonal metabolic framework for one-carbon utilization

Metabolic engineering often entails concurrent engineering of substrate utilization, central metabolism and product synthesis pathways, inevitably creating interdependency with native metabolism. Here we report an alternative approach using synthetic pathways for C1 bioconversion that generate multicarbon products directly from C1 units and hence are orthogonal to the host metabolic network. The engineered pathways are based on formyl-CoA elongation (FORCE) reactions catalysed by the enzyme 2-hydroxyacyl-CoA lyase. We use thermodynamic and stoichiometric analyses to evaluate FORCE pathway variants, including aldose elongation, α-reduction and aldehyde elongation. Promising variants were prototyped in vitro and in vivo using the non-methylotrophic bacterium Escherichia coli. We demonstrate the conversion of formate, formaldehyde and methanol into various products including glycolate, ethylene glycol, ethanol and glycerate. FORCE pathways also have the potential to be integrated with the host metabolism for synthetic methylotrophy by the production of native growth substrates as demonstrated in a two-strain co-culture system.

Are There Biomimetic Lessons from Genetic Regulatory Networks for Developing a Lunar Industrial Ecology?

We examine the prospect for employing a bio-inspired architecture for a lunar industrial ecology based on genetic regulatory networks. The lunar industrial ecology resembles a metabolic system in that it comprises multiple chemical processes interlinked through waste recycling. Initially, we examine lessons from factory organisation which have evolved into a bio-inspired concept, the reconfigurable holonic architecture. We then examine genetic regulatory networks and their application in the biological cell cycle. There are numerous subtleties that would be challenging to implement in a lunar industrial ecology but much of the essence of biological circuitry (as implemented in synthetic biology, for example) is captured by traditional electrical engineering design with emphasis on feedforward and feedback loops to implement robustness.

Bow-tie architecture of gene regulatory networks in species of varying complexity

The gene regulatory network (GRN) architecture plays a key role in explaining the biological differences between species. We aim to understand species differences in terms of some universally present dynamical properties of their gene regulatory systems. A network architectural feature associated with controlling system-level dynamical properties is the bow-tie, identified by a strongly connected subnetwork, the core layer, between two sets of nodes, the in and the out layers. Though a bow-tie architecture has been observed in many networks, its existence has not been extensively investigated in GRNs of species of widely varying biological complexity. We analyse publicly available GRNs of several well-studied species from prokaryotes to unicellular eukaryotes to multicellular organisms. In their GRNs, we find the existence of a bow-tie architecture with a distinct largest strongly connected core layer. We show that the bow-tie architecture is a characteristic feature of GRNs. We observe an increasing trend in the relative core size with species complexity. Using studied relationships of the core size with dynamical properties like robustness and fragility, flexibility, criticality, controllability and evolvability, we hypothesize how these regulatory system properties have emerged differently with biological complexity, based on the observed differences of the GRN bow-tie architectures.

Utilizing the Heterogeneity of Clinical Data for Model Refinement and Rule Discovery Through the Application of Genetic Algorithms to Calibrate a High-Dimensional Agent-Based Model of Systemic Inflammation

Introduction: Accounting for biological heterogeneity represents one of the greatest challenges in biomedical research. Dynamic computational and mathematical models can be used to enhance the study and understanding of biological systems, but traditional methods for calibration and validation commonly do not account for the heterogeneity of biological data, which may result in overfitting and brittleness of these models. Herein we propose a machine learning approach that utilizes genetic algorithms (GAs) to calibrate and refine an agent-based model (ABM) of acute systemic inflammation, with a focus on accounting for the heterogeneity seen in a clinical data set, thereby avoiding overfitting and increasing the robustness and potential generalizability of the underlying simulation model. Methods: Agent-based modeling is a frequently used modeling method for multi-scale mechanistic modeling. However, the same properties that make ABMs well suited to representing biological systems also present significant challenges with respect to their construction and calibration, particularly with respect to the selection of potential mechanistic rules and the large number of associated free parameters. We have proposed that machine learning approaches (such as GAs) can be used to more effectively and efficiently deal with rule selection and parameter space characterization; the current work applies GAs to the challenge of calibrating a complex ABM to a specific data set, while preserving biological heterogeneity reflected in the range and variance of the data. This project uses a GA to augment the rule-set for a previously validated ABM of acute systemic inflammation, the Innate Immune Response ABM (IIRABM) to clinical time series data of systemic cytokine levels from a population of burn patients. The genome for the GA is a vector generated from the IIRABM's Model Rule Matrix (MRM), which is a matrix representation of not only the constants/parameters associated with the IIRABM's cytokine interaction rules, but also the existence of rules themselves. Capturing heterogeneity is accomplished by a fitness function that incorporates the sample value range ("error bars") of the clinical data. Results: The GA-enabled parameter space exploration resulted in a set of putative MRM rules and associated parameterizations which closely match the cytokine time course data used to design the fitness function. The number of non-zero elements in the MRM increases significantly as the model parameterizations evolve toward a fitness function minimum, transitioning from a sparse to a dense matrix. This results in a model structure that more closely resembles (at a superficial level) the structure of data generated by a standard differential gene expression experimental study. Conclusion: We present an HPC-enabled machine learning/evolutionary computing approach to calibrate a complex ABM to complex clinical data while preserving biological heterogeneity. The integration of machine learning, HPC, and multi-scale mechanistic modeling provides a pathway forward to more effectively representing the heterogeneity of clinical populations and their data.

