Growth strategy of microbes on mixed carbon sources

A classic problem in microbiology is that bacteria display two types of growth behavior when cultured on a mixture of two carbon sources: the two sources are sequentially consumed one after another (diauxie) or they are simultaneously consumed (co-utilization). The search for the molecular mechanism of diauxie led to the discovery of the lac operon. However, questions remain as why microbes would bother to have different strategies of taking up nutrients. Here we show that diauxie versus co-utilization can be understood from the topological features of the metabolic network. A model of optimal allocation of protein resources quantitatively explains why and how the cell makes the choice. In case of co-utilization, the model predicts the percentage of each carbon source in supplying the amino acid pools, which is quantitatively verified by experiments. Our work solves a long-standing puzzle and provides a quantitative framework for the carbon source utilization of microbes.


Supplementary Note 1.3 Biomass components and precursor pools
For microbes, biomass consists of multiple components such as proteins, RNA, DNA, lipids, and glycogen, etc. (Fig. 1). Based on the topology of metabolic network, we classify the precursors of biomass components into seven pools. Specifically, each pool is named depending on its entrance  [5][6][7] . Note that there are some overlapping components between Pools a1, a2, a3 and a4 owing to joint synthesis of precursors. For convenience, we lump sum Pools a1-a4 as Pool a and use the term precursor pools to denote both amino acid pools and the precursor pools for other components.

Supplementary Note 1.4 Group A and Group B carbon sources
Denote carbon sources entering the upper part of the glycolysis Group A and those joining at other parts of the metabolic network Group B (Fig. 1). Specifically, all Group A carbon sources join through G6P/F6P. Glycerol enters from the upper part of glycolysis but not G6P/F6P, thus we classify glycerol as a quasi-Group A carbon source. Group A carbon sources can be co-utilized 3 with Group B sources, whereas substrates paired from Group A usually display diauxie. In most cases, glycerol follow all the traits of Group A sources, yet from the network topology, glycerol can be co-utilized with another Group A source of low concentration such as glucose and lactose (as recently observed in experiment 8 ) under optimal conditions.

Supplementary Note 1.5 Intermediate nodes
In a real metabolic network (Fig. 1), there are multiple intermediate nodes in delivering carbon flux from carbon sources to precursor pools. We consider a simple case containing one carbon  the optimal point. In either case, cells will only use the preferable carbon source, which corresponds to the case of diauxie.

Supplementary Note 2.2 Branch efficiency
In real cases, multiple intermediate nodes deliver carbon flux before branches converge to a common node. To take into account the cost of the intermediate enzymes, consider a model depicted in Fig. 2b [ 2] A , but their ratio, to make the decision. Ratio sensing was recently observed in the budding yeast Saccharomyces cerevisiae cultured in glucose-galactose mixed medium 11  Meanwhile, the mechanism of ratio sensing demands resources. It could well be that the microbe cares only about the most frequently encountered (or the most important) combinations of nutrients and would not invest resources to ratio sense the others.

Supplementary Note 3. The reason for co-utilization
The topologies of the metabolic network with one carbon source from Group A and the other from Group B are shown in Supplementary Fig. 3a The nutrient supplier of Pool 1 is then determined by At the intersection node N: then A supplies Pool 1 and B provides Pool 2, both substrates are co-utilized. In this case, the enzyme utilization efficiency  of the mixed medium A+B is (see Supplementary Equation 1) while the enzyme utilization efficiency  of a single substrate medium like A1 is  Table 3). Take the case of glucose-pyruvate co-utilization for example (Supplementary Table 3 and Supplementary Fig. 4a

Supplementary Note 4.3 Energy production
In microbial growth, a considerable amount of carbon sources needs to be allocated for energy production. Adenosine triphosphate (ATP), the molecular unit of energy currency, facilitates intracellular energy transfer. Taking the growth of E. coli in glucose as an example, it is estimated that 1-2×10 9 glucose molecules (7×10 9 carbon atoms/cell, BNID 103010) are required to build the biomass of a new cell 12 [12][13][14] . For anaerobic respiration, 3-6×10 9 glucose molecules 12 are estimated to be required for energy production of a new cell. For aerobic microbial growth in mixed carbon sources with saturated carbon source concentrations, the ratio of energy/biomass allocation is estimated to be 20%-50% [12][13][14] , and we denote this ratio as EM r .

