Coarse-Grained Resource Allocation Modeling for Decoding and Rewiring Microbial Metabolism

Empirical characterization of coarse-grained proteome sectors in rapid growth

Proteins can be viewed as cellular workers that support a wide range of functions, including nutrient transport, metabolic reactions, translational processes, and structural maintenance. At the same time, proteins could take up more than 55% of the cellular biomass in certain microbes, consuming a significant fraction of cellular precursor resources [19]. Examining their distribution therefore provides insight into investment strategies of cellular resource. Using database-based annotations of protein function, the proteome can be divided into coarse-grained sectors [20]. In this way, coarse-grained modeling begins by grouping proteins according to their functional roles, providing a generic view of the cell (Figure 1a).

Early work by Scott et al. demonstrated that during exponential or balanced growth in Escherichia coli, the proteome can be organized into three major sectors that show distinct relationships to the growth rate (Figure 1b) [21]. The ribosomal sector R, which drives protein synthesis, increases linearly with growth rate. The metabolic sector E, composed of enzymes for nutrient uptake and metabolic reactions, decreases as growth increases. The housekeeping sector Z remains relatively constant across growth conditions. Under coarse-grained descriptions, nutrients are brought into the cell through the E sector and converted into amino acids, which are then consumed by the R sector to build proteins (Figure 1b, left). The balance between the R and E sectors determines the size of the amino acid pool and sets the cellular growth rate. This linear relationship has since been observed in other bacterial species [22, 23] and in yeast [24, 25]. Under conditions defined by different nutrient sources, the proteome can be further partitioned into finer sectors while still preserving linear scaling relationships [26]. Additional partitions may include the sector for cell division, which links cell size to growth rate [27], and the sector associated with chaperone activity and contributing to temperature stress responses [28]. Together, these observations relate proteome allocation to growth maintenance and physiological balance across diverse settings.

The relationship between the R and E sectors suggests that their balance plays a central role in setting the growth rate of E. coli, raising key questions about how this balance is regulated. Scott et al. investigated this by examining amino acid homeostasis, focusing on how the supply and consumption of amino acids control proteome partitioning [54]. Their modeling framework assumed that amino acids regulate the two fluxes in opposite directions: accumulating amino acids inhibit the E sector, whereas high amino acid levels stimulate the R sector, described using Hill type functions. They found that the regulation ensures the buffering range of the amino acid pool and helps maintain stable R and E fractions under fluctuations in amino acid availability [29]. Subsequent studies expanded this view by identifying explicit regulatory mechanisms, including allosteric inhibition within amino acid biosynthesis pathways and the actions of global signaling molecules such as ppGpp, GTP and cAMP (Figure 1c, left) [23, 29–31]. Experimental perturbations and modeling studies further showed that disrupting either amino acid mediated feedback or global signals lowers growth rate and shifts proteome allocation away from its optimal configuration (Figure 1c, right) [23, 30–34]. These analyses validate that maintaining the R–E balance is crucial for sustaining fast growth and reflects strategic adjustments in cellular investment to optimize fitness. However, determining which regulatory mechanism dominates specific environmental contexts remains an open question.

Enzyme allocation and the metabolic shift toward overflow during rapid growth

As the cellular growth rate increases, many organisms begin to release carbon resources rather than convert them into biomass. This overflow behavior has been observed in E. coli producing acetate [35], in S. cerevisiae producing ethanol (the Crabtree effect) [36, 37], and in tumor cell lines producing lactate (the Warburg effect) [38]. These carbon outfluxes appear as byproducts of fermentation, raising a central question: why do fast growing cells engage in fermentation rather than respiration, even though fermentation yields less ATP per molecule of substrate? This phenomenon is counterintuitive, as it suggests that cells favor a seemingly wasteful strategy at conditions of high nutrient availability.

To understand this strategy, researchers have examined how cells allocate metabolic enzymes that generate ATP and how these pathways are regulated. As illustrated in Figure 1d, the coarse-grained E sector can be subdivided into finer sectors associated with respiration, fermentation, transport, and anabolic reactions [24, 25, 35, 39, 40]. These modeling frameworks enable investigation of the allocation between respiratory and fermentative pathways. As growth rate increases, cells require more ribosomes to support rapid protein synthesis, yet translation itself demands substantial ATP [39]. As noted earlier, there is a trade-off between R and E sectors, where faster growth reduces the proteome fraction allocated to the E sector. Basan et al. showed that when the E sector becomes limited while ATP demand continues to rise, the cell shifts toward fermentation because it generates ATP at a faster rate and requires fewer portion of enzymes than respiration [35]. Subsequent studies demonstrated that this proteome efficiency principle holds for E. coli, S. cerevisiae, and mammalian cells [37, 41]. Beyond proteome constraints, studies have also identified physical limitations, such as membrane capacity and cytosolic space, as additional contributors to the shift toward overflow metabolism [24, 42].

