Functional characterization of alternate optimal solutions of Escherichia coli's transcriptional and translational machinery

Abstract

The constraint-based reconstruction and analysis approach has recently been extended to describe Escherichia coli's transcriptional and translational machinery. Here, we introduce the concept of reaction coupling to represent the dependency between protein synthesis and utilization. These coupling constraints lead to a significant contraction of the feasible set of steady-state fluxes. The subset of alternate optimal solutions (AOS) consistent with maximal ribosome production was calculated. The majority of transcriptional and translational reactions were active for all of these AOS, showing that the network has a low degree of redundancy. Furthermore, all calculated AOS contained the qualitative expression of at least 92% of the known essential genes. Principal component analysis of AOS demonstrated that energy currencies (ATP, GTP, and phosphate) dominate the network's capability to produce ribosomes. Additionally, we identified regulatory control points of the network, which include the transcription reactions of sigma70 (RpoD) as well as that of a degradosome component (Rne) and of tRNA charging (ValS). These reactions contribute significant variance among AOS. These results show that constraint-based modeling can be applied to gain insight into the systemic properties of E. coli's transcriptional and translational machinery.

Figure 1

(A–C) Schematic illustration of alternate optimal solutions (AOS), unique solutions, and results of flux variability analysis (FVA) on a linear toy problem is shown.

Figure 2

Schematic representation of the participation of tr/tr enzymes in network reactions. In canonical network formulations, enzyme reaction participation is implied but not explicitly modeled. The tr/tr network produces enzymes; hence, the explicit incorporation of enzymes in their catalyzed reactions is desired. The same approach is applied if the reactant E is a tRNA molecule or a protein.

Figure 3

Schematic representations of the mRNA and protein pools present in the E-matrix. (A) Conceptual representation of flux coupling is shown. In steady-state condition, the influx into node A is equal to the sum of outfluxes. Subsequently, there is a ratio describing the relative outfluxes. (B) In contrast to metabolic networks, the tr/tr network requires that component pools are added to ensure that the network functions are similar to known in vivo features. By introducing loops and appropriate constraints, one can represent different pool sizes of the components. NMPs are nucleotide monophosphates.

Figure 4

Illustration of geometric interpretation of constraints and the corresponding flux span. (A and B) Uncoupled model. (C and D) Coupled model contains a set of 1056 coupling constraints between 528 network reactions. The flux span corresponds to the variability of each network reaction while producing maximum rate of ribosomes. The simulation condition corresponds to doubling time t = 90 min. See also Fig. S1 for a comparison by cellular subsystems.

Figure 5

Distance between AOS in the E_coupled-matrix. To assess the overall distance between the set of AOS, we computed the distance between 10⁶ randomly chosen AOS pairs (doubling time t = 90).

Figure 6

Principal component analyses (PCA). Z scores of the entire E_coupled-matrix network (A) and of the gene expression reactions (B). The PCA analysis was performed on the set of alternate optimal solutions (AOS) (doubling time t = 90 min). Note that there are m reactions in the network and the number of AOS (points) is n = 2m.