基于子图模式的巨强连通体局域结构特征(英文)

对代谢网络的"蝴蝶结"结构进行研究吸引了众多科研人员的关注。当前,基于复杂网络理论的全局拓扑结构特征已经被广泛用于研究这种"蝴蝶结"结构的组织原则,然而基于局域结构特征的研究相对较少。本文分析了10种有机物代谢网络及其相应的巨强连通体部分的网络模体(即频繁的子图)。结果显示代谢网络及其相应的巨强连通体部分的网络模体非常相似,这从局域结构特征的角度论证了代谢网络巨强连通体部分的重要性。     

Observing and interpreting correlations in metabolomic networks

MOTIVATION: Metabolite profiling aims at an unbiased identification and quantification of all the metabolites present in a biological sample. Based on their pair-wise correlations, the data obtained from metabolomic experiments are organized into metabolic correlation networks and the key challenge is to deduce unknown pathways based on the observed correlations. However, the data generated is fundamentally different from traditional biological measurements and thus the analysis is often restricted to rather pragmatic approaches, such as data mining tools, to discriminate between different metabolic phenotypes. METHODS AND RESULTS: We investigate to what extent the data generated networks reflect the structure of the underlying biochemical pathways. The purpose of this work is 2-fold: Based on the theory of stochastic systems, we first introduce a framework which shows that the emergent correlations can be interpreted as a 'fingerprint' of the underlying biophysical system. This result leads to a systematic relationship between observed correlation networks and the underlying biochemical pathways. In a second step, we investigate to what extent our result is applicable to the problem of reverse engineering, i.e. to recover the underlying enzymatic reaction network from data. The implications of our findings for other bioinformatics approaches are discussed.     

Motif search in graphs: application to metabolic networks

The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and motifs that could be considered as the building blocks of a network are being suggested. In this work, we introduce a new definition of motif in the context of metabolic networks. Unlike in previous works on (other) biochemical networks, this definition is not based only on topological features. We propose instead to use an alternative definition based on the functional nature of the components that form the motif, which we call a reaction motif. After introducing a formal framework motivated by biological considerations, we present complexity results on the problem of searching for all occurrences of a reaction motif in a network and introduce an algorithm that is fast in practice in most situations. We then show an initial application to the study of pathway evolution. Finally, we give some general features of the observed number of occurrences in order to highlight some structural features of metabolic networks     

Attractor Metabolic Networks

Background

The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity.

Methodology/Principal Findings

In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network.

Conclusions/Significance

We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns, modify the efficiency in the connection between the multienzymatic complexes, and stably retain these modifications. Here for the first time, we have introduced the general concept of attractor metabolic network, in which this dynamic behavior is observed.     

Exploring biological network structure using exponential random graph models

MOTIVATION: The functioning of biological networks depends in large part on their complex underlying structure. When studying their systemic nature many modeling approaches focus on identifying simple, but prominent, structural components, as such components are easier to understand, and, once identified, can be used as building blocks to succinctly describe the network. RESULTS: In recent social network studies, exponential random graph models have been used extensively to model global social network structure as a function of their 'local features'. Starting from those studies, we describe the exponential random graph models and demonstrate their utility in modeling the architecture of biological networks as a function of the prominence of local features. We argue that the flexibility, in terms of the number of available local feature choices, and scalability, in terms of the network sizes, make this approach ideal for statistical modeling of biological networks. We illustrate the modeling on both genetic and metabolic networks and provide a novel way of classifying biological networks based on the prevalence of their local features.     

The Notch signalling system: recent insights into the complexity of a conserved pathway

Notch signalling links the fate of one cell to that of an immediate neighbour and consequently controls differentiation, proliferation and apoptotic events in multiple metazoan tissues. Perturbations in this pathway activity have been linked to several human genetic disorders and cancers. Recent genome-scale studies in Drosophila melanogaster have revealed an extraordinarily complex network of genes that can affect Notch activity. This highly interconnected network contrasts our traditional view of the Notch pathway as a simple linear sequence of events. Although we now have an unprecedented insight into the way in which such a fundamental signalling mechanism is controlled by the genome, we are faced with serious challenges in analysing the underlying molecular mechanisms of Notch signal control.     

Deciphering the molecular mechanism of the cancer formation by chromosome structural dynamics

Cancer reflects the dysregulation of the underlying gene network, which is strongly related to the 3D genome organization. Numerous efforts have been spent on experimental characterizations of the structural alterations in cancer genomes. However, there is still a lack of genomic structural-level understanding of the temporal dynamics for cancer initiation and progression. Here, we use a landscape-switching model to investigate the chromosome structural transition during the cancerization and reversion processes. We find that the chromosome undergoes a non-monotonic structural shape-changing pathway with initial expansion followed by compaction during both of these processes. Furthermore, our analysis reveals that the chromosome with a more expanding structure than those at both the normal and cancer cell during cancerization exhibits a sparse contact pattern, which shows significant structural similarity to the one at the embryonic stem cell in many aspects, including the trend of contact probability declining with the genomic distance, the global structural shape geometry and the spatial distribution of loci on the chromosome. In light of the intimate structure-function relationship at the chromosomal level, we further describe the cell state transition processes by the chromosome structural changes, suggesting an elevated cell stemness during the formation of the cancer cells. We show that cell cancerization and reversion are highly irreversible processes in terms of the chromosome structural transition pathways, spatial repositioning of chromosomal loci and hysteresis loop of contact evolution analysis. Our model draws a molecular-scale picture of cell cancerization from the chromosome structural perspective. The process contains initial reprogramming towards the stem cell followed by the differentiation towards the cancer cell, accompanied by an initial increase and subsequent decrease of the cell stemness.     