These frameworks also explain why overflow becomes more pronounced under engineering or stress conditions. The production of nonfunctional or recombinant proteins increases proteome burden and accelerates overflow [16, 35, 43]. Under nitrogen limitation, ATP is wasted through the ammonium futile cycle, and amino acid scarcity restricts protein production, which further intensifies overflow [44, 45]. In addition, by incorporating nutrient uptake kinetics and protein biosynthesis dynamics into coarse-grained models, recent studies have captured the onset of overflow across diverse conditions, identifying critical resource thresholds that drive cells toward fermentative strategies as growth pressure increases [24, 25, 45–47].

Ribosome activity control governs transitions from slow to fast growth

So far, our discussion has focused on the fast growth regime, where the proteome displays a clear linear relationship between the R sector and the growth rate. However, more recent reports show that this relationship breaks down at slower growth rates in E. coli. Studies have shown that in the slow growth regime, the R sector converges to a minimal basal level, and its abundance no longer scales with growth as it does under fast growth conditions (Figure 1b, right) [48, 49]. This suggests that ribosome abundance is not allocated to support maximal growth in this regime. Instead, ribosomes transition from abundance control to activity control: while roughly 80% of ribosomes are active during fast growth, only about 20% are active during slow growth (Figure 1f) [48]. This shift overturns the long-standing assumption that growth rate is determined primarily by the amount of ribosomes [21]. It also raises a key question: why would cells adopt an apparently suboptimal allocation strategy in which they maintain ribosome overcapacity rather than adjust abundance to match slow growth demands?

A compelling explanation for the shift from abundance control to activity control lies in the timing of regulatory responses. Activity regulation allows rapid adjustment through allosteric mechanisms or post-translational modifications, whereas altering ribosome abundance requires the much slower processes of transcription and translation [50]. Slow growth conditions can be represented by nutrient-stressed environments, and transitions to richer media can be viewed as nutrient upshifts (Figure 1g) [49, 51]. Cells that maintain ribosome overcapacity respond more rapidly when nutrients improve and achieve substantially higher post-shift growth rates than cells that lack this spare ribosomal pool [49], reflecting a fundamental tradeoff between maximizing current growth and enabling rapid recovery [51, 52]. Thus, what appears to be a suboptimal proteome allocation is instead an adaptive strategy. By prioritizing rapid responsiveness through activity control, cells position themselves to exploit sudden improvements in nutrient availability during nutrient stressed conditions.

A deeper understanding of this adaptive strategy requires examining how ribosome activity is regulated at the molecular level. Recent modeling frameworks have incorporated detailed regulatory pathways for this effort, and their framework successfully captured changes in ribosome abundance and activity across growth rates [25, 32, 53–55]. As illustrated in Figure 1f, ribosomes can be categorized into three functional states: free ribosomes not yet assembled into translating complexes; active ribosomes bound to mRNA and incorporating aminoacyl-tRNAs during peptide elongation; and inactive or stalled ribosomes associated with uncharged tRNAs. Calabrese et al. further showed that protein degradation mediated by non-translating ribosomes, which is typically neglected and considered much slower compared to the timescale of cellular growth rate in fast growth regime, becomes non-negligible in slow growth regime [54]. Knowing that the distribution among ribosomes states is governed by the relative levels of charged and uncharged tRNAs, this directly links ribosome activity back to amino acid availability and metabolic regulations [32, 55, 56]. Collectively, these modeling efforts reveal how molecular regulation of ribosome activity links metabolic state to growth controls.

Recent work further suggests that the dominant regulatory strategy depends on both environmental conditions and bacterial species. Although nutrient limitations induce similar patterns of proteome reallocation, responses to antibiotic stress differ markedly across bacterial species. During antibiotic stress, E. coli primarily adapts through proteome reallocation, whereas Bacillus subtilis relies predominantly on allosteric regulation to modulate metabolic activity while maintaining a relatively constant proteome composition [23]. Rather than maximizing growth, the regulatory strategy adopted by B. subtilis prioritizes physiological adaptability, resulting in a suboptimal proteome allocation. These findings indicate that bacteria have evolved distinct strategies between proteome abundance and activity control, reflecting adaptations to their specific ecological and physiological niches.