Why Do Big Data and Machine Learning Entail the Fractional Dynamics?

Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional calculus (FC) is based on fractional-order thinking (FOT) and has been shown to help us to understand complex systems better, improve the processing of complex signals, enhance the control of complex systems, increase the performance of optimization, and even extend the enabling of the potential for creativity. In this article, the authors discuss the fractional dynamics, FOT and rich fractional stochastic models. First, the use of fractional dynamics in big data analytics for quantifying big data variability stemming from the generation of complex systems is justified. Second, we show why fractional dynamics is needed in machine learning and optimal randomness when asking: "is there a more optimal way to optimize?". Third, an optimal randomness case study for a stochastic configuration network (SCN) machine-learning method with heavy-tailed distributions is discussed. Finally, views on big data and (physics-informed) machine learning with fractional dynamics for future research are presented with concluding remarks.

Robust Physiological Metrics From Sparsely Sampled Networks

Physiological and biochemical networks are highly complex, involving thousands of nodes as well as a hierarchical structure. True network structure is also rarely known. This presents major challenges for applying classical network theory to these networks. However, complex systems generally share the property of having a diffuse or distributed signal. Accordingly, we should predict that system state can be robustly estimated with sparse sampling, and with limited knowledge of true network structure. In this review, we summarize recent findings from several methodologies to estimate system state via a limited sample of biomarkers, notably Mahalanobis distance, principal components analysis, and cluster analysis. While statistically simple, these methods allow novel characterizations of system state when applied judiciously. Broadly, system state can often be estimated even from random samples of biomarkers. Furthermore, appropriate methods can detect emergent underlying physiological structure from this sparse data. We propose that approaches such as these are a powerful tool to understand physiology, and could lead to a new understanding and mapping of the functional implications of biological variation.

Emergence and propagation of epistasis in metabolic networks

Epistasis is often used to probe functional relationships between genes, and it plays an important role in evolution. However, we lack theory to understand how functional relationships at the molecular level translate into epistasis at the level of whole-organism phenotypes, such as fitness. Here, I derive two rules for how epistasis between mutations with small effects propagates from lower- to higher-level phenotypes in a hierarchical metabolic network with first-order kinetics and how such epistasis depends on topology. Most importantly, weak epistasis at a lower level may be distorted as it propagates to higher levels. Computational analyses show that epistasis in more realistic models likely follows similar, albeit more complex, patterns. These results suggest that pairwise inter-gene epistasis should be common, and it should generically depend on the genetic background and environment. Furthermore, the epistasis coefficients measured for high-level phenotypes may not be sufficient to fully infer the underlying functional relationships.

How higher goals are constructed and collapse under stress: A hierarchical Bayesian control systems perspective

In this paper, we show that organisms can be modeled as hierarchical Bayesian control systems with small world and information bottleneck (bow-tie) network structure. Such systems combine hierarchical perception with hierarchical goal setting and hierarchical action control. We argue that hierarchical Bayesian control systems produce deep hierarchies of goal states, from which it follows that organisms must have some form of 'highest goals'. For all organisms, these involve internal (self) models, external (social) models and overarching (normative) models. We show that goal hierarchies tend to decompose in a top-down manner under severe and prolonged levels of stress. This produces behavior that favors short-term and self-referential goals over long term, social and/or normative goals. The collapse of goal hierarchies is universally accompanied by an increase in entropy (disorder) in control systems that can serve as an early warning sign for tipping points (disease or death of the organism). In humans, learning goal hierarchies corresponds to personality development (maturation). The failure of goal hierarchies to mature properly corresponds to personality deficits. A top-down collapse of such hierarchies under stress is identified as a common factor in all forms of episodic mental disorders (psychopathology). The paper concludes by discussing ways of testing these hypotheses empirically.

