Intracellular fluxes shape all cellular functions, and understanding how they are shaped by the joint effects of enzyme abundances and metabolite concentrations in vivo currently requires gathering matched quantitative proteomic and metabolomic data sets from resource-intensive experiments. Here, we present KineFlux, a hybrid approach that combines machine learning with enzyme-constrained metabolic models to accurately predict steady-state flux distributions using only quantitative proteomic data. KineFlux builds machine learning models for metabolite concentration effects on reaction fluxes, obtained by using fluxomics and proteomics data from a training set of experiments. Using fluxomic and proteomic data sets of Escherichia coli and Saccharomyces cerevisiae, we show that the steady-state flux distributions predicted by KineFlux are in line with fluxes estimated by classical approaches. We also demonstrate that the machine learning models embedded in KineFlux are transferrable at marginal loss of accuracy using independent testing data from E. coli. Therefore, KineFlux expands the usability of enzyme-constrained models towards accurate prediction of genome-scale flux distributions compatible with metabolite concentration effects without knowledge of enzyme kinetics.

Traits in any organism are not independent, but show considerable integration, observed in a form of couplings and trade-offs. Therefore, improvement in one trait may affect other traits, often in undesired direction. To account for this problem, crop breeding increasingly relies on multi-trait genomic prediction (MT-GP) approaches that leverage the availability of genetic markers from different populations along with advances in high-throughput precision phenotyping. While significant progress has been made to jointly model multiple traits using a variety of statistical and machine learning approaches, there is no systematic comparison of advantages and shortcomings of the existing classes of MT-GP models. Here, we fill this knowledge gap by first classifying the existing MT-GP models and briefly summarizing their general principles, modeling assumptions, and potential limitations. We then perform an extensive comparative analysis with 10 traits measured in an Oryza sativa diversity panel using cross-validation scenarios relevant in breeding practice. Finally, we discuss directions that can enable the building of next generation MT-GP models in addressing pressing challenges in crop breeding.

Metabolites acting as substrates and regulators of all biochemical reactions play an important role in maintaining the functionality of cellular metabolism. Despite advances in the constraint-based framework for genome-scale metabolic modeling, we lack reliable proxies for metabolite concentrations that can be efficiently determined and that allow us to investigate the relationship between metabolite concentrations in specific metabolic states in the absence of measurements. Here, we introduce a constraint-based approach, the flux-sum coupling analysis (FSCA), which facilitates the study of the interdependencies between metabolite concentrations by determining coupling relationships based on the flux-sum of metabolites. Application of FSCA on metabolic models of Escherichia coli, Saccharomyces cerevisiae, and Arabidopsis thaliana showed that the three coupling relationships are present in all models and pinpointed similarities in coupled metabolite pairs. Using the available concentration measurements of E. coli metabolites, we demonstrated that the coupling relationships identified by FSCA can capture the qualitative associations between metabolite concentrations and that flux-sum is a reliable proxy for metabolite concentration. Therefore, FSCA provides a novel tool for exploring and understanding the intricate interdependencies between the metabolite concentrations, advancing the understanding of metabolic regulation, and improving flux-centered systems biology approaches.

The increasing availability of enzyme turnover number measurements from experiments and of turnover number predictions from deep learning models prompts the use of these enzyme parameters in precise metabolic engineering. Yet, there is no computational approach that allows the prediction of metabolic engineering strategies that rely on the modification of turnover numbers. It is also unclear if modifications of turnover numbers without alterations in the host's transcriptional regulatory machinery suffice to increase the production of chemicals of interest. Here, we present a constraint-based modeling approach, termed Overcoming Kinetic rate Obstacles (OKO), that uses enzyme-constrained metabolic models to predict in silico strategies to increase the production of a given chemical, while ensuring specified cell growth. We demonstrate that the application of OKO to enzyme-constrained metabolic models of Escherichia coli and Saccharomyces cerevisiae results in strategies that can at least double the production of over 40 compounds with little penalty to growth. Interestingly, we show that the overproduction of compounds of interest does not entail only an increase in the values of turnover numbers. Lastly, we demonstrate that a refinement of OKO, allowing also for manipulation of enzyme abundance, facilitates the usage of the available compendia and deep learning models of turnover numbers in the design of precise metabolic engineering strategies. Our results expand the usage of genome-scale metabolic models toward the identification of targets for protein engineering, allowing their direct usage in the generation of innovative metabolic engineering designs for various biotechnological applications.

