Network motifs provide signatures that characterize metabolism

Exploring Emergent Properties in Enzymatic Reaction Networks: Design and Control of Dynamic Functional Systems

The intricate and complex features of enzymatic reaction networks (ERNs) play a key role in the emergence and sustenance of life. Constructing such networks in vitro enables stepwise build up in complexity and introduces the opportunity to control enzymatic activity using physicochemical stimuli. Rational design and modulation of network motifs enable the engineering of artificial systems with emergent functionalities. Such functional systems are useful for a variety of reasons such as creating new-to-nature dynamic materials, producing value-added chemicals, constructing metabolic modules for synthetic cells, and even enabling molecular computation. In this review, we offer insights into the chemical characteristics of ERNs while also delving into their potential applications and associated challenges.

What makes a reaction network "chemical"?

BACKGROUND

Reaction networks (RNs) comprise a set X of species and a set [Formula: see text] of reactions [Formula: see text], each converting a multiset of educts [Formula: see text] into a multiset [Formula: see text] of products. RNs are equivalent to directed hypergraphs. However, not all RNs necessarily admit a chemical interpretation. Instead, they might contradict fundamental principles of physics such as the conservation of energy and mass or the reversibility of chemical reactions. The consequences of these necessary conditions for the stoichiometric matrix [Formula: see text] have been discussed extensively in the chemical literature. Here, we provide sufficient conditions for [Formula: see text] that guarantee the interpretation of RNs in terms of balanced sum formulas and structural formulas, respectively.

RESULTS

Chemically plausible RNs allow neither a perpetuum mobile, i.e., a "futile cycle" of reactions with non-vanishing energy production, nor the creation or annihilation of mass. Such RNs are said to be thermodynamically sound and conservative. For finite RNs, both conditions can be expressed equivalently as properties of the stoichiometric matrix [Formula: see text]. The first condition is vacuous for reversible networks, but it excludes irreversible futile cycles and-in a stricter sense-futile cycles that even contain an irreversible reaction. The second condition is equivalent to the existence of a strictly positive reaction invariant. It is also sufficient for the existence of a realization in terms of sum formulas, obeying conservation of "atoms". In particular, these realizations can be chosen such that any two species have distinct sum formulas, unless [Formula: see text] implies that they are "obligatory isomers". In terms of structural formulas, every compound is a labeled multigraph, in essence a Lewis formula, and reactions comprise only a rearrangement of bonds such that the total bond order is preserved. In particular, for every conservative RN, there exists a Lewis realization, in which any two compounds are realized by pairwisely distinct multigraphs. Finally, we show that, in general, there are infinitely many realizations for a given conservative RN.

CONCLUSIONS

"Chemical" RNs are directed hypergraphs with a stoichiometric matrix [Formula: see text] whose left kernel contains a strictly positive vector and whose right kernel does not contain a futile cycle involving an irreversible reaction. This simple characterization also provides a concise specification of random models for chemical RNs that additionally constrain [Formula: see text] by rank, sparsity, or distribution of the non-zero entries. Furthermore, it suggests several interesting avenues for future research, in particular, concerning alternative representations of reaction networks and infinite chemical universes.

A Convergent Functional Genomics Analysis to Identify Biological Regulators Mediating Effects of Creatine Supplementation

Creatine (Cr) and phosphocreatine (PCr) are physiologically essential molecules for life, given they serve as rapid and localized support of energy- and mechanical-dependent processes. This evolutionary advantage is based on the action of creatine kinase (CK) isozymes that connect places of ATP synthesis with sites of ATP consumption (the CK/PCr system). Supplementation with creatine monohydrate (CrM) can enhance this system, resulting in well-known ergogenic effects and potential health or therapeutic benefits. In spite of our vast knowledge about these molecules, no integrative analysis of molecular mechanisms under a systems biology approach has been performed to date; thus, we aimed to perform for the first time a convergent functional genomics analysis to identify biological regulators mediating the effects of Cr supplementation in health and disease. A total of 35 differentially expressed genes were analyzed. We identified top-ranked pathways and biological processes mediating the effects of Cr supplementation. The impact of CrM on miRNAs merits more research. We also cautiously suggest two dose-response functional pathways (kinase- and ubiquitin-driven) for the regulation of the Cr uptake. Our functional enrichment analysis, the knowledge-based pathway reconstruction, and the identification of hub nodes provide meaningful information for future studies. This work contributes to a better understanding of the well-reported benefits of Cr in sports and its potential in health and disease conditions, although further clinical research is needed to validate the proposed mechanisms.