Supplementary Note 4.4 Pool suppliers influenced by the TCA cycle
In TCA cycle, oxaloacetate goes back to itself if reactions flow through the whole cycle (with production of CO 2 and ATPs). To quantify the influence of TCA cycle on  , we consider microbes of exponential growth at certain growth rate, with the TCA cycle depicted in Supplementary Fig. 4c. Since biomass production and energy production are continuous, we assume the total stoichiometry of carbon which means that the value of  should be the same after 1 round of TCA cycle.
Combined with the experiment data we obtained, we roughly estimate  to be 0.55 for all the aerobic growth with saturated carbon source concentrations.

Supplementary Note 4.5 Pool suppliers in practice for optimal growth
To summarize, for optimal growth of E.coli,  Supplementary Table 4.

Supplementary Note 4.6 Note on pathways we have considered
Besides the metabolite pathways listed in Fig. 1 (with enzyme parameters shown in Supplementary Table 1) Oxaloacetate can spontaneously decompose to pyruvate and CO 2 when added into solution 16 . We confirmed this result with our experiment (shown above) and found that the quick decarboxylation of oxaloacetate would result in high concentration of pyruvate. This essentially changes the types of carbon sources in the culturing medium. As a result, we do not predict combinations including oxaloacetate.

Supplementary Note 4.8 Enzymes of gluconeogenesis
For optimal growth, there should be no gluconeogenesis enzymes when there is carbon flux of glycolysis. In reality, microbes need to dealing with the frequently varying environments.
Empirically, it was found in E.coli that microbes reserve a portion of gluconeogenesis enzymes when using Group A carbon sources, with the enzymes expression level anti-correlated with the carbon fluxes down through the glycolysis 17 . This may enable microbes to balance growth and prepare for potential changing environments 17 .  Table 1). For some transporters with no direct experimental data, we estimated the order of magnitude for their parameters 12 (labeled as "Estimated" in Supplementary Table 1).

Supplementary Note 4.9 Predictions compared with experiments
Admittedly the reported turnover numbers (or k cat values) of enzymes are likely to be associated with errors (e.g. measurement errors and in vitro versus in vivo errors), and the estimated parameters for transporters probably involve even large errors. However, it is still rather nontrivial to observe the consistency between model predictions (Supplementary Table 4 Table 6) and of the in-practice pool suppliers (Supplementary Table 7 Table   4 or blue text lines in Supplementary Table 7

Supplementary Note 5. Reversible reactions
Reversible reactions are common in metabolic network (Fig. 1). To analyze the influence of this factor, we consider the scheme that where i E is the enzyme catalyzing the reversible reaction between substrate i S and 1 i S  . We can approximate the details of the reaction as follows: where    is maximized and ii k    , which means that at optimal conditions analysis applies to irreversible cases is valid for reversible reactions.
One prediction of the reversible reaction analysis is that metabolites at the upper part of glycolysis (e.g. G6P, fructose 1,6-bisphosphatase (FBP)) owns a much higher concentration when bacteria cultured in Group A carbon sources (e.g. glucose) compared to that bacteria cultured in carbon sources entering from lower parts of glycolysis or TCA cycle. Recent studies 17 found that G6P and FBP have a much higher concentration when bacteria cultured with glucose than that shifting into acetate (entering from the bottom of glycolysis), which agree well with our reversible reaction analysis.

Supplementary Note 5.1 Influence of the reversible reactions
Note that optimal conditions operate at a non-equilibrium steady state that metabolic flux coming from external carbon sources working at maximum rate. Were the carbon flux drops for a while (e.g. bacteria take a short rest when consuming sugars), the reversible reaction between Here, competitive inhibition is common in metabolic network (e.g. ATP regulates phosphofructokinase-1 in glycolysis) while the two other types have not been observed for enzymes with a single substrates 5 . For competitive inhibition, the Michaelis-Menten kinetics is In these two cases (reversible inhibition type b &c), however, i  is clearly dependent on the concentration of I . We discuss more general regulations below including these two cases.

Supplementary Note 6.4 Enzyme regulations by metabolites that permits any function form
Here we assume that reaction rates  Supplementary Fig. 1b, either A1 or A2 will be utilized depending on the growth rate of individual mediums, yet unable to predict the turning point (or ratio sensing behavior); in the case of Supplementary Fig. 1d, three strategies (using only A; using only B; or using A and B) are permitted, yet unable to predict if A and B would be co-utilized, neither does 23 the carbon supply percentage in cases of co-utilization.

Supplementary Note 6.5 Exceptional cases
On qualitative aspect, there are two exceptional cases of the branch efficiency analysis . According to Supplementary Equation 1,

Supplementary Figures
Supplementary Figure 1. Coarse-grained models of metabolism and biomass production.