Protein allocation determines the activity of cellular pathways and affects growth across all organisms. Therefore, different experimental and machine learning approaches have been developed to quantify and predict protein abundance and how they are allocated to different cellular functions, respectively. Yet, despite advances in protein quantification, it remains challenging to predict condition-specific allocation of enzymes in metabolic networks. Here, using protein-constrained metabolic models, we propose a family of constrained-based approaches, termed PARROT, to predict how much of each enzyme is used based on the principle of minimizing the difference between a reference and an alternative growth condition. To this end, PARROT variants model the minimization of enzyme reallocation using four different (combinations of) distance functions. We demonstrate that the PARROT variant that minimizes the Manhattan distance between the enzyme allocation of a reference and an alternative condition outperforms existing approaches based on the parsimonious distribution of fluxes or enzymes for both Escherichia coli and Saccharomyces cerevisiae. Further, we show that the combined minimization of flux and enzyme allocation adjustment leads to inconsistent predictions. Together, our findings indicate that minimization of protein allocation rather than flux redistribution is a governing principle determining steady-state pathway activity for microorganism grown in alternative growth conditions.

Intracellular fluxes represent a joint outcome of cellular transcription and translation and reflect the availability and usage of nutrients from the environment. While approaches from the constraint-based metabolic framework can accurately predict cellular phenotypes, such as growth and exchange rates with the environment, accurate prediction of intracellular fluxes remains a pressing problem. Parsimonious flux balance analysis (pFBA) has become an approach of choice to predict intracellular fluxes by employing the principle of efficient usage of protein resources. Nevertheless, comparative analyses of intracellular flux predictions from pFBA against fluxes estimated from labeling experiments remain scarce. Here, we posited that steady-state flux distributions derived from the principle of maximizing multi-reaction dependencies are of improved accuracy and precision than those resulting from pFBA. To this end, we designed a constraint-based approach, termed complex-balanced FBA (cbFBA), to predict steady-state flux distributions that support the given specific growth rate and exchange fluxes. We showed that the steady-state flux distributions resulting from cbFBA in comparison to pFBA show better agreement with experimentally measured fluxes from 17 Escherichia coli strains and are more precise, due to the smaller space of alternative solutions. We also showed that the same principle holds in eukaryotes by comparing the predictions of pFBA and cbFBA against experimentally derived steady-state flux distributions from 26 knock-out mutants of Saccharomyces cerevisiae. Furthermore, our results showed that intracellular fluxes predicted by cbFBA provide better support for the principle of minimizing metabolic adjustment between mutants and wild types. Together, our findings point that other principles that consider the dynamics and coordination of steady states may govern the distribution of intracellular fluxes.

Despite extensive research efforts, reconstruction of gene regulatory networks (GRNs) from transcriptomics data remains a pressing challenge in systems biology. While non-linear approaches for reconstruction of GRNs show improved performance over simpler alternatives, we do not yet have understanding if joint modelling of multiple target genes may improve performance, even under linearity assumptions. To address this problem, we propose two novel approaches that cast the GRN reconstruction problem as a blend between regularized multivariate regression and graphical models that combine the L2,1-norm with classical regularization techniques. We used data and networks from the DREAM5 challenge to show that the proposed models provide consistently good performance in comparison to contenders whose performance varies with data sets from simulation and experiments from model unicellular organisms Escherichia coli and Saccharomyces cerevisiae. Since the models' formulation facilitates the prediction of master regulators, we also used the resulting findings to identify master regulators over all data sets as well as their plasticity across different environments. Our results demonstrate that the identified master regulators are in line with experimental evidence from the model bacterium E. coli. Together, our study demonstrates that simultaneous modelling of several target genes results in improved inference of GRNs and can be used as an alternative in different applications.