Intrinsic limitations in mainstream methods of identifying network motifs in biology

Background

Network motifs are connectivity structures that occur with significantly higher frequency than chance, and are thought to play important roles in complex biological networks, for example in gene regulation, interactomes, and metabolomes. Network motifs may also become pivotal in the rational design and engineering of complex biological systems underpinning the field of synthetic biology. Distinguishing true motifs from arbitrary substructures, however, remains a challenge.

Results

Here we demonstrate both theoretically and empirically that implicit assumptions present in mainstream methods for motif identification do not necessarily hold, with the ramification that motif studies using these mainstream methods are less able to effectively differentiate between spurious results and events of true statistical significance than is often presented. We show that these difficulties cannot be overcome without revising the methods of statistical analysis used to identify motifs.

Conclusions

Present-day methods for the discovery of network motifs, and, indeed, even the methods for defining what they are, are critically reliant on a set of incorrect assumptions, casting a doubt on the scientific validity of motif-driven discoveries. The implications of these findings are therefore far-reaching across diverse areas of biology.

Efficiently counting complex multilayer temporal motifs in large-scale networks

This paper proposes novel algorithms for efficiently counting complex network motifs in dynamic networks that are changing over time. Network motifs are small characteristic configurations of a few nodes and edges, and have repeatedly been shown to provide insightful information for understanding the meso-level structure of a network. Here, we deal with counting more complex temporal motifs in large-scale networks that may consist of millions of nodes and edges. The first contribution is an efficient approach to count temporal motifs in multilayer networks and networks with partial timing, two prevalent aspects of many real-world complex networks. We analyze the complexity of these algorithms and empirically validate their performance on a number of real-world user communication networks extracted from online knowledge exchange platforms. Among other things, we find that the multilayer aspects provide significant insights in how complex user interaction patterns differ substantially between online platforms. The second contribution is an analysis of the viability of motif counting algorithms for motifs that are larger than the triad motifs studied in previous work. We provide a novel categorization of motifs of size four, and determine how and at what computational cost these motifs can still be counted efficiently. In doing so, we delineate the “computational frontier” of temporal motif counting algorithms.

Revealing the metabolic characteristics of human embryonic stem cells by genome-scale metabolic modeling

Embryonic stem cells (ESCs) are characterized by a dual capacity, self-renewal and pluripotency, which can be regulated by metabolism. A better understanding of ESC metabolism and regulatory mechanisms is pivotal for research into development, ageing, and cancer treatment. However, a systematic and comprehensive delineation of human ESC metabolism is still lacking. Here, we reconstructed the first genome-scale metabolic model (GEM) of human ESCs (hESCs). By GEM simulation and analyses, hESC global metabolic characteristics including essential metabolites and network motifs were identified. Potential metabolic subsystems responsible for self-renewal and pluripotency were also identified by analyses and experiments. This first GEM of hESCs provides a novel view and resource for stem cell metabolism research and will contribute to the elucidation of their metabolic characteristics.

