Metabolic robustness and network modularity: a model study

Background

Several studies have mentioned network modularity—that a network can easily be decomposed into subgraphs that are densely connected within and weakly connected between each other—as a factor affecting metabolic robustness. In this paper we measure the relation between network modularity and several aspects of robustness directly in a model system of metabolism.

Methodology/Principal Findings

By using a model for generating chemical reaction systems where one can tune the network modularity, we find that robustness increases with modularity for changes in the concentrations of metabolites, whereas it decreases with changes in the expression of enzymes. The same modularity scaling is true for the speed of relaxation after the perturbations.

Conclusions/Significance

Modularity is not a general principle for making metabolism either more or less robust; this question needs to be addressed specifically for different types of perturbations of the system.     

Metabolic shifts in Zymomonas mobilis in response to growth conditions

Abstract Extensive work on ethanol production with the Gram-negative bacterium Zymomonas mobilis has revealed that this is a promising microorganism for industrial use. Concise knowledge of the physiology and metabolism of this organism provides the basis for further improvements by genetic engineering and for the optimization of Zymomonas -specific fermentation processes.     

Determinate growth and modularity in a gorgonian octocoral

Growth rates of branches of colonies of the gorgonian Pseudopterogorgia elisabethae were monitored for 2 years on a reef at San Salvador Island, Bahamas. Images of 261 colonies were made at 6-month intervals and colony and branch growth analyzed. Branch growth rates differed between colonies and between the time intervals in which the measurements were made. Colonies developed a plumelike morphology through a pattern of branch origination and determinate growth in which branch growth rates were greatest at the time the branch originated and branches seldom grew beyond a length of 8 cm. A small number of branches had greater growth rates, did not stop growing, and were sites for the origination of subsequent "generations" of branches. The rate of branch origination decreased with each generation of branching, and branch growth rates were lower on larger colonies, leading to determinate colony growth. Although colonial invertebrates like P. elisabethae grow through the addition of polyps, branches behave as modules with determinate growth. Colony form and size is generated by the iterative addition of branches.     

Identifying protein complexes based on density and modularity in protein-protein interaction network

Background

Identifying protein complexes is crucial to understanding principles of cellular organization and functional mechanisms. As many evidences have indicated that the subgraphs with high density or with high modularity in PPI network usually correspond to protein complexes, protein complexes detection methods based on PPI network focused on subgraph's density or its modularity in PPI network. However, dense subgraphs may have low modularity and subgraph with high modularity may have low density, which results that protein complexes may be subgraphs with low modularity or with low density in the PPI network. As the density-based methods are difficult to mine protein complexes with low density, and the modularity-based methods are difficult to mine protein complexes with low modularity, both two methods have limitation for identifying protein complexes with various density and modularity.

Results

To identify protein complexes with various density and modularity, including those have low density but high modularity and those have low modularity but high density, we define a novel subgraph's fitness, f _ρ , as f _ρ = (density) ^ρ *(modularity)^1-ρ, and propose a novel algorithm, named LF_PIN, to identify protein complexes by expanding seed edges to subgraphs with the local maximum fitness value. Experimental results of LF-PIN in S.cerevisiae show that compared with the results of fitness equal to density (ρ = 1) or equal to modularity (ρ = 0), the LF-PIN identifies known protein complexes more effectively when the fitness value is decided by both density and modularity (0<ρ<1). Compared with the results of seven competing protein complex detection methods (CMC, Core-Attachment, CPM, DPClus, HC-PIN, MCL, and NFC) in S.cerevisiae and E.coli, LF-PIN outperforms other seven methods in terms of matching with known complexes and functional enrichment. Moreover, LF-PIN has better performance in identifying protein complexes with low density or with low modularity.

Conclusions

By considering both the density and the modularity, LF-PIN outperforms other protein complexes detection methods that only consider density or modularity, especially in identifying known protein complexes with low density or low modularity.

     

Metabolic conditions in Chlorella

1. The effect of nitrate reduction and assimilation on the CO(2)/O(2) quotient of gas exchange has been used as an index of the relative rates of carbon and nitrogen assimilation in Chlorella pyrenoidosa. Changes in over-all metabolism induced by starvation, high light intensity, and nitrogen deficiency have been studied in comparison with the metabolism of cells growing at light-limiting intensities. 2. Starvation, which results in depletion of carbohydrate reserves, gives rise to a high CO(2)/O(2) quotient ( approximately 0.9) during photosynthesis and, therefore, a high C/N assimilation ratio. Starved cells apparently restore their normal C/N ratio before becoming growing cells. 3. Under photosynthesis-saturating light intensities cells show the high CO(2)/O(2) quotient (0.9) indicative of a high C/N assimilation ratio. Return to low light intensities is followed by the abnormally low CO(2)/O(2) quotient ( approximately 0.4) of a low C/N assimilation ratio. High light intensity apparently gives rise to a condition of a limiting rate of nitrogen assimilation and to an overflow metabolism analogous to that found in other microorganisms. 4. Nitrogen deficiency leads to a completely carbohydrate metabolism in short time experiments and makes still more pronounced the effects characteristic of high light intensity alone. 5. Considerations of nutritional economy sustain the experimental evidence in establishing the metabolism of cells growing under light-limiting intensities as the normal or reference metabolic condition in Chlorella.     

