Pathways in Escherichia coli show large differences in the extent to which enzymes from the same pathway are expressed in a coordinated manner.Using dynamic optimization, we show that regulation of the initial and terminal reactions of a pathway is the minimum requirement for a precise control of flux.We find that in E. coli a regulation of initial and terminal reactions is predominantly used to control pathways with low costs of enzymes while a regulation of all enzymes occurs if protein costs are high.A trade-off between minimization of protein investment and minimization of response time can explain the preference for transcriptional regulation at key positions (leading to high protein costs, but low response time) or coordinated transcriptional regulation of all enzymes (leading to low protein costs, but high response time).
The increasing availability and decreasing prices of experimental techniques have led to an explosion in the number of available experimental data sets (Ishii et al, 2007; Lu et al, 2007; Bennett et al, 2009; Lewis et al, 2010). However, approaches to integrate these diverse data sets into a coherent model of cellular mechanisms have lagged behind (Palsson and Zengler, 2010). In this study, we want to contribute to this effort through the analysis of a large number of data sets in order to identify global principles in the regulation of metabolism in Escherichia coli. While previous studies have shed light onto the link between the transcriptional regulation of metabolism and its structure (Ihmels et al, 2004; Reed and Palsson, 2004; Schwartz et al, 2007; Seshasayee et al, 2009), the extent to which transcriptional regulation controls metabolism has remained elusive.
To address this problem, we investigated the coexpression of enzymes within the same pathway in all biochemically annotated subsystems of E. coli metabolism. As a reference for metabolic pathways, we used elementary flux patterns, a recently introduced concept for pathway analysis in genome-scale metabolic networks (Kaleta et al, 2009). Through this analysis, we found that while pathways in many subsystems of metabolism show a high degree of coexpression, pathways in the subsystems cofactor and prosthetic group biosynthesis, glycerophospholipid metabolism, murein recycling, nucleotide salvage pathway and pentose phosphate pathway show only weak coexpression. We refer to these subsystems with a low coordination of transcriptional regulation as transcriptionally sparsely regulated subsystems.
In order to understand these different patterns of regulation, we constructed a simplified model of a linear metabolic pathway that converts a substrate s via four intermediates into a product p. We then used dynamic optimization to identify a regulatory program (i.e. a time course for the enzyme concentrations), which allows the cell to maintain the concentration of the product p in a changing environment while obeying a set of physiological constraints. As an objective function we used the minimization of the level of transcriptional regulation, specified through absolute deviations of enzyme concentrations from their initial values, and the minimization of protein costs. Protein costs are measured as the sum of the initial enzyme concentrations.
The optimization results revealed that for a full control of the flux through a pathway, transcriptional regulation of initial and terminal reactions of the pathway is sufficient (sparse transcriptional regulation). Regulation of the first reaction is required to control the flux into the pathway, and hence, the intermediate concentrations. In contrast, regulation at the terminal position is required to tightly control the rate of synthesis of the product. By performing the same optimization for randomly chosen kinetic parameters, we found that this pattern is also optimal in most cases with differences in the catalytic properties of enzymes. Moreover, we found that with increasing enzyme costs (i.e. increasing enzyme concentrations), there is a shift from sparse transcriptional regulation to coordinated transcriptional regulation of all enzymes within a pathway (pervasive transcriptional regulation).
To verify these predictions, we analyzed the position-specific frequency of regulatory events in the pathways of the transcriptionally sparsely regulated subsystems. We could confirm that there is a significant increase in the frequency of transcriptional regulation at the end and a less pronounced increase at the beginning of pathways. Performing the same analysis for post-translational regulation, we found that there is a statistically significant increase at the beginning of pathways. Thus, the control at the beginning of pathways is achieved through a combination of transcriptional and post-translational regulation. In other subsystems that were not identified as transcriptionally sparsely regulated, we did not find this pattern of transcriptional regulation while the same pattern of post-translational regulation could be observed. By analyzing protein abundance data, we confirmed that particularly pathways within subsystems, for which enzyme costs are low, are transcriptionally sparsely regulated.
Having confirmed the predictions made by the optimization, we found that there appears to be a mechanism favoring sparse transcriptional regulation in pathways with low-cost enzymes. We suggest an evolutionary trade-off between the cellular objectives of protein cost minimization and response time minimization as a cause of this mechanism. The optimal strategy to reduce average protein costs is to transcriptionally control enzymes within a pathway. However, responses on a transcriptional level are usually very slow. In contrast, short response times can be achieved through a constitutive expression of enzymes with a focused regulation of key steps within a pathway. The interplay between the two cellular objectives leads to the observation that particularly pathways with highly abundant and thus costly enzymes are transcriptionally pervasively regulated (Figure 7A). In contrast, pathways with low abundance enzymes are transcriptionally sparsely regulated (Figure 7B). In agreement with these results, we found that pathways such as the pentose phosphate pathway, for which rapid response times are required, are sparsely regulated even if they contain costly enzymes (Figure 7C). Finally, if the fitness advantage achieved through following either of the cellular objectives is low, sparse transcriptional regulation is the minimum requirement to control flux through a pathway (Figure 7D).
In summary, our results demonstrate that, in contrast to the classical picture, regulation of key positions of metabolic pathways is sufficient for full control of flux and is implemented in vivo. This pattern of sparse regulation is particularly useful if a higher fitness advantage can be achieved through rapid response times compared to the fitness advantage achieved through the reduced protein cost of pervasive transcriptional regulation.
Analysis of optimal strategies for the control of metabolic pathways in Escherichia coli reveals that the extent of transcriptional regulation reflects an evolutionary trade-off between the minimization of response time and protein costs.
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.