Organization of feed-forward loop motifs reveals architectural principles in natural and engineered networks

Network motifs are significantly overrepresented subgraphs that have been proposed as building blocks for natural and engineered networks. Detailed functional analysis has been performed for many types of motif in isolation, but less is known about how motifs work together to perform complex tasks. To address this issue, we measure the aggregation of network motifs via methods that extract precisely how these structures are connected. Applying this approach to a broad spectrum of networked systems and focusing on the widespread feed-forward loop motif, we uncover striking differences in motif organization. The types of connection are often highly constrained, differ between domains, and clearly capture architectural principles. We show how this information can be used to effectively predict functionally important nodes in the metabolic network of Escherichia coli. Our findings have implications for understanding how networked systems are constructed from motif parts and elucidate constraints that guide their evolution.

Extending the Applicability of Graphlets to Directed Networks

With recent advances in high-throughput cell biology, the amount of cellular biological data has grown drastically. Such data is often modeled as graphs (also called networks) and studying them can lead to new insights into molecule-level organization. A possible way to understand their structure is by analyzing the smaller components that constitute them, namely network motifs and graphlets. Graphlets are particularly well suited to compare networks and to assess their level of similarity due to the rich topological information that they offer but are almost always used as small undirected graphs of up to five nodes, thus limiting their applicability in directed networks. However, a large set of interesting biological networks such as metabolic, cell signaling, or transcriptional regulatory networks are intrinsically directional, and using metrics that ignore edge direction may gravely hinder information extraction. Our main purpose in this work is to extend the applicability of graphlets to directed networks by considering their edge direction, thus providing a powerful basis for the analysis of directed biological networks. We tested our approach on two network sets, one composed of synthetic graphs and another of real directed biological networks, and verified that they were more accurately grouped using directed graphlets than undirected graphlets. It is also evident that directed graphlets offer substantially more topological information than simple graph metrics such as degree distribution or reciprocity. However, enumerating graphlets in large networks is a computationally demanding task. Our implementation addresses this concern by using a state-of-the-art data structure, the g-trie, which is able to greatly reduce the necessary computation. We compared our tool to other state-of-the art methods and verified that it is the fastest general tool for graphlet counting.

Graphlet-based Characterization of Directed Networks

We are flooded with large-scale, dynamic, directed, networked data. Analyses requiring exact comparisons between networks are computationally intractable, so new methodologies are sought. To analyse directed networks, we extend graphlets (small induced sub-graphs) and their degrees to directed data. Using these directed graphlets, we generalise state-of-the-art network distance measures (RGF, GDDA and GCD) to directed networks and show their superiority for comparing directed networks. Also, we extend the canonical correlation analysis framework that enables uncovering the relationships between the wiring patterns around nodes in a directed network and their expert annotations. On directed World Trade Networks (WTNs), our methodology allows uncovering the core-broker-periphery structure of the WTN, predicting the economic attributes of a country, such as its gross domestic product, from its wiring patterns in the WTN for up-to ten years in the future. It does so by enabling us to track the dynamics of a country's positioning in the WTN over years. On directed metabolic networks, our framework yields insights into preservation of enzyme function from the network wiring patterns rather than from sequence data. Overall, our methodology enables advanced analyses of directed networked data from any area of science, allowing domain-specific interpretation of a directed network's topology.

Predicting network functions with nested patterns

Identifying suitable patterns in complex biological interaction networks helps understanding network functions and allows for predictions at the pattern level: by recognizing a known pattern, one can assign its previously established function. However, current approaches fail for previously unseen patterns, when patterns overlap and when they are embedded into a new network context. Here we show how to conceptually extend pattern-based approaches. We define metabolite patterns in metabolic networks that formalize co-occurrences of metabolites. Our probabilistic framework decodes the implicit information in the networks' metabolite patterns to predict metabolic functions. We demonstrate the predictive power by identifying 'indicator patterns', for instance, for enzyme classification, by predicting directions of novel reactions and of known reactions in new network contexts, and by ranking candidate network extensions for gap filling. Beyond their use in improving genome annotations and metabolic network models, we expect that the concepts transfer to other network types.

