First, assume that the concentrations of central carbon metabolites, energy cofactors, and other macromolecules are constant and that their contribution to the biomass balance can be ignored. This leads to the revised rate equations

$$v_r(r) = k'_r r, \quad v_{mer}(m_{er}) = k'_{mer} m_{er}, \quad v_{mef}(m_{ef}) = k'_{mef} m_{ef}, \dots \qquad (67)$$

where the constants $k'_r, k'_{mer}, k'_{mef}, \dots$ lump the effects of the catalytic efficiency of the enzymes and the concentrations of central carbon metabolites and energy cofactors. Moreover, the assumption reduces the biomass to total protein mass:

$$B = \beta'(M_u + R + M_c + M_{er} + M_{ef}), \qquad (68)$$

and consequently,

$$1/\beta' = m_c + m_{er} + m_{ef} + r + m_u, \qquad (69)$$

where $1/\beta'$ is the total protein concentration. Note that, with this simplification, the total protein concentration is constant, independently from the resource allocation strategy adopted by the cell.

A second assumption is that energy dissipation and the degradation of macromolecules can be neglected, which means that $\gamma = k_d = 0$. The absence of protein degradation, together with the revised biomass definition, leads to the proportionality of growth rate and protein synthesis rate:

$$\mu = \frac{1}{B} \frac{dB}{dt} = \frac{\beta'}{B} \frac{dV_r}{dt} = \beta' v_r. \qquad (70)$$

The absence of energy dissipation, in combination with the omission of other macromolecules, leads to a revised energy balance:

$$0 = n_{mer} v_{mer} + n_{mef} v_{mef} - n_r v_r, \qquad (71)$$

which with Equation 70 gives

$$n_{mer} v_{mer} + n_{mef} v_{mef} = \frac{n_r}{\beta'} \mu, \qquad (72)$$

and hence

$$n_{mer} k'_{mer} m_{er} + n_{mef} k'_{mef} m_{ef} = \frac{n_r}{\beta'} \mu. \qquad (73)$$

Third, assume that in the mass balance for the central carbon metabolites the contributions from growth dilution and spontaneous degradation can be neglected in comparison with the utilization of these metabolites for protein synthesis. Then Equation 41 reduces to

$$v_{mc} = v_{mer} + \rho_{mef} v_{mef} + \rho_{ru} v_r, \qquad (74)$$

which with the energy balance of Equation 71 can be rewritten as

$$v_{mc} = \left( \rho_{mef} - \frac{n_{mef}}{n_{mer}} \right) v_{mef} + \left( \rho_{ru} - \frac{n_r}{n_{mer}} \right) v_r \approx \left( \rho_{ru} - \frac{n_r}{n_{mer}} \right) v_r, \qquad (75)$$

bearing in mind that both $\rho_{mef}$ and $n_{mef}/n_{mer}$ assume values in the range 1–2. That is, the substrate uptake rate is approximately proportional to the protein synthesis rate.

Now, using the protein mass balance of Equation 69, we can express the total concentration of energy proteins as follows:

$$m_{er} + m_{ef} = (1/\beta' - m_u) - m_c - r, \qquad (76)$$

which with Equation 75 and the rate equations for the glucose uptake and protein synthesis rates give

$$m_{er} + m_{ef} = (1/\beta' - m_u) - \frac{1}{\beta' e_s} \left( \rho_{ru} - \frac{n_r}{n_{mer}} + \frac{e_s}{k'_r} \right) \mu \qquad (77)$$
$$ = m_e^{max} - \frac{\alpha}{\beta'} \mu, \qquad (78) $$

where $m_e^{max} = 1/\beta' - m_u$, making the further assumption that $m_u = \beta'/\chi_u$ is constant, and $\alpha = (1/e_s)(\rho_{ru} - n_r/n_{mer} + e_s/k'_r)$. Equation 78 expresses that the concentration (or equivalently for constant $1/\beta'$, the fraction) of proteins involved in energy metabolism linearly decreases with the growth rate. Basan et al., 2015a, posit the same linear relationship, based on proteomics data for the NCM3722 strain (Hui et al., 2015).

When combining Equations 72 and 78, we can solve for the two unknowns $m_{ef}$ and $m_{er}$ as a function of $\mu$:

$$ m_{ef} = \frac{\left( \frac{n_r}{\beta' n_{mer} k'_{mer}} + \frac{\alpha}{\beta'} \right) \mu - m_e^{max}}{\left( \frac{n_{mef} k'_{mef}}{n_{mer} k'_{mer}} - 1 \right)}, \qquad (79) $$

$$ m_{er} = \frac{\left( \frac{n_r}{\beta' n_{mef} k'_{mef}} + \frac{\alpha}{\beta'} \right) \mu - m_e^{max}}{\left( \frac{n_{mer} k'_{mer}}{n_{mef} k'_{mef}} - 1 \right)}. \qquad (80) $$

The model is only valid in the range of growth rates where both concentrations are positive. By means of the simplified expressions for the respiration and fermentation fluxes (Equation 67), we can compute the total ATP production rate $n_{mer} k'_{mer} m_{er} + n_{mef} k'_{mef} m_{ef}$ using the above expressions. The ATP production rates of Basan et al., 2015a, are rescaled by using protein fractions instead of protein concentrations, which gives rise to $J_{E,f} \equiv n_{mef} k'_{mef} \beta' m_{ef}$ and $J_{E,r} \equiv n_{mer} k'_{mer} \beta' m_{er}$. Developing the expressions for $J_{E,f}$ and $J_{E,r}$ by means of Equations 79 and 80 yields equations that are equivalent to Eqs S12 and S13, respectively, of Basan et al., 2015a, after appropriately renaming the parameters ($\epsilon_f = n_{mef} k'_{mef}$, $\epsilon_r = n_{mer} k'_{mer}$, $\sigma = n_r$, $b = \alpha$, and $\phi_{E,max} = \beta' m_e^{max}$).

The model of Basan et al., 2015a, predicts a trade-off between respiration and fermentation when the growth rate increases, because the protein cost of fermentation is lower than the protein cost of respiration, that is, $n_{mef} k'_{mef} > n_{mer} k'_{mer}$. This relation, which is preserved for the parameter values for growth on glucose in our model (Appendix 2—table 2), implies that when the growth rate increases, the concentration of fermentation enzymes increases at the expense of the concentration of respiration enzymes. Due to the lower protein cost of fermentation, however, the total ATP production rate increases.

As explained in the Discussion section, our model makes less stringent assumptions, which notably allows metabolite and total protein concentrations to vary with different resource allocation strategies. As a consequence, there are ways to increase the total ATP production rate without shifting resources from energy-efficient but costly respiration (high $n_{mer}$ but low $n_{mer} k'_{mer}$) to energy-inefficient but cheap fermentation (low $n_{mef}$ but high $n_{mef} k'_{mef}$). In particular, in our model, growth rate and growth yield can be simultaneously increased, by trading off proteins against metabolites, thus enabling a more efficient use of proteomic resources.
# Appendix 2

## Model calibration

### Reference datasets and model calibration strategy

Model calibration was performed using published reference datasets with measurements of growth rates and fluxes (Haverkorn van Rijsewijk et al., 2011; Gerosa et al., 2015; Peebo et al., 2015), protein concentrations (Schmidt et al., 2016), and metabolite concentrations (Gerosa et al., 2015; Bennett et al., 2009; Park et al., 2016). The datasets concern the E. coli BW25113 strain: either batch growth in minimal medium with glucose or glycerol, or continuous growth in minimal medium with glucose. We also used auxiliary data for other strains at comparable growth rates, when necessary. Moreover, we adopted a top-down model calibration procedure, in order to enforce consistency across different data types.

### Step 1

We used the total biomass density and measured biomass proportions of proteins and metabolites to derive total protein and metabolite concentrations.

### Step 2

We used proteomics and metabolomics data to derive the concentrations of the different protein and metabolite categories distinguished in the model.

### Step 3

We used published data to reconstruct the biomass degradation rate for growth on glucose and glycerol.

### Step 4

We used the measured substrate uptake and acetate secretion rates, the growth rate, and the derived protein and metabolite concentrations to reconstruct the other metabolic fluxes from the carbon mass balance.

### Step 5

We derived the kinetic parameters from literature data and from the fluxes and the concentrations obtained in the previous steps.

The above procedure does not require computational parameter fitting, since all parameters are unambiguously fixed by the data, literature information, and suitable hypotheses motivated by experimental results. We explain the procedure in detail for batch growth of the reference strain, and then summarize the results for continuous growth and for an alternative strain. In what follows, observed fluxes, growth rates, and concentrations, as well as kinetic parameters derived from this information, are denoted by a hat $\hat{\beta}$ symbol.

