Optimal regulatory strategies for metabolic pathways in Escherichia coli depending on protein costs Frank Wessely1,4, Martin Bartl2, Reinhard Guthke3, Pu Li2, Stefan Schuster1 and Christoph Kaleta1,* 1 Department of Bioinformatics, Friedrich Schiller University Jena, Jena, Germany, 2 Department of Simulation and Optimal Processes, Institute for Automation and Systems Engineering, Ilmenau University of Technology, Ilmenau, Germany and 3 Research Group Systems Biology/Bioinformatics, Leibniz Institute for Natural Product Research and Infection Biology���Hans Knoll �� Institute, Jena, Germany 4 Present address: School of Veterinary Medicine and Science, University of Nottingham, Sutton Bonington Campus, Loughborough LE12 5RD, UK * Corresponding author. Department of Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany. Tel.: �� 49 3641 949583 Fax: �� 49 3641 946452 E-mail: Christoph.Kaleta@uni-jena.de Received 30.11.10 accepted 12.6.11 While previous studies have shed light on the link between the structure of metabolism and its transcriptional regulation, the extent to which transcriptional regulation controls metabolism has not yet been fully explored. In this work, we address this problem by integrating a large number of experimental data sets with a model of the metabolism of Escherichia coli. Using a combination of computational tools including the concept of elementary flux patterns, methods from network inference and dynamic optimization, we find that transcriptional regulation of pathways reflects the protein investment into these pathways. While pathways that are associated to a high protein cost are controlled by fine-tuned transcriptional programs, pathways that only require a small protein cost are transcriptionally controlled in a few key reactions. As a reason for the occurrence of these different regulatory strategies, we identify an evolutionary trade-off between the conflicting requirements to reduce protein investment and the requirement to be able to respond rapidly to changes in environmental conditions. Molecular Systems Biology 7: 515 published online 19 July 2011 doi:10.1038/msb.2011.46 Subject Categories: metabolic and regulatory networks simulation and data analysis Keywords: cost-optimal regulatory strategies evolutionary optimization genome-scale metabolic networks proteomics transcriptomics Introduction In recent years, the increasing availability and decreasing prices of experimental techniques in molecular biology have led to an explosion in the number of available experimental data sets (Ishii et al, 2007 Lu et al, 2007 Faith et al, 2008 Bennett et al, 2009 Lewis et al, 2010). These data sets cover a broad range of aspects of cellular systems, for example, transcript levels, protein abundances, metabolite concentrations or fluxes of a large number of metabolic reactions. However, analytical methods to integrate these data sets into a comprehensive understanding of organisms have lagged behind (Palsson and Zengler, 2010) and, thus, there is a great need for theoretical tools that allow us to build more comprehensive models of cellular mechanisms (Heinemann and Sauer, 2010). Whole-cell models of metabolism have been shown to be a suitable framework to simplify this integration (Feist and Palsson, 2008 Oberhardt et al, 2009 Lewis et al, 2010 Ruppin et al, 2010). Using these large-scale models of metabolism to analyze transcriptomic data sets, a number of recent studies have been able to show a link between the structure of metabolic networks and their transcriptional regulation (Stelling et al, 2002 Ihmels et al, 2004 Reed and Palsson, 2004 Kharchenko et al, 2005 Schwartz et al, 2007 Notebaart et al, 2008 Seshasayee et al, 2009 Marashi and Bockmayr, 2011). However, the extent to which transcriptional regulation controls metabolism has not yet been analyzed in detail despite of a large body of earlier theoretical work on the control of metabolism (Heinrich and Schuster, 1996). Although there is a relationship between the structure of metabolism and its regulation, the results from some of these studies indicate that it is not very strong (Stelling et al, 2002 Reed and Palsson, 2004 Notebaart et al, 2008 Marashi and Bockmayr, 2011). Indeed, the picture emerges that transcrip- tional regulation of metabolism is less pervasive than was previously thought (Heinemann and Sauer, 2010). In our study, which integrates a large array of experimental and bibliomic data sets, we analyzed the extent to which transcriptional regulation controls metabolism in Escherichia coli. As experimental data sets, we used gene-expression profiles of E. coli from the Many Microbe Microarrays Database (M3D Faith et al, 2008) and genome-wide protein abundance data (Lu et al, 2007). We used bibliomic data sets on the transcriptional regulatory network controlling metabolism stored in RegulonDB (Gama-Castro et al, 2008) and EcoCyc (Keseler et al, 2005), information on the post-translational regulation of enzymes (allosteric regulation and phosphoryla- tion) from EcoCyc and Phosida (Gnad et al, 2007). Molecular Systems Biology 7 Article number 515 doi:10.1038/msb.2011.46 Citation: Molecular Systems Biology 7:515 & 2011 EMBO and Macmillan Publishers Limited All rights reserved 1744-4292/11 www.molecularsystemsbiology.com & 2011 EMBO and Macmillan Publishers Limited Molecular Systems Biology 2011 1