Genomic Variation, Evolvability, and the Paradox of Mental Illness

Twentieth-century genetics was hard put to explain the irregular behavior of neuropsychiatric disorders. Autism and schizophrenia defy a principle of natural selection; they are highly heritable but associated with low reproductive success. Nevertheless, they persist. The genetic origins of such conditions are confounded by the problem of variable expression, that is, when a given genetic aberration can lead to any one of several distinct disorders. Also, autism and schizophrenia occur on a spectrum of severity, from mild and subclinical cases to the overt and disabling. Such irregularities reflect the problem of missing heritability; although hundreds of genes may be associated with autism or schizophrenia, together they account for only a small proportion of cases. Techniques for higher resolution, genomewide analysis have begun to illuminate the irregular and unpredictable behavior of the human genome. Thus, the origins of neuropsychiatric disorders in particular and complex disease in general have been illuminated. The human genome is characterized by a high degree of structural and behavioral variability: DNA content variation, epistasis, stochasticity in gene expression, and epigenetic changes. These elements have grown more complex as evolution scaled the phylogenetic tree. They are especially pertinent to brain development and function. Genomic variability is a window on the origins of complex disease, neuropsychiatric disorders, and neurodevelopmental disorders in particular. Genomic variability, as it happens, is also the fuel of evolvability. The genomic events that presided over the evolution of the primate and hominid lineages are over-represented in patients with autism and schizophrenia, as well as intellectual disability and epilepsy. That the special qualities of the human genome that drove evolution might, in some way, contribute to neuropsychiatric disorders is a matter of no little interest.

Environmental flexibility does not explain metabolic robustness

Cells show remarkable resilience against genetic and environmental perturbations. However, its evolutionary origin remains obscure. In order to leverage methods of systems biology for examining cellular robustness, a computationally accessible way of quantification is needed. Here, we present an unbiased metric of structural robustness in genome-scale metabolic models based on concepts prevalent in reliability engineering and fault analysis. The probability of failure (PoF) is defined as the (weighted) portion of all possible combinations of loss-of-function mutations that disable network functionality. It can be exactly determined if all essential reactions, synthetic lethal pairs of reactions, synthetic lethal triplets of reactions etc. are known. In theory, these minimal cut sets (MCSs) can be calculated for any network, but for large models the problem remains computationally intractable. Herein, we demonstrate that even at the genome scale only the lowest-cardinality MCSs are required to efficiently approximate the PoF with reasonable accuracy. Building on an improved theoretical understanding, we analysed the robustness of 489 E. coli, Shigella, Salmonella, and fungal genome-scale metabolic models (GSMMs). In contrast to the popular "congruence theory", which explains the origin of genetic robustness as a byproduct of selection for environmental flexibility, we found no correlation between network robustness and the diversity of growth-supporting environments. On the contrary, our analysis indicates that amino acid synthesis rather than carbon metabolism dominates metabolic robustness.

The sustainability and the survivability of Kyoto's traditional craft industry revealed from supplier-customer network

Due to the changes in consumer demand and generational transformations, Kyoto’s traditional craft industry has suffered substantial revenue losses in recent years. This research aimed to characterize Kyoto’s traditional craft industry by analyzing the supplier-customer network involving individual firms within the Kyoto region. In the process, we clarify the community structure, key firms, network topological characteristics, bow-tie structure, robustness, the vulnerability of the supplier-customer network as crucial factors for sustainable growth. The community and bow-tie structure analysis became clear that the traditional craft industry continues to occupy an important position in Kyoto’s industrial network. Furthermore, we clarify the relationship between modern and traditional craft industries’ network characteristics and their relative profitability and productivity. It became evident that the traditional craft industry has a different network structure from the modern consumer games and electric machinery industries. The modern industries have the strongly coupled component, and the attendant firms there create high value-added and play a significant role in driving the entire industry, while more traditional craft industries, such as the Nishijin silk fabrics and Kyoto doll industries, do not have this strongly coupled component. Moreover, the traditional crafts industry does not have a central firm or a dense network for integrating information, which is presumed to be a factor in the decline of the traditional craft industry.

How to Build a Biological Machine Using Engineering Materials and Methods

We present work in 3D printing electric motors from basic materials as the key to building a self-replicating machine to colonise the Moon. First, we explore the nature of the biological realm to ascertain its essence, particularly in relation to the origin of life when the inanimate became animate. We take an expansive view of this to ascertain parallels between the biological and the manufactured worlds. Life must have emerged from the available raw material on Earth and, similarly, a self-replicating machine must exploit and leverage the available resources on the Moon. We then examine these lessons to explore the construction of a self-replicating machine using a universal constructor. It is through the universal constructor that the actuator emerges as critical. We propose that 3D printing constitutes an analogue of the biological ribosome and that 3D printing may constitute a universal construction mechanism. Following a description of our progress in 3D printing motors, we suggest that this engineering effort can inform biology, that motors are a key facet of living organisms and illustrate the importance of motors in biology viewed from the perspective of engineering (in the Feynman spirit of “what I cannot create, I cannot understand”).