## Reconstruction of concentrations, rates, and fluxes for batch growth

### Total biomass concentration 1/β

The total concentration of biomass in the cell, in units Cmmol gDW⁻¹, is referred to in our model as 1/β. Using the definition of yield (Equation 2 in the main text), we have 1/β = Yvmc/μ. With the values reported by Morin et al., 2016, for the MG1655 strain, we estimate

$$1/\beta = 40.65 \text{ Cmmol gDW}^{-1}. \qquad (81)$$

This value is close to the theoretical value obtained from the fact that the carbon mass fraction of biomass is approximately 0.5 (Folsom and Carlson, 2015):

$$1 \text{ gDW} = 0.5 \text{ CgDW} = \frac{0.5}{12.01 \cdot 10^{-3}} = 41.6 \text{ Cmmol}, \qquad (82)$$

where CgDW refers to Cgram dry weight and the molecular weight of C equals 12.01 g mol⁻¹. Another way to determine the total biomass concentration is to use the estimated elementary biomass composition of E. coli. von Stockar and Liu, 1999, report CH₁.₇₇O₀.₄₉N₀.₂₄, which with the
molecular weights of H, O, and N yields an estimate of 40.03 Cmmol gDW⁻¹, again close to the value proposed above.

## Metabolite concentrations c, a, a*, and a₀

A recent quantification of 43 abundant metabolites in the *E. coli* BW25113 strain growing in minimal medium with glucose or glycerol learns that these metabolites sum up to a concentration of 0.89 Cmmol gDW⁻¹ and 0.69 Cmmol gDW⁻¹, respectively (*Gerosa et al., 2015*). When comparing the metabolites quantified by Gerosa et al. with those measured in a broader screen carried out by *Park et al., 2016*, we conclude that 56% of the metabolite mass is covered by the study of Gerosa et al. As a consequence, we estimate the total metabolite concentrations in growth on glucose and glycerol to be 1.6 Cmmol gDW⁻¹ and 1.2 Cmmol gDW⁻¹, respectively. With the biomass density value of 1/β, these concentrations correspond to 3.9% and 3.0% of the total biomass. The estimates correspond well to the older estimate that metabolites constitute 3.5% of the total biomass, obtained for the *E. coli* B/r strain growing at a rate of around 1 hr⁻¹ (*Neidhardt, 1996*), and a more recent estimate of 2.9% (*Feist et al., 2007*).

Analysis of the data of *Gerosa et al., 2015*, shows that central carbon metabolites account for 22% of the total free metabolite concentration during growth in minimal medium with glucose. We therefore estimate the concentration of the pool of central metabolites in this condition as

$$ \hat{c} = 0.22 \cdot 1.6 = 0.35 \text{ Cmmol gDW}^{-1}. \qquad (83) $$

For growth on glycerol, the fraction of central metabolites is 17%, so that

$$ \hat{c} = 0.17 \cdot 0.92 = 0.20 \text{ Cmmol gDW}^{-1}. \qquad (84) $$

As explained in Appendix 1, we consider pools of charged and discharged energy cofactors expressed as ATP equivalents. Following the arguments of *Basan et al., 2015b*, 1 NADH or 1 NADPH molecule can be converted into 2 ATP molecules. With these conversion factors, we obtain from the ATP/ ADP, NADH/NAD+, NADPH/NADP+ concentrations reported by *Gerosa et al., 2015*, the following estimates of the concentrations of energy cofactors during growth on glucose:

$$ \hat{a}^* = 0.009 \text{ mmol gDW}^{-1}, \quad \hat{a} = 0.011 \text{ mmol gDW}^{-1}. \qquad (85) $$

The values for growth on glycerol are

$$ \hat{a}^* = 0.005 \text{ mmol gDW}^{-1}, \quad \hat{a} = 0.010 \text{ mmol gDW}^{-1}. \qquad (86) $$

Accordingly, $\hat{a}_0 = 0.020 \text{ mmol gDW}^{-1}$ for growth on glucose, and $\hat{a}_0 = 0.015 \text{ mmol gDW}^{-1}$ for growth on glycerol. Recall that ATP and ADP are not included in the mass balance (Appendix 1).

## Protein concentrations m<sub>u</sub>, r, m<sub>c</sub>, and m<sub>er</sub> + m<sub>ef</sub>

Estimates of the total protein concentration of *E. coli* reported in the literature vary significantly (*Milo, 2013*). For example, older values for the B/r strain indicate a mass fraction of 0.55 (*Neidhardt, 1996*), for cells growing with a doubling time of 40 min ($\mu = 1.04 \text{ hr}^{-1}$). In their quantification of the NCM3722 strain, *Basan et al., 2015b*, report a value of 0.67 for the protein fraction of dry biomass of cells growing in batch in minimal medium with glucose at a rate of 0.99 hr⁻¹. For growth on other carbon sources at rates of 0.42–0.43, this fraction increases to 0.73–0.76. *Valgepea et al., 2013*, find that for glucose-limited growth in a bioreactor at a rate of 0.4 hr⁻¹, the MG1655 strain, another K-12 descendant, has a protein dry biomass fraction equal to 0.53. *Milo, 2013*, cites an old reference value of 0.24 g mL⁻¹, which with an estimated total (dry) biomass concentration of 0.33 g mL⁻¹ yields a protein mass fraction of 0.73, in agreement with the values of Basan et al.

We based our estimates on the data from *Basan et al., 2015b*, who report protein dry mass fractions for batch growth in different media at different growth rates. From within the range of reported values, we chose the dry mass fractions for growth rates corresponding to the observed growth rates of the BW25113 strain in minimal medium with glucose or glycerol (*Appendix 2—figure 1*). This resulted in protein dry mass fractions of 0.72 (glucose) and 0.73 (glycerol). Like the carbon mass fraction of biomass, the carbon mass fraction of protein is approximately 0.5 (Supplementary table 3 in *Feist et al., 2007*). As a consequence, the above protein dry mass fractions also denote the protein fractions of the total biomass concentration expressed in units Cmmol gDW⁻¹.
In our model, the process of protein synthesis includes the synthesis of amino acids from central metabolites (Appendix 1). For reasons of consistency, we therefore add the concentrations of free amino acids to the total protein concentration. Given that amino acids account for around 50% of metabolites (Bennett et al., 2009), and the total metabolite concentrations were estimated to take up 3.9% and 3.0% of the total biomass during growth on glucose and glycerol, respectively, the total protein concentrations amount to a fraction of 0.74 of the total biomass density, for both glucose and glycerol.

The proteomics data of Schmidt et al., 2016, provide information on the mass fractions of each of the protein categories distinguished in the model. This information, together with the total protein concentration established above, allows us to compute the concentrations $m_u$, $r$, $m_c$, and $m_{er} + m_{ef}$ (in units Cmmol gDW⁻¹). The use of mass fractions, instead of the absolute values also reported by Schmidt et al., has the advantage of ensuring the consistency of the protein concentrations with the uptake, secretion, and growth rates reconstructed below. In the case of growth in minimal medium with glucose, we thus estimate that

$$ \hat{m}_u = 0.37 \cdot 0.74 \cdot 1/\hat{\beta} = 11.1 \text{ Cmmol gDW}^{-1}, \qquad (87) $$

$$ \hat{r} = 0.44 \cdot 0.74 \cdot 1/\hat{\beta} = 13.2 \text{ Cmmol gDW}^{-1}, \qquad (88) $$

$$ \hat{m}_c = 0.09 \cdot 0.74 \cdot 1/\hat{\beta} = 2.7 \text{ Cmmol gDW}^{-1}, \qquad (89) $$

$$ \hat{m}_{er} + \hat{m}_{ef} = 0.10 \cdot 0.74 \cdot 1/\hat{\beta} = 3.0 \text{ Cmmol gDW}^{-1}. \qquad (90) $$

while for minimal medium with glycerol we obtain

$$ \hat{m}_u = 0.36 \cdot 0.74 \cdot 1/\hat{\beta} = 10.9 \text{ Cmmol gDW}^{-1}, \qquad (91) $$

$$ \hat{r} = 0.38 \cdot 0.74 \cdot 1/\hat{\beta} = 11.5 \text{ Cmmol gDW}^{-1}, \qquad (92) $$

$$ \hat{m}_c = 0.10 \cdot 0.74 \cdot 1/\hat{\beta} = 3.0 \text{ Cmmol gDW}^{-1}, \qquad (93) $$

$$ \hat{m}_{er} + \hat{m}_{ef} = 0.16 \cdot 0.74 \cdot 1/\hat{\beta} = 4.8 \text{ Cmmol gDW}^{-1}, \qquad (94) $$

The above mass fractions correspond to the following resource allocation parameters for growth on glucose:

$$ \hat{\chi}_u = 0.37, \quad \hat{\chi}_r = 0.44, \quad \hat{\chi}_c = 0.09, \qquad (95) $$

and growth on glycerol:

$$ \hat{\chi}_u = 0.36, \quad \hat{\chi}_r = 0.38, \quad \hat{\chi}_c = 0.10. \qquad (96) $$

We will discuss in a later section how to distribute the total concentration $\hat{m}_{er} + \hat{m}_{ef}$ over the respiration and fermentation protein classes (and thus determine the resource allocation parameters $\chi_{er}$ and $\chi_{ef}$).

## Concentration of other macromolecules u

The biomass definition in the model enforces the concentration u of other macromolecules (RNA, DNA, lipids in the cell membrane) to equal the difference between the total biomass concentration and the sum of the total protein and metabolite concentrations. For growth on glucose, we thus find that

$$ \hat{u} = 10.2 \text{ Cmmol gDW}^{-1}, \qquad (97) $$

whereas for growth on glycerol, we also obtain

$$ \hat{u} = 10.2 \text{ Cmmol gDW}^{-1}. \qquad (98) $$
The estimated values, and all other concentration values derived above, are summarized in **Appendix 2—table 1**.