Using these data sets, we show that there are large differences in the degree of transcriptional control between different subsystems of metabolism. While some pathways show a strong coexpression of the corresponding enzymes, there appears to be no coexpression in other pathways. In order to explain these observations, we used dynamic optimization on a simple model of a linear pathway to identify a regulatory program that allows the flux through a pathway to be controlled. For the optimization we used the minimization of transcriptional regulatory interactions and protein costs as an objective function.���Cost��� of a particular protein refers to the total weight of this protein present in the cell. The results of the optimization show that for tight control of flux, initial and terminal reactions in a pathway need to be transcriptionally regulated and that this regulatory program is used in particular to control pathways with low abundance and thus low costs of enzymes. In contrast, in pathways with highly abundant and thus costly enzymes, all enzymes are predicted to be transcriptionally regulated. Analyzing the positional regulation within pathways show- ing a low degree of coexpression of enzymes, we can confirm the utilization of the predicted minimal regulatory program and find that regulation at initial pathway positions is exerted mainly through post-translational means. Thus, the extent of transcriptional regulation is even further reduced through post-translational regulation. Moreover, we confirm that the occurrence of the different regulatory programs is related to the costs of enzymes within a pathway. Finally, we show that the cost-dependent control of metabolic pathways can be explained by a subtle balance between two conflicting evolutionary objectives: the pressure to be able to react as quickly as possible to a change in environmental conditions and the requirement to minimize the enzyme investment necessary to achieve this response. Results Identification of elementary flux patterns An outline of our approach to identify coexpressed elementary flux patterns is shown in Figure 1. Our analysis is based on the genome-scale metabolic network of E. coli, iAF1260 (Feist et al, 2007). We allowed for the unconstrained inflow and outflow of every metabolite that can be taken up by the cell in order to model the set of conditions under which the microarray data have been obtained (see Materials and methods). In order to identify reactions that need to be regulated in a similar manner, we computed the elementary flux patterns of the 35 biochemically annotated subsystems of iAF1260 (Table I). Elementary flux patterns (Kaleta et al, 2009) are defined as the basic routes of physiological feasible fluxes through a particular subsystem of metabolism. Hence, they correspond to basic metabolic routes through each subsystem. We obtained a total of 6584 elementary flux patterns (see Supplementary Information S2 for a list). We translated the elementary flux patterns into the gene sets encoding the enzymes catalyzing them and performed several filtering steps in order to remove elementary flux patterns, which either gave rise to the same gene set or translated into a gene set of size one. After this final filtering step, 775 elementary flux patterns remained (see Supplementary Information S3 for a size distribution). Due to this filtering, no elementary flux patterns remained in eight subsystems, which mainly contain very small elementary flux patterns that did not translate into gene sets of size of at least two. For a detailed discussion of this issue see Supplementary Information S2. The 27 subsystems for which elementary flux patterns remained are listed in Table I. Network analysis Gene-expression analysis Gene expression profiles M3D 1 4297 Genes 1 907 Chips Similarity matrix S 1 4297 Genes 1 4297 Genes Mutual information CLR Select iAF1260 metabolic genes Hierarchical clustering g1... g1257 g1 g2 g4 g5 g9 g10 g9 g10 g1 g2 g4 g5 g5 g4 g1 g2 g. . . Coexpressed gene sets E. coli iAF1260 Subsystem 1 Subsystem 2 Growth substrate Internal metabolite Biomass component g1 g2 g3 g4+g5 g9+g10 g11 g12 g8 g6/g7 g13 g14 g15 +g16 Elementary flux patterns (6584) Subsystem 1 Subsystem 2 g1 g2 g4 g5 g9 g10 g1 g3 g9 g10 g6 g8 g9 g10 g7 g8 g9 g10 g11 g12 g11 g13 g14 g15 g16. . . 17 522 gene sets from 775 EFPs Filtering + translation into gene sets Overlap Compute for each subsystem Figure 1 Outline of the analysis. Elementary flux patterns were identified for each metabolic subsystem and then translated into the corresponding gene sets using the gene���protein���reaction associations of the model. Gene sets were compared on a subsystem basis to sets of coexpressed genes determined from a large compendium of microarrays from the Many Microbe Microarrays Database (M3D). In the schematic depiction of iAF1260, gene���protein���reaction associations are shown below the reactions. In case of ���/��� isoenzymes are catalyzing a reaction, in the case of ��� �� ��� a protein complex catalyzes a reaction. EFPs, elementary flux patterns. Regulation of metabolism in Escherichia coli F Wessely et al 2 Molecular Systems Biology 2011 & 2011 EMBO and Macmillan Publishers Limited