Physical and functional modularity of the protein network in yeast

While protein-protein interactions have been studied largely as a network graph without physicality, here we analyze two protein complex data sets of Saccharomyces cerevisiae to relate physical and functional modularity to the network topology. We study for the first time the number of different protein complexes as a function of the protein complex size and find that it follows an exponential decay with a characteristic number of about 7. This reflects the dynamics of complex formation and dissociation in the cell. The analysis of the protein usage by complexes shows an extensive sharing of subunits that is due to the particular organization of the proteome into physical complexes and functional modules. This promiscuity accounts for the high clustering in the protein net-work graph. Our results underscore the need to include the information contained in observed protein complexes into protein network analyses.     

Metabolic flexibility of SUP05 under low DO growth conditions

Chemoautotrophic bacteria from the SUP05 clade often dominate anoxic waters within marine oxygen minimum zones (OMZs) where they use energy gained from the oxidation of reduced sulfur to fuel carbon fixation. Some of these SUP05 bacteria are facultative aerobes that can use either nitrate or oxygen as a terminal electron acceptor making them ideally suited to thrive at the boundaries of OMZs where they experience fluctuations in dissolved oxygen (DO). SUP05 metabolism in these regions, and therefore the biogeochemical function of SUP05, depends largely on their sensitivity to oxygen. We evaluated growth and quantified differences in gene expression in Ca. T. autotrophicus strain EF1 from the SUP05 clade under high DO (22 μM), anoxic, and low DO (3.8 μM) concentrations. We show that strain EF1 cells respire oxygen and nitrate and that cells have higher growth rates, express more genes, and fix more carbon when oxygen becomes available for aerobic respiration. Evidence that facultatively aerobic SUP05 are more active and respire nitrate when oxygen becomes available at low concentrations suggests that they are an important source of nitrite across marine OMZ boundary layers.     

Metabolic rate of Arctic charr eggs depends on their parentage

The metabolic rate (specific heat output) of individual eyed-stage eggs of Arctic charr Salvelinus alpinus (Linnaeus, 1758) originating from different families was measured with direct microcalorimetry. Metabolic rates varied between 2.3–7.9 μW ind⁻¹ and 0.06–0.22 μW mg⁻¹. Absolute heat output was unrelated to egg size, but size-scaled or specific heat output was negatively correlated with egg size, measured as diameter, dry mass or fresh mass. Metabolic rates varied significantly between families, suggesting that genetic and/or maternal effects affect embryonic metabolism in Arctic charr. Heat output increased almost linearly from 3.4 to 16.7 μW ind⁻¹ (0.09–0.67 μW mg⁻¹) during the embryonic development. Although the metabolic rate varied between the families and egg metabolic rate increased during development, there was an unexpected disconnect between metabolic rate and hatching time.     

Metabolic control by S6 kinases depends on dietary lipids

Targeted deletion of S6 kinase (S6K) 1 in mice leads to higher energy expenditure and improved glucose metabolism. However, the molecular mechanisms controlling these effects remain to be fully elucidated. Here, we analyze the potential role of dietary lipids in regulating the mTORC1/S6K system. Analysis of S6K phosphorylation in vivo and in vitro showed that dietary lipids activate S6K, and this effect is not dependent upon amino acids. Comparison of male mice lacking S6K1 and 2 (S6K-dko) with wt controls showed that S6K-dko mice are protected against obesity and glucose intolerance induced by a high-fat diet. S6K-dko mice fed a high-fat diet had increased energy expenditure, improved glucose tolerance, lower fat mass gain, and changes in markers of lipid metabolism. Importantly, however, these metabolic phenotypes were dependent upon dietary lipids, with no such effects observed in S6K-dko mice fed a fat-free diet. These changes appear to be mediated via modulation of cellular metabolism in skeletal muscle, as shown by the expression of genes involved in energy metabolism. Taken together, our results suggest that the metabolic functions of S6K in vivo play a key role as a molecular interface connecting dietary lipids to the endogenous control of energy metabolism.     