## Degradation rate $\gamma$

The model includes a degradation constant $\gamma$ that accounts for one of the main causes of so-called maintenance costs of the cell, the turnover of macromolecules and other biomass components. We show that the biomass degradation constant can be determined by means of the well-known Pirt model for maintenance, defined by

$$v_{mc} = \frac{\mu}{y_{max}} + k_m, \qquad (99)$$

where $v_{mc}$ [Cmmol gDW⁻¹ hr⁻¹] is the substrate uptake rate, $Y_{max}$ [gDW Cmmol⁻¹] the maximum biomass yield without maintenance, and $k_m$ [Cmmol gDW⁻¹ hr⁻¹] the so-called maintenance coefficient (Pirt, 1965).

By substituting expressions for $Y_{max}$ and $\mu$ from our model (Appendix 1) into Equation 99, we obtain

$$\begin{aligned} v_{mc} &= \frac{\beta(v_{mc} - v_{mer} - \rho_{mef}v_{mef} - (\rho_{ru} - 1)(v_r + v_{mu}) - \gamma/\beta)}{\beta(v_{mc} - v_{mer} - \rho_{mef}v_{mef} - (\rho_{ru} - 1)(v_r + v_{mu}))} \cdot v_{mc} + k_m \\ &= v_{mc} - \frac{\gamma}{y_{max}} + k_m, \end{aligned} \qquad (100)$$

or

$$\gamma = k_m \cdot Y_{max}. \qquad (101)$$

Data for growth of the E. coli MG1655 strain in minimal medium with glucose, by Esquerré et al., 2014, indicate a maintenance coefficient of $k_m = 0.35$ mmol$_{glc}$ gDW⁻¹ hr⁻¹ and a maximal yield $Y_{max} = 76.2$ gDW mol⁻¹$_{glc}$, practically identical to the values reported for the same strain in the same medium by Nanchen et al., 2006 ($k_m = 0.37$ mmol$_{glc}$ gDW⁻¹ hr⁻¹, $Y_{max} = 76$ gDW mol⁻¹$_{glc}$). Using the values from Esquerré et al., 2014, we find $\hat{\gamma} = 0.027$ hr⁻¹. By the same reasoning as above, the maintenance rate for growth in minimal medium with glycerol can be obtained. Classical experiments indicate that the rate is 1.2 times the rate for glucose (Farmer and Jones, 1976), so $\hat{\gamma} = 0.032$ hr⁻¹.

## Substrate uptake flux $v_{mc}$, fermentation flux $v_{mef}$, and biosynthesis fluxes $v_{mu}$, $v_r$
The datasets used from Haverkorn van Rijsewijk et al., 2011, and Gerosa et al., 2015, consist of measured fluxes and the growth rate of the E. coli BW25113 strain, during exponential growth in minimal medium with glucose and glycerol, respectively. In particular, the glucose or glycerol uptake rate $v_{mc}$ [mmol$_{glc}$/gly gDW⁻¹ hr⁻¹], the acetate secretion rate $v_{mef}$ [mmol$_{ace}$ gDW⁻¹ hr⁻¹], and the growth rate $\mu$ [hr⁻¹] were measured. The values for glucose are $\hat{v}_{mc} = 8.26$ mmol$_{glc}$ gDW⁻¹ hr⁻¹, $\hat{v}_{mef} = 4.89$ mmol$_{ace}$ gDW⁻¹ hr⁻¹, and $\hat{\mu} = 0.61$ hr⁻¹. These values are very close to those reported by Morin et al., 2016, for the MG1655 strain. In the case of growth on glycerol, we have $\hat{v}_{mc} = 11.3$ mmol$_{gly}$ gDW⁻¹ hr⁻¹ and $\hat{\mu} = 0.49$ hr⁻¹, while the acetate secretion rate was found to be small: $\hat{v}_{mef} = 0.60$ mmol$_{ace}$ gDW⁻¹ hr⁻¹. (Gerosa et al., 2015, actually report a glycerol uptake rate of 10.14 mmol$_{glc}$ gDW⁻¹ hr⁻¹, but explain that uptake rates were computed by dividing the measured growth rates by the measured biomass yields [see Extended Experimental Procedures]. In the case of glycerol, the growth rate and the biomass yield were found to be 0.49 hr⁻¹ and 0.47 gDW g⁻¹, respectively (Data S1), which with a molecular weight of 92.09 g mol⁻¹ gives a value of 0.49/(0.47 · 92.09 · 0.001) = 11.3 mmol gDW⁻¹ hr⁻¹ for the glycerol uptake rate).

In agreement with the biomass concentration units, we express mass fluxes in terms of the amount of carbon flowing through the system [Cmmol gDW⁻¹ hr⁻¹]. Bearing in mind that the carbon content of glucose is 6 C and that of acetate 2 C, we obtain the following rates:

$$\hat{v}_{mc} = 8.26 \cdot 6 = 49.6 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}, \qquad (102)$$

$$\hat{v}_{mef} = 4.89 \cdot 2 = 9.8 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}. \qquad (103)$$

Similarly, for growth on glycerol we have

$$\hat{v}_{mc} = 11.3 \cdot 3 = 33.9 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}, \qquad (104)$$
$$ \hat{v}_{mef} = 0.60 \cdot 2 = 1.2 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}, \qquad (105) $$

where we have used the fact that the carbon content of glycerol is 3 C.

The measured fluxes, together with the growth and degradation rates and the total biomass concentration, fix the biosynthesis fluxes in the model. This can be shown by rewriting the equations in the model in the following way:

$$ v_{mu} = (\mu + \gamma) u, \qquad (106) $$

$$ v_r = (\mu + \gamma)(m_u + r + m_c + m_{er} + m_{ef}). \qquad (107) $$

Values for $v_{mu}$ and $v_r$ can be directly computed from the values for the concentrations and rates in the right-hand sides of Equations 106 and 107 that were derived above. This yields for growth on glucose:

$$ \hat{v}_{mu} = 6.5 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}, \qquad (108) $$

$$ \hat{v}_r = 19.2 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}, \qquad (109) $$

and for growth on glycerol:

$$ \hat{v}_{mu} = 5.3 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}, \qquad (110) $$

$$ \hat{v}_r = 15.8 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}. \qquad (111) $$

## Respiration flux $v_{mer}$ and CO$_2$ correction factors $\rho_{ru}$ and $\rho_{mef}$

In the flux datasets mentioned above, CO$_2$ released by the cells was not directly measured. The CO$_2$ flux can be derived from the carbon mass balance, bearing in mind that almost all of the carbon not integrated into biomass leaves the cells as CO$_2$ or acetate (Gerosa et al., 2015; Gottschalk, 1986). The carbon mass balance is given by the definition of the growth rate, which provides an expression for the total CO$_2$ outflux $v_{CO_2}$. We have

$$ v_{CO_2} = v_{mer} + (\rho_{mef} - 1) v_{mef} + (\rho_{ru} - 1) (v_r + v_{mu}) = v_{mc} - v_{mef} - \frac{\mu + \gamma}{\beta}, \qquad (112) $$

where $\rho_{ru} - 1 > 0$ is the correction factor accounting for the release of CO$_2$ during the synthesis of amino acids, proteins, and other biomass components and $\rho_{mef} - 1 > 0$ the correction factor accounting for the CO$_2$ released during the conversion of glucose to acetate (Appendix 1). That is, the total CO$_2$ flux is composed of the CO$_2$ released during respiration ($v_{mer}$), fermentation ($\rho_{mef} - 1$) $v_{mef}$), and the CO$_2$ released during macromolecular synthesis ($\rho_{ru} - 1$) ($v_r + v_{mu}$). Basan et al., 2015a, argue that the latter CO$_2$ outflux is proportional to the growth rate over a wide range of conditions, with a proportionality constant $\eta$:

$$ (\rho_{ru} - 1)(v_r + v_{mu}) = \eta \mu. \qquad (113) $$

The value of $\eta$ is estimated at 7.2 Cmmol gDW$^{-1}$ (Basan et al., 2015a), so that for a growth rate of .61 hr$^{-1}$ in the case of minimal medium with glucose, the CO$_2$ outflux associated to biosynthesis equals 4.4 Cmmol gDW$^{-1}$ hr$^{-1}$. Moreover, with the values for $v_r$ and $v_{mu}$ derived above, we find

$$ \hat{\rho}_{ru} = \frac{\hat{\eta} \hat{\mu}}{\hat{v}_r + \hat{v}_{mu}} + 1 = 1.17. \qquad (114) $$

That is, 17% of the carbon flux toward macromolecular synthesis is lost as CO$_2$. The total CO$_2$ outflux can be directly computed from Equation 112, giving

$$ \hat{v}_{CO_2} = 13.9 \text{ Cmmol gDW}^{-1} \text{ hr}^{-1}. \qquad (115) $$

For each acetate molecule, one CO$_2$ is produced (Basan et al., 2015a), so that $\hat{\rho}_{mef} = 1.5$. The respiration-associated CO$_2$ outflux can now be reconstructed as

$$ \hat{v}_{mer} = \hat{v}_{CO_2} - (\hat{\rho}_{mef} - 1) v_{mef} - (\hat{\rho}_{ru} - 1) (\hat{v}_r + \hat{v}_{mu}) = 4.6 \text{ Cmmol gDW}^{-1} \text{ h}^{-1}. \qquad (116) $$
In the case of growth on glycerol, we find $\hat{v}_{CO_2} = 11.5$ Cmmol gDW$^{-1}$ hr$^{-1}$ and $\hat{v}_{mer} = 7.3$ Cmmol gDW$^{-1}$ hr$^{-1}$, while the value for $\rho_{ru}$ is the same as for glucose (1.17). The reconstructed flux measurements are summarized in **Appendix 2—table 1**, whereas the flux correction factors for CO$_2$ release are included in **Appendix 2—table 2**.