Composition and functions of microbial communities affect important traits in diverse hosts, from crops to humans. Yet, mechanistic understanding of how metabolism of individual microbes is affected by the community composition and metabolite leakage is lacking. Here, we first show that the consensus of automatically generated metabolic reconstructions improves the quality of the draft reconstructions, measured by comparison to reference models. We then devise an approach for gap filling, termed COMMIT, that considers metabolites for secretion based on their permeability and the composition of the community. By applying COMMIT with two soil communities from the Arabidopsis thaliana culture collection, we could significantly reduce the gap-filling solution in comparison to filling gaps in individual reconstructions without affecting the genomic support. Inspection of the metabolic interactions in the soil communities allows us to identify microbes with community roles of helpers and beneficiaries. Therefore, COMMIT offers a versatile fully automated solution for large-scale modelling of microbial communities for diverse biotechnological applications.

MOTIVATION: Genomic selection (GS) is currently deemed the most effective approach to speed up breeding of agricultural varieties. It has been recognized that consideration of multiple traits in GS can improve accuracy of prediction for traits of low heritability. However, since GS forgoes statistical testing with the idea of improving predictions, it does not facilitate mechanistic understanding of the contribution of particular single nucleotide polymorphisms (SNP). RESULTS: Here, we propose a L2,1-norm regularized multivariate regression model and devise a fast and efficient iterative optimization algorithm, called L2,1-joint, applicable in multi-trait GS. The usage of the L2,1-norm facilitates variable selection in a penalized multivariate regression that considers the relation between individuals, when the number of SNPs is much larger than the number of individuals. The capacity for variable selection allows us to define master regulators that can be used in a multi-trait GS setting to dissect the genetic architecture of the analyzed traits. Our comparative analyses demonstrate that the proposed model is a favorable candidate compared to existing state-of-the-art approaches. Prediction and variable selection with datasets from Brassica napus, wheat and Arabidopsis thaliana diversity panels are conducted to further showcase the performance of the proposed model. AVAILABILITY AND IMPLEMENTATION: : The model is implemented using R programming language and the code is freely available from https://github.com/alainmbebi/L21-norm-GS. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Prediction of protein complexes from protein-protein interaction (PPI) networks is an important problem in systems biology, as they control different cellular functions. The existing solutions employ algorithms for network community detection that identify dense subgraphs in PPI networks. However, gold standards in yeast and human indicate that protein complexes can also induce sparse subgraphs, introducing further challenges in protein complex prediction. RESULTS: To address this issue, we formalize protein complexes as biclique spanned subgraphs, which include both sparse and dense subgraphs. We then cast the problem of protein complex prediction as a network partitioning into biclique spanned subgraphs with removal of minimum number of edges, called coherent partition. Since finding a coherent partition is a computationally intractable problem, we devise a parameter-free greedy approximation algorithm, termed Protein Complexes from Coherent Partition (PC2P), based on key properties of biclique spanned subgraphs. Through comparison with nine contenders, we demonstrate that PC2P: (i) successfully identifies modular structure in networks, as a prerequisite for protein complex prediction, (ii) outperforms the existing solutions with respect to a composite score of five performance measures on 75% and 100% of the analyzed PPI networks and gold standards in yeast and human, respectively, and (iii,iv) does not compromise GO semantic similarity and enrichment score of the predicted protein complexes. Therefore, our study demonstrates that clustering of networks in terms of biclique spanned subgraphs is a promising framework for detection of complexes in PPI networks. AVAILABILITY AND IMPLEMENTATION: https://github.com/SaraOmranian/PC2P. