Origin of structural difference in metabolic networks with respect to temperature

<p>Abstract</p> <p>Background</p> <p>Metabolism is believed to adaptively shape-shift with changing environment. In recent years, a structural difference with respect to temperature, which is an environmental factor, has been revealed in metabolic networks, implying that metabolic networks transit with temperature. Subsequently, elucidatation of the origin of these structural differences due to temperature is important for understanding the evolution of life. However, the origin has yet to be clarified due to the complexity of metabolic networks.</p> <p>Results</p> <p>Consequently, we propose a simple model with a few parameters to explain the transitions. We first present mathematical solutions of this model using mean-field approximation, and demonstrate that this model can reproduce structural properties, such as heterogeneous connectivity and hierarchical modularity, in real metabolic networks both qualitatively and quantitatively. We next show that the model parameters correlate with optimal growth temperature. In addition, we present a relationship between multiple cyclic properties and optimal growth temperature in metabolic networks.</p> <p>Conclusion</p> <p>From the proposed model, we find that such structural properties are determined by the emergence of a short-cut path, which reduces the minimum distance between two nodes on a graph. Furthermore, we investigate correlations between model parameters and growth temperature; as a result, we find that the emergence of the short-cut path tends to be inhibited with increasing temperature. In addition, we also find that the short-cut path bypasses a relatively long path at high temperature when the emergence of the new path is not inhibited. Even further, additional network analysis provides convincing evidence of the reliability of the proposed model and its conclusions on the possible origins of differences in metabolic network structure.</p

Popularity versus Similarity in Growing Networks

Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribution of the number of connections that nodes have follows power laws observed in many real networks. Preferential attachment has been directly validated for some real networks, including the Internet. Preferential attachment can also be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks, or duplication. Here we show that popularity is just one dimension of attractiveness. Another dimension is similarity. We develop a framework where new connections, instead of preferring popular nodes, optimize certain trade-offs between popularity and similarity. The framework admits a geometric interpretation, in which popularity preference emerges from local optimization. As opposed to preferential attachment, the optimization framework accurately describes large-scale evolution of technological (Internet), social (web of trust), and biological (E.coli metabolic) networks, predicting the probability of new links in them with a remarkable precision. The developed framework can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon

Conserved Ising Model on the Human Connectome

Dynamical models implemented on the large scale architecture of the human brain may shed light on how function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the \it{critical state}) the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of an homeostatic principle imposed to neural activity

Elasticity sampling links thermodynamics to metabolic control

Metabolic networks can be turned into kinetic models in a predefined steady state by sampling the reaction elasticities in this state. Elasticities for many reversible rate laws can be computed from the reaction Gibbs free energies, which are determined by the state, and from physically unconstrained saturation values. Starting from a network structure with allosteric regulation and consistent metabolic fluxes and concentrations, one can sample the elasticities, compute the control coefficients, and reconstruct a kinetic model with consistent reversible rate laws. Some of the model variables are manually chosen, fitted to data, or optimised, while the others are computed from them. The resulting model ensemble allows for probabilistic predictions, for instance, about possible dynamic behaviour. By adding more data or tighter constraints, the predictions can be made more precise. Model variants differing in network structure, flux distributions, thermodynamic forces, regulation, or rate laws can be realised by different model ensembles and compared by significance tests. The thermodynamic forces have specific effects on flux control, on the synergisms between enzymes, and on the emergence and propagation of metabolite fluctuations. Large kinetic models could help to simulate global metabolic dynamics and to predict the effects of enzyme inhibition, differential expression, genetic modifications, and their combinations on metabolic fluxes. MATLAB code for elasticity sampling is freely available

The solution space of metabolic networks: producibility, robustness and fluctuations

Flux analysis is a class of constraint-based approaches to the study of biochemical reaction networks: they are based on determining the reaction flux configurations compatible with given stoichiometric and thermodynamic constraints. One of its main areas of application is the study of cellular metabolic networks. We briefly and selectively review the main approaches to this problem and then, building on recent work, we provide a characterization of the productive capabilities of the metabolic network of the bacterium E.coli in a specified growth medium in terms of the producible biochemical species. While a robust and physiologically meaningful production profile clearly emerges (including biomass components, biomass products, waste etc.), the underlying constraints still allow for significant fluctuations even in key metabolites like ATP and, as a consequence, apparently lay the ground for very different growth scenarios.Comment: 10 pages, prepared for the Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japa

Metabolic Network Modularity in Archaea Depends on Growth Conditions

Network modularity is an important structural feature in metabolic networks. A previous study suggested that the variability in natural habitat promotes metabolic network modularity in bacteria. However, since many factors influence the structure of the metabolic network, this phenomenon might be limited and there may be other explanations for the change in metabolic network modularity. Therefore, we focus on archaea because they belong to another domain of prokaryotes and show variability in growth conditions (e.g., trophic requirement and optimal growth temperature), but not in habitats because of their specialized growth conditions (e.g., high growth temperature). The relationship between biological features and metabolic network modularity is examined in detail. We first show the absence of a relationship between network modularity and habitat variability in archaea, as archaeal habitats are more limited than bacterial habitats. Although this finding implies the need for further studies regarding the differences in network modularity, it does not contradict previous work. Further investigations reveal alternative explanations. Specifically, growth conditions, trophic requirement, and optimal growth temperature, in particular, affect metabolic network modularity. We have discussed the mechanisms for the growth condition-dependant changes in network modularity. Our findings suggest different explanations for the changes in network modularity and provide new insights into adaptation and evolution in metabolic networks, despite several limitations of data analysis