**Appendix 2—table 1.** Reconstruction of growth and degradation rates, fluxes, and concentrations from published datasets for the case of batch growth of E. coli in minimal medium with glucose or glycerol, as explained in the text.

The uncertainty intervals for the rates, fluxes, and metabolite concentrations are standard deviations reported in the source publications, after unit conversion. The uncertainty interval for the total biomass concentration was obtained by propagating the errors of the measurements in the right-hand side of $1/\beta = Yv_{mc}/\mu$ (Morin et al., 2016). The uncertainty interval for the total protein concentration was obtained by combining the latter error with the standard error of the mean for the total protein fraction predicted by the linear model fitted to the data in **Appendix 2—figure 1**. The resulting error was distributed over the individual protein categories according to their mass fractions. References: a Haverkorn van Rijsewijk et al., 2011, b Gerosa et al., 2015, c Esquerré et al., 2014, d Farmer and Jones, 1976, e Morin et al., 2016, f Basan et al., 2015b, g Schmidt et al., 2016, h Park et al., 2016.

<table><thead><tr><th>Rates</th><th>Unit</th><th>Glucose</th><th>Glycerol</th><th>Reference</th></tr></thead><tbody><tr><td>μ̂</td><td>hr<sup>-1</sup></td><td>0.61 ± 0.01</td><td>0.49 ± 0.01</td><td>a, b</td></tr><tr><td>γ̂</td><td>hr<sup>-1</sup></td><td>0.027</td><td>0.032</td><td>c, d</td></tr><tr><td colspan="5">Uptake, secretion, biosynthesis fluxes</td></tr><tr><td>ν̂<sub>mc</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>49.6 ± 5</td><td>33.9 ± 1.0</td><td>a</td></tr><tr><td>ν̂<sub>mer</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>4.6</td><td>7.3</td><td>Derived</td></tr><tr><td>ν̂<sub>mef</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>9.8 ± 3.0</td><td>1.2 ± 0.4</td><td>a</td></tr><tr><td>ν̂<sub>mu</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>6.5</td><td>5.3</td><td>Derived</td></tr><tr><td>ν̂<sub>r</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>19.2</td><td>15.8</td><td>Derived</td></tr><tr><td colspan="5">Total biomass concentration</td></tr><tr><td>1/β̂</td><td>Cmmol gDW<sup>-1</sup></td><td>40.65 ± 2.0</td><td>40.65 ± 2.0</td><td>e</td></tr><tr><td colspan="5">Protein concentrations</td></tr><tr><td>m̂<sub>u</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>11.1 ± 0.5</td><td>10.9 ± 0.5</td><td>e, f, g</td></tr><tr><td>r̂</td><td>Cmmol gDW<sup>-1</sup></td><td>13.2 ± 0.6</td><td>11.5 ± 0.6</td><td>e, f, g</td></tr><tr><td>m̂<sub>c</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>2.7 ± 0.1</td><td>3.0 ± 0.1</td><td>e, f, g</td></tr><tr><td>m̂<sub>er</sub> + m̂<sub>ef</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>3.0 ± 0.1</td><td>4.8 ± 0.2</td><td>e, f, g</td></tr><tr><td>m̂<sub>er</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>1.9</td><td>4.4</td><td>Derived</td></tr><tr><td>m̂<sub>ef</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>1.1</td><td>0.47</td><td>Derived</td></tr><tr><td colspan="5">Metabolite concentrations</td></tr><tr><td>ĉ</td><td>Cmmol gDW<sup>-1</sup></td><td>0.35 ± 0.002</td><td>0.20 ± 0.002</td><td>b, h</td></tr><tr><td>â*</td><td>mmol gDW<sup>-1</sup></td><td>0.009 ± 0.0002</td><td>0.005 ± 0.0003</td><td>b</td></tr><tr><td>â</td><td>mmol gDW<sup>-1</sup></td><td>0.011 ± 0.0006</td><td>0.010 ± 0.0005</td><td>b</td></tr></tbody></table>

Appendix 2—table 1 Continued on next page
<table><caption>Appendix 2—table 1 Continued</caption><thead><tr><th>Rates</th><th>Unit</th><th>Glucose</th><th>Glycerol</th><th>Reference</th></tr></thead><tbody><tr><td>â<sub>0</sub></td><td>mmol gDW<sup>-1</sup></td><td>0.020 ± 0.0008</td><td>0.015 ± 0.0008</td><td>b</td></tr><tr><td colspan="5">Concentration of other biomass</td></tr><tr><td>û</td><td>Cmmol gDW<sup>-1</sup></td><td>10.2</td><td>10.2</td><td>Derived</td></tr></tbody></table>

<figure><img src="image_13.png" /></figure>

**Appendix 2—figure 1.** Protein dry mass fraction for different growth rates of E. coli. The protein dry mass fraction (g gDW⁻¹) as a function of the steady-state growth rate was computed from data for the NCM3722 wild-type strain grown in different media (red dots) or for a strain carrying a plasmid for the gratuitous overexpression of a protein (blue dots) (Appendix Table S4 in Basan et al., 2015b). We interpolated the data (black line) to provide an estimate of the protein dry mass fractions at the growth rates corresponding to batch growth of the BW25113 strain in minimal medium with either glucose or glycerol (μ = 0.61 hr⁻¹ or μ = 0.49 hr⁻¹, respectively).

**Appendix 2—table 2.** Estimation of the values of the kinetic parameters in the model, in the case of batch growth of E. coli in minimal medium with glucose or glycerol, as explained in the text.

<table><thead><tr><th>Parameter</th><th>Glucose</th><th>Glycerol</th><th>Unit</th></tr></thead><tbody><tr><td>ρ̂<sub>ru</sub></td><td>1.17</td><td>1.17</td><td>–</td></tr><tr><td>ρ̂<sub>mef</sub></td><td>1.5</td><td>1.5</td><td>–</td></tr><tr><td>k̂<sub>r</sub></td><td>2.9</td><td>3.6</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>mu</sub></td><td>1.2</td><td>1.3</td><td>hr<sup>-1</sup></td></tr><tr><td>ε̂<sub>s</sub></td><td>18.3</td><td>11.2</td><td>hr<sup>-1</sup></td></tr></tbody></table>

Appendix 2—table 2 Continued on next page
<table><caption>Appendix 2—table 2 Continued</caption><thead><tr><th>Parameter</th><th>Glucose</th><th>Glycerol</th><th>Unit</th></tr></thead><tbody><tr><td>ŷ<sub>mer</sub></td><td>5.0</td><td>4.4</td><td>hr<sup>-1</sup></td></tr><tr><td>ŷ<sub>mef</sub></td><td>17.4</td><td>6.7</td><td>hr<sup>-1</sup></td></tr><tr><td>ŷ<sub>a</sub></td><td>2279</td><td>6462</td><td>hr<sup>-1</sup></td></tr><tr><td>K̂<sub>r</sub></td><td>0.29</td><td>0.28</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>mu</sub></td><td>0.29</td><td>0.28</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>mer</sub></td><td>0.29</td><td>0.28</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>mef</sub></td><td>0.29</td><td>0.28</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>ar</sub></td><td>0.0009</td><td>0.0005</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amer</sub></td><td>0.0011</td><td>0.001</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amef</sub></td><td>0.0011</td><td>0.001</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amu</sub></td><td>0.0009</td><td>0.0005</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>n̂<sub>mer</sub></td><td>4.3</td><td>4.7</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>mef</sub></td><td>2.0</td><td>2.3</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>r</sub></td><td>0.77</td><td>0.09</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>mu</sub></td><td>0.65</td><td>0.65</td><td>mmol Cmmol<sup>-1</sup></td></tr></tbody></table>

## Estimation of parameter values for batch growth

The model contains 20 kinetic parameters. Estimation of all of these values from the data in **Appendix 2—table 1** would lead to identifiability problems. However, as shown below, making appropriate assumptions based on experimental observations allows all parameters to be unambiguously fixed.

### Parameters in energy balance equation $n_{me}$, $n_{mer}$, $n_{mef}$, $n_r$, $n_{mu}$, $k_a$

We remind that the energy cofactor rate equation at steady state, or energy balance, is given by

$$0 = n_{mer} v_{mer} + n_{mef} v_{mef} - n_r v_r - n_{mu} v_{mu} - v_d, \quad (117)$$

where $v_d = k_a a^*$.

