Editor's evaluation: An optimal regulation of fluxes dictates microbial growth in and out of steady state

Abstract

Article Figures and data Abstract Editor's evaluation Introduction Discussion Methods Appendix 1 Data availability References Decision letter Author response Article and author information Metrics Abstract Effective coordination of cellular processes is critical to ensure the competitive growth of microbial organisms. Pivotal to this coordination is the appropriate partitioning of cellular resources between protein synthesis via translation and the metabolism needed to sustain it. Here, we extend a low-dimensional allocation model to describe the dynamic regulation of this resource partitioning. At the core of this regulation is the optimal coordination of metabolic and translational fluxes, mechanistically achieved via the perception of charged- and uncharged-tRNA turnover. An extensive comparison with ≈ 60 data sets from Escherichia coli establishes this regulatory mechanism’s biological veracity and demonstrates that a remarkably wide range of growth phenomena in and out of steady state can be predicted with quantitative accuracy. This predictive power, achieved with only a few biological parameters, cements the preeminent importance of optimal flux regulation across conditions and establishes low-dimensional allocation models as an ideal physiological framework to interrogate the dynamics of growth, competition, and adaptation in complex and ever-changing environments. Editor's evaluation This valuable study provides a synthesis of sector models for cellular resource partitioning in microbes and shows how a simple flux balance model can quantitatively explain growth phenomena from numerous published experimental data sets. The evidence is convincing, and the study should be of interest to the microbial physiology community. https://doi.org/10.7554/eLife.84878.sa0 Decision letter Reviews on Sciety eLife's review process Introduction Growth and reproduction is central to life. This is particularly true of microbial organisms where the ability to quickly accumulate biomass is critical for competition in ecologically diverse habitats. Understanding which cellular processes are key in defining growth has thus become a fundamental goal in the field of microbiology. Pioneering physiological and metabolic studies throughout the 20th century laid the groundwork needed to answer this question (Monod, 1935; Monod, 1937; Monod, 1941; Monod, 1947; Monod, 1966; Campbell, 1957; Schaechter et al., 1958; Kjeldgaard et al., 1958; Cooper and Helmstetter, 1968; Donachie et al., 1976; Jun et al., 2018), with the extensive characterization of cellular composition across growth conditions at both the elemental (Heldal et al., 1985; Loferer-Krößbacher et al., 1998; Lawford and Rousseau, 1996) and molecular (Schaechter et al., 1958; Kjeldgaard et al., 1958; Watson, 1976; Britten and Mcclure, 1962) levels showing that the dry mass of microbial cells is primarily composed of proteins and RNA. Seminal studies further revealed that the cellular RNA content is strongly correlated with the growth rate (Schaechter et al., 1958; Kjeldgaard et al., 1958; Gausing, 1977), an observation which has held for many microbial species (Karpinets et al., 2006). As the majority of RNAs are ribosomal, these observations suggested that protein synthesis via ribosomes is a major determinant of biomass accumulation in nutrient replete conditions (Koch, 1988; Hernandez and Bremer, 1993; Magasanik et al., 1959). Given that the cellular processes involved in biosynthesis, particularly those of protein synthesis, are well conserved between species and domains (Doris et al., 2015; Davidovich et al., 2009; Bruell et al., 2008), these findings have inspired hope that fundamental principles of microbial growth can be found despite the enormous diversity of microbial species and the variety of habitats they occupy. The past decade has seen a flurry of experimental studies further establishing the importance of protein synthesis in defining growth. Approaches include modern ‘-omics’ techniques with molecular-level resolution (Taniguchi et al., 2010; Bennett et al., 2009; Schmidt et al., 2016; Valgepea et al., 2013; Peebo et al., 2015; Li et al., 2014; Balakrishnan et al., 2021b; Mori et al., 2021; Belliveau et al., 2021; Metzl-Raz et al., 2017; Paulo et al., 2015; Paulo et al., 2016; Xia et al., 2021; Jahn et al., 2018), measurements of many core physiological processes and their coordination (Dai et al., 2016; Basan et al., 2015; You et al., 2013; Wu et al., 2022; Di Bartolomeo et al., 2020; Li et al., 2018; Jahn et al., 2018; Zavřel et al., 2019; Parker et al., 2020), and the perturbation of major cellular processes like translation (Scott et al., 2010; Hui et al., 2015; Dai et al., 2016; Towbin et al., 2017). Together, these studies advanced a more thorough description of how cells allocate their ribosomes to the synthesis of different