Hubs with network motifs organize modularity dynamically in the protein-protein interaction network of yeast

Background

It has been recognized that modular organization pervades biological complexity. Based on network analysis, ‘party hubs’ and ‘date hubs’ were proposed to understand the basic principle of module organization of biomolecular networks. However, recent study on hubs has suggested that there is no clear evidence for coexistence of ‘party hubs’ and ‘date hubs’. Thus, an open question has been raised as to whether or not ‘party hubs’ and ‘date hubs’ truly exist in yeast interactome.

Methodology

In contrast to previous studies focusing on the partners of a hub or the individual proteins around the hub, our work aims to study the network motifs of a hub or interactions among individual proteins including the hub and its neighbors. Depending on the relationship between a hub''s network motifs and protein complexes, we define two new types of hubs, ‘motif party hubs’ and ‘motif date hubs’, which have the same characteristics as the original ‘party hubs’ and ‘date hubs’ respectively. The network motifs of these two types of hubs display significantly different features in spatial distribution (or cellular localizations), co-expression in microarray data, controlling topological structure of network, and organizing modularity.

Conclusion

By virtue of network motifs, we basically solved the open question about ‘party hubs’ and ‘date hubs’ which was raised by previous studies. Specifically, at the level of network motifs instead of individual proteins, we found two types of hubs, motif party hubs (mPHs) and motif date hubs (mDHs), whose network motifs display distinct characteristics on biological functions. In addition, in this paper we studied network motifs from a different viewpoint. That is, we show that a network motif should not be merely considered as an interaction pattern but be considered as an essential function unit in organizing modules of networks.     

Photosynthesis in sugar beet depends on root growth

Summary Sugar-beet plants, germinated in growth cabinets at 20°C and transplanted into the field after 3 weeks, developed much larger roots than plants grown from seed drilled directly into the soil. At the end of the season, the roots of transplants were 39% greater than from drilled seed—an increase of 14 m tons per hectare. The increased yield was mainly due to a sustained increase in photosynthesis because of the larger sink for carbohydrates provided by plants from the growth cabinets.     

Synergistic growth in bacteria depends on substrate complexity

Both positive and negative interactions among bacteria take place in the environment. We hypothesize that the complexity of the substrate affects the way bacteria interact with greater cooperation in the presence of recalcitrant substrate. We isolated lignocellulolytic bacteria from salt marsh detritus and compared the growth, metabolic activity and enzyme production of pure cultures to those of three-species mixed cultures in lignocellulose and glucose media. Synergistic growth was common in lignocellulose medium containing carboxyl methyl cellulose, xylan and lignin but absent in glucose medium. Bacterial synergism promoted metabolic activity in synergistic mixed cultures but not the maximal growth rate (μ). Bacterial synergism also promoted the production of β-1,4-glucosidase but not the production of cellobiohydrolase or β-1,4-xylosidase. Our results suggest that the chemical complexity of the substrate affects the way bacteria interact. While a complex substrate such as lignocellulose promotes positive interactions and synergistic growth, a labile substrate such as glucose promotes negative interactions and competition. Synergistic interactions among indigenous bacteria are suggested to be important in promoting lignocellulose degradation in the environment.     

The inner-mitochondrial distribution of Oxa1 depends on the growth conditions and on the availability of substrates

The Oxa1 protein is a well-conserved integral protein of the inner membrane of mitochondria. It mediates the insertion of both mitochondrial- and nuclear-encoded proteins from the matrix into the inner membrane. We investigated the distribution of budding yeast Oxa1 between the two subdomains of the contiguous inner membrane--the cristae membrane (CM) and the inner boundary membrane (IBM)--under different physiological conditions. We found that under fermentable growth conditions, Oxa1 is enriched in the IBM, whereas under nonfermentable (respiratory) growth conditions, it is predominantly localized in the CM. The enrichment of Oxa1 in the CM requires mitochondrial translation; similarly, deletion of the ribosome-binding domain of Oxa1 prevents an enrichment of Oxa1 in the CM. The predominant localization in the IBM under fermentable growth conditions is prevented by inhibiting mitochondrial protein import. Furthermore, overexpression of the nuclear-encoded Oxa1 substrate Mdl1 shifts the distribution of Oxa1 toward the IBM. Apparently, the availability of nuclear- and mitochondrial-encoded substrates influences the inner-membrane distribution of Oxa1. Our findings show that the distribution of Oxa1 within the inner membrane is dynamic and adapts to different physiological needs.     

