Dynamic regulatory on/off minimization for biological systems under internal temporal perturbations

<p>Abstract</p> <p>Background</p> <p>Flux balance analysis (FBA) together with its extension, dynamic FBA, have proven instrumental for analyzing the robustness and dynamics of metabolic networks by employing only the stoichiometry of the included reactions coupled with adequately chosen objective function. In addition, under the assumption of minimization of metabolic adjustment, dynamic FBA has recently been employed to analyze the transition between metabolic states.</p> <p>Results</p> <p>Here, we propose a suite of novel methods for analyzing the dynamics of (internally perturbed) metabolic networks and for quantifying their robustness with limited knowledge of kinetic parameters. Following the biochemically meaningful premise that metabolite concentrations exhibit smooth temporal changes, the proposed methods rely on minimizing the significant fluctuations of metabolic profiles to predict the time-resolved metabolic state, characterized by both fluxes and concentrations. By conducting a comparative analysis with a kinetic model of the Calvin-Benson cycle and a model of plant carbohydrate metabolism, we demonstrate that the principle of regulatory on/off minimization coupled with dynamic FBA can accurately predict the changes in metabolic states.</p> <p>Conclusions</p> <p>Our methods outperform the existing dynamic FBA-based modeling alternatives, and could help in revealing the mechanisms for maintaining robustness of dynamic processes in metabolic networks over time.</p

Concurrent Conditional Clustering of Multiple Networks: COCONETS

<div><p>The accumulation of high-throughput data from different experiments has facilitated the extraction of condition-specific networks over the same set of biological entities. Comparing and contrasting of such multiple biological networks is in the center of differential network biology, aiming at determining general and condition-specific responses captured in the network structure (<i>i.e.</i>, included associations between the network components). We provide a novel way for comparison of multiple networks based on determining network clustering (<i>i.e.</i>, partition into communities) which is optimal across the set of networks with respect to a given cluster quality measure. To this end, we formulate the optimization-based problem of concurrent conditional clustering of multiple networks, termed COCONETS, based on the modularity. The solution to this problem is a clustering which depends on all considered networks and pinpoints their preserved substructures. We present theoretical results for special classes of networks to demonstrate the implications of conditionality captured by the COCONETS formulation. As the problem can be shown to be intractable, we extend an existing efficient greedy heuristic and applied it to determine concurrent conditional clusters on coexpression networks extracted from publically available time-resolved transcriptomics data of <i>Escherichia coli</i> under five stresses as well as on metabolite correlation networks from metabolomics data set from <i>Arabidopsis thaliana</i> exposed to eight environmental conditions. We demonstrate that the investigation of the differences between the clustering based on all networks with that obtained from a subset of networks can be used to quantify the specificity of biological responses. While a comparison of the <i>Escherichia coli</i> coexpression networks based on seminal properties does not pinpoint biologically relevant differences, the common network substructures extracted by COCONETS are supported by existing experimental evidence. Therefore, the comparison of multiple networks based on concurrent conditional clustering offers a novel venue for detection and investigation of preserved network substructures.</p></div

Condition-specific network properties and pairwise network similarities for eight environmental conditions in <i>Arabidopsis thaliana</i>.

<p>The upper part of the table includes seven seminal network properties together with the thresholds used to establish the edges in the correlation networks of metabolites under eight investigated stresses: 4 C and darkness (4-D), 21 C and darkness (21-D), 32 C and darkness (32-D), 4 C and light (4-L), 21 C and low-light (21-LL), 21 C and high light (21-HL), and 32 C and light (32-L). The lower part of the table includes the Jaccard similarity between the edge-sets of the condition-specific networks.</p

Illustration of COCONETS.

<p>Given are three networks in the top row. The clusters in the optimal clustering for each network are marked in different colors (red and blue). The optimal concurrent conditional clustering of the two networks given in the middle row is of value 0 and is suboptimal for the network to the left. The optimal clusterings for any of the two networks shown in the bottom row are suboptimal concurrent conditional clustering; the shown clustering yields a value of −0.24, while the optimal clustering is of value 0, whereby all nodes form a single cluster (not shown).</p

Clustering tree based on the adjusted Rand index values for the investigated CoCo clusterings.

<p>The clusterings from single networks are based on the greedy heuristic for approximating the MODULARITY problem. All other clusterings are based on the greedy heuristic for COCONETS. The tree is derived by agglomerative clustering with a distance matrix derived from the adjusted Rand index values for all pairwise comparisons of the obtained CoCo clusterings. The stress conditions are denoted as follows: cold (c), heat (h), lactose diauxie (ld), oxidative (o), and stationary phase (s); their pairwise combinations are marked with ‘/’, and the clustering over all five stresses, by ‘all’. The number of clusters in each CoCo clustering is included next to the abbreviations for the stresses.</p

Illustration of network comparison based on community structure.

<p>Shown are three networks, , , and . Nodes belonging to the same community in each network are marked by the same color. Networks and differ in 11 edges, while networks and do not share 4 edges. Nevertheless, the community structures between and are equivalent, while this is not the case for the community structures in and .</p

Structured patterns in geographic variability of metabolic phenotypes in arabidopsis thaliana

Understanding molecular factors determining local adaptation is a key challenge, particularly relevant for plants, which are sessile organisms coping with a continuously fluctuating environment. Here we introduce a rigorous network-based approach for investigating the relation between geographic location of accessions and heterogeneous molecular phenotypes. We demonstrate for Arabidopsis accessions that not only genotypic variability but also flowering and metabolic phenotypes show a robust pattern of isolation-by-distance. Our approach opens new avenues to investigate relations between geographic origin and heterogeneous molecular phenotypes, like metabolite profiles, which can easily be obtained in species where genome data is not yet available

Structured patterns in geographic variability of metabolic phenotypes in arabidopsis thaliana

Understanding molecular factors determining local adaptation is a key challenge, particularly relevant for plants, which are sessile organisms coping with a continuously fluctuating environment. Here we introduce a rigorous network-based approach for investigating the relation between geographic location of accessions and heterogeneous molecular phenotypes. We demonstrate for Arabidopsis accessions that not only genotypic variability but also flowering and metabolic phenotypes show a robust pattern of isolation-by-distance. Our approach opens new avenues to investigate relations between geographic origin and heterogeneous molecular phenotypes, like metabolite profiles, which can easily be obtained in species where genome data is not yet available

Metabolic efficiency underpins performance trade-offs in growth of arabidopsis thaliana

Growth often involves a trade-off between the performance of contending tasks; metabolic plasticity can play an important role. Here we grow 97 Arabidopsis thaliana accessions in three conditions with a differing supply of carbon and nitrogen and identify a trade-off between two tasks required for rosette growth: increasing the physical size and increasing the protein concentration. We employ the Pareto performance frontier concept to rank accessions based on their multitask performance; only a few accessions achieve a good trade-off under all three growth conditions. We determine metabolic efficiency in each accession and condition by using metabolite levels and activities of enzymes involved in growth and protein synthesis. We demonstrate that accessions with high metabolic efficiency lie closer to the performance frontier and show increased metabolic plasticity. We illustrate how public domain data can be used to search for additional contending tasks, which may underlie the sub-optimality in some accessions