Complete Topological Mapping of a Cellular Protein Interactome Reveals Bow-Tie Motifs as Ubiquitous Connectors of Protein Complexes

The network topology of a protein interactome is shaped by the function of each protein, making it a resource of functional knowledge in tissues and in single cells. Today, this resource is underused, as complete network topology characterization has proved difficult for large protein interactomes. We apply a matrix visualization and decoding approach to a physical protein interactome of a dendritic cell, thereby characterizing its topology with no prior assumptions of structure. We discover 294 proteins, each forming topological motifs called "bow-ties" that tie together the majority of observed protein complexes. The central proteins of these bow-ties have unique network properties, display multifunctional capabilities, are enriched for essential proteins, and are widely expressed in other cells and tissues. Collectively, the bow-tie motifs are a pervasive and previously unnoted topological trend in cellular interactomes. As such, these results provide fundamental knowledge on how intracellular protein connectivity is organized and operates.

Structural and functional analyses of microbial metabolic networks reveal novel insights into genome-scale metabolic fluxes

We present here an integrated analysis of structures and functions of genome-scale metabolic networks of 17 microorganisms. Our structural analyses of these networks revealed that the node degree of each network, represented as a (simplified) reaction network, follows a power-law distribution, and the clustering coefficient of each network has a positive correlation with the corresponding node degree. Together, these properties imply that each network has exactly one large and densely connected subnetwork or core. Further analyses revealed that each network consists of three functionally distinct subnetworks: (i) a core, consisting of a large number of directed reaction cycles of enzymes for interconversions among intermediate metabolites; (ii) a catabolic module, with a largely layered structure consisting of mostly catabolic enzymes; (iii) an anabolic module with a similar structure consisting of virtually all anabolic genes; and (iv) the three subnetworks cover on average ∼56, ∼31 and ∼13% of a network's nodes across the 17 networks, respectively. Functional analyses suggest: (1) cellular metabolic fluxes generally go from the catabolic module to the core for substantial interconversions, then the flux directions to anabolic module appear to be determined by input nutrient levels as well as a set of precursors needed for macromolecule syntheses; and (2) enzymes in each subnetwork have characteristic ranges of kinetic parameters, suggesting optimized metabolic and regulatory relationships among the three subnetworks.

Division of labour promotes the spread of information in colony emigrations by the ant Temnothorax rugatulus

The fitness of group-living animals often depends on how well members share information needed for collective decision-making. Theoretical studies have shown that collective choices can emerge in a homogeneous group of individuals following identical rules, but real animals show much evidence for heterogeneity in the degree and nature of their contribution to group decisions. In social insects, for example, the transmission and processing of information is influenced by a well-organized division of labour. Studies that accurately quantify how this behavioural heterogeneity affects the spread of information among group members are still lacking. In this paper, we look at nest choices during colony emigrations of the ant Temnothorax rugatulus and quantify the degree of behavioural heterogeneity of workers. Using clustering methods and network analysis, we identify and characterize four behavioural castes of workers-primary, secondary, passive and wandering-covering distinct roles in the spread of information during an emigration. This detailed characterization of the contribution of each worker can improve models of collective decision-making in this species and promises a deeper understanding of behavioural variation at the colony level.

The hourglass organization of the Caenorhabditis elegans connectome

We approach the C. elegans connectome as an information processing network that receives input from about 90 sensory neurons, processes that information through a highly recurrent network of about 80 interneurons, and it produces a coordinated output from about 120 motor neurons that control the nematode's muscles. We focus on the feedforward flow of information from sensory neurons to motor neurons, and apply a recently developed network analysis framework referred to as the "hourglass effect". The analysis reveals that this feedforward flow traverses a small core ("hourglass waist") that consists of 10-15 interneurons. These are mostly the same interneurons that were previously shown (using a different analytical approach) to constitute the "rich-club" of the C. elegans connectome. This result is robust to the methodology that separates the feedforward from the feedback flow of information. The set of core interneurons remains mostly the same when we consider only chemical synapses or the combination of chemical synapses and gap junctions. The hourglass organization of the connectome suggests that C. elegans has some similarities with encoder-decoder artificial neural networks in which the input is first compressed and integrated in a low-dimensional latent space that encodes the given data in a more efficient manner, followed by a decoding network through which intermediate-level sub-functions are combined in different ways to compute the correlated outputs of the network. The core neurons at the hourglass waist represent the information bottleneck of the system, balancing the representation accuracy and compactness (complexity) of the given sensory information.