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Large-scale metabolic models are widely used to design metabolic engineering strategies for diverse biotechnological applications. However, the existing computational approaches focus on alteration of reaction fluxes and often neglect the manipulations of gene expression to implement these strategies. RESULTS: Here, we find that the association of genes with multiple reactions leads to infeasibility of engineering strategies at the flux level, since they require contradicting manipulations of gene expression. Moreover, we identify that all of the existing approaches to design gene knockout strategies do not ensure that the resulting design may also require other gene alterations, such as up- or downregulations, to match the desired flux distribution. To address these issues, we propose a constraint-based approach, termed GeneReg, that facilitates the design of feasible metabolic engineering strategies at the gene level and that is readily applicable to large-scale metabolic networks. We show that GeneReg can identify feasible strategies to overproduce ethanol in Escherichia coli and lactate in Saccharomyces cerevisiae, but overproduction of the TCA cycle intermediates is not feasible in five organisms used as cell factories under default growth conditions. Therefore, GeneReg points at the need to couple gene regulation and metabolism to design rational metabolic engineering strategies. AVAILABILITY AND IMPLEMENTATION: https://github.com/MonaRazaghi/GeneReg. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Constraint-based modeling approaches allow the estimation of maximal in vivo enzyme catalytic rates that can serve as proxies for enzyme turnover numbers. Yet, genome-scale flux profiling remains a challenge in deploying these approaches to catalogue proxies for enzyme catalytic rates across organisms. RESULTS: Here, we formulate a constraint-based approach, termed NIDLE-flux, to estimate fluxes at a genome-scale level by using the principle of efficient usage of expressed enzymes. Using proteomics data from Escherichia coli, we show that the fluxes estimated by NIDLE-flux and the existing approaches are in excellent qualitative agreement (Pearson correlation > 0.9). We also find that the maximal in vivo catalytic rates estimated by NIDLE-flux exhibits a Pearson correlation of 0.74 with in vitro enzyme turnover numbers. However, NIDLE-flux results in a 1.4-fold increase in the size of the estimated maximal in vivo catalytic rates in comparison to the contenders. Integration of the maximum in vivo catalytic rates with publically available proteomics and metabolomics data provide a better match to fluxes estimated by NIDLE-flux. Therefore, NIDLE-flux facilitates more effective usage of proteomics data to estimate proxies for kcatomes. AVAILABILITY AND IMPLEMENTATION: https://github.com/Rudan-X/NIDLE-flux-code. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Actin filaments (AFs) are dynamic structures that substantially change their organization over time. The dynamic behavior and the relatively low signal-to-noise ratio during live-cell imaging have rendered the quantification of the actin organization a difficult task. RESULTS: We developed an automated image-based framework that extracts AFs from fluorescence microscopy images and represents them as networks, which are automatically analyzed to identify and compare biologically relevant features. Although the source code is freely available, we have now implemented the framework into a graphical user interface that can be installed as a Fiji plugin, thus enabling easy access by the research community. AVAILABILITY AND IMPLEMENTATION: CytoSeg 2.0 is open-source software under the GPL and is available on Github: https://github.com/jnowak90/CytoSeg2.0. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Biological networks across scales exhibit hierarchical organization that may constrain network function. Yet, understanding how these hierarchies arise due to the operational constraint of the networks and whether they impose limits to molecular phenotypes remains elusive. Here we show that metabolic networks include a hierarchy of reactions based on a natural flux ordering that holds for every steady state. We find that the hierarchy of reactions is reflected in experimental measurements of transcript, protein and flux levels of Escherichia coli under various growth conditions as well as in the catalytic rate constants of the corresponding enzymes. Our findings point at resource partitioning and a fine-tuning of enzyme levels in E. coli to respect the constraints imposed by the network structure at steady state. Since reactions in upper layers of the hierarchy impose an upper bound on the flux of the reactions downstream, the hierarchical organization of metabolism due to the flux ordering has direct applications in metabolic engineering.

