Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction

Abstract

Growth is a fundamental process of life. Growth requirements are well-characterized experimentally for many microbes; however, we lack a unified model for cellular growth. Such a model must be predictive of events at the molecular scale and capable of explaining the high-level behavior of the cell as a whole. Here, we construct an ME-Model for Escherichia coli--a genome-scale model that seamlessly integrates metabolic and gene product expression pathways. The model computes ~80% of the functional proteome (by mass), which is used by the cell to support growth under a given condition. Metabolism and gene expression are interdependent processes that affect and constrain each other. We formalize these constraints and apply the principle of growth optimization to enable the accurate prediction of multi-scale phenotypes, ranging from coarse-grained (growth rate, nutrient uptake, by-product secretion) to fine-grained (metabolic fluxes, gene expression levels). Our results unify many existing principles developed to describe bacterial growth.

Figure 1

Growth demands and coupling constraints leading to growth rate-dependent changes in enzyme and ribosome efficiency. (A) Three growth rate-dependent demand functions derived from empirical observations determine the basic requirements for cell replication (detailed in Supplementary information). (B) Coupling constraints link gene expression to metabolism through the dependence of reaction fluxes on enzyme concentrations. (C, D) RNA:protein ratio predicted by the ME-Model with two different coupling constraint scenarios, one for variable translation rate versus growth rate (red lines) and one for constant translation rate (orange lines). Experimental data in (C) obtained from Scott et al (2010). (E) Phosphotransferase system (PTS) transient activity following a glucose pulse in a glucose-limited chemostat culture (red) and glucose uptake before the glucose pulse (blue) is plotted as a function of growth rate. The data shown were obtained from O’Brien et al (1980)). Data from μ>0.7 h⁻¹ were omitted. (F) Data from (E) are used to plot glucose uptake as a fraction of PTS activity. The resulting value is the fractional enzyme saturation (black line). The fractional enzyme saturation predicted by the ME-Model is plotted as a function of growth rate under carbon limitation (red dots). (G) The cartoon depicts changes in extra- (blue) and intra- (green) cellular substrate (circle) and product (triangle) concentrations and metabolic enzyme (orange) and ribosome (purple/maroon) levels as the concentration of a growth-limiting nutrient (and growth rate) increases. The dials show k_eff/k_cat, the effective catalytic rate over the maximum for metabolic enzymes (orange) and ribosomes (purple/maroon).

Figure 2

Predicted growth, yield, and secretion. (A) Predicted growth rate is plotted as a function of the glucose uptake rate bound imposed in glucose minimal media. Three regions of growth are labeled Strictly Nutrient-Limited (SNL), Janusian, and Batch (i.e., excess of substrate) based on the dominant active constraints (nutrient and/or proteome limitation). The proteome-activity constraint inherent in the ME-Model results in a maximal growth rate and substrate uptake rate. The behavior of a genome-scale metabolic model (M-Model) is depicted with an arrow. (B) Predicted growth rates as a function of uptake of a limiting nutrient with glucose in excess. The shaded regions correspond to those as labeled in (A). (C) Experimental (triangle) and ME-Model-predicted (circle) acetate secretion in Nitrogen- (blue) and Carbon- (red) limited glucose minimal medium are plotted as a function of growth rate. Data were obtained from Zhuang et al (2011). The root-mean-square error (RMSE) between data and the ME-Model is 0.12 (for comparison, RMSE=0.40 for the M-Model). (D) Experimental (triangle) and ME-Model-predicted (circle) carbon yield (gDW Biomass/g Glucose) in Carbon- (red) and Nitrogen- (blue) limited glucose minimal medium are plotted as a function of growth rate. Data were obtained from Zhuang et al (2011). RMSE between data and the ME-Model is 0.04 (for comparison, RMSE=0.07 for the M-Model). (E) The cartoon depicts changes in extra- (blue) and intra- (green) cellular substrate (circle) and product (triangle) concentrations and metabolic enzyme (blue/orange) and ribosome (purple/maroon) levels during the Janusian region. Metabolic enzymes are saturated throughout the entire Janusian region. To increase the growth rate, the cell expresses metabolic pathways that have lower operating costs. (Pathways with the smaller blue proteins taken to be 0.25 the cost of the pathways with larger orange proteins.) A higher glucose uptake and turnover results, but energy yield is lower and some carbon is ‘wasted’ and secreted (brown triangles). The dials show k_eff/k_cat, the effective catalytic rate over the maximum for metabolic enzymes (blue/orange) and ribosomes (purple/maroon).

Figure 3

Central carbon metabolic flux patterns under glucose-limited and glucose-excess conditions. (A–C) Relative fluxes from ¹³C experiments are plotted versus the fluxes predicted by the ME-Model. (A, B) Comparison of nutrient-limited model solutions with chemostat culture conditions and (C) comparison of the batch ME-Model solution with batch culture data. All simulations and experiments correspond to growth in glucose minimal media. Fluxes are normalized so that glucose uptake is 100. Insets show the main flux changes under increasing glucose concentrations. The only model parameter that is modulated is the glucose uptake rate bound. Data were obtained from Nanchen et al (2006) and Schuetz et al (2007). The ME-Model flux for the reaction ‘pyk’ is taken to include phosphoenolpyruvate (PEP) to pyruvate (PYR) conversion via the phosphotransferase system (PTS). Flux splits shown as insets were computed using the ME-Model. The percentages indicate the percent carbon (Glucose) converted to CO₂ (for branch labeled ‘TCA’), acetate, and biomass. Both the TCA and acetate branches contribute to ATP production. The total mmol ATP per gDW biomass produced is indicated.

Figure 4

Growth rate-dependent gene expression under glucose limitation. (A) Gene expression changes predicted by the ME-Model to occur in the Strictly Nutrient-Limited (SNL) growth region indicated in light blue under glucose limitation in minimal media are analyzed. (B) ME-Model-computed relative gene–enzyme pair expression is plotted as a function of growth rate; the normalized in silico expression profiles are clustered hierarchically (see Materials and methods). Solid lines are expression profiles of individual gene–enzyme pairs and dotted black lines are the centroid of each cluster. Each leaf node is colored and qualitatively labeled by function. The number of genes in each leaf node is indicated and listed in Supplementary Table S8A. Asterisks indicate clusters with monotonic expression changes that significantly match the directionality observed in expression data (Wilcoxon signed-rank test, P<1 × 10⁻⁴). Expression data were obtained from a previous study (Nahku et al, 2010), in which E. coli was cultivated in a chemostat at dilution rates 0.3 h⁻¹ and ∼0.5 h⁻¹.

Figure 5

Gene expression during the Janusian region. (A) Gene expression changes predicted by the ME-Model to occur in the Janusian growth region indicated in purple under glucose limitation in minimal media are analyzed. (B) Simulated expression profiles are clustered using signed power (β=25) correlation similarity and average agglomeration. A freely available R package was used (Langfelder and Horvath, 2008). Eleven clusters resulted. Two small clusters were removed because they represented stochastic expression of alternative isozymes. The first principal component of the remaining nine clusters is displayed and grouped qualitatively by function. (C) Many of the expression modules correspond to genes of central carbon energy metabolism. Reactions are colored according to the module color in (B).