The ATP yield coefficients $n_{mer}$ and $n_{mef}$ describe how many energy cofactor molecules (ATP) can be regenerated from a molecule of substrate (glucose or glycerol), in units mmol<sub>ATP</sub> Cmmol. **Basan et al., 2015b**, describe a procedure for deriving the yield coefficients $n_{mer}$ and $n_{mef}$ from the reaction stoichiometry of the metabolic pathways used during growth on glucose. Aerobic respiration generates 4 ATP, 8 NADH, 2 NADPH, and 2 FADH<sub>2</sub> from one molecule of glucose, equivalent to 26 ATP, whereas aerobic fermentation (acetate overflow) leads to 4 ATP and 4 NADH, equivalent to 12 ATP. As a consequence,

$$\hat{n}_{mer} = 26 \text{ ATP/Glc} = 26/6 = 4.3 \text{ mmol Cmmol}^{-1}, \quad (118)$$

$$\hat{n}_{mef} = 12 \text{ ATP/Glc} = 12/6 = 2 \text{ mmol Cmmol}^{-1}, \quad (119)$$

bearing in mind that glucose contains 6 C atoms. Restricting central metabolism to the glycolysis and TCA pathways, like **Basan et al., 2015b**, and focusing on the main flux of glycerol catabolism through the lower part of the glycolysis pathway, the ATP yield of glycerol respiration can be determined as 2 ATP, 4 NADH, 1 NADPH, and 2 FADH<sub>2</sub>, equivalent to 14 ATP. Similarly, for aerobic fermentation we find 2 ATP, 2 NADH, and 1 FADH<sub>2</sub>, equivalent to 7 ATP. This yields
$$ \hat{n}_{mer} = 14 \text{ ATP/Gly} = 14/3 = 4.7 \text{ mmol Cmmol}^{-1}, \qquad (120) $$

$$ \hat{n}_{mef} = 7 \text{ ATP/Gly} = 7/3 = 2.3 \text{ mmol Cmmol}^{-1}, \qquad (121) $$

given that glycerol contains 3 C atoms.

The coefficient $n_r$ describes the ATP costs of protein synthesis. Kaleta et al., 2013, compute the amount of ATP needed for the elongation of a protein by one amino acid, including the net ATP costs of the synthesis of the amino acids from central metabolites and mRNA synthesis. They find that the ATP costs of the synthesis of many amino acids are negative (i.e. their synthesis yields ATP), while the ATP costs of mRNA synthesis are negligible in comparison with the translation costs. For glucose, the median total ATP costs are 3.7 ATP/amino acid. This equals 3.7/4.8=0.77 mmol$_{ATP}$ Cmmol$_{aa}^{-1}$, where the mean C content of amino acids, weighted for the amino acid composition of biomass, is estimated at 4.8 (data from Feist et al., 2007). That is,

$$ \hat{n}_r = 0.77 \text{ mmol Cmmol}^{-1}. \qquad (122) $$

These theoretical costs are close to the value of 0.94 mmol$_{ATP}$ Cmmol$_{aa}^{-1}$ obtained from the review of Russell and Cook, who base their estimate on calculations by Stouthamer (Russell and Cook, 1995). (The value of 0.94 mmol$_{ATP}$ Cmmol$_{aa}^{-1}$ is obtained by converting the value given in Table 1 of Russell and Cook, 1995, bearing in mind that the calculations were done for a protein fraction of biomass equal to 0.52 and using a carbon mass fraction of protein equal to 0.5; Feist et al., 2007.) For glycerol, where the synthesis of many amino acids is energetically favorable (Kaleta et al., 2013), the median total ATP costs are much lower: 0.44 ATP/amino acid. This amounts to 0.44/4.8=0.09 mmol$_{ATP}$ Cmmol$_{aa}^{-1}$, and hence

$$ \hat{n}_r = 0.09 \text{ mmol Cmmol}^{-1}. \qquad (123) $$

The coefficient $n_{mu}$ describes the ATP costs of the synthesis of other macromolecules (RNA, DNA, etc.). From the review of Russell and Cook, 1995, under the assumption that the average carbon mass fraction of other macromolecules is also equal to 0.5, we find that these ATP costs equal 0.65 mmol$_{ATP}$ Cmmol$_{macromolecule}^{-1}$, so that

$$ \hat{n}_{mu} = 0.65 \text{ mmol Cmmol}^{-1}. \qquad (124) $$

This value applies to growth on glucose, but in the absence of information specific to growth on glycerol, we use the same value for the latter condition.

It has been well established that the estimated ATP production exceeds the estimated ATP consumption for macromolecular synthesis by a factor of 2–3 in the case of growth on minimal medium with glucose (Feist et al., 2007; Russell and Cook, 1995). This suggests a dissipation of energy which is also observed in our case: the ratio of $\hat{n}_{mer} \hat{v}_{mer} + \hat{n}_{mef} \hat{v}_{mef}$ and $\hat{n}_r \hat{v}_r + \hat{n}_{mu} \hat{v}_{mu}$ equals 2.1 in the case of glucose, and increases to 7.5 in the case of glycerol. The difference is due to the costs of osmoregulation, motility, and other maintenance processes (van Bodegom, 2007), but also to energy spilling, a factor that remains little understood (Russell and Cook, 1995). As explained in Appendix 1, we model all of the above forms of energy dissipation by a first-order reaction with constant $k_a$ whose value can be computed by closing the energy balance (Equation 117):

$$ \hat{k}_a = \frac{\hat{n}_{mer} \hat{v}_{mer} + \hat{n}_{mef} \hat{v}_{mef} - \hat{n}_r \hat{v}_r - \hat{n}_{mu} \hat{v}_{mu}}{\hat{a}^*}. \qquad (125) $$

In the case of batch growth on glucose, we thus find an approximate value

$$ \hat{k}_a = 2279 \text{ hr}^{-1}, \qquad (126) $$

and for glycerol,

$$ \hat{k}_a = 6426 \text{ hr}^{-1}. \qquad (127) $$
## Parameter in rate equation for central carbon metabolism e_s

As explained in Appendix 1, the macroreaction for central carbon metabolism simplifies to the following simple rate equation:

$$v_{mc} = e_s m_c. \qquad (128)$$

With the value for $m_c$ derived in the previous section (Appendix 2—table 1), we obtain the following estimates for glucose:

$$\hat{e}_s = 18.3 \text{ hr}^{-1}, \qquad (129)$$

and for glycerol:

$$\hat{e}_s = 11.2 \text{ hr}^{-1}. \qquad (130)$$

## Parameters in the rate equations for the synthesis of proteins and other biomass components $K_r, K_{mu}, K_{ar}, K_{amu}, k_{r1}$ and $k_{mu}$

The rate equations for the macroreactions corresponding to protein synthesis and the synthesis of other macromolecules are restated as a reminder:

$$v_r = k_r r \frac{a^*}{a^* + K_{ar}} \frac{c}{c + K_r}, \qquad (131)$$

$$v_{mu} = k_{mu} m_u \frac{a^*}{a^* + K_{amu}} \frac{c}{c + K_{mu}}. \qquad (132)$$

The above reactions consume central metabolites (c) and charged energy cofactors (ATP) ($a^*$).

Very little information is available on the in vivo values of half-saturation constants occurring in the kinetic expressions of the macroreactions. However, previous metabolomics assays have yielded general observations on enzyme saturation (the ratio of reaction substrates and half-saturation constants) that will be exploited here (Bennett et al., 2009). These will be refined by combining available measurements with a recent compilation of $K_m$ values for E. coli (Dourado et al., 2021; Park et al., 2016).

First, in the case of central carbon metabolism, 'substrate concentrations are close to $K_m$ for many reactions' (Bennett et al., 2009). We have computed, for metabolites in central carbon metabolism of E. coli quantified by Gerosa et al., 2015, the ratio of metabolite concentrations and values of the half-saturation constants of the reactions in which the metabolites participate (Dourado et al., 2021). Taking the geometric mean of the ratios, we found an average value of substrate saturation of 1.2 for glucose and 0.72 for glycerol (Supplementary file 3). Assuming that this value is approximately valid for all reactions consuming central carbon metabolites in our model, we estimate for glucose

$$\hat{K}_r = \hat{K}_{mu} \approx \frac{\hat{c}}{1.2} = 0.29 \text{ Cmmol gDW}^{-1}, \qquad (133)$$

and for glycerol

$$\hat{K}_r = \hat{K}_{mu} \approx \frac{\hat{c}}{0.72} = 0.28 \text{ Cmmol gDW}^{-1}, \qquad (134)$$

Note that we deal with apparent half-saturation constants that account for possible metabolic regulation.

Second, ATP and NAD+ were found to saturate their enzymes with 'cofactor concentration typically exceeding their $K_m$ value by more than 10-fold' (Bennett et al., 2009). This motivates the following approximate values for the half-saturation constants occurring in the energy terms of the biosynthesis rate equations:

$$\hat{K}_{ar} = \hat{K}_{amu} \approx \frac{\hat{a}^*}{10} \text{ mmol gDW}^{-1}, \qquad (135)$$

with different values for growth on glucose and glycerol (0.0009 vs 0.0005 mmol gDW$^{-1}$).
Together with the values for the fluxes and enzyme concentrations, we can now derive values for the unknown catalytic constants $k_r$ and $k_{mu}$ from **Equations 131 and 132**. In the case of growth on glucose, we have

$$ \hat{k}_r = 2.9 \text{ hr}^{-1}, \quad \hat{k}_{mu} = 1.2 \text{ hr}^{-1}, \qquad (136) $$

whereas for growth on glycerol we find

$$ \hat{k}_r = 3.6 \text{ hr}^{-1}, \quad \hat{k}_{mu} = 1.3 \text{ hr}^{-1}. \qquad (137) $$

Note that the estimates for $k_r$ are comparable to values used for the maximum translation capacity in previous work (5.9 hr$^{-1}$ in Scott et al., 2010; 3.6 hr$^{-1}$ in Giordano et al., 2016).