proteins depending on their metabolic state and the environmental conditions they encounter, called ribosomal allocation. Tied to the experimental studies, different theoretical ribosomal allocation models have further been formulated to dissect how ribosomal allocation influences growth (Molenaar et al., 2009; Karr et al., 2012; Scott et al., 2014; Weiße et al., 2015; Maitra and Dill, 2015; Giordano et al., 2016; Mori et al., 2017; Erickson et al., 2017; Towbin et al., 2017; Mori et al., 2017; Korem Kohanim et al., 2018; Macklin et al., 2020; Hu et al., 2020; Dourado and Lercher, 2020; Roy et al., 2021; Mori et al., 2021; Serbanescu et al., 2020; Balakrishnan et al., 2021a; Balakrishnan et al., 2021b). For example, high-dimensional models have been formulated which simulate hundreds to thousands of biological reactions (Karr et al., 2012; Macklin et al., 2020) providing a detailed view of the emergence of distinct internal physiological states and the underlying processes which sustain them. Alternatively, other theoretical considerations follow coarse-grained approaches of moderate dimensionality which group different classes metabolic reactions together and mathematizicing their dynamics (Roy et al., 2021; Hu et al., 2020). Distinct from these is an array of extremely low-dimensional models, pioneered by Molenaar et al., 2009, which have been developed to describe growth phenomena in varied conditions and physiological limits that rely on only a few parameters (Molenaar et al., 2009; Scott et al., 2014; Bosdriesz et al., 2015; Giordano et al., 2016; Towbin et al., 2017; Korem Kohanim et al., 2018; Erickson et al., 2017; Mairet et al., 2021; Balakrishnan et al., 2021a) (a more detailed overview of the different modeling approaches is provided in Appendix 1 - Allocation models to study microbial growth). In this work, we build on low-dimensional allocation models (Scott et al., 2014; Giordano et al., 2016; Bosdriesz et al., 2015; Dourado and Lercher, 2020; Hu et al., 2020) and the results from dozens of experimental studies to synthesize a self-consistent and quantitatively predictive description of resource allocation and growth. At the core of our model is the dynamic reallocation of resources between the translational and metabolic machinery, which is sensitive to the metabolic state of the cell. We demonstrate how ‘optimal allocation’—meaning an allocation towards ribosomes which contextually maximizes the steady-state growth rate—emerges when the flux of amino acids through translation to generate new proteins and the flux of uncharged-tRNA through metabolism to provide charged-tRNA required for translation are mutually maximized, given the environmental conditions and corresponding physiological constraints. This regulatory scheme, which we term flux-parity regulation, can be mechanistically achieved by a global regulator (e.g., guanosine tetraphosphate, ppGpp, in bacteria) capable of simultaneously measuring the turnover of charged- and uncharged-tRNA pools and routing protein synthesis. The explanatory power of the flux-parity regulation circuit is confirmed by extensive comparison of model predictions with ≈ 60 data sets from Escherichia coli, spanning more than half a century of studies using varied methodologies. This comparison demonstrates that a simple argument of flux-sensitive regulation is sufficient to predict bacterial growth phenomena in and out of steady state and across diverse physiological perturbations. The accuracy of the predictions, coupled with the minimalism of the model, establishes the optimal regulation and cements the centrality of protein synthesis in defining microbial growth. The mechanistic nature of the theory—predicated on a minimal set of biologically meaningful parameters—provides a low-dimensional framework that can be used to explore complex phenomena at the intersection of physiology, ecology, and evolution without requiring extensive characterization of the myriad biochemical processes which drive them. A simple allocation model describes translation-limited growth We begin by formulating a simplified model of growth which follows the flow of mass from nutrients in the environment to biomass by building upon and extending the general logic of low-dimensional resource allocation models (Molenaar et al., 2009; Scott et al., 2010; Scott et al., 2014; Dai et al., 2016; Giordano et al., 2016). Specifically, we focus on the accumulation of protein biomass, as protein constitutes the majority of microbial dry mass (Churchward et al., 1982; Feijó Delgado et al., 2013) and peptide bond formation commonly accounts for ≈80% of the cellular energy budget (Stouthamer, 1973; Belliveau et al., 2021). Furthermore, low-dimensional allocation models utilize a simplified representation of the proteome where proteins can be categorized into only a few functional classes (Molenaar et al., 2009; Scott et al., 2014; Hui et al., 2015; Maitra and Dill, 2015; Dourado and Lercher, 2020). In