Consistency analysis of metabolic correlation networks

<p>Abstract</p> <p>Background</p> <p>Metabolic correlation networks are derived from the covariance of metabolites in replicates of metabolomics experiments. They constitute an interesting intermediate between topology (i.e. the system's architecture defined by the set of reactions between metabolites) and dynamics (i.e. the metabolic concentrations observed as fluctuations around steady-state values in the metabolic network).</p> <p>Results</p> <p>Here we analyze, how such a correlation network changes over time, and compare the relative positions of metabolites in the correlation networks with those in established metabolic networks derived from genome databases. We find that network similarity indeed decreases with an increasing time difference between these networks during a day/night course and, counter intuitively, that proximity of metabolites in the correlation network is no indicator of proximity of the metabolites in the metabolic network.</p> <p>Conclusion</p> <p>The organizing principles of correlation networks are distinct from those of metabolic reaction maps. Time courses of correlation networks may in the future prove an important data source for understanding these organizing principles.</p

Evaluation of rate law approximations in bottom-up kinetic models of metabolism.

BackgroundThe mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.ResultsIn this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.ConclusionsOverall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches

Uniform sampling of steady states in metabolic networks: heterogeneous scales and rounding

The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case of inferring the feasible steady states in models of metabolic networks, since they can show heterogeneous time scales . In this work we focus on rounding procedures based on building an ellipsoid that closely matches the sampling space, that can be used to define an efficient hit-and-run (HR) Markov Chain Monte Carlo. In this way the uniformity of the sampling of the convex space of interest is rigorously guaranteed, at odds with non markovian methods. We analyze and compare three rounding methods in order to sample the feasible steady states of metabolic networks of three models of growing size up to genomic scale. The first is based on principal component analysis (PCA), the second on linear programming (LP) and finally we employ the lovasz ellipsoid method (LEM). Our results show that a rounding procedure is mandatory for the application of the HR in these inference problem and suggest that a combination of LEM or LP with a subsequent PCA perform the best. We finally compare the distributions of the HR with that of two heuristics based on the Artificially Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good agreement with the results of the HR for the small network, while on genome scale models present inconsistencies.Comment: Replacement with major revision

Extracting the hierarchical organization of complex systems

Extracting understanding from the growing ``sea'' of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract the hierarchical organization of complex biological, social, and technological networks. We define an ensemble of hierarchically nested random graphs, which we use to validate the method. We then apply our method to real-world networks, including the air-transportation network, an electronic circuit, an email exchange network, and metabolic networks. We find that our method enables us to obtain an accurate multi-scale descriptions of a complex system.Comment: Figures in screen resolution. Version with full resolution figures available at http://amaral.chem-eng.northwestern.edu/Publications/Papers/sales-pardo-2007.pd

The relationship between metabolic rate and sociability is altered by food-deprivation

Individuals vary in the extent to which they associate with conspecifics, but little is known about the energetic underpinnings of this variation in sociability. Group-living allows individuals to find food more consistently, but within groups, there can be competition for food items. Individuals with an increased metabolic rate could display decreased sociability to reduce competition. Long-term food deprivation (FD) may alter any links between sociability and metabolic rate by affecting motivation to find food. We examined these issues in juvenile qingbo carp Spinibarbus sinensis, to understand how FD and metabolic rate affect sociability. Like many aquatic ectotherms, this species experiences seasonal bouts of FD. Individuals were either: (i) food-deprived for 21 days; or (ii) fed a maintenance ration (control). Fish from each treatment were measured for standard metabolic rate (SMR) and tested for sociability twice: once in the presence of a control stimulus shoal and once with a food-deprived stimulus shoal. Control individuals ventured further from stimulus shoals over a 30-min trial, while food-deprived fish did not change their distance from stimulus shoals as trials progressed. Control fish with a higher SMR were least sociable. Well-fed controls showed decreased sociability when exposed to food-deprived stimulus shoals, but there was evidence of consistency in relative sociability between exposures to different shoal types. Results contrast with previous findings that several days of fasting causes individuals to decrease associations with conspecifics. Prolonged FD may cause individuals to highly prioritize food acquisition, and the decreased vigilance that would accompany continuous foraging may heighten the need for the antipredator benefits of shoaling. Conversely, decreased sociability in well-fed fish with a high SMR probably minimizes intraspecific competition, allowing them to satisfy an increased energetic demand while foraging. Together, these results suggest that FD – a challenge common for many ectothermic species – can affect individual sociability as well as the attractiveness of groups towards conspecifics. In addition, the lack of a link between SMR and sociability in food-deprived fish suggests that, in situations where group membership is linked to fitness, the extent of correlated selection on metabolic traits may be context-dependent

On the effects of alternative optima in context-specific metabolic model predictions

Recent methodological developments have facilitated the integration of high-throughput data into genome-scale models to obtain context-specific metabolic reconstructions. A unique solution to this data integration problem often may not be guaranteed, leading to a multitude of context-specific predictions equally concordant with the integrated data. Yet, little attention has been paid to the alternative optima resulting from the integration of context-specific data. Here we present computational approaches to analyze alternative optima for different context-specific data integration instances. By using these approaches on metabolic reconstructions for the leaf of Arabidopsis thaliana and the human liver, we show that the analysis of alternative optima is key to adequately evaluating the specificity of the predictions in particular cellular contexts. While we provide several ways to reduce the ambiguity in the context-specific predictions, our findings indicate that the existence of alternative optimal solutions warrant caution in detailed context-specific analyses of metabolism

The specificity and robustness of long-distance connections in weighted, interareal connectomes

Brain areas' functional repertoires are shaped by their incoming and outgoing structural connections. In empirically measured networks, most connections are short, reflecting spatial and energetic constraints. Nonetheless, a small number of connections span long distances, consistent with the notion that the functionality of these connections must outweigh their cost. While the precise function of these long-distance connections is not known, the leading hypothesis is that they act to reduce the topological distance between brain areas and facilitate efficient interareal communication. However, this hypothesis implies a non-specificity of long-distance connections that we contend is unlikely. Instead, we propose that long-distance connections serve to diversify brain areas' inputs and outputs, thereby promoting complex dynamics. Through analysis of five interareal network datasets, we show that long-distance connections play only minor roles in reducing average interareal topological distance. In contrast, areas' long-distance and short-range neighbors exhibit marked differences in their connectivity profiles, suggesting that long-distance connections enhance dissimilarity between regional inputs and outputs. Next, we show that -- in isolation -- areas' long-distance connectivity profiles exhibit non-random levels of similarity, suggesting that the communication pathways formed by long connections exhibit redundancies that may serve to promote robustness. Finally, we use a linearization of Wilson-Cowan dynamics to simulate the covariance structure of neural activity and show that in the absence of long-distance connections, a common measure of functional diversity decreases. Collectively, our findings suggest that long-distance connections are necessary for supporting diverse and complex brain dynamics.Comment: 18 pages, 8 figure