Overall biomass yield on multiple nutrient sources

Overall biomass yield on multiple nutrient sources | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Overall biomass yield on multiple nutrient sources Uwe Sauer, Ohad Golan, Olivia Gampp, Lina Eckert This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4219475/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Feb, 2025 Read the published version in npj Systems Biology and Applications → Version 1 posted 10 You are reading this latest preprint version Abstract Microorganisms utilize nutrients primarily to generate biomass and replicate. When a single nutrient source is available, the produced biomass increases linearly with the initial amount of the available nutrient. This linear trend can be predicted to high accuracy by “black box models” that consider growth as a single chemical reaction with nutrients as substrates and biomass as a product. Since natural environments typically feature multiple nutrients, we extended the black box framework to include catabolism, anabolism, and biosynthesis of biomass precursors to quantify co-utilization of multiple nutrients on microbial biomass production. The model differentiates between different types of nutrients: degradable nutrients that first must be catabolized before they can be used from non-degradable nutrients that can only be used as a biomass precursor. Experimentally, we demonstrated that contradictory to the model predictions, there is a mutual effect between different nutrients on Escherichia coli’s nutrient utilization, where the ability to utilize one is affected by the other; i.e., for some combinations the produced biomass was no longer linear to the initial amount of nutrients. To capture such mutual effects with a black box model, we phenomenologically added an interaction between the metabolic processes used in utilizing the nutrient sources. The phenomenological model qualitatively captures the experimental observations and, unexpectedly, predicts that the produced biomass does not only depend on the combination of nutrient sources but also on their relative initial amounts – a prediction we validated experimentally. Moreover, the model predicts which metabolic processes – catabolism, anabolism, or precursor biosynthesis – is affected in each nutrient combination. Biological sciences/Systems biology/Biochemical networks Biological sciences/Systems biology/Bioenergetics Biological sciences/Systems biology/Dynamical systems Biological sciences/Systems biology/Systems analysis Biological sciences/Biophysics/Bioenergetics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Author summary Understanding microbial nutrient utilization efficiency is critical for maximizing productivity and minimizing environmental impact in agricultural and biotechnology settings, as well as for improving our understanding of ecological systems and how they are impacted by changes in nutrient availability. Previous models suggest that the availability of one nutrient should not affect the utilization efficiency of another. However, our study found that the availability of a second nutrient not only effects the utilization efficiency of the first but can also lead to a decrease in gain from the first nutrient. Following these results, we used mathematical modeling and simulations to determine how different nutrient combinations affect various growth processes, ultimately leading to changes in overall biomass yield. These findings highlight the complex interplay between multiple nutrient sources and challenge previous models. Our study suggests that careful consideration of nutrient interactions is essential for achieving optimal yields and may help guide the development of more effective nutrient management strategies in agricultural and biotechnology settings, as well as understanding of ecological systems. Introduction Natural environments are characterized by a broad spectrum of physicochemical parameters that collectively define constraints within which species survive and thrive. Of particular importance to niche occupancy by different microbes are the type of nutrients and their temporal availability. For example, bacteria growing in a riverbed might experience continuous nutrient flux and high spatial homogeneity while bacteria growing in pulsating environments, such as tidal wetlands or at the sea bottom, receive nutrients only sporadically [ 1 , 2 ]. Different physiological traits provide fitness advantages for different nutrient dynamics. Continuous nutrient flux environments favor organisms with higher growth rate so that they can exploit the otherwise washed out nutrients, while environments of sporadic nutrient flux and high spatial heterogeneity favor organisms that utilize resources more efficiently [ 3 – 6 ]. In conditions of continuous nutrient flux, the biomass produced per consumed nutrient is physiologically defined as the biomass yield parameter that describes the efficiency of nutrient utilization [ 7 – 9 ]. Theoretical models, known as ‘black box models’, predict the biomass yield for growth on a single nutrient source in conditions of continuous flux such as those observed in chemostat experiments to high accuracy [ 10 – 12 ]. These models consider growth as a single chemical reaction with the nutrients as substrates and the produced biomass and secreted byproducts as products. By calculating the change in free energy of the whole reaction, the biomass yield is predicted. Here, we adopt these models to qualitatively predict and then test the overall biomass yield in batch cultures of Escherichia coli , where the outgoing flux of nutrients is limited so that all available nutrients are utilized, including reutilization of secreted byproducts, a condition akin to a single nutrient pulse in natural pulsating environments. Since natural environments typically contain multiple nutrients [ 13 – 15 ], we investigate whether the overall biomass yield of a nutrient depends on the availability and metabolic properties of a second nutrient, for example if it can be degraded or only used as a building block for biomass. Generally, black box models describe scenarios without mutual effects between nutrients; hence, the overall biomass yield of each nutrient is independent of the availability of another. We tested this prediction experimentally by titrating a second nutrient to batch cultures grown on a single carbon source, demonstrating that the overall biomass yield depends not only on the availability but also on the initial amount of other nutrients, and that this mutual effect can be negative. To explain these observations, we expanded the black box model to consider whether a second nutrient can only be used for biomass synthesis or also degraded for energy generation and included mutual effects between the metabolic processes of the nutrient sources. The model qualitatively captures the experimental observations and explains how the combination of nutrients affects metabolism. Furthermore, using the model, we determine the mutual effect of different nutrient combinations on growth processes. Results Growth on a single nutrient source The classical system to investigate the efficiency of nutrient utilization in pulsating environments where organisms have sufficient time to fully utilize all available nutrients in a single nutrient pulse are batch cultures. Here we follow growth of E. coli until depletion of the initial nutrient source and potential secreted byproducts when stationary phase is reached in M9 minimal medium with glucose, malate, or aspartate as sole carbon sources [ 16 , 17 ]. These carbon sources were chosen as respiro-fermentative, strictly respiratory, and a degradable biomass component. The produced biomass ( \({\Delta }B\) ), that is the biomass reached at stationary phase minus the biomass at inoculation, was recorded as the optical density at 600nm, converted to cellular dry weight using a predetermined conversion factor [ 18 ], and plotted against the initial nutrient amount (Fig. 1 ; S1 Fig). The produced biomass shows a good linear fit to the initial amount of the sole carbon source (Fig. 1 B) and as such, can be described by [ 16 ]: $${\Delta }B={Y}_{X/D}{N}_{D}$$ (1) where \({N}_{D}\) is the initial amount of nutrient \(D\) and \({Y}_{X/D}\) the overall biomass yield for organism \(X\) on nutrient \(D\) which describes the efficiency of full utilization of the available nutrient. To predict the produced biomass, we used a black box formalism [ 10 ] that separates the growth reaction of chemotrophic organisms to a two-reaction process (Fig. 2 A). The first is a catabolic reaction that releases Gibbs free energy by breakdown of nutrients. The second is the anabolic reaction that uses the released free energy for the synthesis of new biomass. The overall Gibbs energy dissipation \({\Delta }{G}_{X}\) of the growth process is given by ([ 10 ], S1A text): $${\Delta }{G}_{X}=\frac{1}{{Y}_{X/D}}{\Delta }{G}_{cat}+{\Delta }{G}_{an}$$ (2) where the subscripts cat , and an refer to the Gibbs energy of dissipation of the catabolic and anabolic reactions, respectively. Given that all secreted byproducts are utilized in the here investigated growth conditions, the free energy of the secreted byproducts can be set to 0, the overall biomass yield may be predicted as [ 10 ]: $${Y}_{X/D}=\frac{{\Delta }{G}_{cat}}{{\Delta }{G}_{X}-{\Delta }{G}_{an}}$$ (3) Combining equations (1) and (3) predicts a linear correlation of the produced biomass as function of initial nutrient amount with a slope that depends only on the type of nutrient through \({\Delta }{G}_{cat}\) . This prediction fits well with all measured nutrients and is consistent with previous results [ 16 , 17 ] (Fig. 1 B, S1 Fig). Growth on multiple nutrient sources Since organisms typically encounter multiple nutrients in natural environments, we next asked whether the availability of one nutrient affects the overall biomass yield of another. To enable a black box model to capture such effects, we added another reaction that depends on the type of second nutrient: A) degradable nutrients that first must be catabolized before they can be used, such as a sugar; B) non-degradable nutrients that can be used only as a biomass precursor, such as the non-degradable amino acid methionine in E. coli ; and C) nutrients that can be both catabolized or used directly as a biomass precursor, such as the amino acid aspartate in E. coli . For the combination of two degradable nutrients the added reaction is catabolic (S1B text, Fig. 2 B). In this case, the overall Gibbs energy dissipation gives: $${\Delta }{G}_{X}=\frac{1}{{Y}_{X/{N}_{1}}}{\Delta }{G}_{cat}^{{N}_{1}}+\frac{1}{{Y}_{X/{N}_{2}}}{\Delta }{G}_{cat}^{{N}_{2}} +{\Delta }{G}_{an}$$ (4) where \({\Delta }{G}_{cat}^{{N}_{i}}\) is the Gibbs energy of dissipation for the catabolic process of nutrient \(i\) . When the second nutrient source is a non-degradable biomass precursor, we split the anabolic reaction into two – a reaction for biosynthesis of the biomass precursor and a reaction for the general anabolic process (S1C text, Fig. 2 C). The overall Gibbs energy of dissipation in this case gives: $${\Delta }{G}_{X}=\frac{1}{{Y}_{X/{N}_{1}}}{\Delta }{G}_{cat}+{\Delta }{G}_{an}^{bsyn}+{\Delta }{G}_{bsyn}(1-{M}_{utl})$$ (5) where \({\Delta }{G}_{bsyn}\) is the Gibbs energy of dissipation for synthesis of the biomass precursor and \({\Delta }{G}_{an}^{bsyn}\) is the dissipation energy for the general anabolic process minus that of the biomass precursor. The function \({M}_{utl}\) describes the ratio of available biomass precursor to that required to generate the produced biomass during the growth process. It is dependent on biomass precursor availability such that when all the necessary biomass precursor is available in the environment, the function assumes the maximal value of 1 and the cost for this precursor biosynthesis is alleviated. Combining equations (4) or (5) with Eq. (1) shows that regardless of the type of nutrient supplemented, the produced biomass is predicted to be a linear sum of the biomass gained from the available nutrients and the overall biomass yield of each nutrient is independent of the availability of others (S1B-C text, Fig. 2 D): $${\Delta }B={Y}_{X/N1 }{N}_{1}+{Y}_{X/N2}{N}_{2}$$ (6) where \({N}_{i}\) is the amount of nutrient \(i\) in the growth medium and \({Y}_{X/Ni }\) is the overall biomass yield of nutrient \(i\) . To test the prediction that the overall biomass yield of a nutrient is independent of the availability of others, we compared the overall biomass yield of E. coli for different nutrients, henceforth referred to as the measured nutrient, in the presence or absence of a second nutrient, termed the base nutrient. To do so, the initial amount of the measured