Self-maintenance and self-reproduction in an abstract cell model

Living cells must maintain their membranes by active metabolism. The membrane is not static but a dynamic structure that has evolved along with its internal reactions. When we reflect on the emergence and evolution of primitive cells, we should not forget the mutual dependency between membranes and metabolic cycles inside the cell. In this paper, we present a simple abstract model of the self-maintaining cell. A metabolic cycle will produce a self-assembling membrane that will enclose the metabolic cycle. We show that a self-maintaining cell has the potential to reproduce itself spontaneously. Further, we have demonstrated two different ways of cellular reproduction depending on the mobility of chemicals. In the first case, a cell releases autocatalytic chemicals that create new cells outside the mother cell. In the second case, a cell grows larger and divides itself into daughter cells by creating a new internal dividing membrane.     

A topological look into the evolution of developmental programs

Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and inventing new cell types. A hurdle to understanding developmental evolution is the difficulty of even describing the intertwined network of spatiotemporal processes underlying the development of complex multicellular organisms. Nonetheless, an overview of developmental trajectories can be obtained from cell type lineage maps. Here, we propose that these lineage maps can also reveal how developmental programs evolve: the modes of evolving new cell types in an organism should be visible in its developmental trajectories and therefore in the geometry of its cell type lineage map. This idea is demonstrated using a parsimonious generative model of developmental programs, which allows us to reliably survey the universe of all possible programs and examine their topological features. We find that, contrary to belief, tree-like lineage maps are rare, and lineage maps of complex multicellular organisms are likely to be directed acyclic graphs in which multiple developmental routes can converge on the same cell type. Although cell type evolution prescribes what developmental programs come into existence, natural selection prunes those programs that produce low-functioning organisms. Our model indicates that additionally, lineage map topologies are correlated with such a functional property: the ability of organisms to regenerate.     

Community Structure and Multi-Modal Oscillations in Complex Networks

In many types of network, the relationship between structure and function is of great significance. We are particularly interested in community structures, which arise in a wide variety of domains. We apply a simple oscillator model to networks with community structures and show that waves of regular oscillation are caused by synchronised clusters of nodes. Moreover, we show that such global oscillations may arise as a direct result of network topology. We also observe that additional modes of oscillation (as detected through frequency analysis) occur in networks with additional levels of topological hierarchy and that such modes may be directly related to network structure. We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems. We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.     

Self-assembling enzymes and the origins of the cytoskeleton

The bacterial cytoskeleton is composed of a complex and diverse group of proteins that self-assemble into linear filaments. These filaments support and organize cellular architecture and provide a dynamic network controlling transport and localization within the cell. Here, we review recent discoveries related to a newly appreciated class of self-assembling proteins that expand our view of the bacterial cytoskeleton and provide potential explanations for its evolutionary origins. Specifically, several types of metabolic enzymes can form structures similar to established cytoskeletal filaments and, in some cases, these structures have been repurposed for structural uses independent of their normal roles. The behaviors of these enzymes suggest that some modern cytoskeletal proteins may have evolved from dual-role proteins with catalytic and structural functions.     

Beyond topology: coevolution of structure and flux in metabolic networks

Interactions between the structure of a metabolic network and its functional properties underlie its evolutionary diversification, but the mechanism by which such interactions arise remains elusive. Particularly unclear is whether metabolic fluxes that determine the concentrations of compounds produced by a metabolic network, are causally linked to a network's structure or emerge independently of it. A direct empirical study of populations where both structural and functional properties vary among individuals’ metabolic networks is required to establish whether changes in structure affect the distribution of metabolic flux. In a population of house finches (Haemorhous mexicanus), we reconstructed full carotenoid metabolic networks for 442 individuals and uncovered 11 structural variants of this network with different compounds and reactions. We examined the consequences of this structural diversity for the concentrations of plumage‐bound carotenoids produced by flux in these networks. We found that concentrations of metabolically derived, but not dietary carotenoids, depended on network structure. Flux was partitioned similarly among compounds in individuals of the same network structure: within each network, compound concentrations were closely correlated. The highest among‐individual variation in flux occurred in networks with the strongest among‐compound correlations, suggesting that changes in the magnitude, but not the distribution of flux, underlie individual differences in compound concentrations on a static network structure. These findings indicate that the distribution of flux in carotenoid metabolism closely follows network structure. Thus, evolutionary diversification and local adaptations in carotenoid metabolism may depend more on the gain or loss of enzymatic reactions than on changes in flux within a network structure.     