this work, we consider proteins to be either ribosomal (i.e., a structural component of the ribosome, excluding ternary complex members like EF-Tu), metabolic (i.e., enzymes catalyzing synthesis of charged-tRNA molecules from environmental nutrients), or being involved in all other biological processes (e.g., lipid synthesis, DNA replication, energy generation, and chemotaxis) Molenaar et al., 2009; Scott et al., 2010; Scott et al., 2014; Hui et al., 2015; Figure 1—figure supplement 1; in Appendix 1 What makes the fraction of ‘other’ proteins?, we outline in more detail how individual protein species are partitioned between the ‘metabolic’ and ‘other’ sectors depending on their functional annotations. Simple allocation models further do not distinguish between different cells but only consider the overall turnover of nutrients and biomass. To this end, we explicitly consider a well-mixed batch culture growth as reference scenario where the nutrients are considered to be in abundance. This low-dimensional view of living matter may at first seem like an unfair approximation, ignoring the decades of work interrogating the multitudinous biochemical and biophysical processes of cell-homeostasis and growth (Macklin et al., 2020; Karr et al., 2012; Hui et al., 2015; Grigaitis et al., 2021; Noree et al., 2019). However, at least in nutrient replete conditions, many of these processes appear not to impose a fundamental limit on the rate of growth in the manner that protein synthesis does (Belliveau et al., 2021). In Appendix 1 The major simplifications of low-dimensional allocation models and why they might work we discuss this along with other simplifications in more detail. To understand protein synthesis and biomass growth within the low-dimensional allocation framework, consider the flux diagram (Figure 1A, Molenaar et al., 2009; Giordano et al., 2016; Belliveau et al., 2021; Balakrishnan et al., 2021b; Scott et al., 2014) showing the masses of the three protein classes, precursors which are required for protein synthesis (including charged-tRNA molecules, free amino acids, cofactors, etc.), nutrients which are required for the synthesis of precursors, and the corresponding fluxes through the key biochemical processes (arrows). This diagram emphasizes that growth is autocatalytic in that the synthesis of ribosomes is undertaken by ribosomes which imposes a strict speed limit on growth (Dill et al., 2011; Belliveau et al., 2021; Kafri et al., 2016). While this may imply that the rate of growth monotonically increases with increasing ribosome abundance, it is important to remember that metabolic proteins are needed to supply the ribosomes with the precursors needed to form peptide bonds. Herein lies the crux of ribosomal allocation models: the abundance of ribosomes is constrained by the need to synthesize other proteins and growth is a result of how new protein synthesis is partitioned between ribosomal, metabolic, and other proteins. How is this partitioning determined, and how does it affect growth? Figure 1 with 4 supplements see all Download asset Open asset A simple model of ribosomal allocation and hypothetical regulatory strategies. (A) The flow of mass through the self-replicating system. Biomolecules and biosynthetic processes are shown as gray and white boxes, respectively. Nutrients in the environment passed through cellular metabolism to produce ‘precursor’ molecules which are then consumed through the process of translation to produce new protein biomass, either as metabolic proteins (purple arrow), ribosomal proteins (gold arrow), or ‘other’ proteins (gray arrow). (B) Annotated equations of the model with key parameters highlighted in blue. An interactive figure where these equations can be numerically integrated is provided on paper website (cremerlab.github.io/flux_parity). (C) Key model parameters, their units, typical values in E. coli, and their appropriate references. This is also provided as Supplementary file 1. The steady-state values of (D) the growth rate λ and (E) the relative translation rate γ⁢(cp⁢c*)/γm⁢a⁢x, are plotted as functions of the allocation towards ribosomes for different metabolic rates (colored lines). (F) Analytical solutions for candidate scenarios for regulation of ribosomal allocation with fixed allocation, allocation to prioritize translation rate, and allocation to optimal growth rate highlighted in gray, green, and blue respectively. (G) A list of collated data sets of E. coli ribosomal allocation and translation speed measurements spanning 55 years of research. Details regarding these sources and method of data collation is provided in Supplementary file 2. A comparison of the observations with predicted growth-rate dependence of ribosomal allocation (H) and translation speeds (I) for the three allocation strategies. An interactive version of the panels allowing the free adjustment of parameters is available on the associated paper website (cremerlab.github.io/flux_parity). Figure 1—source data 1 Collated measurements of ribosomal mass fractions in E. coli. https://cdn.elifesciences.org/articles/84878/elife-84878-fig1-data1-v2.csv Download elife-84878-fig1-data1-v2.csv Figure 1—source data 2 Collated measurements of translation speeds per ribosome in E. coli. https://cdn.elifesciences.org/articles/84878/elife-84878-fig1-data2-v2.csv Download elife-84878-fig1-data2-v2.csv To answer these questions, we must understand how these different fluxes interact at a quantitative level and thus must mathematize the biology underlying the boxes and arrows in Figure 1A. Taking inspiration from previous models of allocation (Molenaar et al., 2009; Scott et al., 2010; Scott et al., 2014; Giordano et al., 2016; Dourado and Lercher, 2020), we enumerate a minimal set of coupled differential equations which captures the flow of mass through metabolism and translation (Figure 1B, with the dimensions and value ranges of the parameters listed in Figure 1C and Supplementary file 1). While we present a step-by-step introduction of this model in ‘Methods,’ we here focus on a summary of the underlying biological intuition and implications of the approach. We begin by codifying the assertion that protein synthesis is key in determining growth. The synthesis of new total protein mass M depends on the total proteinaceous mass of ribosomes MR⁢b present in the system and their corresponding average translation rate γ (Figure 1Bi). As ribosomes rely on precursors to work, it is reasonable to assert that this translation rate must be dependent on the concentration of precursors cp⁢c such that γ≡γ⁢(cp⁢c) (Scott et al., 2014; Giordano et al., 2016), for which a simple Michaelis–Menten relation is biochemically well motivated (Figure 1Bii). With changing precursor concentrations, the translation rate γ varies between a maximum value γm⁢a⁢x, representing rapid synthesis, and a minimum value γm⁢i⁢n, representing the slowest achievable translation rate. In our model, this minimum rate γm⁢i⁢n is zero and corresponds to the condition where there are no available precursors to support translation. The standing precursor concentration cp⁢c is set by a combination of processes (Figure 1Biii), namely the production of new precursors through metabolism (synthesis), their degradation through translation (consumption), and their dilution as the total cell volume grows. The synthesis is driven by the abundance of metabolic proteins MM⁢b in the system and the speed by which they convert nutrients into novel precursors. As the metabolic networks at play are complex, low-dimensional allocation models describe the process of metabolism using an average metabolic rate ν in lieu of mathematicizing the network’s individual components. As such, the metabolic rate is difficult to directly measure but generally depends on the quality and concentration of nutrients in the environment (see below, Figure 1—figure supplement 2 and ‘Methods’). In the following, we focus on a growth regime in which nutrient concentrations are saturating. In such a scenario, metabolism operates at a nutrient-specific maximal metabolic rate ν≡νm⁢a⁢x. Finally, the relative magnitude of the ribosomal, metabolic, and ‘other’ protein masses is dictated by ϕR⁢b, ϕM⁢b, and ϕO, three allocation parameters which range between zero and one to describe the fraction of ribosomes being utilized in synthesizing the corresponding protein pools. Importantly, as ribosomes only translate one protein at a time, the allocation parameters follow the constraint ϕR⁢b+ϕM⁢b+ϕO=1 (Figure 1Biv). For readers familiar with allocation models, we emphasize that we here use ϕX to denote allocation parameters rather than mass fractions, MX/M; both quantities are only equivalent in the steady-state regime. Together, the introduced equations provide a full mathematicization of the mass flow diagram shown in Figure 1A. For constant allocation parameters (ϕR⁢b*,ϕM⁢b*), a steady-state regime emerges from this system of differential equation. Particularly, the precursor concentration is stationary in time (cp⁢c=cp⁢c*), meaning the rate of synthesis is exactly equal to the rate of consumption and dilution. Furthermore, the translation rate γ⁢(cp⁢c*) is constant during steady-state growth and the mass abundances of ribosomes and metabolic proteins are equivalent to the corresponding allocation parameters, e.g. MR⁢bM≡ϕR⁢b*. As a consequence, biomass is increasing exponentially d⁢Md⁢t=λ⁢M, with the growth rate λ=γ⁢(cp⁢c*)⁢ϕR⁢b*. The emergence of a steady state and analytical solutions describing steady growth are further discussed in Figure 1—figure supplement 2 and Figure 1—figure supplement 3. Notably, dilution is important to obtain a steady state as has been highlighted previously by Giordano et al., 2016 and Dourado and Lercher, 2020 but is often neglected (Appendix Precursors concentrations and the importance of dilution by cell growth). Figure 1D and E show how the steady-state