Metabolic network motifs can provide novel insights into evolution: The evolutionary origin of Eukaryotic organelles as a case study

Phylogenetic trees are typically constructed using genetic and genomic data, and provide robust evolutionary relationships of species from the genomic point of view. We present an application of network motif mining and analysis of metabolic pathways that when used in combination with phylogenetic trees can provide a more complete picture of evolution. By using distributions of three-node motifs as a proxy for metabolic similarity, we analyze the ancestral origin of Eukaryotic organelles from the metabolic point of view to illustrate the application of our motif mining and analysis network approach. Our analysis suggests that the hypothesis of an early proto-Eukaryote could be valid. It also suggests that a δ- or ϵ-Proteobacteria may have been the endosymbiotic partner that gave rise to modern mitochondria. Our evolutionary analysis needs to be extended by building metabolic network reconstructions of species from the phylum Crenarchaeota, which is considered to be a possible archaeal ancestor of the eukaryotic cell. In this paper, we also propose a methodology for constructing phylogenetic trees that incorporates metabolic network signatures to identify regions of genomically-estimated phylogenies that may be spurious. We find that results generated from our approach are consistent with a parallel phylogenetic analysis using the method of feature frequency profiles.

Network motif frequency vectors reveal evolving metabolic network organisation

At the systems level many organisms of interest may be described by their patterns of interaction, and as such, are perhaps best characterised via network or graph models. Metabolic networks, in particular, are fundamental to the proper functioning of many important biological processes, and thus, have been widely studied over the past decade or so. Such investigations have revealed a number of shared topological features, such as a short characteristic path-length, large clustering coefficient and hierarchical modular structure. However, the extent to which evolutionary and functional properties of metabolism manifest via this underlying network architecture remains unclear. In this paper, we employ a novel graph embedding technique, based upon low-order network motifs, to compare metabolic network structure for 383 bacterial species categorised according to a number of biological features. In particular, we introduce a new global significance score which enables us to quantify important evolutionary relationships that exist between organisms and their physical environments. Using this new approach, we demonstrate a number of significant correlations between environmental factors, such as growth conditions and habitat variability, and network motif structure, providing evidence that organism adaptability leads to increased complexities in the resultant metabolic networks.

The biological networks in studying cell signal transduction complexity: The examples of sperm capacitation and of endocannabinoid system

Cellular signal transduction is a complex phenomenon, which plays a central role in cell surviving and adaptation. The great amount of molecular data to date present in literature, together with the adoption of high throughput technologies, on the one hand, made available to scientists an enormous quantity of information, on the other hand, failed to provide a parallel increase in the understanding of biological events. In this context, a new discipline arose, the systems biology, aimed to manage the information with a computational modeling-based approach. In particular, the use of biological networks has allowed the making of huge progress in this field.

Here we discuss two possible application of the use of biological networks to explore cell signaling: the study of the architecture of signaling systems that cooperate in determining the acquisition of a complex cellular function (as it is the case of the process of activation of spermatozoa) and the organization of a single specific signaling systems expressed by different cells in different tissues (i.e. the endocannabinoid system). In both the cases we have found that the networks follow a scale free and small world topology, likely due to the evolutionary advantage of robustness against random damages, fastness and specific of information processing, and easy navigability.

Network motifs that recur across species, including gene regulatory and protein-protein interaction networks

Cellular molecules interact in complex ways, giving rise to a cell's functional outcomes. Conscientious efforts have been made in recent years to better characterize these patterns of interactions. It has been learned that many of these interactions can be represented abstractly as a network and within a network there in many instances are network motifs. Network motifs are subgraphs that are statistically overrepresented within networks. To date, specific network motifs have been experimentally identified across various species and also within specific, intracellular networks; however, motifs that recur across species and major network types have not been systematically characterized. We reason that recurring network motifs could potentially have important implications and applications for toxicology and, in particular, toxicity testing. Therefore, the goal of this study was to determine the set of intracellular, network motifs found to recur across species of both gene regulatory and protein-protein interaction networks. We report the recurrence of 13 intracellular, network motifs across species. Ten recurring motifs were found across both protein-protein interaction networks and gene regulatory networks. The significant pair motif was found to recur only in gene regulatory networks. The diamond and one-way cycle reversible step motifs were found to recur only in protein-protein interaction networks. This study is the first formal review of recurring, intracellular network motifs across species. Within toxicology, combining our understanding of recurring motifs with mechanism and mode of action knowledge could result in more robust and efficient toxicity testing models. We are sure that our results will support research in applying network motifs to toxicity testing.

