Metabolic flux balance analysis and the in silico analysis of Escherichia coli K-12 gene deletions

Abstract

representations of integrated metabolic functions can be constructed and analyzed using flux balance analysis (FBA). FBA is particularly well-suited to study metabolic networks based on genomic, biochemical, and strain specific information. isogenic strains. results lead to a further understanding of the complex genotype-phenotype relation. Supplementary information:

Background

representations of integrated metabolic functions can be constructed and analyzed using flux balance analysis (FBA). FBA is particularly well-suited to study metabolic networks based on genomic, biochemical, and strain specific information.

Results

isogenic strains.

Conclusions

results lead to a further understanding of the complex genotype-phenotype relation.

Supplementary information:

Introduction

]. However, it is becoming evident that cellular functions are intricate and the integrated function of biological systems involves many complex interactions among the molecular components within the cell. To understand the complexity inherent in cellular networks, approaches that focus on the systemic properties of the network are also required.

].

].

strains.

Flux balance analysis

] (see the supplementary information for an FBA primer). The mass balance constraints in a metabolic network can be represented mathematically by a matrix equation:

S • v = 0 Equation 1

represents all fluxes in the metabolic network, including the internal fluxes, transport fluxes and the growth flux.

.

In addition to the mass balance constraints, we imposed constraints on the magnitude of individual metabolic fluxes.

Equation 2

). When a metabolite was not available in the medium, the transport flux was constrained to zero. The transport flux for metabolites capable of leaving the metabolic network (i.e. acetate, ethanol, lactate, succinate, formate, and pyruvate) was always unconstrained in the net outward direction.

within the feasible set is not reachable by the cell under a given condition due to other constraints not considered in the analysis (i.e. maximal internal fluxes and gene regulation). The feasible set can be further reduced by imposing additional constraints (i.e. kinetic or gene regulatory constraints), and in the limiting condition where all constraints are known, the feasible set may reduce to a single point.

], and was formulated as shown below:

Minimize -Z

= <c • v> Equation 3

was defined as the unit vector in the direction of the growth flux, and the growth flux was defined in terms of the biosynthetic requirements:

(Equation 4)

] (see Appendix 4)), and the growth flux was modeled as a single reaction that converts all the biosynthetic precursors into biomass.

Phenotype Phase Plane Analysis

), where each solution in this space corresponds to a feasible metabolic flux distribution.

.

One demarcation line in the PhPP was defined as the line of optimality (LO). The LO represents the optimal relation between exchange fluxes defined on the axes of the PhPP.

Alterations of the genotype

).

.

).

= 0.

Optimal production of the twelve biosynthetic precursors and the metabolic cofactors.

deletion; red corresponds to 0.0, yellow corresponds to 0-50% of the wild-type production, blue corresponds to 50-100% of the wild-type, and no color coding is illustrated when the production is unchanged from the wild-type. Data for other carbon sources is available online. G6P, glucose-6-phosphate; F6P, fructose-6-phosphate; R5P, ribose-5-phosphate; E4P,erythrose 4-phosphate; T3P1, glyceraldehyde 3-phosphate; 3PG, 3-phosphoglycerate; PEP, phosphoenolpyruvate; PYR, pyruvate; ACCOA, acetyl-CoA; AKG, α-ketoglutarate; SUCCOA, succinyl-CoA; OA, oxaloacetate.

Additional material

Appendix 1: Metabolic map

metabolic reactions in the model

Appendix 3: Metabolite abbreviations

Results

strains.

).

].

deletion strains were limited in their production capability of high-energy phosphate bonds under all conditions, and were unable to produce any of the biosynthetic precursors in phase 6 even with the serine degradation pathway.

].

deletion strain was limited in its production capabilities of several amino acids (arg, gly, his- not shown in table), but under anaerobic conditions, these capabilities were not limited with respect to the wild-type.

deletion strain discussed below).

deletion strains to the wild-type to provide a more complete definition of optimal phenotypes.

and to demonstrate the use of FBA to interpret and analyze cellular metabolism.

metabolic genotype theoretically supported biomass production, the feasible steady states were restricted to a limited phase of the phase plane and the flexibility of the metabolic network was reduced to one dimension.

was characterized by increased PPP fluxes to bypass the TPI block. The PPP operated cyclically; thus, leading to a high production of NADPH. Due to the high NADPH production in the PPP, the TCA cycle flux was optimally reduced and functioned only to produce the biosynthetic precursors.

strain.

).

].

Discussion

Given the central importance of this question, we will discuss the general applicability, limitations, and future prospects for FBA and functional genomics.

].

analysis can help identify missing or incorrect functional assignments; for example, by identifying sets of metabolic reactions that are not connected to the metabolic network by the mass balance constraints.

].

Conclusions

mutant phenotypes.

Additional material

Appendix 1: Metabolic map

metabolic reactions in the model

Appendix 3: Metabolite abbreviations