Multi-layer regulation strategies for cellular adaptation in fluctuating environments

To integrate observations across fast-growth, slow-growth, and transitional regimes, recent coarse-grained modeling frameworks are developed to capture regulatory dynamics during environmental shifts [25, 32, 45, 55–59]. Feast-and-famine experiments are further applied to elucidate how cells dynamically adapt to fluctuating nutrient environments (Figure 1g) [32, 56, 60, 61]. During feast and famine cycles, cells repeatedly experience nutrient upshifts and downshifts. Unlike nutrient upshift, nutrient downshifts such as transitions to poorer amino acids or carbon diauxic shifts typically induce a pronounced lag phase [62–64]. This lag reflects the time required for cells to rebuild depleted metabolite pools and reconfigure central metabolic pathways to sustain growth [25, 60, 65]. Similar to the trade-off observed during nutrient upshifts between pre-shift growth rate and post-shift performance, nutrient downshifts also reveal a trade-off in which faster pre-shift growth comes at the cost of slower adaptation to nutrient decline [63, 65]. Schink et al. demonstrated this trade-off in carbon diauxie, where modeling analysis shows that E. coli and Pseudomonas aeruginosa adopt distinct proteome strategies during the switch between glycolysis and gluconeogenesis; reducing lag time for either strain requires futile cycling of carbon and ATP, lowering steady-state efficiency [65]. Moreover, pre-exposure to less favorable environments in the feast-and-famine cycle reduces lag times, and the findings lie in the slow dynamics of the proteome reallocation, which can be manifested as a form of cellular memory [25, 60].

Building on these observations, modeling efforts increasingly converge with concepts from control theory, which offers another perspective for interpreting cellular decision-making strategies under fluctuating conditions [66]. Within this view, regulatory strategies such as amino acid mediated feedforward control [29], ppGpp-based feedback control [56], ultrasensitive regulatory responses [33, 56], metabolite buffering [29, 67] can be understood as components of coordinated control architectures. Control theoretic formulations further recast growth transitions as optimal control problems. Due to the separation of timescales between ribosome synthesis and ppGpp signaling, the ppGpp response during nutrient shifts can resemble a bang-bang control strategy, switching abruptly between regulatory states to optimize biomass accumulation under changing environments [56, 58, 61]. In this perspective, cellular regulatory networks function as control systems to dynamically optimize growth across changing nutrient conditions.

Heterologous gene expression imposes metabolic burden on host cell

In synthetic biology, microbes are often programmed to give rise to new functions with the introduction of exogeneous genes. These synthetic genes encode desired functions that redirect cellular resources toward the production of target bioproducts. Inevitably, heterologous gene expression imposes a metabolic load on the host, as cellular resources must be diverted to synthesize nonnative proteins and products (Figure 2a). In this section, we review modeling efforts that elucidate how cells adapt to heterologous gene expression and enable quantitative assessment of synthetic gene performance under diverse environmental conditions.

Early quantitative studies showed that expression of nonfunctional proteins leads to an approximately linear decrease in growth rate, as demonstrated by Scott et al. using a coarse-grained framework in which heterologous proteins are treated as an additional proteome sector, denoted as the H sector (Figure 2b) [21]. Subsequent work extended this view through minimal mechanistic models that explicitly couple precursor pools and protein synthesis, thereby inferring how cellular resources are allocated during heterologous gene expression [27, 55]. This diversion of resources leads to a reduction in growth and is commonly referred to as metabolic burden. More detailed models revealed that metabolic burden arises from competition for shared transcriptional and translational machinery, including RNA polymerase and ribosomes [68, 69], as well as from depletion of precursor pools such as amino acids, the energy carrier ATP, and membrane capacity [10, 70]. Notably, protein translation alone consumes roughly half of the cellular energy budget [71]. Together, these studies establish metabolic burden as an emergent consequence of constrained cellular resources.

Circuit-induced burden induces emergent behavior in circuit performances

In addition to competing with native cellular processes, heterologous genes also compete with one another for limited resources. This competition induces tradeoffs among introduced genes, which can be captured by isocost relationships that define feasible design spaces for synthetic outcomes (Figure 2c). These tradeoffs depend on plasmid copy number, promoter strength, and ribosome binding site (RBS) strength, highlighting the combined roles of transcriptional and translational resource allocation in shaping heterologous gene expression [68, 71–73].