Computational analyses of synergism in small molecular network motifs

Cellular functions and responses to stimuli are controlled by complex regulatory networks that comprise a large diversity of molecular components and their interactions. However, achieving an intuitive understanding of the dynamical properties and responses to stimuli of these networks is hampered by their large scale and complexity. To address this issue, analyses of regulatory networks often focus on reduced models that depict distinct, reoccurring connectivity patterns referred to as motifs. Previous modeling studies have begun to characterize the dynamics of small motifs, and to describe ways in which variations in parameters affect their responses to stimuli. The present study investigates how variations in pairs of parameters affect responses in a series of ten common network motifs, identifying concurrent variations that act synergistically (or antagonistically) to alter the responses of the motifs to stimuli. Synergism (or antagonism) was quantified using degrees of nonlinear blending and additive synergism. Simulations identified concurrent variations that maximized synergism, and examined the ways in which it was affected by stimulus protocols and the architecture of a motif. Only a subset of architectures exhibited synergism following paired changes in parameters. The approach was then applied to a model describing interlocked feedback loops governing the synthesis of the CREB1 and CREB2 transcription factors. The effects of motifs on synergism for this biologically realistic model were consistent with those for the abstract models of single motifs. These results have implications for the rational design of combination drug therapies with the potential for synergistic interactions.

Cellular responses to stimuli are controlled by complex regulatory networks that comprise many molecular components. Understanding such networks is critical for understanding normal cellular functions and pathological conditions. Because the complexity of these networks often precludes intuitive insights, a useful approach is to study mathematical models of small network motifs having reduced complexity yet consisting of key regulatory components of the more complex networks. Computational studies have analyzed the behavior of small motifs, and have begun to describe the ways in which variations in parameters affect their functional properties. Here, we investigated how variations in pairs of parameters act synergistically (or antagonistically) to alter responses of ten common network motifs. Simulations identified parameter variations that maximized synergism, and examined the ways in which synergism was affected by stimulus protocols and motif architecture. The results have implications for the rational design of combination drug therapies where a goal is to identify drugs that when administered together have a greater effect than would be predicted by simple addition of single-drug effects (i.e., super-additive effects), thereby allowing for lower drug doses, minimizing undesirable effects.

Network representations and methods for the analysis of chemical and biochemical pathways

Systems biologists increasingly use network representations to investigate biochemical pathways and their dynamic behaviours. In this critical review, we discuss four commonly used network representations of chemical and biochemical pathways. We illustrate how some of these representations reduce network complexity but result in the ambiguous representation of biochemical pathways. We also examine the current theoretical approaches available to investigate the dynamic behaviour of chemical and biochemical networks. Finally, we describe how the critical chemical and biochemical pathways responsible for emergent dynamic behaviour can be identified using network mining and functional mapping approaches.

Identification of breast cancer patients based on human signaling network motifs

Identifying breast cancer patients is crucial to the clinical diagnosis and therapy for this disease. Conventional gene-based methods for breast cancer diagnosis ignore gene-gene interactions and thus may lead to loss of power. In this study, we proposed a novel method to select classification features, called “Selection of Significant Expression-Correlation Differential Motifs” (SSECDM). This method applied a network motif-based approach, combining a human signaling network and high-throughput gene expression data to distinguish breast cancer samples from normal samples. Our method has higher classification performance and better classification accuracy stability than the mutual information (MI) method or the individual gene sets method. It may become a useful tool for identifying and treating patients with breast cancer and other cancers, thus contributing to clinical diagnosis and therapy for these diseases.