nutrient was varied for each batch culture experiment at constant initial amounts of the base nutrient between 0 and 1.2 g/l for glucose, acetate, or aspartate and 0 and 0.06 g/l for methionine. The produced biomass was plotted against the initial amount of the measured nutrient and the overall biomass yield was determined as the slope of a linear fit of that curve (Fig. 3 A,B). In combination with glucose, succinate, or acetate as base nutrients, we determined the overall biomass yield of xylose and methionine as measured nutrients, as examples of degradable or non-degradable nutrients, respectively (Fig. 3 ). The initial amount of base nutrient determines the intercept with the Y-axis and was chosen such that the measured parameters remain within measurable range. The overall biomass yield was highly dependent on the base nutrient. For xylose, the overall biomass yield was higher on succinate as base nutrient than on glucose or when used alone, and for methionine the overall yield was by far the highest on glucose (Fig. 3 C,D). For most combinations, the influence of the second nutrient was monotonous across the tested concentrations, i.e., the overall biomass yield of the measured nutrient can be determined from the slope of a linear fit (Fig. 3 A,B). An exception was the non-monotonous behavior of methionine as the measured nutrient in combination with glucose as a base nutrient (Fig. 3 B). At low initial amounts of methionine (below 3 \({\mu }\text{g}\) ), increasing initial amounts of methionine unexpectedly decreased the produced biomass. In the higher range of initial amounts (above 3 \({\mu }\text{g}\) ), increasing methionine initial amounts increased the produced biomass linearly. Thus, the overall biomass yield of a measured nutrient is dependent on the base nutrient, consequently black box theory cannot capture the produced biomass of multiple nutrient sources. To enable the model to describe such mutual effects, we expand it to include such effects phenomenologically. To do so, we coupled a function that is dependent on the combination of available nutrients to the Gibbs energy dissipation of each reaction in the growth processes. For simplicity, we assumed these functions are linear to the initial nutrient amount. As such, the overall Gibbs energy dissipation of growth on two degradable nutrient sources is described as (S1D text): $${\Delta }{G}_{X}=\frac{1}{{Y}_{X/{N}_{1}}}{\Delta }{G}_{cat}^{{N}_{1}}{f}_{cat1}\left({N}_{2}\right)+\frac{1}{{Y}_{X/{N}_{2}}}{\Delta }{G}_{cat}^{{N}_{2}}{f}_{cat2}\left({N}_{1}\right)+{\Delta }{G}_{an}{f}_{an}\left({N}_{1},{N}_{2}\right)$$ (7) where \({f}_{cat}\left({N}_{i}\right)\) , \({f}_{an}\left({N}_{i}\right)\) are linear functions to the initial amounts of nutrient source \(i\) , with coefficients \({\text{m}}_{\text{c}\text{a}\text{t}}^{{\text{N}}_{\text{j}}} , {\text{m}}_{\text{a}\text{n}}^{{\text{N}}_{\text{j}}}\) respectively. These functions phenomenologically depict the mutual effect of the nutrient combination on the growth processes. Combining equations (1) and (7) predicts the produced biomass: $${\Delta }B=\frac{{\Delta }{G}_{cat}^{{N}_{1}}{N}_{1}+{\Delta }{G}_{cat}^{{N}_{2}}{N}_{2}+{\Delta }{\text{m}}_{\text{C}\text{A}\text{T}}^{{\text{N}}_{1}{N}_{2}}{N}_{1}{N}_{2}}{{\Delta }{G}_{X}-{\Delta }{G}_{an}{f}_{an}\left({N}_{1}, {N}_{2}\right)}$$ (8) where \({\Delta }{\text{m}}_{\text{C}\text{A}\text{T}}^{{\text{N}}_{1}{N}_{2}}={\Delta }{G}_{cat}^{{N}_{1}}{m}_{cat}^{{N}_{1}}+{\Delta }{G}_{cat}^{{N}_{2}}{m}_{cat}^{{N}_{2}}\) and \({f}_{an}\left({N}_{1}, {N}_{2}\right)=1+{m}_{an}^{{N}_{1}}{N}_{1}+{m}_{an}^{{N}_{2}}{N}_{2}\) . Given a mutual effect between nutrients, the produced biomass is thus made of three terms, two describing the direct effect of catabolism of the two nutrient sources and a third term describing the mutual catabolic effect depending on availability of both substrates. Although the last term of the model is based on the phenomenological observation, the range of model solutions is limited. Exploring this solution space shows that, depending on the type of mutualism, qualitatively different relationships are predicted between available nutrients and biomass formation (Fig. 4 A) – a positive mutual catabolic effect increases the overall biomass yield (Fig. 4 A, orange curve) while a negative catabolic effect decreases it (Fig. 4 A, purple curve). The expanded model can capture the experimentally observed mutual effect of increased overall biomass yield with a positive mutual catabolic effect (compare increased slope for different base nutrients in Fig. 3 A to the orange curve in Fig. 4 A). For growth on a combination of a degradable nutrient and a non-degradable biomass precursor, the overall Gibbs energy dissipation is described as (S1E text): $${\Delta }{G}_{X}=\frac{1}{{Y}_{X/D }}{\Delta }{G}_{cat}{f}_{cat}\left(M\right)+{\Delta }{G}_{an}{f}_{an}\left(N,M\right)+{\Delta }{G}_{bsyn}^{M} {f}_{bsyn}\left(N\right)(1-{M}_{utl})$$ (9) where \({f}_{cat}\left({M}_{utl}\right)\) , \({f}_{an}\left(N,{M}_{utl}\right)\) , \({f}_{bsyn}\left({M}_{utl}\right)\) are linear functions with coefficients \({m}_{cat}\) , \({m}_{an }^{N}\) , \({m}_{an }^{M}\) , \({m}_{sbyn}\) respectively. These functions depict the mutual effect between the nutrient sources on the Gibbs free energy of each growth reaction. Solving equations (1) and (9) for the produced biomass gives a quadratic equation: $${\Delta }{B}^{2}-\frac{{\Delta }B}{{\Delta }{G}_{A}} \left(N{\Delta }{G}_{cat}+{M}^{{\prime }}\left({m}_{an }^{M}{\Delta }{G}_{an}-\left(1+{m}_{sbyn}N\right){\Delta }{G}_{bsyn }^{M}\right) \right)-N\frac{{\Delta }{G}_{cat}}{{\Delta }{G}_{A}}{m}_{cat}{M}^{{\prime }}=0$$ (10) $$\text{w}\text{h}\text{e}\text{r}\text{e} {\Delta }{G}_{A}=\left({\Delta }{G}_{X}-{\Delta }{G}_{an}(1-N{m}_{an }^{N})-{\Delta }{G}_{bsyn}^{M}\left(1+{m}_{sbyn}N\right)\right) \text{a}\text{n}\text{d} {M}^{{\prime }}={M}_{utl}{\Delta }B.$$ Unlike the solution for growth on two degradable nutrient sources, solving Eq. (10) for the produced biomass shows that a mutual effect between a biomass precursor and a degradable nutrient can give rise to non-monotonous solutions. Figure 4 B explores the solution space of possible mutual effects between a precursor and a degradable nutrient. The case of a negative catabolic effect (Fig. 4 B, orange curve) fits qualitatively well with the experimental observation of the biomass precursor methionine on glucose as base nutrient (Fig. 3 B, green data points). The coefficients of the linear functions depicting the mutual effect between the nutrients are a key output of the model since they infer how each combination of nutrients effects the different growth reactions. Fitting these coefficients to the experimental results of methionine growing with glucose as a base nutrient gives a qualitative fit to a negative value for the catabolic parameter (coefficient \({m}_{cat})\) , revealing that methionine decreases the catabolic efficiency of glucose. Furthermore, the overall biomass yield of methionine on glucose in the linear region is higher than that on succinate or acetate (Fig. 3 D), suggesting a mutual effect on another metabolic process in one of these combinations, potentially the precursor biosynthesis processes (coefficient \({m}_{sbyn})\) . For all combinations of two degradable nutrients, the overall biomass yield increased as compared to growth on sole nutrient sources (Fig. 3 C), a result that fits a positive mutual effect on the catabolic process (coefficient \({m}_{cat})\) . An unexpected model prediction is noticeable in equations (9) and (10) where the initial amounts of the two available nutrients are coupled in at least one term. Hence, the model predicts that the overall biomass yield of a measured nutrient depends not only on the availability of a base nutrient, but also on the relative initial amounts of the nutrients. For a combination of two degradable nutrient sources with a positive catabolic effect, as observed experimentally for xylose on the two base nutrients (Fig. 3 A,C), the overall biomass yield is predicted to increase with increasing initial amounts of the base nutrient (Fig. 4 C). For the combination of a degradable nutrient and a biomass precursor, such as methionine on glucose, with a negative catabolic effect and positive effect on precursor biosynthesis, the model predicts a shift of the curves for the non-linear part as well as an increase in the slope of the linear part with increasing initial amounts of base nutrient (Fig. 4 D). To test these predictions, we determined the produced biomass on xylose and methionine as the measured nutrients on different initial amounts of succinate and glucose as the base nutrients, respectively (Fig. 5 A,B). The overall biomass yield of xylose (i.e., slope of the curve) increased linearly with the initial amount of the base nutrient succinate (Fig. 5 A, C). This observation fits well with the model prediction for a positive catabolic effect between two degradable nutrients (Fig. 4 C). The curve of the produced biomass on methionine exhibits a more complex dependency on the initial amount of glucose as the base nutrient. Above \(5 {\mu }\text{g}\) methionine, the slope of all curves increased linearly with the amount of the base nutrient glucose, but below \(5 {\mu }\text{g}\) methionine there was no linear dependency and the amount of base nutrient varied the curve shape (Fig. 5 B, D). This observation fits well with the theoretical prediction (Fig. 4 D) that this nutrient combination not only has a positive effect on the precursor biosynthesis reaction (i.e., the linear dependency at higher methionine supplementation), but also a negative catabolic effect where at low methionine concentrations, in some cases, more methionine leads to lower biomass gain. Which mechanism underlies the negative catabolic effect of methionine on glucose? The growth curves followed the classical diauxic shift with exponential growth on glucose and a second phase on previously secreted acetate (S2A Fig). For the example of 160 \({\mu }\text{g}\) glucose as the base nutrient (Fig. 5 , pink curve), the first phase lasted 4-4.5 hours and growth on acetate resumed between 7–10 hours (S2A Fig). In both phases, the biomass gain (calculated as the biomass at the end minus the biomass at the beginning) increased linearly with methionine amounts greater than 2 \({\mu }\text{g}\) (S2B, C Fig). The biomass gain was much higher than the trendline in the absence of or at very low methionine concentrations. During exponential growth on glucose in the first phase, methionine decreased the gain in biomass but increased the growth rate (S2D Fig.). Given the diauxic shift from growth on glucose to previously secreted acetate (S2E Fig), the most plausible explanation for the higher biomass gain without or low methionine in the second phase is due to higher acetate secretion in the first phase. To test whether methionine supplementation indeed reduced acetate secretion, we varied acetate secretion rates by altering steady state growth through an inducible promoter for the glucose uptake gene ptsG that limits glucose uptake [ 19 ]. Comparing acetate secretion in the presence and absence of methionine shows that methionine indeed decreases acetate secretion (S2F Fig). Thus, the negative catabolic effect of methionine on glucose catabolism appears to be a combination of a lower biomass gain during the first growth phase, with a higher growth rate and less acetate secretion, and a lower biomass gain in the second phase because less acetate was secreted. At the lowest amounts of methionine (0 and 1.43 \({\mu }\text{g}\) ) we noted a shorter lag time for growth on acetate (S2A Fig, compare red and black curves to the other curves). Growth with 1.43 \({\mu }\text{g}\) methionine was somewhat special as it followed the biomass trendline in the first growth phase but could not sustain the higher growth rate throughout this growth phase (S2A Fig, red curve between 2-4h), presumably because methionine was used up, which explains why its biomass gain in the second phase was indistinguishable from the no methionine condition (S2C Fig). Consistently, 1.43 \({\mu }\text{g}\) methionine was below the amount necessary to produce the biomass reached at the end of the first growth phase (about 1.7 \({\mu }\text{g}\) of methionine is required to generate 0.8 \(\text{g}\text{D}\text{C}\text{W}\) of biomass [ 20 ]). Growth with a second nutrient that can be degraded and used as a biomass precursor So far, we focused on degradable nutrients or nutrients that can only be used as biomass precursors. Some nutrients such as degradable amino acids, however, can be directly used both as biomass precursors or energy source. Given the complex curves observed for the