growth rate λ and translation rate γ⁢(cp⁢c*) are dependent on the allocation towards ribosomes ϕR⁢b*. The figures also show the dependence on the metabolic rate νm⁢a⁢x which we here assert to be a proxy for the ‘quality’ of the nutrients in the environment (with increasing νm⁢a⁢x, less metabolic proteins are required to obtain the same synthesis of precursors). The non-monotonic dependence of the steady-state growth rate on the ribosome allocation and the metabolic rate poses a critical question: What biological mechanisms determine the allocation towards ribosomes in a particular environment and what criteria must be met for the allocation to ensure efficient growth? Different strategies for regulation of allocation predicts different phenomenological behavior While cells might employ many different ways to regulate allocation, we here consider three specific allocation scenarios to illustrate the importance of allocation on growth. These candidate scenarios either strictly maintain the total ribosomal content (scenario I), maintain a high rate of translation (scenario II), or optimize the steady-state growth rate (scenario III). We derive analytical solutions for these scenarios (as has been previously performed for scenario III; Giordano et al., 2016; Dourado and Lercher, 2020; Figure 1F and ‘Methods’), and ultimately compare these predictions to observations with E. coli to show this organisms’ optimal allocation of resources. The simplest and perhaps most näive regulatory scenario is one in which the allocation towards ribosomes is completely fixed and independent of the environmental conditions. This strategy (scenario I in Figure 1F, gray) represents a locked-in physiological state where a specific constant fraction of all proteins is ribosomal. This imposes a strict speed limit for growth when all ribosomes are translating close to their maximal rate, γ⁢(cp⁢c*)≈γm⁢a⁢x. If the fixed allocation is low (e.g., ϕR⁢b(I)=0.2), then this speed limit could be reached at moderate metabolic rates. A more complex regulatory scenario is one in which the allocation towards ribosomes is adjusted to prioritize the translation rate. This strategy (scenario II in Figure 1F, green) requires that the ribosomal allocation is adjusted such that a constant internal concentration of precursors cp⁢c* is maintained across environmental conditions, irrespective of the metabolic rate. In the case where this standing precursor concentration is large (cp⁢c*≫KMcp⁢c), all ribosomes will be translating close to their maximal rate. The third and final regulatory scenario is one in which the allocation towards ribosomes is adjusted such that the steady-state growth rate is maximized. The analytical solution which describes this scenario (scenario III in Figure 1F) resembles previous analytical solutions by Giordano et al., 2016; Dourado and Lercher, 2020. More illustratively, the strategy can be thought of as one in which the allocation towards ribosomes is tuned across conditions such that the observed growth rate rests at the peak of the curves in Figure 1D. Notably, this does not imply that the translation rate is constantly high across conditions (as in scenario II). Rather, the translation rate is also adjusted and approaches its maximal value γm⁢a⁢x only in very rich conditions (high metabolic rates). All allocation scenarios and their consequence on growth are discussed in further detail in Figure 1—figure supplement 4 and the corresponding interactive figure on the paper website (cremerlab.github.io/flux_parity). E. coli regulates its ribosome content to optimize growth Thus far, our modeling of microbial growth has remained ‘organism agnostic’ without pinning parameters to the specifics of any one microbe’s physiology. To probe the predictive power of this simple allocation model and test the plausibility of the three different strategies for regulation of ribosomal allocation, we performed a systematic and comprehensive survey of data from a vast array quantitative studies of the well-characterized bacterium E. coli. This analysis, consisting of 26 studies spanning 55 years of research (listed in Supplementary file 2 and as Figure 1—source data 1 and Figure 1—source data 2) using varied experimental methods, goes well beyond previous attempts to compare allocation models to data (Scott et al., 2010; Hui et al., 2015; Erickson et al., 2017; Giordano et al., 2016; Bosdriesz et al., 2015; Hu et al., 2020; Dourado and Lercher, 2020; Serbanescu et al., 2020; Hu et al., 2020; Roy et al., 2021; Maitra and Dill, 2015; Weiße et al., 2015). These data, shown in Figure 1H and I (markers), present a highly consistent view of E. coli physiology where the allocation towards ribosomes (equivalent to ribosomal mass fraction in steady-state balanced growth) and the translation rate demonstrate a strong dependence on the steady-state growth rate in different carbon sources. The pronounced correlation between the allocation towards