Molecular basis for evolving modularity in the yeast protein interaction network

Scale-free networks are generically defined by a power-law distribution of node connectivities. Vastly different graph topologies fit this law, ranging from the assortative, with frequent similar-degree node connections, to a modular structure. Using a metric to determine the extent of modularity, we examined the yeast protein network and found it to be significantly self-dissimilar. By orthologous node categorization, we established the evolutionary trend in the network, from an “emerging” assortative network to a present-day modular topology. The evolving topology fits a generic connectivity distribution but with a progressive enrichment in intramodule hubs that avoid each other. Primeval tolerance to random node failure is shown to evolve toward resilience to hub failure, thus removing the fragility often ascribed to scale-free networks. This trend is algorithmically reproduced by adopting a connectivity accretion law that disfavors like-degree connections for large-degree nodes. The selective advantage of this trend relates to the need to prevent a failed hub from inducing failure in an adjacent hub. The molecular basis for the evolutionary trend is likely rooted in the high-entropy penalty entailed in the association of two intramodular hubs.     

Production of plant growth modulating volatiles is widespread among rhizosphere bacteria and strongly depends on culture conditions

Recent studies have suggested that bacterial volatiles play an important role in bacterial-plant interactions. However, few reports of bacterial species that produce plant growth modulating volatiles have been published, raising the question whether this is just an anecdotal phenomenon. To address this question, we performed a large screen of strains originating from the soil for volatile-mediated effects on Arabidopsis thaliana. All of the 42 strains tested showed significant volatile-mediated plant growth modulation, with effects ranging from plant death to a sixfold increase in plant biomass. The effects of bacterial volatiles were highly dependent on the cultivation medium and the inoculum quantity. GC-MS analysis of the tested strains revealed over 130 bacterial volatile compounds. Indole, 1-hexanol and pentadecane were selected for further studies because they appeared to promote plant growth. None of these compounds triggered a typical defence response, using production of ethylene and of reactive oxygen species (ROS) as read-outs. However, when plants were challenged with the flg-22 epitope of bacterial flagellin, a prototypical elicitor of defence responses, additional exposure to the volatiles reduced the flg-22-induced production of ethylene and ROS in a dose-dependent manner, suggesting that bacterial volatiles may act as effectors to inhibit the plant's defence response.     

Metabolic network sensitivity analysis

A linear sensitivity analysis of metabolic regulation in nonsteady states is described. This treatment considers the effects of enzymatic and nonenzymatic reactions and spontaneous rapid equilibria. Sensitivity coefficients summarizing the influence of metabolite concentrations on reaction rates and pathway net flux are defined, as are sensitivity coefficients summarizing the effects of enzymes on metabolite concentrations and net flux. The sensitivity analysis is implemented in an easily used set of computer programs. A four-enzyme test model was shown to be resistant to intuitive interpretation. Sensitivity analysis showed a shift of control from the end of the enzymic sequence to the beginning of the sequence with changing metabolic state. The homeostatic behavior of the test system was shown to depend on the nonenzymatic reactions as well as on the enzymes. Under certain conditions metabolic regulation is shared so intimately among enzymes and spontaneous reactions that separation of their effects is impossible.     

Metabolic network alignment in large scale by network compression

Metabolic network alignment is a system scale comparative analysis that discovers important similarities and differences across different metabolisms and organisms. Although the problem of aligning metabolic networks has been considered in the past, the computational complexity of the existing solutions has so far limited their use to moderately sized networks. In this paper, we address the problem of aligning two metabolic networks, particularly when both of them are too large to be dealt with using existing methods. We develop a generic framework that can significantly improve the scale of the networks that can be aligned in practical time. Our framework has three major phases, namely the compression phase, the alignment phase and the refinement phase. For the first phase, we develop an algorithm which transforms the given networks to a compressed domain where they are summarized using fewer nodes, termed supernodes, and interactions. In the second phase, we carry out the alignment in the compressed domain using an existing network alignment method as our base algorithm. This alignment results in supernode mappings in the compressed domain, each of which are smaller instances of network alignment problem. In the third phase, we solve each of the instances using the base alignment algorithm to refine the alignment results. We provide a user defined parameter to control the number of compression levels which generally determines the tradeoff between the quality of the alignment versus how fast the algorithm runs. Our experiments on the networks from KEGG pathway database demonstrate that the compression method we propose reduces the sizes of metabolic networks by almost half at each compression level which provides an expected speedup of more than an order of magnitude. We also observe that the alignments obtained by only one level of compression capture the original alignment results with high accuracy. Together, these suggest that our framework results in alignments that are comparable to existing algorithms and can do this with practical resource utilization for large scale networks that existing algorithms could not handle. As an example of our method's performance in practice, the alignment of organism-wide metabolic networks of human (1615 reactions) and mouse (1600 reactions) was performed under three minutes by only using a single level of compression.