combination of biomass precursor and degradable nutrient, we expected that a degradable amino acid in combination with a degradable nutrient would also produce non-monotonous curves. To investigate the effects of such nutrient combinations, we measured the produced biomass on the degradable amino acid aspartate on different initial amounts of glucose and acetate as base nutrients (Fig. 6 A,B). The combination of aspartate and acetate led to a complex curve with two linear phases separated by a double shift in slope at intermediate concentrations (between \(100-150 {\mu }\text{g}\) , Fig. 6 A). The first phase at low initial amounts of aspartate resulted in a linear slope that increases with initial amount of acetate while the slope of the second phase shows only a low dependency on acetate initial amounts (Fig. 6 C). Aspartate on glucose also shows a complex curve with two linear phases (Fig. 6 B). In this nutrient combination, the slope of the first phase is independent of the initial amount of glucose yet the length of this phase increases with increasing initial glucose amounts (Fig. 6 D). The slope of the second linear phase increases with increasing glucose initial amounts. The complex behavior observed in these experiments cannot be captured even with the mutual effect model presented here. We hypothesize that the ratio of how much aspartate is utilized as a biomass precursor to how much is catabolized affects the overall biomass yield. The multiple utilization possibilities add an additional degree of freedom to the system and as such, capturing the behavior of these nutrients in a model requires time-resolved intracellular flux information. Discussion In conditions of low nutrient flux, organisms utilize all nutrients in the environment and reabsorb previously secreted byproducts to fuel further growth. Here we asked whether the availability of one nutrient affects the utilization efficiency of another? We showed that different nutrient combinations have different mutual effects on an organism’s ability to generate biomass, presumably by changing intracellular metabolism, secretion, and reabsorption of secreted byproducts. While microbial utilization of multiple nutrients has been extensively studied, yielding significant findings like the diauxic shift [ 21 – 23 ] or the complex interplay of factors in multiple nutrient environments [ 24 – 27 ], these studies don’t differentiate between different nutrient types, focus on specific growth phases and as such are incapable of capturing the biomass gain from the entire growth curve. To address this challenge and gain a more comprehensive understanding, we expanded previous black box models to depict the full growth process for growth on multiple nutrients. We expanded the model to account for the effect of different nutrient types and incorporated a phenomenological representation of mutual effects between nutrient sources. The expanded black box model was able to qualitatively capture the experimental observation and further predicts that the overall biomass yield of a nutrient depends not only on the availability of other nutrients but also on the ratio of initial amounts of the different nutrients. Given the coarse granularity of a black box model, it does not identify the specific metabolic reactions. However, by fitting the model to experimental measurements, the model can determine which coarse-grained metabolic process – catabolism, anabolism or precursor biosynthesis – in each nutrient combination is the cause of the mutual effect. This leads to generate hypotheses on which specific pathways are affected. For instance, we observed that for E. coli growing on glucose, methionine supplementation decreases the catabolic efficiency of glucose utilization, and provide circumstantial evidence that this is caused by a combination of the effect of methionine on the growth rate and reduced acetate secretion. For all nutrient combinations, the initial amount of the base nutrient had a positive effect on the overall biomass yield of the measured nutrient, for at least some region of the measured range. This result is consistent with previous reports, for example, the supplementation of growth media with casamino acids or yeast extract has been shown to increase the carbon utilization efficiency of succinate or asparagine in batch culture experiments of Enterobacter aerogenes and Pseudomonas perfectomarinus [ 28 ]. Similarly, the utilization of mixtures of different dissolved organic carbon sources by bacterial communities in aquatic systems has been found to be more efficient than the utilization of a single source [ 29 – 33 ]. Moreover, the carbon utilization efficiency of Candida utilis , P. oxalaticus , Saccharomyces cerevisiae , Paracoccus denitrificans , and Thiobacilius versutus has been found to be higher than theoretically predicted when a nutrient source that can be utilized solely as an energy source was supplemented during balanced growth conditions [ 34 – 36 ]. It is tempting to conclude that the underlying reason for this deviation from the theoretical prediction is similar in all cases, regardless of the experimental setup and measured parameter, i.e., biomass yield as measured in a chemostat continuous culture [ 7 – 9 ] or the overall biomass yield as measured in batch cultures. Our analysis suggests that the different nutrients affect each other’s catabolism, although the specific metabolic pathways that are affected remain unresolved. One potential explanation could lie in the concept of maintenance energy, which can potentially vary depending on nutrient availability. A maintenance energy that decreases due to supplementation of a second nutrient would consequently increase the efficiency of nutrient utilization. To further investigate these mechanisms and identify a possible global mechanism, a more detailed resolution of metabolic pathways and their fluxes will be necessary, possibly by combining the thermodynamic black-box approach presented here with genome-scale metabolic models [ 37 , 38 ]. Inherent to the black box models is the conception that the biomass produced is ultimately constrained by the energy available in the system. These models hinge on a thermodynamic balance, where the energy gleaned from catabolic processes is weighed against the energy expended in anabolic processes. While these models address the energy balance, implications for the carbon balance can extrapolated from the results. Given the conservation of carbon in the system, our findings suggest that the combination of nutrients could have a substantial impact on CO 2 production as the primary carbon byproduct during growth. In cases where a base nutrient augments the yield of the measured nutrient, CO 2 production per nutrient utilized would decrease, while a base nutrient that diminishes the yield of the measured nutrient can result in an increase in CO 2 production per nutrient utilized. Understanding the influence of nutrient combinations on CO 2 production opens up broader ecological considerations, especially when changes in CO 2 production can significantly impact the environment [ 39 , 40 ]. Microbes metabolize a wide range of compounds, which affects the dynamics of organic matter and CO 2 emissions [ 41 – 43 ], potentially impacting agricultural productivity, ocean nutrient balance, and the global climate [ 43 ]. For example, heterotrophic microbes respire 60 gigatonnes of terrestrial organic matter annually, roughly six times the annual anthropogenic emissions. Given that microbes utilize multiple nutrients in most growth environments, understanding the interplay between different nutrients, as explored in this study, could pave the way for more informed research in ecological systems, and even aid in mitigating the environmental impact of agriculture and the biotechnology industry by decreasing CO 2 emissions. Nutrient utilization efficiency is important in other contexts, including evolution, microbiome-host interactions and synthetic biology. For example, different nutrient combinations have been shown to impact the gut microbiome [ 44 , 45 ], sometimes unintuitively where supplementation of another nutrient such as an amino acid reduces the overall biomass gain of gut bacteria [ 46 ]. Our observation showing the effects of amino acid supplementation on the overall biomass yield and specifically the reduced biomass gain due to supplementation of methionine could help elucidate the phenomenon. The analysis presented here was done for a single organism and experimentally tested on E. coli , but since the abstracted reactions occur in any metabolic system our approach can be extended to analyze growth of consortia or even larger ecological systems. It remains an open question whether there are general principles governing the here described mutual effects or whether each nutrient combination has its own unique mechanism in a given organism. Materials and methods Strains and growth essays: In the growth essays the NCM3722 strain [ 47 , 48 ] as used and in the acetate secretion essay NQ1243 [ 19 ]. Each experiment was carried out in three steps: seed culture, pre-culture and experimental culture. For seed culture, one colony from fresh LB agar plate was inoculated into test tube with M9 minimal medium with 4 gr/l glucose and cultured in 37ºC shaking at 350 rpm for 8–9 hours. The cell culture was then diluted to OD 600 = 0.1–0.2 in pre-warmed shake flask with m9 minimal medium with the same base nutrient as the experiment and left to grow for two hours in 37ºC shaking at 350 rpm (pre-culture). The cell culture was then diluted to OD 600 = 0.03–0.08 in pre-warmed 96 deep well plate with 1 ml. Each well contained medium with the experimental growth conditions (M9 minimal medium with nutrients according to experiment, each condition was set in triplicates) and mixed thoroughly. 200 µl cell culture from every well was then transferred to 96 deep well transparent essay plate and placed in Tecan microplate reader (Tecan infinite M200) for growth measurement. Microplate reader was programmed to maintain temperature at 37ºC, maximal shaking and measure OD 600 every 10 minutes. Data analysis: The OD measured by the microplate reader was linearized using a premeasured calibration curve. Growth curves obtained in the microplate reader were compared to growth curves obtained in shake flask and were equivalent. The optical density was then converted to dry weight according to known calibration \(0.396\frac{gDW}{L OD}\) [49]. The final biomass point was recorded at 3–5 hours after maximal OD was reached. All linear fits were done to the average of the triplicate measurements by method of least-mean-square[ 50 ] in the range that displayed a clear linear trend. Acetate secretion rate experiment: The experiment was done at 37ºC shaker shaking at 350 rpm in three steps: seed culture, pre-culture and experimental culture. For seed culture, one colony from fresh LB agar plate was inoculated into test tube with M9 minimal medium with 4 gr/l glucose and cultured in 37ºC shaking at 350 rpm for 8–9 hours. The culture was then diluted in pre-warmed 96 deep well plate to an OD 600 of 0.05–0.4 so that all cultures reached exponential phase at the same time. Each growth condition in the deep well plate was run in triplicates. All conditions contained m9 minimal medium, 4 gr/l glucose and different concentrations of the inducer for the glucose uptake promoter 3methyl-benzyl. Half of the growth conditions contained 0.1 gr/l methionine. Every 30 min, 40 µl culture from every well were collected and used to measure OD 600 using Tecan microplate reader (Tecan Infinite M200). Another 100 µl culture from every well was collected, centrifuged at 15,000 rpm, the supernatant was collected and immediately frozen. Supernatant were used to measure acetate concentrations using Acetate assay kit (Megazyme Acetic Acid Assay Kit). The slope of the plot of acetate concentrations versus OD 600 for all replicates (multiplied with the measured growth rate) was used to determine the acetate secretion rate. Declarations Acknowledgments OGo and US acknowledge support by Marie Skłodowska-Curie Actions ITN “SynCrop” (grant agreement no. 764591). Figures were generated using Biorender. We would like to extend our gratitude to Hidde de Jong for insightful discussions and valuable feedback. References Stocker R. Marine microbes see a sea of gradients. Science. 2012. pp. 628–633. doi: 10.1126/science.1208929 Odum WE, Odum EP, Odum HT. 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Entropy. 2020. doi: 10.3390/e22030277 Soon W, Baliunas SL, Robinson AB, Robinson ZW. Environmental Effects of Increased Atmospheric Carbon Dioxide. Energy & Environment. 