### Parameters in the rate equations for energy metabolism $K_{mer}$, $K_{mef}$, $K_{amer}$, $K_{amef}$, $k_{mer}$, and $k_{mef}$

We repeat the rate equations for energy metabolism, for the two macroreactions (respiration and fermentation):

$$ v_{mer} = k_{mer} m_{er} \frac{a_0 - a^*}{a_0 - a^* + K_{amer}} \frac{c}{c + K_{mer}}, \qquad (138) $$

$$ v_{mef} = k_{mef} m_{ef} \frac{a_0 - a^*}{a_0 - a^* + K_{mef}} \frac{c}{c + K_{mef}}, \qquad (139) $$

The arguments given in the previous section for fixing the values of the half-saturation constants also apply in this case, so that we obtain

$$ \hat{K}_{mer} = \hat{K}_{mef} = 0.29 \text{ Cmmol gDW}^{-1}, \qquad (140) $$

$$ \hat{K}_{amer} = \hat{K}_{amef} = 0.0011 \text{ mmol gDW}^{-1}, \qquad (141) $$

for growth on glucose, and

$$ \hat{K}_{mer} = \hat{K}_{mef} = 0.28 \text{ Cmmol gDW}^{-1}, \qquad (142) $$

$$ \hat{K}_{amer} = \hat{K}_{amef} = 0.001 \text{ mmol gDW}^{-1}, \qquad (143) $$

for growth on glycerol.

In the previous section, we were only able to reconstruct the total concentration of enzymes involved in energy metabolism (Appendix 2—table 1), but not the fractions involved in aerobic respiration or fermentation. Let $\hat{m}_e = \hat{m}_{er} + \hat{m}_{ef}$. In order to derive the concentrations $m_{er}$ and $m_{ef}$, we follow approximately the same procedure as Basan et al., 2015b, but for the proteomics data of Schmidt et al., 2016. We divide the proteins labeled as taking part in energy metabolism into enzymes only playing a role in respiration (pyruvate decarboxylation, TCA cycle), enzymes only playing a role in fermentation (acetate pathway), and other enzymes, notably those constituting the electron transport chain and ATP synthases using the proton gradient for ATP production. The latter category is involved in both (aerobic) respiration and fermentation, and we divide the protein mass according to the ratio of the respiration and fermentation fluxes. For growth on glucose, we find fractions 0.45, 0.01, and 0.54 for the three protein categories, whereas for glycerol we find 0.37, 0.01, and 0.62, respectively (Supplementary file 4). This gives rise to the following estimates for glucose,

$$ \hat{m}_{er} = (0.45 + 0.54 \frac{\hat{v}_{mer}}{\hat{v}_{mer} + \hat{v}_{mef}}) \hat{m}_{e} = 1.9 \text{ Cmmol gDW}^{-1}, \qquad (144) $$

$$ \hat{m}_{ef} = (0.01 + 0.54 \frac{\hat{v}_{mef}}{\hat{v}_{mer} + \hat{v}_{mef}}) \hat{m}_{e} = 1.1 \text{ Cmmol gDW}^{-1}, \qquad (145) $$
and for glycerol

$$ \hat{m}_{er} = (0.37 + 0.62 \frac{\hat{v}_{mer}}{\hat{v}_{mer} + \hat{v}_{mef}}) \hat{m}_{e} = 4.4 \text{ Cmmol gDW}^{-1}, \qquad (146) $$

$$ \hat{m}_{ef} = (0.01 + 0.62 \frac{\hat{v}_{mef}}{\hat{v}_{mer} + \hat{v}_{mef}}) \hat{m}_{e} = 0.47 \text{ Cmmol gDW}^{-1}. \qquad (147) $$

Together with the values for the fluxes and metabolite concentrations, we can now estimate values for the unknown apparent catalytic constants $k_{mer}$ and $k_{mef}$ from **Equations 138 and 139**. In the case of growth on glucose, we have

$$ \hat{k}_{mer} = 5.0 \text{ hr}^{-1}, \quad \hat{k}_{mef} = 17.4 \text{ hr}^{-1}, \qquad (148) $$

and for growth on glycerol,

$$ \hat{k}_{mer} = 4.4 \text{ hr}^{-1}, \quad \hat{k}_{mef} = 6.7 \text{ hr}^{-1}. \qquad (149) $$

All parameter values derived in this and the previous sections are summarized in **Appendix 2—table 2**.

## Data and parameter estimates for continuous growth

The model calibration procedure for the other conditions considered, continuous growth in a chemostat, in minimal medium with glucose at dilution rates of 0.2 hr⁻¹, 0.35 hr⁻¹, and 0.5 hr⁻¹, is the same as for batch growth. Not all source data used above are available for continuous growth. In their absence, we use the corresponding data for batch growth as a proxy. In particular, total protein and metabolite concentrations were obtained from Gerosa et al., 2015, and Basan et al., 2015b, by selecting the (interpolated) values for batch growth at rates corresponding to the dilution rates (Appendix 2—figure 1). In addition, for the case of growth at a dilution rate of 0.2 hr⁻¹, where no significant acetate overflow is detected, we set the acetate secretion rate to 5% of the acetate secretion rate during continuous growth at 0.35 hr⁻¹, that is, a value below the detection limit. This allows the same model with respiration and fermentation to be used over all conditions.

The data used for calibration is shown in **Appendix 2—table 3** and the values for the parameters obtained after calibration are listed in **Appendix 2—table 4**.

**Appendix 2—table 3.** Reconstruction of growth and degradation rates, fluxes, and concentrations from published datasets for the case of continuous growth of E. coli in minimal medium with glucose at different dilution rates (D0.2: 0.2 hr⁻¹, D0.35: 0.35 hr⁻¹, D0.5: 0.5 hr⁻¹).

For the error bars, see **Appendix 2—table 1**. References: a Peebo et al., 2015, b Esquerré et al., 2014, c Morin et al., 2016, d Basan et al., 2015b, e Schmidt et al., 2016, f Gerosa et al., 2015, g Park et al., 2016.

<table><thead><tr><th>Rates</th><th>Unit</th><th>D0.2</th><th>D0.35</th><th>D0.5</th><th>Reference</th></tr></thead><tbody><tr><td>μ̂</td><td>hr<sup>-1</sup></td><td>0.2</td><td>0.35</td><td>0.5</td><td>a</td></tr><tr><td>γ̂</td><td>hr<sup>-1</sup></td><td>0.027</td><td>0.027</td><td>0.027</td><td>b</td></tr><tr><td colspan="6">Uptake, secretion, and biosynthesis fluxes</td></tr><tr><td>ν̂<sub>mc</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>16.0</td><td>26.2</td><td>37.4</td><td>a</td></tr><tr><td>ν̂<sub>mer</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>5.3</td><td>8.1</td><td>9.4</td><td>Derived</td></tr><tr><td>ν̂<sub>mef</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>0.02</td><td>0.16</td><td>2.0</td><td>a</td></tr><tr><td>ν̂<sub>mu</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>1.9</td><td>3.4</td><td>5.2</td><td>Derived</td></tr></tbody></table>

Appendix 2—table 3 Continued on next page
<table><caption>Appendix 2—table 3 Continued</caption><thead><tr><th>Rates</th><th>Unit</th><th>D0.2</th><th>D0.35</th><th>D0.5</th><th>Reference</th></tr></thead><tbody><tr><td>ν̂<sub>r</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>7.3</td><td>11.8</td><td>16.1</td><td>Derived</td></tr><tr><td colspan="6">Total biomass concentration</td></tr><tr><td>1/β̂</td><td>Cmmol gDW<sup>-1</sup></td><td>40.65 ± 2.0</td><td>40.65 ± 2.0</td><td>40.65 ± 2.0</td><td>c</td></tr><tr><td colspan="6">Protein concentrations</td></tr><tr><td>μ̂<sub>u</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>11.2 ± 0.6</td><td>11.2 ± 0.6</td><td>10.4 ± 0.5</td><td>c, d, e</td></tr><tr><td>ρ̂</td><td>Cmmol gDW<sup>-1</sup></td><td>9.3 ± 0.5</td><td>9.4 ± 0.5</td><td>11.0 ± 0.5</td><td>c, d, e</td></tr><tr><td>μ̂<sub>c</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>3.5 ± 0.2</td><td>3.4 ± 0.2</td><td>3.3 ± 0.2</td><td>c, d, e</td></tr><tr><td>μ̂<sub>er</sub> + μ̂<sub>ef</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>8.0 ± 0.4</td><td>7.2 ± 0.4</td><td>5.8 ± 0.3</td><td>c, d, e</td></tr><tr><td>μ̂<sub>er</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>7.9</td><td>7.1</td><td>5.2</td><td>Derived</td></tr><tr><td>μ̂<sub>ef</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>0.05</td><td>0.1</td><td>0.6</td><td>Derived</td></tr><tr><td colspan="6">Metabolite concentrations</td></tr><tr><td>μ̂</td><td>Cmmol gDW<sup>-1</sup></td><td>0.35 ± 0.002</td><td>0.35 ± 0.002</td><td>0.35 ± 0.002</td><td>f, g</td></tr><tr><td>μ̂*</td><td>mmol gDW<sup>-1</sup></td><td>0.005</td><td>0.006</td><td>0.008</td><td>f</td></tr><tr><td>μ̂</td><td>mmol gDW<sup>-1</sup></td><td>0.011</td><td>0.015</td><td>0.016</td><td>f</td></tr><tr><td>μ̂<sub>0</sub></td><td>mmol gDW<sup>-1</sup></td><td>0.016</td><td>0.021</td><td>0.024</td><td>f</td></tr><tr><td colspan="6">Concentration of other biomass</td></tr><tr><td>μ̂</td><td>Cmmol gDW<sup>-1</sup></td><td>8.2</td><td>9.0</td><td>9.8</td><td>Derived</td></tr></tbody></table>