ribosomes and the steady-state growth rate immediately rules out scenario I, where allocation is constant, as a plausible regulatory strategy used by E. coli, regardless of its precise value. Similarly, the presence of a dependence of the translation speed on the growth rate rules out scenario II, where the translation rate is prioritized across growth rates and maintained at a constant value. The observed phenomenology for both the ribosomal allocation and the translation speed is only consistent with the logic of regulatory scenario III where the allocation towards ribosomes is tuned to optimize growth rate. This logic is quantitatively confirmed when we compute the predicted dependencies of these quantities on the steady-state growth rate for the three scenarios diagrammed in Figure 1F based on literature values for key parameters (outlined in Supplementary file 1). Deviations from the prediction for scenario III are only evident for the ribosomal content at very slow steady growth (λ≤0.5 hr-1), which are hardly observed in any ecologically relevant conditions and can be attributed to additional biological and experimental factors, including protein degradation (Calabrese et al., 2021) and cultures which have not yet reached steady state, factors we discuss in Appendix 1 – Additional considerations relevant at slow growth. The inactivation of ribosomes is another such explanation, though a growth rate-independent inactive fraction is not sufficient to explain the observations, Appendix 1 —Inactive ribosomes. Importantly, the agreement between theory and observations works with a minimal number of parameters and does not require the inclusion of fitting parameters. All fixed model parameters such as the maximum translation rate γm⁢a⁢x and the Michaelis–Menten constant for translation KMcp⁢c have distinct biological meaning and can be either directly measured or inferred from data (Supplementary file 1). Furthermore, we discuss the necessity of other parameters such as the ‘other protein sector’ ϕO (Appendix 1— What makes the fraction of 'other' proteins?), its degeneracy with the maximum metabolic rate νm⁢a⁢x, and inclusion of ribosome inactivation and minimal ribosome content (Appendix 1— Inactive ribosomes). We, furthermore, provide an interactive figure on the paper website (cremerlab.github.io/flux_parity) where the parametric sensitivity of these regulatory scenarios and the agreement/disagreement with data can be directly explored. Notably there is no combination of parameter values that would allow scenario I or II to adequately describe both the ribosomal allocation and the translation speed as a function of growth rate. These findings are in line with a recent higher-dimensional modeling study (Hu et al., 2020), which, based on the optimization of a reaction network with >200 components, rationalized the variation in translation speed with growth as a manifestation of efficient protein synthesis. Together, these results confirm that scenario III can accurately describe observations over a very broad range of conditions, in strong support of the popular but often questioned presumption that E. coli optimally tunes its ribosomal content to promote fast growth (Giordano et al., 2016; Bosdriesz et al., 2015; Towbin et al., 2017). In Appendix 1 – Application of the model to Saccharomyces cerevisiae, we present a similar analysis for yeast, which, in line with previous studies (Metzl-Raz et al., 2017; Xia et al., 2021; Paulo et al., 2015; Paulo et al., 2016; Kostinski and Reuveni, 2021), suggests that this eukaryote likely follows a similar optimal allocation strategy, although data for ribosomal content and the translation rate is scarce. The strong correlation between ribosome content and growth rate has further been reported for other microbial organisms in line with an optimal allocation (Karpinets et al., 2006; Jahn et al., 2018; Zavřel et al., 2019; Jahn et al., 2021), though the absence of translation rate measurements precludes confirmation. An interesting exception is the methanogenic archaeon Methanococcus maripaludis, which appears to maintain constant allocation, in agreement with scenario I (Müller et al., 2021). The presented analysis thus suggests that E. coli and possibly many other microbes closely follow an optimal ribosome allocation behavior to support efficient growth. Moreover, the good agreement between experiments and data establishes that a simple low-dimensional allocation model can describe growth with notable quantitative accuracy. However, this begs the question: how do cells coordinate their complex machinery to ensure optimal allocation? Optimal allocation results from a mutual maximization of translational and metabolic flux To optimize the steady-state growth rate, cells must have some means of coordinating the flow of mass through metabolism and protein synthesis. In the ribosomal allocation model, this reduces to a regulatory mechanism in which the allocation paramet