Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomerative approach.

The tricarboxylic acid (TCA) cycle is a crucial component of respiratory metabolism in both photosynthetic and heterotrophic plant organs. All of the major genes of the tomato TCA cycle have been cloned recently, allowing the generation of a suite of transgenic plants in which the majority of the enzymes in the pathway are progressively decreased. Investigations of these plants have provided an almost complete view of the distribution of control in this important pathway. Our studies suggest that citrate synthase, aconitase, isocitrate dehydrogenase, succinyl CoA ligase, succinate dehydrogenase, fumarase and malate dehydrogenase have control coefficients flux for respiration of −0.4, 0.964, −0.123, 0.0008, 0.289, 0.601 and 1.76, respectively; while 2‐oxoglutarate dehydrogenase is estimated to have a control coefficient of 0.786 in potato tubers. These results thus indicate that the control of this pathway is distributed among malate dehydrogenase, aconitase, fumarase, succinate dehydrogenase and 2‐oxoglutarate dehydrogenase. The unusual distribution of control estimated here is consistent with specific non‐cyclic flux mode and cytosolic bypasses that operate in illuminated leaves. These observations are discussed in the context of known regulatory properties of the enzymes and some illustrative examples of how the pathway responds to environmental change are given.

Photosynthesis is the basis for life, and its optimization is a key biotechnological aim given the problems of population explosion and environmental deterioration. We describe a method to resolve intracellular fluxes in intact Arabidopsis thaliana rosettes based on time-dependent labeling patterns in the metabolome. Plants photosynthesizing under limiting irradiance and ambient CO₂ in a custom-built chamber were transferred into a ¹³CO₂-enriched environment. The isotope labeling patterns of 40 metabolites were obtained using liquid or gas chromatography coupled to mass spectrometry. Labeling kinetics revealed striking differences between metabolites. At a qualitative level, they matched expectations in terms of pathway topology and stoichiometry, but some unexpected features point to the complexity of subcellular and cellular compartmentation. To achieve quantitative insights, the data set was used for estimating fluxes in the framework of kinetic flux profiling. We benchmarked flux estimates to four classically determined flux signatures of photosynthesis and assessed the robustness of the estimates with respect to different features of the underlying metabolic model and the time-resolved data set.

The model organism Arabidopsis thaliana is readily used in basic research due to resource availability and relative speed of data acquisition. A major goal is to transfer acquired knowledge from Arabidopsis to crop species. However, the identification of functional equivalents of well-characterized Arabidopsis genes in other plants is a nontrivial task. It is well documented that transcriptionally coordinated genes tend to be functionally related and that such relationships may be conserved across different species and even kingdoms. To exploit such relationships, we constructed whole-genome coexpression networks for Arabidopsis and six important plant crop species. The interactive networks, clustered using the HCCA algorithm, are provided under the banner PlaNet (http://aranet.mpimp-golm.mpg.de). We implemented a comparative network algorithm that estimates similarities between network structures. Thus, the platform can be used to swiftly infer similar coexpressed network vicinities within and across species and can predict the identity of functional homologs. We exemplify this using the PSA-D and chalcone synthase-related gene networks. Finally, we assessed how ontology terms are transcriptionally connected in the seven species and provide the corresponding MapMan term coexpression networks. The data support the contention that this platform will considerably improve transfer of knowledge generated in Arabidopsis to valuable crop species.

Genome-wide association studies have been successful in identifying genes involved in polygenic traits and are valuable for crop improvement. Tomato (Solanum lycopersicum) is a major crop and is highly appreciated worldwide for its health value. We used a core collection of 163 tomato accessions composed of S. lycopersicum, S. lycopersicum var cerasiforme, and Solanum pimpinellifolium to map loci controlling variation in fruit metabolites. Fruits were phenotyped for a broad range of metabolites, including amino acids, sugars, and ascorbate. In parallel, the accessions were genotyped with 5,995 single-nucleotide polymorphism markers spread over the whole genome. Genome-wide association analysis was conducted on a large set of metabolic traits that were stable over 2 years using a multilocus mixed model as a general method for mapping complex traits in structured populations and applied to tomato. We detected a total of 44 loci that were significantly associated with a total of 19 traits, including sucrose, ascorbate, malate, and citrate levels. These results not only provide a list of candidate loci to be functionally validated but also a powerful analytical approach for finding genetic variants that can be directly used for crop improvement and deciphering the genetic architecture of complex traits.

A large-scale metabolic quantitative trait loci (mQTL) analysis was performed on the well-characterized Solanum pennellii introgression lines to investigate the genomic regions associated with secondary metabolism in tomato fruit pericarp. In total, 679 mQTLs were detected across the 76 introgression lines. Heritability analyses revealed that mQTLs of secondary metabolism were less affected by environment than mQTLs of primary metabolism. Network analysis allowed us to assess the interconnectivity of primary and secondary metabolism as well as to compare and contrast their respective associations with morphological traits. Additionally, we applied a recently established real-time quantitative PCR platform to gain insight into transcriptional control mechanisms of a subset of the mQTLs, including those for hydroxycinnamates, acyl-sugar, naringenin chalcone, and a range of glycoalkaloids. Intriguingly, many of these compounds displayed a dominant-negative mode of inheritance, which is contrary to the conventional wisdom that secondary metabolite contents decreased on domestication. We additionally performed an exemplary evaluation of two candidate genes for glycolalkaloid mQTLs via the use of virus-induced gene silencing. The combined data of this study were compared with previous results on primary metabolism obtained from the same material and to other studies of natural variance of secondary metabolism.