1999;10: 439–468. doi: 10.1260/0958305991499694 Solomon S, Plattner G-K, Knutti R, Friedlingstein P. Irreversible climate change due to carbon dioxide emissions. Proceedings of the National Academy of Sciences. 2009;106: 1704–1709. doi: 10.1073/pnas.0812721106 Karhu K, Auffret MD, Dungait JAJ, Hopkins DW, Prosser JI, Singh BK, et al. Temperature sensitivity of soil respiration rates enhanced by microbial community response. Nature. 2014;513: 81–84. Frey SD, Lee J, Melillo JM, Six J. The temperature response of soil microbial efficiency and its feedback to climate. Nat Clim Chang. 2013;3: 395–398. Manzoni S, Taylor P, Richter A, Porporato A, Ågren GI. Environmental and stoichiometric controls on microbial carbon-use efficiency in soils. New Phytologist. 2012;196: 79–91. Wu L, Tang Z, Chen H, Ren Z, Ding Q, Liang K, et al. Mutual interaction between gut microbiota and protein/amino acid metabolism for host mucosal immunity and health. Animal Nutrition. 2021;7: 11–16. Beaumont M, Roura E, Lambert W, Turni C, Michiels J, Chalvon-Demersay T. Selective nourishing of gut microbiota with amino acids: A novel prebiotic approach? Front Nutr. 2022;9: 1066898. Tramontano M, Andrejev S, Pruteanu M, Klünemann M, Kuhn M, Galardini M, et al. Nutritional preferences of human gut bacteria reveal their metabolic idiosyncrasies. Nat Microbiol. 2018;3: 514–522. doi: 10.1038/s41564-018-0123-9 Lyons E, Freeling M, Kustu S, Inwood W. Using genomic sequencing for classical genetics in E. coli K12. PLoS One. 2011;6. doi: 10.1371/journal.pone.0016717 Soupene E, Van Heeswijk WC, Plumbridge J, Stewart V, Bertenthal D, Lee H, et al. Physiological studies of Escherichia coli strain MG1655: Growth defects and apparent cross-regulation of gene expression. J Bacteriol. 2003;185: 5611–5626. doi: 10.1128/JB.185.18.5611-5626.2003 Myers JA, Curtis BS, Curtis WR. Improving accuracy of cell and chromophore concentration measurements using optical density. BMC Biophys. 2013;6: 1–16. Bevington PR, Robinson DK, Blair JM, Mallinckrodt AJ, McKay S. Data reduction and error analysis for the physical sciences. Computers in Physics. 1993;7: 415–416. Supplementary Figures Supplementary Figures 1 and 2 are not available with this version<. Additional Declarations (Not answered) Supplementary Files Supplementarynote1.docx Supporting information captions S1 text. Mathematical model Cite Share Download PDF Status: Published Journal Publication published 10 Feb, 2025 Read the published version in npj Systems Biology and Applications → Version 1 posted Editorial decision: revise 18 Jun, 2024 Reviewer # 3 agreed at journal 08 May, 2024 Review # 1 received at journal 08 May, 2024 Review # 2 received at journal 07 May, 2024 Reviewer # 2 agreed at journal 28 Apr, 2024 Reviewer # 1 agreed at journal 22 Apr, 2024 Reviewers invited by journal 09 Apr, 2024 Submission checks completed at journal 05 Apr, 2024 Editor assigned by journal 04 Apr, 2024 First submitted to journal 04 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4219475","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":289363624,"identity":"a52e983c-05d2-4f1f-a656-ea3e5a6c3cb1","order_by":0,"name":"Uwe Sauer","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYNCCCgkGBgkGNoYEBgsgjwckdICAljNwLUAGGzFaGNsYIFoYiNEi337G8HHlPIto+dkNbA8eAF3IL997+ANDzR2cWgzO5Bgbnt0mkbvhzgF2gwSgCyXb+BIMGI49w62FIcdMshGkRSKBTSKxTYLB4BiPQQJjw2HcDut/Y/6zcY5E7vwZUC32QC0H8GlhuJFjxtjYIJHbcANmCxuPYQM+LQY3nhVLNhwD+eVgO8gvPBLHcowZEo7hc1jyxo8NNXW582c3H3v4o8JGjr/5jPGHDzV4HIYAjA0gEhwpwDgdBaNgFIyCUUAJAAALsVGQr0MYBgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-5923-0770","institution":"ETH Zurich","correspondingAuthor":true,"prefix":"","firstName":"Uwe","middleName":"","lastName":"Sauer","suffix":""},{"id":289363625,"identity":"c078e579-477c-46e5-8715-b0107f84c3a8","order_by":1,"name":"Ohad Golan","email":"","orcid":"https://orcid.org/0000-0001-6513-3275","institution":"ETHZ","correspondingAuthor":false,"prefix":"","firstName":"Ohad","middleName":"","lastName":"Golan","suffix":""},{"id":289363626,"identity":"0148476f-69bc-4551-b59e-20c52c16c035","order_by":2,"name":"Olivia Gampp","email":"","orcid":"","institution":"ETHZ","correspondingAuthor":false,"prefix":"","firstName":"Olivia","middleName":"","lastName":"Gampp","suffix":""},{"id":289363627,"identity":"ec8a89ef-2903-41be-9173-ef5768dfcab8","order_by":3,"name":"Lina Eckert","email":"","orcid":"https://orcid.org/0000-0001-5827-3018","institution":"ETHZ","correspondingAuthor":false,"prefix":"","firstName":"Lina","middleName":"","lastName":"Eckert","suffix":""}],"badges":[],"createdAt":"2024-04-04 19:00:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4219475/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4219475/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41540-025-00497-y","type":"published","date":"2025-02-10T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":54582670,"identity":"94f2ff5b-7f2d-4640-a960-ef8ec5e3ae06","added_by":"auto","created_at":"2024-04-12 15:01:17","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":226279,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eOverall biomass yield of malate\u003c/strong\u003e (A) Growth curves of \u003cem\u003eE. coli\u003c/em\u003e for different initial amounts of malate. Curves are averages of three biological replicates. The produced biomass (\u003cimg width=\"31\" height=\"19\" src=\"file:///C:/Users/rpt0628/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif\"/\u003e) is the final biomass reached in stationary phase minus the initial biomass at inoculation. (B)\u003cstrong\u003e \u003c/strong\u003eThe produced biomass of the different growth curves in Fig 1A as function of the initial nutrient amount. The slope of the linear fit is the overall biomass yield (fit parameter R\u003csup\u003e2\u003c/sup\u003e\u0026gt;0.9). Bars of standard errors of the biological replicates are too small to be noticeable. Data for glucose and aspartate experiments are shown in S1 Fig.\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4219475/v1/67e3c9f1d425ddd82263f055.png"},{"id":54582667,"identity":"bf7dad00-7e17-4691-92d3-bd883250276d","added_by":"auto","created_at":"2024-04-12 15:01:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":112252,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExpansion of black box model to include multiple nutrients\u003c/strong\u003e (A) The overall growth process is split into two reactions – a catabolic process in which free energy is released and an anabolic process in which new biomass is formed. The ring in the middle of the cell represents the coupling of anabolism and catabolism by ATP and other biochemical process. (B) Schematics of black box model expansion for two degradable nutrients. A catabolic reaction is added for each nutrient. (C)\u003cstrong\u003e \u003c/strong\u003eSchematics of model expansion for a combination of a degradable nutrient and a second nutrient that can only be used as a biomass precursor. The anabolic reaction is separated into two reactions – one for the biosynthesis of the biomass precursor and a second for the rest of the anabolic process excluding the biosynthesis reaction of the biomass precursor. (D)\u003cstrong\u003e \u003c/strong\u003eBlack box model prediction for growth on two nutrient sources without mutual effect. The model predicts the produced biomass is a linear sum of the biomass gained from each nutrient. The overall biomass yield, the slope of the curve, is independent of availability of different nutrients.\u003c/p\u003e","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4219475/v1/0c4ffbca21793078560c5da7.png"},{"id":54582662,"identity":"ca2374c3-fe1a-4e13-b841-9473fcab98b9","added_by":"auto","created_at":"2024-04-12 15:01:15","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":129488,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProduced biomass and biomass yield on different nutrient bases\u003c/strong\u003e (A-B) The produced biomass as function of initial amounts of the measured nutrients: xylose with or without different base nutrient sources (A, black– no base, green – 160 \u003cimg width=\"15\" height=\"19\" src=\"file:///C:/Users/rpt0628/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif\"/\u003e\u0026nbsp;glucose, orange –160 \u003cimg width=\"15\" height=\"19\" src=\"file:///C:/Users/rpt0628/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif\"/\u003e\u0026nbsp;succinate), and methionine with different base nutrient sources (B, green – 160 \u003cimg width=\"15\" height=\"19\" src=\"file:///C:/Users/rpt0628/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif\"/\u003e\u0026nbsp;glucose, orange – 80 \u003cimg width=\"15\" height=\"19\" src=\"file:///C:/Users/rpt0628/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif\"/\u003e\u0026nbsp;succinate, purple – 160 \u003cimg width=\"15\" height=\"19\" src=\"file:///C:/Users/rpt0628/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif\"/\u003e\u0026nbsp;acetate). Error bars depicting standard error for three biological replicates are in several cases not visible. Curves show a linear fit to the average of the three biological replicates of the linear region (fit parameter R\u003csup\u003e2\u003c/sup\u003e\u0026gt;0.9). (C-D)\u003cstrong\u003e \u003c/strong\u003eThe overall biomass yield (slope of the fits above) for xylose and methionine for growth on the different base nutrients. Error bars depict error of fit parameter. The overall biomass yield is dependent on the nutrient base.\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4219475/v1/eb00aa73b5dbac170cf2ad0c.png"},{"id":54582671,"identity":"0dfa1be8-5e2a-46e2-9df7-e37d40d18663","added_by":"auto","created_at":"2024-04-12 15:01:17","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":84891,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExpanded model solution space including mutual effects between two nutrients \u003c/strong\u003e(A-B)\u003cstrong\u003e \u003c/strong\u003eSimulations\u003cstrong\u003e \u003c/strong\u003eof expanded\u003cstrong\u003e \u003c/strong\u003emodel with different mutual effects for growth on two degradable nutrient sources (A) and a biomass precursor in combination with a degradable nutrient (B). Initial nutrient amount of the base nutrient were kept constant in all simulations. (C)\u003cstrong\u003e \u003c/strong\u003eSimulations of expanded model for growth on two degradable nutrients for different initial amounts of base nutrient with positive catabolic mutual effect. The overall biomass yield (slope) increases with increasing initial amount of base nutrient. (D\u003cstrong\u003e) \u003c/strong\u003eSimulations of expanded model for growth on a biomass precursor and a degradable base nutrient with a negative catabolic effect and positive effect on precursor biosynthesis. Increased initial amount of base nutrient shifts the initial decreasing part and increases the slope (the overall biomass yield) of the linear part.\u003c/p\u003e","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4219475/v1/477dee3bef2c1072508a8e45.png"},{"id":54582669,"identity":"ac112cf8-2bbc-48ee-b659-1da31d3d030d","added_by":"auto","created_at":"2024-04-12 15:01:16","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":122765,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEffects of initial amounts of base nutrients on the overall biomass yield\u003c/strong\u003e (A-B)\u003cstrong\u003e \u003c/strong\u003eThe produced biomass as a function of the initial amount of xylose (A) and methionine (B) at different initial amounts of the base nutrient succinate (A) and glucose (B)\u003cstrong\u003e. \u003c/strong\u003eData points are average of three biological replicates and error bars are standard error that are too small to notice. Curves are linear fits in the linear region to the average of the three biological replicates (fit parameter R\u003csup\u003e2\u003c/sup\u003e\u0026gt;0.9 for all fits except for methionine on 40 \u003cimg width=\"15\" height=\"19\" src=\"file:///C:/Users/rpt0628/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif\"/\u003e\u0026nbsp;glucose which showed a good fit to a constant (p-value\u0026lt;0.05)). (C-D)\u003cstrong\u003e \u003c/strong\u003eThe overall biomass yield as a function of initial nutrient amount as calculate from the conditions in A-B. Curves show linear fit region (fit parameter R\u003csup\u003e2\u003c/sup\u003e\u0026gt;0.9).\u0026nbsp; Error bars depict error of fit parameter.