Universal hypotrochoidic law for random matrices with cyclic correlations

The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate the generalization of this law to random matrices exhibiting higher-order cyclic correlations between k tuples of matrix entries. We show that the eigenvalue spectrum in this ensemble is bounded by a hypotrochoid curve with k-fold rotational symmetry. This hypotrochoid law applies to full matrices as well as sparse ones, and thereby holds with remarkable universality. We further extend our analysis to matrices and graphs with competing cycle motifs, which are described more generally by polytrochoid spectral boundaries.

The central role of peripheral nodes in directed network dynamics

Many social, technological, and biological systems with asymmetric interactions display a variety of collective phenomena, such as opinion formation and synchronization. This has motivated much research on the dynamical impact of local and mesoscopic structure in directed networks. However, the unique constraints imposed by the global organization of directed networks remain largely undiscussed. Here, we control the global organization of directed Erdős–Rényi networks, and study its impact on the emergence of synchronization and ferromagnetic ordering, using Kuramoto and Ising dynamics. In doing so, we demonstrate that source nodes – peripheral nodes without incoming links – can disrupt or entirely suppress the emergence of collective states in directed networks. This effect is imposed by the bow-tie organization of directed networks, where a large connected core does not uniquely ensure the emergence of collective states, as it does for undirected networks.

Effects of Sphagnum Leachate on Competitive Sphagnum Microbiome Depend on Species and Time

Plant specialized metabolites play an important role in soil carbon (C) and nutrient fluxes. Through anti-microbial effects, they can modulate microbial assemblages and associated microbial-driven processes, such as nutrient cycling, so to positively or negatively cascade on plant fitness. As such, plant specialized metabolites can be used as a tool to supplant competitors. These compounds are little studied in bryophytes. This is especially notable in peatlands where Sphagnum mosses can dominate the vegetation and show strong interspecific competition. Sphagnum mosses form carpets where diverse microbial communities live and play a crucial role in Sphagnum fitness by regulating C and nutrient cycling. Here, by means of a microcosm experiment, we assessed to what extent moss metabolites of two Sphagnum species (S. fallax and S. divinum) modulate the competitive Sphagnum microbiome, with particular focus on microbial respiration. Using a reciprocal leachate experiment, we found that interactions between Sphagnum leachates and microbiome are species-specific. We show that both Sphagnum leachates differed in compound richness and compound relative abundance, especially sphagnum acid derivates, and that they include microbial-related metabolites. The addition of S. divinum leachate on the S. fallax microbiome immediately reduced microbial respiration (−95%). Prolonged exposition of S. fallax microbiome to S. divinum leachate destabilized the food web structure due to a modulation of microbial abundance. In particular, leachate addition decreased the biomass of testate amoebae and rotifers but increased that of ciliates. These changes did not influence microbial CO₂ respiration, suggesting that the structural plasticity of the food web leads to its functional resistance through the replacement of species that are functionally redundant. In contrast, S. fallax leachate neither affected S. divinum microbial respiration, nor microbial biomass. We, however, found that S. fallax leachate addition stabilized the food web structure associated to S. divinum by changing trophic interactions among species. The differences in allelopathic effects between both Sphagnum leachates might impact their competitiveness and affect species distribution at local scale. Our study further paves the way to better understand the role of moss and microbial specialized metabolites in peatland C dynamics.

Emergence of Hierarchical Modularity in Evolving Networks Uncovered by Phylogenomic Analysis

Networks describe how parts associate with each other to form integrated systems which often have modular and hierarchical structure. In biology, network growth involves two processes, one that unifies and the other that diversifies. Here, we propose a biphasic (bow-tie) theory of module emergence. In the first phase, parts are at first weakly linked and associate variously. As they diversify, they compete with each other and are often selected for performance. The emerging interactions constrain their structure and associations. This causes parts to self-organize into modules with tight linkage. In the second phase, variants of the modules diversify and become new parts for a new generative cycle of higher level organization. The paradigm predicts the rise of hierarchical modularity in evolving networks at different timescales and complexity levels. Remarkably, phylogenomic analyses uncover this emergence in the rewiring of metabolomic and transcriptome-informed metabolic networks, the nanosecond dynamics of proteins, and evolving networks of metabolism, elementary functionomes, and protein domain organization.