Cellular functions are shaped by reaction networks whose dynamics are determined by the concentrations of underlying components. However, cellular mechanisms ensuring that a component's concentration resides in a given range remain elusive. We present network properties which suffice to identify components whose concentration ranges can be efficiently computed in mass-action metabolic networks. We show that the derived ranges are in excellent agreement with simulations from a detailed kinetic metabolic model of Escherichia coli. We demonstrate that the approach can be used with genome-scale metabolic models to arrive at predictions concordant with measurements from Escherichia coli under different growth scenarios. By application to 14 genome-scale metabolic models from diverse species, our approach specifies the cellular determinants of concentration ranges that can be effectively employed to make predictions for a variety of biotechnological and medical applications.

The integration of experimental data into genome-scale metabolic models can greatly improve flux predictions. This is achieved by restricting predictions to a more realistic context-specific domain, like a particular cell or tissue type. Several computational approaches to integrate data have been proposed-generally obtaining context-specific (sub)models or flux distributions. However, these approaches may lead to a multitude of equally valid but potentially different models or flux distributions, due to possible alternative optima in the underlying optimization problems. Although this issue introduces ambiguity in context-specific predictions, it has not been generally recognized, especially in the case of model reconstructions. In this study, we analyze the impact of alternative optima in four state-of-the-art context-specific data integration approaches, providing both flux distributions and/or metabolic models. To this end, we present three computational methods and apply them to two particular case studies: leaf-specific predictions from the integration of gene expression data in a metabolic model of Arabidopsis thaliana, and liver-specific reconstructions derived from a human model with various experimental data sources. The application of these methods allows us to obtain the following results: (i) we sample the space of alternative flux distributions in the leaf- and the liver-specific case and quantify the ambiguity of the predictions. In addition, we show how the inclusion of ℓ1-regularization during data integration reduces the ambiguity in both cases. (ii) We generate sets of alternative leaf- and liver-specific models that are optimal to each one of the evaluated model reconstruction approaches. We demonstrate that alternative models of the same context contain a marked fraction of disparate reactions. Further, we show that a careful balance between model sparsity and metabolic functionality helps in reducing the discrepancies between alternative models. Finally, our findings indicate that alternative optima must be taken into account for rendering the context-specific metabolic model predictions less ambiguous.

MOTIVATION: Understanding the rerouting of metabolic reaction fluxes upon perturbations has the potential to link changes in molecular state of a cellular system to alteration of growth. Yet, differential flux profiling on a genome-scale level remains one of the biggest challenges in systems biology. This is particularly relevant in plants, for which fluxes in autotrophic growth necessitate time-consuming instationary labeling experiments and costly computations, feasible for small-scale networks. RESULTS: Here we present a computationally and experimentally facile approach, termed iReMet-Flux, which integrates relative metabolomics data in a metabolic model to predict differential fluxes at a genome-scale level. Our approach and its variants complement the flux estimation methods based on radioactive tracer labeling. We employ iReMet-Flux with publically available metabolic profiles to predict reactions and pathways with altered fluxes in photo-autotrophically grown Arabidopsis and four photorespiratory mutants undergoing high-to-low CO2 acclimation. We also provide predictions about reactions and pathways which are most strongly regulated in the investigated experiments. The robustness and variability analyses, tailored to the formulation of iReMet-Flux, demonstrate that the findings provide biologically relevant information that is validated with external measurements of net CO2 exchange and biomass production. Therefore, iReMet-Flux paves the wave for mechanistic dissection of the interplay between pathways of primary and secondary metabolisms at a genome-scale. AVAILABILITY AND IMPLEMENTATION: The source code is available from the authors upon request. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SUMMARY: Automated analysis of imaged phenotypes enables fast and reproducible quantification of biologically relevant features. Despite recent developments, recordings of complex networked structures, such as leaf venation patterns, cytoskeletal structures or traffic networks, remain challenging to analyze. Here we illustrate the applicability of img2net to automatedly analyze such structures by reconstructing the underlying network, computing relevant network properties and statistically comparing networks of different types or under different conditions. The software can be readily used for analyzing image data of arbitrary 2D and 3D network-like structures. AVAILABILITY AND IMPLEMENTATION: img2net is open-source software under the GPL and can be downloaded from http://mathbiol.mpimp-golm.mpg.de/img2net/, where supplementary information and datasets for testing are provided. CONTACT: [email protected].

Constraint-based approaches have been used for integrating data in large-scale metabolic networks to obtain insights into metabolism of various organisms. Due to the underlying steady-state assumption, these approaches are usually not suited for making predictions about metabolite levels. Here, we ask whether we can make inferences about the variability of metabolite levels from a constraint-based analysis based on the integration of transcriptomics data. To this end, we analyze time-resolved transcriptomics and metabolomics data from Arabidopsis thaliana under a set of eight different light and temperature conditions. In a previous study, the gene expression data have already been integrated in a genome-scale metabolic network to predict pathways, termed modulators and sustainers, which are differentially regulated with respect to a biochemically meaningful data-driven null model. Here, we present a follow-up analysis which bridges the gap between flux- and metabolite-centric methods. One of our main findings demonstrates that under certain environmental conditions, the levels of metabolites acting as substrates in modulators or sustainers show significantly lower temporal variations with respect to the remaining measured metabolites. This observation is discussed within the context of a systems-view of plasticity and robustness of metabolite contents and pathway fluxes. Our study paves the way for investigating the existence of similar principles in other species for which both genome-scale networks and high-throughput metabolomics data of high quality are becoming increasingly available.

Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign "share of control" to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions.

MOTIVATION: Metabolic engineering aims at modulating the capabilities of metabolic networks by changing the activity of biochemical reactions. The existing constraint-based approaches for metabolic engineering have proven useful, but are limited only to reactions catalogued in various pathway databases. RESULTS: We consider the alternative of designing synthetic strategies which can be used not only to characterize the maximum theoretically possible product yield but also to engineer networks with optimal conversion capability by using a suitable biochemically feasible reaction called 'stoichiometric capacitance'. In addition, we provide a theoretical solution for decomposing a given stoichiometric capacitance over a set of known enzymatic reactions. We determine the stoichiometric capacitance for genome-scale metabolic networks of 10 organisms from different kingdoms of life and examine its implications for the alterations in flux variability patterns. Our empirical findings suggest that the theoretical capacity of metabolic networks comes at a cost of dramatic system's changes. CONTACT: [email protected], or [email protected] SUPPLEMENTARY INFORMATION: Supplementary tables are available at Bioinformatics online.

MOTIVATION: Network-centered studies in systems biology attempt to integrate the topological properties of biological networks with experimental data in order to make predictions and posit hypotheses. For any topology-based prediction, it is necessary to first assess the significance of the analyzed property in a biologically meaningful context. Therefore, devising network null models, carefully tailored to the topological and biochemical constraints imposed on the network, remains an important computational problem. RESULTS: We first review the shortcomings of the existing generic sampling scheme-switch randomization-and explain its unsuitability for application to metabolic networks. We then devise a novel polynomial-time algorithm for randomizing metabolic networks under the (bio)chemical constraint of mass balance. The tractability of our method follows from the concept of mass equivalence classes, defined on the representation of compounds in the vector space over chemical elements. We finally demonstrate the uniformity of the proposed method on seven genome-scale metabolic networks, and empirically validate the theoretical findings. The proposed method allows a biologically meaningful estimation of significance for metabolic network properties.

SUMMARY: Analysis of biological networks requires assessing the statistical significance of network-based predictions by using a realistic null model. However, the existing network null model, switch randomization, is unsuitable for metabolic networks, as it does not include physical constraints and generates unrealistic reactions. We present JMassBalance, a tool for mass-balanced randomization and analysis of metabolic networks. The tool allows efficient generation of large sets of randomized networks under the physical constraint of mass balance. In addition, various structural properties of the original and randomized networks can be calculated, facilitating the identification of the salient properties of metabolic networks with a biologically meaningful null model. AVAILABILITY AND IMPLEMENTATION: JMassBalance is implemented in Java and freely available on the web at http://mathbiol.mpimp-golm.mpg.de/massbalance/. CONTACT: [email protected].

BACKGROUND: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. RESULTS: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. CONCLUSIONS: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices.

MOTIVATION: Comprehensive understanding of cellular processes requires development of approaches which consider the energetic balances in the cell. The existing approaches that address this problem are based on defining energy-equivalent costs which do not include the effects of a changing environment. By incorporating these effects, one could provide a framework for integrating 'omics' data from various levels of the system in order to provide interpretations with respect to the energy state and to elicit conclusions about putative global energy-related response mechanisms in the cell. RESULTS: Here we define a cost measure for amino acid synthesis based on flux balance analysis of a genome-scale metabolic network, and develop methods for its integration with proteomics and metabolomics data. This is a first measure which accounts for the effect of different environmental conditions. We applied this approach to a genome-scale network of Arabidopsis thaliana and calculated the costs for all amino acids and proteins present in the network under light and dark conditions. Integration of function and process ontology terms in the analysis of protein abundances and their costs indicates that, during the night, the cell favors cheaper proteins compared with the light environment. However, this does not imply that there is squandering of resources during the day. The results from the association analysis between the costs, levels and well-defined expenses of amino acid synthesis, indicate that our approach not only captures the adjustment made at the switch of conditions, but also could explain the anticipation of resource usage via a global energy-related regulatory mechanism of amino acid and protein synthesis.

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.