\u003c/p\u003e","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4219475/v1/c713578cdcd111f0a306905d.png"},{"id":54582656,"identity":"903d0f53-3b36-42de-bc7d-44cdd2502b7d","added_by":"auto","created_at":"2024-04-12 15:01:13","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":138086,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEffects of initial amounts of base nutrients on the overall biomass yield \u003c/strong\u003e\u0026nbsp;(A-B)\u003cstrong\u003e \u003c/strong\u003eThe produced biomass as function of initial nutrient amount of aspartate for different initial amounts of the base nutrient ((A) – glucose, (B) – acetate)\u003cstrong\u003e. \u003c/strong\u003eData points are average of three biological replicates and error bars are standard error that are too small to notice. Curves are linear fits to the average of the three replicates in the linear regions (fit parameter R\u003csup\u003e2\u003c/sup\u003e\u0026gt;0.9). (C-D\u003cstrong\u003e) \u003c/strong\u003eThe overall biomass yield as function of initial nutrient amount as calculated from the conditions in A-B respectively. Black data points show the slope of the first linear phase and blue data points show the second. Curves show linear fit (fit parameter R\u003csup\u003e2\u003c/sup\u003e\u0026gt;0.9 for first linear fit on acetate and second linear phase on glucose, the other fits show a good fit to a constant (p-value\u0026lt;0.05)). Error bars depict error of fit parameter.\u003c/p\u003e","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4219475/v1/c4f0877c057fd93a8b09564e.png"},{"id":75984611,"identity":"c854ccce-6bfe-4c13-8755-2bdeab9a15d9","added_by":"auto","created_at":"2025-02-11 08:11:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1496914,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4219475/v1/d24ca8bf-cc8e-4406-b672-7ab6ff2aa7cb.pdf"},{"id":54582668,"identity":"ae431de8-9722-409f-88cc-8b75538ec6a8","added_by":"auto","created_at":"2024-04-12 15:01:16","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":37986,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSupporting information captions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eS1 text. Mathematical model\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Supplementarynote1.docx","url":"https://assets-eu.researchsquare.com/files/rs-4219475/v1/d1c6ef30c7d1bebbc48d7eff.docx"}],"financialInterests":"(Not answered)","formattedTitle":"Overall biomass yield on multiple nutrient sources","fulltext":[{"header":"Author summary ","content":"\u003cp\u003eUnderstanding microbial nutrient utilization efficiency is critical for maximizing productivity and minimizing environmental impact in agricultural and biotechnology settings, as well as for improving our understanding of ecological systems and how they are impacted by changes in nutrient availability. Previous models suggest that the availability of one nutrient should not affect the utilization efficiency of another. However, our study found that the availability of a second nutrient not only effects the utilization efficiency of the first but can also lead to a decrease in gain from the first nutrient. Following these results, we used mathematical modeling and simulations to determine how different nutrient combinations affect various growth processes, ultimately leading to changes in overall biomass yield. These findings highlight the complex interplay between multiple nutrient sources and challenge previous models. Our study suggests that careful consideration of nutrient interactions is essential for achieving optimal yields and may help guide the development of more effective nutrient management strategies in agricultural and biotechnology settings, as well as understanding of ecological systems.\u003c/p\u003e"},{"header":"Introduction","content":"\u003cp\u003eNatural environments are characterized by a broad spectrum of physicochemical parameters that collectively define constraints within which species survive and thrive. Of particular importance to niche occupancy by different microbes are the type of nutrients and their temporal availability. For example, bacteria growing in a riverbed might experience continuous nutrient flux and high spatial homogeneity while bacteria growing in pulsating environments, such as tidal wetlands or at the sea bottom, receive nutrients only sporadically [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Different physiological traits provide fitness advantages for different nutrient dynamics. Continuous nutrient flux environments favor organisms with higher growth rate so that they can exploit the otherwise washed out nutrients, while environments of sporadic nutrient flux and high spatial heterogeneity favor organisms that utilize resources more efficiently [\u003cspan additionalcitationids=\"CR4 CR5\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn conditions of continuous nutrient flux, the biomass produced per consumed nutrient is physiologically defined as the biomass yield parameter that describes the efficiency of nutrient utilization [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Theoretical models, known as \u0026lsquo;black box models\u0026rsquo;, predict the biomass yield for growth on a single nutrient source in conditions of continuous flux such as those observed in chemostat experiments to high accuracy [\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. These models consider growth as a single chemical reaction with the nutrients as substrates and the produced biomass and secreted byproducts as products. By calculating the change in free energy of the whole reaction, the biomass yield is predicted. Here, we adopt these models to qualitatively predict and then test the overall biomass yield in batch cultures of \u003cem\u003eEscherichia coli\u003c/em\u003e, where the outgoing flux of nutrients is limited so that all available nutrients are utilized, including reutilization of secreted byproducts, a condition akin to a single nutrient pulse in natural pulsating environments. Since natural environments typically contain multiple nutrients [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], we investigate whether the overall biomass yield of a nutrient depends on the availability and metabolic properties of a second nutrient, for example if it can be degraded or only used as a building block for biomass.\u003c/p\u003e \u003cp\u003eGenerally, black box models describe scenarios without mutual effects between nutrients; hence, the overall biomass yield of each nutrient is independent of the availability of another. We tested this prediction experimentally by titrating a second nutrient to batch cultures grown on a single carbon source, demonstrating that the overall biomass yield depends not only on the availability but also on the initial amount of other nutrients, and that this mutual effect can be negative. To explain these observations, we expanded the black box model to consider whether a second nutrient can only be used for biomass synthesis or also degraded for energy generation and included mutual effects between the metabolic processes of the nutrient sources. The model qualitatively captures the experimental observations and explains how the combination of nutrients affects metabolism. Furthermore, using the model, we determine the mutual effect of different nutrient combinations on growth processes.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eGrowth on a single nutrient source\u003c/h2\u003e \u003cp\u003eThe classical system to investigate the efficiency of nutrient utilization in pulsating environments where organisms have sufficient time to fully utilize all available nutrients in a single nutrient pulse are batch cultures. Here we follow growth of \u003cem\u003eE. coli\u003c/em\u003e until depletion of the initial nutrient source and potential secreted byproducts when stationary phase is reached in M9 minimal medium with glucose, malate, or aspartate as sole carbon sources [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. These carbon sources were chosen as respiro-fermentative, strictly respiratory, and a degradable biomass component. The produced biomass (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }B\\)\u003c/span\u003e\u003c/span\u003e), that is the biomass reached at stationary phase minus the biomass at inoculation, was recorded as the optical density at 600nm, converted to cellular dry weight using a predetermined conversion factor [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], and plotted against the initial nutrient amount (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e; S1 Fig). The produced biomass shows a good linear fit to the initial amount of the sole carbon source (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB) and as such, can be described by [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${\\Delta }B={Y}_{X/D}{N}_{D}$$\u003c/div\u003e\u003c/div\u003e(1) \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{D}\\)\u003c/span\u003e\u003c/span\u003e is the initial amount of nutrient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{X/D}\\)\u003c/span\u003e\u003c/span\u003e the overall biomass yield for organism \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X\\)\u003c/span\u003e\u003c/span\u003e on nutrient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D\\)\u003c/span\u003e\u003c/span\u003e which describes the efficiency of full utilization of the available nutrient.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo predict the produced biomass, we used a black box formalism [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] that separates the growth reaction of chemotrophic organisms to a two-reaction process (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA). The first is a catabolic reaction that releases Gibbs free energy by breakdown of nutrients. The second is the anabolic reaction that uses the released free energy for the synthesis of new biomass. The overall Gibbs energy dissipation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{G}_{X}\\)\u003c/span\u003e\u003c/span\u003e of the growth process is given by ([\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], S1A text):\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$${\\Delta }{G}_{X}=\\frac{1}{{Y}_{X/D}}{\\Delta }{G}_{cat}+{\\Delta }{G}_{an}$$\u003c/div\u003e\u003c/div\u003e(2) \u003c/p\u003e \u003cp\u003ewhere the subscripts \u003cem\u003ecat\u003c/em\u003e, and \u003cem\u003ean\u003c/em\u003e refer to the Gibbs energy of dissipation of the catabolic and anabolic reactions, respectively. Given that all secreted byproducts are utilized in the here investigated growth conditions, the free energy of the secreted byproducts can be set to 0, the overall biomass yield may be predicted as [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]:\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$${Y}_{X/D}=\\frac{{\\Delta }{G}_{cat}}{{\\Delta }{G}_{X}-{\\Delta }{G}_{an}}$$\u003c/div\u003e\u003c/div\u003e(3) \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCombining equations (1) and (3) predicts a linear correlation of the produced biomass as function of initial nutrient amount with a slope that depends only on the type of nutrient through\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{G}_{cat}\\)\u003c/span\u003e\u003c/span\u003e. This prediction fits well with all measured nutrients and is consistent with previous results [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB, S1 Fig).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eGrowth on multiple nutrient sources\u003c/h2\u003e \u003cp\u003eSince organisms typically encounter multiple nutrients in natural environments, we next asked whether the availability of one nutrient affects the overall biomass yield of another. To enable a black box model to capture such effects, we added another reaction that depends on the type of second nutrient: A) degradable nutrients that first must be catabolized before they can be used, such as a sugar; B) non-degradable nutrients that can be used only as a biomass precursor, such as the non-degradable amino acid methionine in \u003cem\u003eE. coli\u003c/em\u003e; and C) nutrients that can be both catabolized or used directly as a biomass precursor, such as the amino acid aspartate in \u003cem\u003eE. coli\u003c/em\u003e. For the combination of two degradable nutrients the added reaction is catabolic (S1B text, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB). In this case, the overall Gibbs energy dissipation gives:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$${\\Delta }{G}_{X}=\\frac{1}{{Y}_{X/{N}_{1}}}{\\Delta }{G}_{cat}^{{N}_{1}}+\\frac{1}{{Y}_{X/{N}_{2}}}{\\Delta }{G}_{cat}^{{N}_{2}} +{\\Delta }{G}_{an}$$\u003c/div\u003e\u003c/div\u003e(4) \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{G}_{cat}^{{N}_{i}}\\)\u003c/span\u003e\u003c/span\u003e is the Gibbs energy of dissipation for the catabolic process of nutrient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e. When the second nutrient source is a non-degradable biomass precursor, we split the anabolic reaction into two \u0026ndash; a reaction for biosynthesis of the biomass precursor and a reaction for the general anabolic process (S1C text, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eC). The overall Gibbs energy of dissipation in this case gives:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$${\\Delta }{G}_{X}=\\frac{1}{{Y}_{X/{N}_{1}}}{\\Delta }{G}_{cat}+{\\Delta }{G}_{an}^{bsyn}+{\\Delta }{G}_{bsyn}(1-{M}_{utl})$$\u003c/div\u003e\u003c/div\u003e(5) \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{G}_{bsyn}\\)\u003c/span\u003e\u003c/span\u003e is the Gibbs energy of dissipation for synthesis of the biomass precursor and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{G}_{an}^{bsyn}\\)\u003c/span\u003e\u003c/span\u003e is the dissipation energy for the general anabolic process minus that of the biomass precursor. The function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({M}_{utl}\\)\u003c/span\u003e\u003c/span\u003e describes the ratio of available biomass precursor to that required to generate the produced biomass during the growth process. It is dependent on biomass precursor availability such that when all the necessary biomass precursor is available in the environment, the function assumes the maximal value of 1 and the cost for this precursor biosynthesis is alleviated.