Circuit-induced burden can further give rise to unexpected dynamical behaviors that deviate from design expectations. For example, noncooperative positive-feedback circuits that are designed to be monostable can exhibit emergent bistability when circuit activation slows host growth (Figure 2d, left) [74, 75]. Similarly, circuit loading is also reported to reshape both the multistability regimes and steady-state expression levels of genetic toggle switches (Figure 2d, right) [74]. Subsequent analyses demonstrated that tuning ribosome binding site (RBS) strength strongly modifies the phase diagrams of toggle switches and repressilator circuits by modulating translational load [69, 76]. Resource competition also constrains the behavior of larger circuit architectures. In cascades of coupled self-activating bistable modules designed to drive sequential transitions, activation of one module can dominate others under limited resource availability, leading to winner-takes-all behavior rather than the intended sequential switching [77].

Host-mediated growth dilution feedback shapes synthetic circuit dynamics

In parallel, host cell growth imposes an implicit negative effect on synthetic circuits through growth mediated dilution of molecular species. Growth dependent changes in global cellular parameters, including ribosome and RNA polymerase abundance as well as cell volume, reduce the effective concentration of constitutively expressed proteins at higher growth rates [78]. Consequently, growth rate has been shown to reshape the bistable regimes of autoactivators and toggle switches by shifting stability boundaries and switching [78–80], and under certain conditions can also give rise to higher order multistability [81]. Because the host supplies resources to circuits while simultaneously diluting circuit components, and because circuit genes compete with each other while collectively imposing burden on the host, circuit behavior emerges from the balance between these opposing effects. Quantitative studies that explicitly disentangled growth dilution from resource loading demonstrated that both mechanisms jointly shape toggle switch dynamics [82]. Related work on cascaded bistable systems further revealed that growth mediated dilution can induce cooperative behavior between competing genes [83].

Since growth rate is tightly coupled to environmental conditions, external perturbations such as nutrient availability and stress also modulate circuit performance. For example, nutrient shifts can reshape toggle switch protein dynamics (Figure 2e) [84], whereas nutrient dependent growth feedback may induce damped oscillations in genetic circuits [85]. Together, these results show that circuit function cannot be decoupled from host physiology or environmental context, and that quantitative modeling frameworks are essential for elucidating how growth, circuit load, and environmental conditions jointly determine synthetic circuit dynamics. Starting from mRNA synthesis, recent mechanistic frameworks simulate whole-cell gene expression [69, 76, 86], and further account for global regulatory feedback, including ppGpp mediated growth control [74], to capture heterologous gene expression across growth conditions.

Design strategies for mitigating circuit-host coupling

Mitigating burden and decoupling synthetic circuits from host physiology has become a central focus in gene circuit design. Several review studies have focused on design principles to address this challenge. Borkowski et al. analyzed cellular capacity limitations and proposed burden monitoring strategies to quantify and manage resource usage [70]. Subsequent work emphasized the incorporation of feedback and feedforward control architectures to regulate circuit behavior and maintain stable function across conditions [80, 87, 88]. Dynamic controllers are particularly important because they enable automatic regulation and enhance robustness to growth fluctuations [87, 88]. These strategies include global control approaches that target shared cellular resources, such as orthogonal ribosomes or ribosome binding site designs (Figure 2f), as well as local control schemes that directly regulate expression of the gene of interest to prevent overexpression and minimize growth inhibition (Figure 2g) [80, 87, 88].

Modeling frameworks provide a powerful platform for integrating and evaluating the design rationale of control strategies. For example, Sechkar et al. used coarse-grained models to explore the parameter space of integral controllers that locally regulate gene expression across nutrient variations [89]. As circuit architectures expand to include multiple functional modules, they impose greater burdens due to increased resource competition and regulatory complexity [77]. Building on this, Chakravarty et al. systematically compared the performance of local and global control strategies in regulating multi-module circuit designs [90]. Beyond controller-based approaches, an alternative strategy is to distribute complex circuit functions across multiple host strains (Figure 2h), thereby reducing gene–gene competition within a single cell [77, 80]. While this division-of-labor approach can substantially alleviate burden, it requires reliable intercellular communication, often mediated by quorum-sensing systems, making circuit performance sensitive to signaling efficiency and population-level coordination [91]. Complementary to burden mitigation, recent studies also sought to minimize the impact of host growth on circuit dynamics by engineering growth-robust circuit architectures. These approaches include stabilizing circuit expression through repressive regulatory designs [92] and buffering transcription factor concentrations via phase separation [93, 117], both of which reduce the impact of growth-mediated dilution and improve circuit robustness across changing physiological conditions.