Figure 1.
Overview of constraint-based reconstruction and analysis.
(A) Schematic illustration of the conversion of a biochemical reaction network into a mathematical format (stoichiometric matrix, S). Since there are normally less columns (reactions) than rows (metabolites) there does not exist a single solution but rather a steady-state solution space containing all possible solutions. (B) The successive addition of constraints will shrink the solution space by eliminating biologically infeasible steady-state solutions. Complete knowledge would reduce the steady-state solution space to a single solution. Since complete knowledge is not available for the majority of biochemical reaction networks the investigation of properties and capabilities of the solution space is very useful. (C) This graphic illustrate the central role of reconstruction of biochemical networks to systems biology and how they serve as a foundation for many applications and problem-specific models.
Figure 2.
(A) Schematic representation of the network components and reactions is shown. In addition to the macromolecular synthesis of RNA and proteins, rRNA and tRNA processing reactions were included in the reconstruction. I: Transcription; II: mRNA degradation; III: translation; IV: protein maturation; V: protein folding; VI: metallo-ion binding; VII: protein complex formation; VIII: ribosome assembly; IX: RNA processing; X: rRNA modification; XI: tRNA modification; XII: tRNA charging (see Table 1 for complete list of subsystems and Figure S1 for a complete protein map). (B) The pentagram shows the five main data sources incorporated in the ‘E-matrix’: EcoCyc [36], CyberCell [70], and tRNA DB [71], the revised genome annotation [32], and the genome sequence (m56, [65]).
Table 1.
Reactions per subsystems.
Table 2.
Overview of the ‘E-matrix’ content.
Figure 3.
Comparison of in vivo [42] and in silico maximal number of ribosomes at different doubling times.
Two sets of constraints were applied to the models: uptake rates for amino acids and NTPs, and maximal possible rates on stable RNA transcription initiation (see text for more details).
Figure 4.
(A) Analysis of the effect of rRNA operon deletion to the ribosome production capability of the network. As expected, the ribosome production rate decreased with decreasing number of available rRNA operons. All possible combinations of operon deletions were considered resulting in different maximal possible ribosome production rates for a given number of remaining rRNA operons. This is due the gene dosage effect since multiple replication forks are present at higher growth rates. (B) Experimental data (orange bars, [46],[48]) suggested much higher ribosome production than we determined in (A). This compensation is achieved by increasing the transcription rate of the remaining rRNA operon. We tested different possible compensation factors and compared the results with the experimental data. The error bars are again caused by different combination of rRNA operons.
Table 3.
List of rRNA transcription units and their basic characteristics.
Figure 5.
Integration of ‘-omics’ data into ‘E-matrix’ as reaction constraints.
(A) This schema illustrates the types of high-throughput data (HT, red boxes) or low-throughput data (LT, blue boxes) that can be directly integrated with the ‘E-matrix’ as it accounts for the different macromolecules measured in these data sets. In contrast, the integration of regulatory information would require the formulation of the regulatory network in matrix format (‘Operon’ or ‘O’-matrix). Furthermore, the metabolic network, here represented as ‘M-matrix’, would enable the mapping of fluxomic, metabolomic and phenomic data. (B–D) Absolute flux span in ‘E-matrix’ while incorporating successively more complex constraints (see text for more details). (B) LB-medium specific constraints were applied on exchange reactions. (C) The upper bounds of stable RNA transcription initiation reactions were constrained. (D) Additional constraints on upper bound of mRNA degradation flux rates were applied.
Figure 6.
Schematic representation is shown of the calculated functional modules, the associated proteins and their canonical assignments.
Functional modules that consist of one protein are not shown.