\u003c/p\u003e \u003cp\u003eCombining equations (4) or (5) with Eq.\u0026nbsp;(1) shows that regardless of the type of nutrient supplemented, the produced biomass is predicted to be a linear sum of the biomass gained from the available nutrients and the overall biomass yield of each nutrient is independent of the availability of others (S1B-C text, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eD):\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$${\\Delta }B={Y}_{X/N1 }{N}_{1}+{Y}_{X/N2}{N}_{2}$$\u003c/div\u003e\u003c/div\u003e(6) \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the amount of nutrient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e in the growth medium and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{X/Ni }\\)\u003c/span\u003e\u003c/span\u003e is the overall biomass yield of nutrient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eTo test the prediction that the overall biomass yield of a nutrient is independent of the availability of others, we compared the overall biomass yield of \u003cem\u003eE. coli\u003c/em\u003e for different nutrients, henceforth referred to as the measured nutrient, in the presence or absence of a second nutrient, termed the base nutrient. To do so, the initial amount of the measured nutrient was varied for each batch culture experiment at constant initial amounts of the base nutrient between 0 and 1.2 g/l for glucose, acetate, or aspartate and 0 and 0.06 g/l for methionine. The produced biomass was plotted against the initial amount of the measured nutrient and the overall biomass yield was determined as the slope of a linear fit of that curve (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA,B). In combination with glucose, succinate, or acetate as base nutrients, we determined the overall biomass yield of xylose and methionine as measured nutrients, as examples of degradable or non-degradable nutrients, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The initial amount of base nutrient determines the intercept with the Y-axis and was chosen such that the measured parameters remain within measurable range.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe overall biomass yield was highly dependent on the base nutrient. For xylose, the overall biomass yield was higher on succinate as base nutrient than on glucose or when used alone, and for methionine the overall yield was by far the highest on glucose (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC,D). For most combinations, the influence of the second nutrient was monotonous across the tested concentrations, i.e., the overall biomass yield of the measured nutrient can be determined from the slope of a linear fit (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA,B). An exception was the non-monotonous behavior of methionine as the measured nutrient in combination with glucose as a base nutrient (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB). At low initial amounts of methionine (below 3 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e), increasing initial amounts of methionine unexpectedly decreased the produced biomass. In the higher range of initial amounts (above 3 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e), increasing methionine initial amounts increased the produced biomass linearly.\u003c/p\u003e \u003cp\u003eThus, the overall biomass yield of a measured nutrient is dependent on the base nutrient, consequently black box theory cannot capture the produced biomass of multiple nutrient sources. To enable the model to describe such mutual effects, we expand it to include such effects phenomenologically. To do so, we coupled a function that is dependent on the combination of available nutrients to the Gibbs energy dissipation of each reaction in the growth processes. For simplicity, we assumed these functions are linear to the initial nutrient amount.\u003c/p\u003e \u003cp\u003eAs such, the overall Gibbs energy dissipation of growth on two degradable nutrient sources is described as (S1D text):\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$${\\Delta }{G}_{X}=\\frac{1}{{Y}_{X/{N}_{1}}}{\\Delta }{G}_{cat}^{{N}_{1}}{f}_{cat1}\\left({N}_{2}\\right)+\\frac{1}{{Y}_{X/{N}_{2}}}{\\Delta }{G}_{cat}^{{N}_{2}}{f}_{cat2}\\left({N}_{1}\\right)+{\\Delta }{G}_{an}{f}_{an}\\left({N}_{1},{N}_{2}\\right)$$\u003c/div\u003e\u003c/div\u003e(7) \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{cat}\\left({N}_{i}\\right)\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{an}\\left({N}_{i}\\right)\\)\u003c/span\u003e\u003c/span\u003e are linear functions to the initial amounts of nutrient source \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e, with coefficients \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{m}}_{\\text{c}\\text{a}\\text{t}}^{{\\text{N}}_{\\text{j}}} , {\\text{m}}_{\\text{a}\\text{n}}^{{\\text{N}}_{\\text{j}}}\\)\u003c/span\u003e\u003c/span\u003erespectively. These functions phenomenologically depict the mutual effect of the nutrient combination on the growth processes. Combining equations (1) and (7) predicts the produced biomass:\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$${\\Delta }B=\\frac{{\\Delta }{G}_{cat}^{{N}_{1}}{N}_{1}+{\\Delta }{G}_{cat}^{{N}_{2}}{N}_{2}+{\\Delta }{\\text{m}}_{\\text{C}\\text{A}\\text{T}}^{{\\text{N}}_{1}{N}_{2}}{N}_{1}{N}_{2}}{{\\Delta }{G}_{X}-{\\Delta }{G}_{an}{f}_{an}\\left({N}_{1}, {N}_{2}\\right)}$$\u003c/div\u003e\u003c/div\u003e(8) \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{\\text{m}}_{\\text{C}\\text{A}\\text{T}}^{{\\text{N}}_{1}{N}_{2}}={\\Delta }{G}_{cat}^{{N}_{1}}{m}_{cat}^{{N}_{1}}+{\\Delta }{G}_{cat}^{{N}_{2}}{m}_{cat}^{{N}_{2}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{an}\\left({N}_{1}, {N}_{2}\\right)=1+{m}_{an}^{{N}_{1}}{N}_{1}+{m}_{an}^{{N}_{2}}{N}_{2}\\)\u003c/span\u003e\u003c/span\u003e. Given a mutual effect between nutrients, the produced biomass is thus made of three terms, two describing the direct effect of catabolism of the two nutrient sources and a third term describing the mutual catabolic effect depending on availability of both substrates. Although the last term of the model is based on the phenomenological observation, the range of model solutions is limited. Exploring this solution space shows that, depending on the type of mutualism, qualitatively different relationships are predicted between available nutrients and biomass formation (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA) \u0026ndash; a positive mutual catabolic effect increases the overall biomass yield (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA, orange curve) while a negative catabolic effect decreases it (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA, purple curve). The expanded model can capture the experimentally observed mutual effect of increased overall biomass yield with a positive mutual catabolic effect (compare increased slope for different base nutrients in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA to the orange curve in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor growth on a combination of a degradable nutrient and a non-degradable biomass precursor, the overall Gibbs energy dissipation is described as (S1E text):\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$${\\Delta }{G}_{X}=\\frac{1}{{Y}_{X/D }}{\\Delta }{G}_{cat}{f}_{cat}\\left(M\\right)+{\\Delta }{G}_{an}{f}_{an}\\left(N,M\\right)+{\\Delta }{G}_{bsyn}^{M} {f}_{bsyn}\\left(N\\right)(1-{M}_{utl})$$\u003c/div\u003e\u003c/div\u003e(9) \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{cat}\\left({M}_{utl}\\right)\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{an}\\left(N,{M}_{utl}\\right)\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{bsyn}\\left({M}_{utl}\\right)\\)\u003c/span\u003e\u003c/span\u003e are linear functions with coefficients \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{cat}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{an }^{N}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{an }^{M}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{sbyn}\\)\u003c/span\u003e\u003c/span\u003e respectively. These functions depict the mutual effect between the nutrient sources on the Gibbs free energy of each growth reaction. Solving equations (1) and (9) for the produced biomass gives a quadratic equation:\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$${\\Delta }{B}^{2}-\\frac{{\\Delta }B}{{\\Delta }{G}_{A}} \\left(N{\\Delta }{G}_{cat}+{M}^{{\\prime }}\\left({m}_{an }^{M}{\\Delta }{G}_{an}-\\left(1+{m}_{sbyn}N\\right){\\Delta }{G}_{bsyn }^{M}\\right) \\right)-N\\frac{{\\Delta }{G}_{cat}}{{\\Delta }{G}_{A}}{m}_{cat}{M}^{{\\prime }}=0$$\u003c/div\u003e\u003c/div\u003e(10) \u003cdiv id=\"Equk\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equk\" name=\"EquationSource\"\u003e\n$$\\text{w}\\text{h}\\text{e}\\text{r}\\text{e} {\\Delta }{G}_{A}=\\left({\\Delta }{G}_{X}-{\\Delta }{G}_{an}(1-N{m}_{an }^{N})-{\\Delta }{G}_{bsyn}^{M}\\left(1+{m}_{sbyn}N\\right)\\right) \\text{a}\\text{n}\\text{d} {M}^{{\\prime }}={M}_{utl}{\\Delta }B.$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eUnlike the solution for growth on two degradable nutrient sources, solving Eq.\u0026nbsp;(10) for the produced biomass shows that a mutual effect between a biomass precursor and a degradable nutrient can give rise to non-monotonous solutions. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB explores the solution space of possible mutual effects between a precursor and a degradable nutrient. The case of a negative catabolic effect (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB, orange curve) fits qualitatively well with the experimental observation of the biomass precursor methionine on glucose as base nutrient (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB, green data points).\u003c/p\u003e \u003cp\u003eThe coefficients of the linear functions depicting the mutual effect between the nutrients are a key output of the model since they infer how each combination of nutrients effects the different growth reactions. Fitting these coefficients to the experimental results of methionine growing with glucose as a base nutrient gives a qualitative fit to a negative value for the catabolic parameter (coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{cat})\\)\u003c/span\u003e\u003c/span\u003e, revealing that methionine decreases the catabolic efficiency of glucose. Furthermore, the overall biomass yield of methionine on glucose in the linear region is higher than that on succinate or acetate (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eD), suggesting a mutual effect on another metabolic process in one of these combinations, potentially the precursor biosynthesis processes (coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{sbyn})\\)\u003c/span\u003e\u003c/span\u003e. For all combinations of two degradable nutrients, the overall biomass yield increased as compared to growth on sole nutrient sources (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC), a result that fits a positive mutual effect on the catabolic process (coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{cat})\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAn unexpected model prediction is noticeable in equations (9) and (10) where the initial amounts of the two available nutrients are coupled in at least one term. Hence, the model predicts that the overall biomass yield of a measured nutrient depends not only on the availability of a base nutrient, but also on the relative initial amounts of the nutrients. For a combination of two degradable nutrient sources with a positive catabolic effect, as observed experimentally for xylose on the two base nutrients (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA,C), the overall biomass yield is predicted to increase with increasing initial amounts of the base nutrient (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eC). For the combination of a degradable nutrient and a biomass precursor, such as methionine on glucose, with a negative catabolic effect and positive effect on precursor biosynthesis, the model predicts a shift of the curves for the non-linear part as well as an increase in the slope of the linear part with increasing initial amounts of base nutrient (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eD).