<table><caption>**Appendix 2—table 4.** Estimation of the values of the kinetic parameters in the model, in the case of continuous growth of *E. coli* in minimal medium with glucose at different dilution rates (D0.2: 0.2 hr⁻¹, D0.35: 0.35 hr⁻¹, D0.5: 0.5 hr⁻¹), as explained in the text.</caption><thead><tr><th>Parameter</th><th>D0.2</th><th>D0.35</th><th>D0.5</th><th>Unit</th></tr></thead><tbody><tr><td>ρ̂<sub>ru</sub></td><td>1.16</td><td>1.17</td><td>1.17</td><td>–</td></tr><tr><td>ρ̂<sub>me</sub></td><td>1.5</td><td>1.5</td><td>1.5</td><td>–</td></tr><tr><td>k̂<sub>r</sub></td><td>1.6</td><td>2.5</td><td>2.9</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>mu</sub></td><td>0.33</td><td>0.61</td><td>1.0</td><td>hr<sup>-1</sup></td></tr><tr><td>ε̂<sub>s</sub></td><td>4.5</td><td>7.6</td><td>11.2</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>mer</sub></td><td>1.3</td><td>2.3</td><td>3.6</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>me</sub></td><td>0.77</td><td>2.98</td><td>6.8</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>a</sub></td><td>3203</td><td>4001</td><td>3633</td><td>hr<sup>-1</sup></td></tr><tr><td>K̂<sub>r</sub></td><td>0.29</td><td>0.29</td><td>0.29</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>mu</sub></td><td>0.29</td><td>0.29</td><td>0.29</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>me</sub></td><td>0.29</td><td>0.29</td><td>0.29</td><td>Cmmol gDW<sup>-1</sup></td></tr></tbody></table>

Appendix 2—table 4 Continued on next page
<table><caption>Appendix 2—table 4 Continued</caption><thead><tr><th>Parameter</th><th>D0.2</th><th>D0.35</th><th>D0.5</th><th>Unit</th></tr></thead><tbody><tr><td>K̂<sub>mef</sub></td><td>0.29</td><td>0.29</td><td>0.29</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>ar</sub></td><td>0.0005</td><td>0.0006</td><td>0.0008</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amer</sub></td><td>0.0011</td><td>0.0015</td><td>0.0016</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amef</sub></td><td>0.0011</td><td>0.0015</td><td>0.0016</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amu</sub></td><td>0.0005</td><td>0.0006</td><td>0.0008</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>n̂<sub>mer</sub></td><td>4.3</td><td>4.3</td><td>4.3</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>mef</sub></td><td>2.0</td><td>2.0</td><td>2.0</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>r</sub></td><td>0.77</td><td>0.77</td><td>0.77</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>mu</sub></td><td>0.65</td><td>0.65</td><td>0.65</td><td>mmol Cmmol<sup>-1</sup></td></tr></tbody></table>

## Data and parameter estimates for MG1655 and NCM3722 strains

In order to test the robustness of our results with respect to the calibration procedure, we calibrated the model for a different *E. coli* strain, MG1655, in the same way as for the reference strain. To this aim, we used published measurements on batch growth of MG1655 in minimal medium with glucose, including metabolite concentrations (*McCloskey et al., 2018*), proteomics data (*Schmidt et al., 2016*), and metabolic fluxes (*Monk et al., 2017*).

The total biomass concentration is the same as for the reference strain (Equation 81). The total metabolite concentration is obtained by *McCloskey et al., 2018*, who reported a value of 3.7 Cmmol gDW⁻¹, equivalent to 9.1% of the total cellular biomass. The fraction of central metabolites is estimated to be 14% of the total metabolic concentration. The total protein concentration is obtained from *Basan et al., 2015b*, who report a protein fraction of 0.71 for the MG1655 strain, to which we add the fraction of free amino acids, estimated as 50% of the total metabolite concentration (*Bennett et al., 2009*). This gives a total protein biomass fraction of 0.76.

Proteins are then distributed over our protein categories, following the mass fraction values reported by *Schmidt et al., 2016*, for the MG1655 strain. Accordingly, we estimate

$$ \hat{m}_u = 0.37 \cdot 0.76 \cdot 1/\hat{\beta} = 11.4 \text{ Cmmol gDW}^{-1}, \qquad (150) $$

$$ \hat{r} = 0.45 \cdot 0.76 \cdot 1/\hat{\beta} = 13.8 \text{ Cmmol gDW}^{-1}, \qquad (151) $$

$$ \hat{m}_c = 0.08 \cdot 0.76 \cdot 1/\hat{\beta} = 2.4 \text{ Cmmol gDW}^{-1}, \qquad (152) $$

$$ \hat{m}_{er} + \hat{m}_{ef} = 0.10 \cdot 0.76 \cdot 1/\hat{\beta} = 3.1 \text{ Cmmol gDW}^{-1}. \qquad (153) $$

Uptake and secretion rates were taken from *Monk et al., 2017*. Comparison of metabolite concentration measurements of *McCloskey et al., 2018*, with $K_m$ values collected by *Dourado et al., 2021*, shows that reactions in central carbon metabolism are more saturated in MG1655 than in the reference strain (2.2 vs 1.2), in agreement with its higher growth rate (*Supplementary file 3*). Accordingly, the half-saturation constant of reactions consuming central metabolites are estimated as

$$ \hat{K}_r = \hat{K}_{mu} = \hat{K}_{mer} = \hat{K}_{mef} \approx \frac{\hat{c}}{2\hat{\beta}} = 0.24 \text{ Cmmol gDW}^{-1}. \qquad (154) $$

The data used for calibration are summarized in *Appendix 2—table 5* and the values for the parameters obtained after calibration are listed in *Appendix 2—table 6*.
**Appendix 2—table 5.** Reconstruction of growth and degradation rates, uptake and secretion fluxes, and protein and metabolite concentrations from published datasets for E. coli MG1655 and NCM3722 strains for the case of batch growth in glucose minimal medium.

The uncertainty intervals for the rates, fluxes, and metabolite concentrations are standard deviations reported in the source publications, after unit conversion. For the NCM3722 strain, as an example of a fast-growing strain with a higher growth yield than the BW25113 reference strain, we only use a subset of observed values in the main text. References: <sup>a</sup>Cheng et al., 2019, <sup>b</sup>Basan et al., 2015a, <sup>c</sup>Esquerré et al., 2014, <sup>d</sup>Farmer and Jones, 1976, <sup>e</sup>Monk et al., 2017, <sup>f</sup>Basan et al., 2015b, <sup>g</sup>Schmidt et al., 2016, <sup>h</sup>Park et al., 2016, <sup>i</sup>McCloskey et al., 2018.