Metabolic control theory: a structural approach

In the general framework of metabolic control theory, we describe a method of mathematical modelling that provides a way of analysing the sensitivity of a metabolic system to perturbations of the environment or of the internal state of this system. The method can be applied to any metabolic system, involving for instance conservation relationships, non-specific external parameters, etc., and leads in particular to a characterization of the control matrices and to a generalization of the summation and connectivity theorems. In this paper, we emphasize the structural characterizations and properties of the systems which depend only on the structure of the metabolic network, and not on the reaction kinetics. The advantage of this approach lies of course in the fact that the structure of the metabolic network is an invariant of the system which depends neither on the environment nor on the internal state of this system. The aim of this paper is to show the efficiency of such a structural approach.     

The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing

BACKGROUND: Epithelial junctional networks assume packing geometries characterized by different cell shapes, neighbor number distributions and areas. The development of specific packing geometries is tightly controlled; in the Drosophila wing epithelium, cells convert from an irregular to a hexagonal array shortly before hair formation. Packing geometry is determined by developmental mechanisms that likely control the biophysical properties of cells and their interactions. RESULTS: To understand how physical cellular properties and proliferation determine cell-packing geometries, we use a vertex model for the epithelial junctional network in which cell packing geometries correspond to stable and stationary network configurations. The model takes into account cell elasticity and junctional forces arising from cortical contractility and adhesion. By numerically simulating proliferation, we generate different network morphologies that depend on physical parameters. These networks differ in polygon class distribution, cell area variation, and the rate of T1 and T2 transitions during growth. Comparing theoretical results to observed cell morphologies reveals regions of parameter space where calculated network morphologies match observed ones. We independently estimate parameter values by quantifying network deformations caused by laser ablating individual cell boundaries. CONCLUSIONS: The vertex model accounts qualitatively and quantitatively for the observed packing geometry in the wing disc and its response to perturbation by laser ablation. Epithelial packing geometry is a consequence of both physical cellular properties and the disordering influence of proliferation. The occurrence of T2 transitions during network growth suggests that elimination of cells from the proliferating disc epithelium may be the result of junctional force balances.     

Robustness and state-space structure of Boolean gene regulatory models

Robustness to perturbation is an important characteristic of genetic regulatory systems, but the relationship between robustness and model dynamics has not been clearly quantified. We propose a method for quantifying both robustness and dynamics in terms of state-space structures, for Boolean models of genetic regulatory systems. By investigating existing models of the Drosophila melanogaster segment polarity network and the Saccharomyces cerevisiae cell-cycle network, we show that the structure of attractor basins can yield insight into the underlying decision making required of the system, and also the way in which the system maximises its robustness. In particular, gene networks implementing decisions based on a few genes have simple state-space structures, and their attractors are robust by virtue of their simplicity. Gene networks with decisions that involve many interacting genes have correspondingly more complicated state-space structures, and robustness cannot be achieved through the structure of the attractor basins, but is achieved by larger attractor basins that dominate the state space. These different types of robustness are demonstrated by the two models: the D. melanogaster segment polarity network is robust due to simple attractor basins that implement decisions based on spatial signals; the S. cerevisiae cell-cycle network has a complicated state-space structure, and is robust only due to a giant attractor basin that dominates the state space.     

Filament formation by metabolic enzymes—A new twist on regulation

Compartmentalization of metabolic enzymes through protein–protein interactions is an emerging mechanism for localizing and regulating metabolic activity. Self-assembly into linear filaments is a common strategy for cellular compartmentalization of enzymes. Polymerization is often driven by changes in the metabolic state of the cell, suggesting that it is a strategy for shifting metabolic flux in response to cellular demand. Although polymerization of metabolic enzymes is widespread, observed from bacteria to humans, we are just beginning to appreciate their role in regulating cellular metabolism. In most cases, one functional role of metabolic enzyme filaments is allosteric control of enzyme activity. Here, we highlight recent findings, providing insight into the structural and functional significance of filamentation of metabolic enzymes in cells.     

Efficient Network Reconstruction from Dynamical Cascades Identifies Small-World Topology of Neuronal Avalanches

Cascading activity is commonly found in complex systems with directed interactions such as metabolic networks, neuronal networks, or disease spreading in social networks. Substantial insight into a system's organization can be obtained by reconstructing the underlying functional network architecture from the observed activity cascades. Here we focus on Bayesian approaches and reduce their computational demands by introducing the Iterative Bayesian (IB) and Posterior Weighted Averaging (PWA) methods. We introduce a special case of PWA, cast in nonparametric form, which we call the normalized count (NC) algorithm. NC efficiently reconstructs random and small-world functional network topologies and architectures from subcritical, critical, and supercritical cascading dynamics and yields significant improvements over commonly used correlation methods. With experimental data, NC identified a functional and structural small-world topology and its corresponding traffic in cortical networks with neuronal avalanche dynamics.