\u003c/p\u003e \u003cp\u003eTo test these predictions, we determined the produced biomass on xylose and methionine as the measured nutrients on different initial amounts of succinate and glucose as the base nutrients, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA,B). The overall biomass yield of xylose (i.e., slope of the curve) increased linearly with the initial amount of the base nutrient succinate (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA, C). This observation fits well with the model prediction for a positive catabolic effect between two degradable nutrients (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eC). The curve of the produced biomass on methionine exhibits a more complex dependency on the initial amount of glucose as the base nutrient. Above \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(5 {\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e methionine, the slope of all curves increased linearly with the amount of the base nutrient glucose, but below \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(5 {\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003emethionine there was no linear dependency and the amount of base nutrient varied the curve shape (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB, D). This observation fits well with the theoretical prediction (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eD) that this nutrient combination not only has a positive effect on the precursor biosynthesis reaction (i.e., the linear dependency at higher methionine supplementation), but also a negative catabolic effect where at low methionine concentrations, in some cases, more methionine leads to lower biomass gain.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhich mechanism underlies the negative catabolic effect of methionine on glucose? The growth curves followed the classical diauxic shift with exponential growth on glucose and a second phase on previously secreted acetate (S2A Fig). For the example of 160 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e glucose as the base nutrient (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, pink curve), the first phase lasted 4-4.5 hours and growth on acetate resumed between 7\u0026ndash;10 hours (S2A Fig). In both phases, the biomass gain (calculated as the biomass at the end minus the biomass at the beginning) increased linearly with methionine amounts greater than 2 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e (S2B, C Fig). The biomass gain was much higher than the trendline in the absence of or at very low methionine concentrations. During exponential growth on glucose in the first phase, methionine decreased the gain in biomass but increased the growth rate (S2D Fig.). Given the diauxic shift from growth on glucose to previously secreted acetate (S2E Fig), the most plausible explanation for the higher biomass gain without or low methionine in the second phase is due to higher acetate secretion in the first phase. To test whether methionine supplementation indeed reduced acetate secretion, we varied acetate secretion rates by altering steady state growth through an inducible promoter for the glucose uptake gene \u003cem\u003eptsG\u003c/em\u003e that limits glucose uptake [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Comparing acetate secretion in the presence and absence of methionine shows that methionine indeed decreases acetate secretion (S2F Fig). Thus, the negative catabolic effect of methionine on glucose catabolism appears to be a combination of a lower biomass gain during the first growth phase, with a higher growth rate and less acetate secretion, and a lower biomass gain in the second phase because less acetate was secreted.\u003c/p\u003e \u003cp\u003eAt the lowest amounts of methionine (0 and 1.43 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e) we noted a shorter lag time for growth on acetate (S2A Fig, compare red and black curves to the other curves). Growth with 1.43 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e methionine was somewhat special as it followed the biomass trendline in the first growth phase but could not sustain the higher growth rate throughout this growth phase (S2A Fig, red curve between 2-4h), presumably because methionine was used up, which explains why its biomass gain in the second phase was indistinguishable from the no methionine condition (S2C Fig). Consistently, 1.43 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e methionine was below the amount necessary to produce the biomass reached at the end of the first growth phase (about 1.7 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e of methionine is required to generate 0.8 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{g}\\text{D}\\text{C}\\text{W}\\)\u003c/span\u003e\u003c/span\u003e of biomass [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eGrowth with a second nutrient that can be degraded and used as a biomass precursor\u003c/h3\u003e\n\u003cp\u003eSo far, we focused on degradable nutrients or nutrients that can only be used as biomass precursors. Some nutrients such as degradable amino acids, however, can be directly used both as biomass precursors or energy source. Given the complex curves observed for the combination of biomass precursor and degradable nutrient, we expected that a degradable amino acid in combination with a degradable nutrient would also produce non-monotonous curves. To investigate the effects of such nutrient combinations, we measured the produced biomass on the degradable amino acid aspartate on different initial amounts of glucose and acetate as base nutrients (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA,B). The combination of aspartate and acetate led to a complex curve with two linear phases separated by a double shift in slope at intermediate concentrations (between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(100-150 {\\mu }\\text{g}\\)\u003c/span\u003e\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA). The first phase at low initial amounts of aspartate resulted in a linear slope that increases with initial amount of acetate while the slope of the second phase shows only a low dependency on acetate initial amounts (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eC). Aspartate on glucose also shows a complex curve with two linear phases (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eB). In this nutrient combination, the slope of the first phase is independent of the initial amount of glucose yet the length of this phase increases with increasing initial glucose amounts (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eD). The slope of the second linear phase increases with increasing glucose initial amounts. The complex behavior observed in these experiments cannot be captured even with the mutual effect model presented here. We hypothesize that the ratio of how much aspartate is utilized as a biomass precursor to how much is catabolized affects the overall biomass yield. The multiple utilization possibilities add an additional degree of freedom to the system and as such, capturing the behavior of these nutrients in a model requires time-resolved intracellular flux information.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn conditions of low nutrient flux, organisms utilize all nutrients in the environment and reabsorb previously secreted byproducts to fuel further growth. Here we asked whether the availability of one nutrient affects the utilization efficiency of another? We showed that different nutrient combinations have different mutual effects on an organism\u0026rsquo;s ability to generate biomass, presumably by changing intracellular metabolism, secretion, and reabsorption of secreted byproducts. While microbial utilization of multiple nutrients has been extensively studied, yielding significant findings like the diauxic shift [\u003cspan additionalcitationids=\"CR22\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] or the complex interplay of factors in multiple nutrient environments [\u003cspan additionalcitationids=\"CR25 CR26\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], these studies don\u0026rsquo;t differentiate between different nutrient types, focus on specific growth phases and as such are incapable of capturing the biomass gain from the entire growth curve.\u003c/p\u003e \u003cp\u003eTo address this challenge and gain a more comprehensive understanding, we expanded previous black box models to depict the full growth process for growth on multiple nutrients. We expanded the model to account for the effect of different nutrient types and incorporated a phenomenological representation of mutual effects between nutrient sources. The expanded black box model was able to qualitatively capture the experimental observation and further predicts that the overall biomass yield of a nutrient depends not only on the availability of other nutrients but also on the ratio of initial amounts of the different nutrients. Given the coarse granularity of a black box model, it does not identify the specific metabolic reactions. However, by fitting the model to experimental measurements, the model can determine which coarse-grained metabolic process \u0026ndash; catabolism, anabolism or precursor biosynthesis \u0026ndash; in each nutrient combination is the cause of the mutual effect. This leads to generate hypotheses on which specific pathways are affected. For instance, we observed that for \u003cem\u003eE. coli\u003c/em\u003e growing on glucose, methionine supplementation decreases the catabolic efficiency of glucose utilization, and provide circumstantial evidence that this is caused by a combination of the effect of methionine on the growth rate and reduced acetate secretion.\u003c/p\u003e \u003cp\u003eFor all nutrient combinations, the initial amount of the base nutrient had a positive effect on the overall biomass yield of the measured nutrient, for at least some region of the measured range. This result is consistent with previous reports, for example, the supplementation of growth media with casamino acids or yeast extract has been shown to increase the carbon utilization efficiency of succinate or asparagine in batch culture experiments of \u003cem\u003eEnterobacter aerogenes\u003c/em\u003e and \u003cem\u003ePseudomonas perfectomarinus\u003c/em\u003e [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Similarly, the utilization of mixtures of different dissolved organic carbon sources by bacterial communities in aquatic systems has been found to be more efficient than the utilization of a single source [\u003cspan additionalcitationids=\"CR30 CR31 CR32\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Moreover, the carbon utilization efficiency of \u003cem\u003eCandida utilis\u003c/em\u003e, \u003cem\u003eP. oxalaticus\u003c/em\u003e, \u003cem\u003eSaccharomyces cerevisiae\u003c/em\u003e, \u003cem\u003eParacoccus denitrificans\u003c/em\u003e, and \u003cem\u003eThiobacilius versutus\u003c/em\u003e has been found to be higher than theoretically predicted when a nutrient source that can be utilized solely as an energy source was supplemented during balanced growth conditions [\u003cspan additionalcitationids=\"CR35\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. It is tempting to conclude that the underlying reason for this deviation from the theoretical prediction is similar in all cases, regardless of the experimental setup and measured parameter, i.e., biomass yield as measured in a chemostat continuous culture [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] or the overall biomass yield as measured in batch cultures. Our analysis suggests that the different nutrients affect each other\u0026rsquo;s catabolism, although the specific metabolic pathways that are affected remain unresolved. One potential explanation could lie in the concept of maintenance energy, which can potentially vary depending on nutrient availability. A maintenance energy that decreases due to supplementation of a second nutrient would consequently increase the efficiency of nutrient utilization. To further investigate these mechanisms and identify a possible global mechanism, a more detailed resolution of metabolic pathways and their fluxes will be necessary, possibly by combining the thermodynamic black-box approach presented here with genome-scale metabolic models [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eInherent to the black box models is the conception that the biomass produced is ultimately constrained by the energy available in the system. These models hinge on a thermodynamic balance, where the energy gleaned from catabolic processes is weighed against the energy expended in anabolic processes. While these models address the energy balance, implications for the carbon balance can extrapolated from the results. Given the conservation of carbon in the system, our findings suggest that the combination of nutrients could have a substantial impact on CO\u003csub\u003e2\u003c/sub\u003e production as the primary carbon byproduct during growth. In cases where a base nutrient augments the yield of the measured nutrient, CO\u003csub\u003e2\u003c/sub\u003e production per nutrient utilized would decrease, while a base nutrient that diminishes the yield of the measured nutrient can result in an increase in CO\u003csub\u003e2\u003c/sub\u003e production per nutrient utilized.