<table><thead><tr><th>Rates</th><th>Unit</th><th>MG1655</th><th>NCM3722</th><th>Reference</th></tr></thead><tbody><tr><td>μ̂</td><td>hr<sup>-1</sup></td><td>0.69 ± 0.02</td><td>0.97 ± 0.05</td><td>a, b</td></tr><tr><td>γ̂</td><td>hr<sup>-1</sup></td><td>0.027</td><td>-</td><td>c, d</td></tr><tr><td colspan="5">Uptake, secretion, and biosynthesis fluxes</td></tr><tr><td>ν̂<sub>mc</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>51.5 ± 8.5</td><td>66.1 ± 4</td><td>a, b, e</td></tr><tr><td>ν̂<sub>mer</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>5.7</td><td>-</td><td>Derived</td></tr><tr><td>ν̂<sub>mef</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>7.8 ± 2.3</td><td>10.3 ± 1.8</td><td>a, b, e</td></tr><tr><td>ν̂<sub>mu</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>7.0</td><td>-</td><td>Derived</td></tr><tr><td>ν̂<sub>r</sub></td><td>Cmmol gDW<sup>-1</sup> hr<sup>-1</sup></td><td>21.7</td><td>-</td><td>Derived</td></tr><tr><td colspan="5">Total biomass concentration</td></tr><tr><td>1/β̂</td><td>Cmmol gDW<sup>-1</sup></td><td>40.65 ± 2.0</td><td>-</td><td>e</td></tr><tr><td colspan="5">Protein concentrations</td></tr><tr><td>p̂</td><td>Cmmol gDW<sup>-1</sup></td><td>30.7 ± 2.0</td><td>29.7 ± 1.9</td><td>e, f</td></tr><tr><td>m̂<sub>u</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>11.4 ± 0.74</td><td>-</td><td>e, f, g</td></tr><tr><td>r̂</td><td>Cmmol gDW<sup>-1</sup></td><td>13.8 ± 0.9</td><td>-</td><td>e, f, g</td></tr><tr><td>m̂<sub>c</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>2.4 ± 0.2</td><td>-</td><td>e, f, g</td></tr><tr><td>m̂<sub>er</sub> + m̂<sub>ef</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>3.1 ± 0.2</td><td>-</td><td>e, f, g</td></tr><tr><td>m̂<sub>er</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>2.2 ± 0.1</td><td>-</td><td>Derived</td></tr><tr><td>m̂<sub>ef</sub></td><td>Cmmol gDW<sup>-1</sup></td><td>0.9 ± 0.04</td><td>-</td><td>Derived</td></tr><tr><td colspan="5">Metabolite concentrations</td></tr><tr><td>ĉ</td><td>Cmmol gDW<sup>-1</sup></td><td>0.5 ± 0.09</td><td>0.8 ± 0.03</td><td>h, i</td></tr><tr><td>â*</td><td>mmol gDW<sup>-1</sup></td><td>0.046</td><td>-</td><td>h, i</td></tr><tr><td>â</td><td>mmol gDW<sup>-1</sup></td><td>0.008</td><td>-</td><td>h, i</td></tr><tr><td>â<sub>0</sub></td><td>mmol gDW<sup>-1</sup></td><td>0.054</td><td>-</td><td>h, i</td></tr><tr><td colspan="5">Concentration of other biomass</td></tr><tr><td>û</td><td>Cmmol gDW<sup>-1</sup></td><td>9.4</td><td>-</td><td>Derived</td></tr></tbody></table>
**Appendix 2—table 6.** Estimation of the values of the kinetic parameters in the model for the *E. coli* MG1655 strain during batch growth in glucose minimal medium from data in Appendix 2—table 5, as explained in the text.

Idem for a model variant with an additional category of growth-rate-independent proteins (*Q*), using data for the BW25113 strain from **Appendix 2—table 1**.

<table><thead><tr><th>Parameter</th><th>MG1655</th><th>Model variant with Q</th><th>Unit</th></tr></thead><tbody><tr><td>ρ̂<sub>ru</sub></td><td>1.17</td><td>1.17</td><td>–</td></tr><tr><td>ρ̂<sub>mef</sub></td><td>1.5</td><td>1.5</td><td>–</td></tr><tr><td>k̂<sub>r</sub></td><td>2.5</td><td>6.1</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>mu</sub></td><td>0.9</td><td>2.5</td><td>hr<sup>-1</sup></td></tr><tr><td>ê<sub>s</sub></td><td>21.0</td><td>38.0</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>mer</sub></td><td>4.1</td><td>10.3</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>mef</sub></td><td>20.4</td><td>36.1</td><td>hr<sup>-1</sup></td></tr><tr><td>k̂<sub>a</sub></td><td>412</td><td>2278</td><td>hr<sup>-1</sup></td></tr><tr><td>K̂<sub>r</sub></td><td>0.24</td><td>0.29</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>mu</sub></td><td>0.24</td><td>0.29</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>mer</sub></td><td>0.24</td><td>0.29</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>mef</sub></td><td>0.24</td><td>0.29</td><td>Cmmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>ar</sub></td><td>0.005</td><td>0.0009</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amer</sub></td><td>0.0008</td><td>0.0011</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amef</sub></td><td>0.0008</td><td>0.0011</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>K̂<sub>amu</sub></td><td>0.005</td><td>0.0009</td><td>mmol gDW<sup>-1</sup></td></tr><tr><td>n̂<sub>mer</sub></td><td>4.3</td><td>4.3</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>mef</sub></td><td>2.0</td><td>2.0</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>r</sub></td><td>0.77</td><td>0.77</td><td>mmol Cmmol<sup>-1</sup></td></tr><tr><td>n̂<sub>mu</sub></td><td>0.65</td><td>0.65</td><td>mmol Cmmol<sup>-1</sup></td></tr></tbody></table>

We also collect in **Appendix 2—table 5** the data for batch growth of the NCM3722 strain in minimal medium with glucose, used in the Results section of the main paper. The data concern the growth rate and growth yield (Cheng et al., 2019), the glucose uptake, and acetate secretion rates reported by Cheng et al., 2019, from experiments carried out by Basan et al., 2015a, the total protein concentration (Basan et al., 2015a), and the total metabolite concentration (Park et al., 2016).

## Calibration of model variant with an additional growth-rate-independent protein category

In Appendix 1, we introduced a model variant with an additional growth-rate-independent protein category, referred to as *Q* (Scott et al., 2010). Estimation of the parameters for this model variant requires the estimation, for every protein category, of the offset of the linear relation between growth rate and proteome fraction (Hui et al., 2015). In order to obtain results comparable to those for the reference model, we have used proteomics data for the BW25113 strain (Schmidt et al., 2016). We considered 22 different growth conditions, excluding stationary phase (no balanced growth) and LB medium (addition of amino acids).
For the R category, the proteome fraction increases with the growth rate and the offset can be computed as $\chi_r^0 = 0.23$ (Appendix 2—figure 2). Unfortunately, in the case of $M_c$, $M_e$, and $M_u$, the data show a decreasing or constant pattern with growth rate, which makes it impossible to determine the offset fraction for these protein categories (Appendix 2—figure 2, panels B–D). We therefore followed a different approach to estimate the growth-rate-independent protein fraction. Assuming a total fraction of growth-rate-independent proteins $\chi_q = 0.52$, as reported for the MG1655 strain by Mori et al., 2016, we split the fraction $\chi_q - \chi_r^0 = 0.29$ over the $M_c$, $M_u$, and $M_e$ categories proportionally to their size:

$$ \begin{aligned} \chi_u^0 &= 0.29 \cdot \frac{0.37}{0.56} = 0.19, \\ \chi_c^0 &= 0.29 \cdot \frac{0.09}{0.56} = 0.05, \\ \chi_e^0 &= 0.29 \cdot \frac{0.10}{0.56} = 0.05. \end{aligned} $$

<figure><img src="image_14.png" /><figcaption>Appendix 2—figure 2. Growth-rate dependency of proteome fractions. Using the data from Schmidt et al., 2016, the proteome fractions over a large variety of growth conditions (growth on different limiting carbon sources, different temperatures, different pH, etc.) are plotted for the categories: (A) ribosomes and translation-affiliated proteins (r/p), (B) enzymes in central carbon metabolism (m_c/p), (C) enzymes in energy metabolism ((m_e + m_c)/p), and (D) other proteins (m_u/p). A linear regression is performed, giving rise to slopes (A) 0.31 ± 0.04, (B) -0.03 ± 0.02, (C) -0.34 ± 0.04, and (D) 0.06 ± 0.03, showing that only the fraction r/p significantly increases with the growth rate.</figcaption></figure>

Notice that the above partitioning is equivalent to assuming that all enzyme categories have the same proportion of growth-rate-independent proteins.

The growth-rate-dependent fractions of the protein categories are then simply obtained from the difference between the total proteome fractions (Schmidt et al., 2016) and the growth-rate-independent fractions:
$$ \chi_u = 0.37 - 0.19 = 0.18, $$

$$ \chi_r = 0.44 - 0.23 = 0.21, $$

$$ \chi_c = 0.09 - 0.05 = 0.04, $$

$$ \chi_e = 0.10 - 0.05 = 0.05. $$

Further calibration of the model is then identical to the calibration of the reference model, using published data for batch growth of BW25113 in glucose minimal medium (Appendix 2—table 1). In particular, from the total biomass concentration (40.65 Cmmol gDW⁻¹) and the protein mass fraction (0.74), we can estimate the following growth-rate-dependent protein concentrations:

$$ \hat{q} = 0.52 \cdot 0.74 \cdot 1/\hat{\beta} = 15.9 \text{ Cmmol gDW}^{-1}, \qquad (155) $$

$$ \hat{r} = 0.21 \cdot 0.74 \cdot 1/\hat{\beta} = 6.3 \text{ Cmmol gDW}^{-1}, \qquad (156) $$

$$ \hat{m}_u = 0.18 \cdot 0.74 \cdot 1/\hat{\beta} = 5.4 \text{ Cmmol gDW}^{-1}, \qquad (157) $$

$$ \hat{m}_c = 0.04 \cdot 0.74 \cdot 1/\hat{\beta} = 1.2 \text{ Cmmol gDW}^{-1}, \qquad (158) $$

$$ \hat{m}_{er} + \hat{m}_{ef} = 0.05 \cdot 0.74 \cdot 1/\hat{\beta} = 1.5 \text{ Cmmol gDW}^{-1}. \qquad (159) $$

Parameter values derived for this model are summarized in Appendix 2—table 6.