\u003c/p\u003e \u003cp\u003eUnderstanding the influence of nutrient combinations on CO\u003csub\u003e2\u003c/sub\u003e production opens up broader ecological considerations, especially when changes in CO\u003csub\u003e2\u003c/sub\u003e production can significantly impact the environment [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Microbes metabolize a wide range of compounds, which affects the dynamics of organic matter and CO\u003csub\u003e2\u003c/sub\u003e emissions [\u003cspan additionalcitationids=\"CR42\" citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], potentially impacting agricultural productivity, ocean nutrient balance, and the global climate [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. For example, heterotrophic microbes respire 60 gigatonnes of terrestrial organic matter annually, roughly six times the annual anthropogenic emissions. Given that microbes utilize multiple nutrients in most growth environments, understanding the interplay between different nutrients, as explored in this study, could pave the way for more informed research in ecological systems, and even aid in mitigating the environmental impact of agriculture and the biotechnology industry by decreasing CO\u003csub\u003e2\u003c/sub\u003e emissions.\u003c/p\u003e \u003cp\u003eNutrient utilization efficiency is important in other contexts, including evolution, microbiome-host interactions and synthetic biology. For example, different nutrient combinations have been shown to impact the gut microbiome [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e], sometimes unintuitively where supplementation of another nutrient such as an amino acid reduces the overall biomass gain of gut bacteria [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Our observation showing the effects of amino acid supplementation on the overall biomass yield and specifically the reduced biomass gain due to supplementation of methionine could help elucidate the phenomenon. The analysis presented here was done for a single organism and experimentally tested on \u003cem\u003eE. coli\u003c/em\u003e, but since the abstracted reactions occur in any metabolic system our approach can be extended to analyze growth of consortia or even larger ecological systems. It remains an open question whether there are general principles governing the here described mutual effects or whether each nutrient combination has its own unique mechanism in a given organism.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eStrains and growth essays:\u003c/h2\u003e \u003cp\u003eIn the growth essays the NCM3722 strain [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e] as used and in the acetate secretion essay NQ1243 [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Each experiment was carried out in three steps: seed culture, pre-culture and experimental culture. For seed culture, one colony from fresh LB agar plate was inoculated into test tube with M9 minimal medium with 4 gr/l glucose and cultured in 37\u0026ordm;C shaking at 350 rpm for 8\u0026ndash;9 hours. The cell culture was then diluted to OD\u003csub\u003e600\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.1\u0026ndash;0.2 in pre-warmed shake flask with m9 minimal medium with the same base nutrient as the experiment and left to grow for two hours in 37\u0026ordm;C shaking at 350 rpm (pre-culture). The cell culture was then diluted to OD\u003csub\u003e600\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.03\u0026ndash;0.08 in pre-warmed 96 deep well plate with 1 ml. Each well contained medium with the experimental growth conditions (M9 minimal medium with nutrients according to experiment, each condition was set in triplicates) and mixed thoroughly. 200 \u0026micro;l cell culture from every well was then transferred to 96 deep well transparent essay plate and placed in Tecan microplate reader (Tecan infinite M200) for growth measurement. Microplate reader was programmed to maintain temperature at 37\u0026ordm;C, maximal shaking and measure OD\u003csub\u003e600\u003c/sub\u003e every 10 minutes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eData analysis:\u003c/h2\u003e \u003cp\u003eThe OD measured by the microplate reader was linearized using a premeasured calibration curve. Growth curves obtained in the microplate reader were compared to growth curves obtained in shake flask and were equivalent. The optical density was then converted to dry weight according to known calibration \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.396\\frac{gDW}{L OD}\\)\u003c/span\u003e\u003c/span\u003e[49]. The final biomass point was recorded at 3\u0026ndash;5 hours after maximal OD was reached. All linear fits were done to the average of the triplicate measurements by method of least-mean-square[\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e] in the range that displayed a clear linear trend.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eAcetate secretion rate experiment:\u003c/h2\u003e \u003cp\u003eThe experiment was done at 37\u0026ordm;C shaker shaking at 350 rpm in three steps: seed culture, pre-culture and experimental culture. For seed culture, one colony from fresh LB agar plate was inoculated into test tube with M9 minimal medium with 4 gr/l glucose and cultured in 37\u0026ordm;C shaking at 350 rpm for 8\u0026ndash;9 hours. The culture was then diluted in pre-warmed 96 deep well plate to an OD\u003csub\u003e600\u003c/sub\u003e of 0.05\u0026ndash;0.4 so that all cultures reached exponential phase at the same time. Each growth condition in the deep well plate was run in triplicates. All conditions contained m9 minimal medium, 4 gr/l glucose and different concentrations of the inducer for the glucose uptake promoter 3methyl-benzyl. Half of the growth conditions contained 0.1 gr/l methionine. Every 30 min, 40 \u0026micro;l culture from every well were collected and used to measure OD\u003csub\u003e600\u003c/sub\u003e using Tecan microplate reader (Tecan Infinite M200). Another 100 \u0026micro;l culture from every well was collected, centrifuged at 15,000 rpm, the supernatant was collected and immediately frozen.\u003c/p\u003e \u003cp\u003eSupernatant were used to measure acetate concentrations using Acetate assay kit (Megazyme Acetic Acid Assay Kit). The slope of the plot of acetate concentrations versus OD\u003csub\u003e600\u003c/sub\u003e for all replicates (multiplied with the measured growth rate) was used to determine the acetate secretion rate.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eOGo and US acknowledge support by Marie Skłodowska-Curie Actions ITN \u0026ldquo;SynCrop\u0026rdquo; (grant agreement no. 764591). Figures were generated using Biorender. We would like to extend our gratitude to Hidde de Jong for insightful discussions and valuable feedback.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eStocker R. 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When a single nutrient source is available, the produced biomass increases linearly with the initial amount of the available nutrient. This linear trend can be predicted to high accuracy by “black box models” that consider growth as a single chemical reaction with nutrients as substrates and biomass as a product. Since natural environments typically feature multiple nutrients, we extended the black box framework to include catabolism, anabolism, and biosynthesis of biomass precursors to quantify co-utilization of multiple nutrients on microbial biomass production. The model differentiates between different types of nutrients: degradable nutrients that first must be catabolized before they can be used from non-degradable nutrients that can only be used as a biomass precursor. Experimentally, we demonstrated that contradictory to the model predictions, there is a mutual effect between different nutrients on \u003cem\u003eEscherichia coli’s\u003c/em\u003e nutrient utilization, where the ability to utilize one is affected by the other; i.e., for some combinations the produced biomass was no longer linear to the initial amount of nutrients. To capture such mutual effects with a black box model, we phenomenologically added an interaction between the metabolic processes used in utilizing the nutrient sources. The phenomenological model qualitatively captures the experimental observations and, unexpectedly, predicts that the produced biomass does not only depend on the combination of nutrient sources but also on their relative initial amounts – a prediction we validated experimentally. Moreover, the model predicts which metabolic processes – catabolism, anabolism, or precursor biosynthesis – is affected in each nutrient combination.\u003c/p\u003e","manuscriptTitle":"Overall biomass yield on multiple nutrient sources","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-12 15:01:01","doi":"10.21203/rs.3.rs-4219475/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"revise","date":"2024-06-18T09:06:02+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-05-08T21:42:31+00:00","index":3,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-05-08T16:06:23+00:00","index":1,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-05-08T03:47:14+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-04-29T00:48:44+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-04-22T16:12:28+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2024-04-09T16:08:06+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-04-05T09:17:36+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-04T18:57:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Systems Biology and Applications","date":"2024-04-04T18:57:54+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-systems-biology-and-applications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjsba","sideBox":"Learn more about [npj Systems Biology and Applications](http://www.nature.com/npjsba/)","snPcode":"41540","submissionUrl":"https://submission.springernature.com/new-submission/41540/3","title":"npj Systems Biology and Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"aee248c6-009f-4467-aafb-e680f6111e18","owner":[],"postedDate":"April 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":30470652,"name":"Biological sciences/Systems biology/Biochemical networks"},{"id":30470653,"name":"Biological sciences/Systems biology/Bioenergetics"},{"id":30470654,"name":"Biological sciences/Systems biology/Dynamical systems"},{"id":30470655,"name":"Biological sciences/Systems biology/Systems analysis"},{"id":30470656,"name":"Biological sciences/Biophysics/Bioenergetics"}],"tags":[],"updatedAt":"2025-02-11T08:11:23+00:00","versionOfRecord":{"articleIdentity":"rs-4219475","link":"https://doi.org/10.1038/s41540-025-00497-y","journal":{"identity":"npj-systems-biology-and-applications","isVorOnly":false,"title":"npj Systems Biology and Applications"},"publishedOn":"2025-02-10 05:00:00","publishedOnDateReadable":"February 10th, 2025"},"versionCreatedAt":"2024-04-12 15:01:01","video":"","vorDoi":"10.1038/s41540-025-00497-y","vorDoiUrl":"https://doi.org/10.1038/s41540-025-00497-y","workflowStages":[]},"version":"v1","identity":"rs-4219475","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4219475","identity":"rs-4219475","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}