- Tutorial
- Open Access
Hands-On Growth Laws Theory Cookbook
PRX Life 4, 012001 – Published 25 March, 2026
DOI: https://doi.org/10.1103/x33x-srz4
Abstract
This tutorial covers the emerging field of coarse-grained cellular growth modeling, and aims to bridge the gap between theoretical foundations and practical application. By adopting an original “cookbook” approach, it is designed to offer a hands-on guide for constructing and analyzing different key aspects of cellular growth, focusing on available results for bacteria and beyond. The tutorial is structured as a series of step-by-step “recipes,” and covers essential concepts, recent literature, and key challenges. It aims to empower a broad audience, from students to seasoned researchers, to replicate, extend, and innovate in this scientific area. Specifically, each section provides detailed, bare-bones models to start working in each area, from basic steady-state growth to variable environments and focusing on different key layers relevant to biosynthesis, transcription, translation, nutrient sensing, and protein degradation, links between cell cycle and growth, ending with ecological insights.
Physics Subject Headings (PhySH)
Article Text
References (300)
- J. Knight, Bridging the culture gap, Nature (London) 419, 244 (2002).
- W. Bialek, Perspectives on theory at the interface of physics and biology, Rep. Prog. Phys. 81, 012601 (2018).
- P. W Anderson, More is different: Broken symmetry and the nature of the hierarchical structure of science, Science 177, 393 (1972).
- S. Jun, F. Si, R. Pugatch, and M. Scott, Fundamental principles in bacterial physiology—History, recent progress, and the future with focus on cell size control: A review, Rep. Prog. Phys. 81, 056601 (2018).
- M. Scott, E. M Mateescu, Z. Zhang, and T. Hwa, Interdependence of cell growth origins and consequences, Science 330, 1099 (2010).
- M. Scott and T. Hwa, Bacterial growth laws and their applications, Curr. Opin. Biotechnol. 22, 559 (2011).
- D. Serbanescu, N. Ojkic, and S. Banerjee, Cellular resource allocation strategies for cell size and shape control in bacteria, FEBS J. 289, 7891 (2021).
- M. Scott and T. Hwa, Shaping bacterial gene expression by physiological and proteome allocation constraints, Nat. Rev. Microbiol. 21, 327 (2022).
- J. B. Deris, M. Kim, Z. Zhang, H. Okano, R. Hermsen, A. Groisman, and T. Hwa, The innate growth bistability and fitness landscapes of antibiotic-resistant bacteria, Science 342, 1237435 (2013).
- Y. Huang, A. Mukherjee, S. Schink, N. C. Benites, and M. Basan, Evolution and stability of complex microbial communities driven by trade-offs, Mol. Syst. Biol. 20, 997 (2024).
- F. J. F. Labourel, V. Daubin, Frédéric Menu, and Etienne Rajon, Proteome allocation and the evolution of metabolic cross-feeding, Evolution 78, 849 (2024).
- L. Pacciani-Mori, S. Suweis, A. Maritan, and A. Giometto, Constrained proteome allocation affects coexistence in models of competitive microbial communities, ISME J. 15, 1458 (2021).
- M. Schaechter, A brief history of bacterial growth physiology, Front. Microbiol. 6, (2015).
- F. J. Bruggeman, R. Planqué, D. Molenaar, and B. Teusink, Searching for principles of microbial physiology, FEMS Microbiol. Rev. 44, 821 (2020).
- N. M. Belliveau, G. Chure, C. L. Hueschen, H. G. Garcia, J. Kondev, D. S. Fisher, J. A. Theriot, and R. Phillips, Fundamental limits on the rate of bacterial growth and their influence on proteomic composition, Cels 12, 924 (2021).
- G. Chure and J. Cremer, An optimal regulation of fluxes dictates microbial growth in and out of steady state, eLife, 12, e84878 (2023).
- I. Golding and A. Amir, Colloquium: Gene expression in growing cells: A biophysical primer, Rev. Mod. Phys. 96, 041001 (2024).
- M. Zim, C. Euler, and M. Scott, Constraints on metabolic network analysis in bacterial physiology, PRX Life 3, 022001 (2025).
- J. Monod, Recherches Sur La Croissance Des Cultures Bactériennes, Ph.D. thesis, Hermann et Cie, Paris, 1942.
- M. Schaechter, O. MaalOe, and N. O. Kjeldgaard, Dependency on medium and temperature of cell size and chemical composition during balanced growth of Salmonella typhimurium, J. Gen. Microbiol. 19, 592 (1958).
- F. C. Neidhardt, Effects of environment on the composition of bacterial cells, Annu. Rev. Microbiol. 17, 61 (1963).
- F. C. Neidhardt and B. Magasanik, Studies on the role of ribonucleic acid in the growth of bacteria, Biochim. Biophys. Acta 42, 99 (1960).
- S. Hui, J. M. Silverman, S. S. Chen, D. W. Erickson, M. Basan, J. Wang, T. Hwa, and J. R. Williamson, Quantitative proteomic analysis reveals a simple strategy of global resource allocation in bacteria, Mol. Syst. Biol. 11, 784 (2015).
- M. Mori, Z. Zhang, A. Banaei-Esfahani, J.-B. Lalanne, H. Okano, B. C. Collins, A. Schmidt, O. T. Schubert, D.-S. Lee, G.-W. Li, R. Aebersold, T. Hwa, and C. Ludwig, From coarse to fine: The absolute Escherichia coli proteome under diverse growth conditions, Mol. Syst. Biol. 17, e9536 (2021).
- S. Klumpp, Z. Zhang, and T. Hwa, Growth rate-dependent global effects on gene expression in bacteria, Cell 139, 1366 (2009).
- S. Klumpp and T. Hwa, Bacterial growth: Global effects on gene expression, growth feedback and proteome partition, Curr. Opin. Biotechnol. 28, 96 (2014).
- P. Greulich, M. Scott, M. R Evans, and R. J Allen, Growth-dependent bacterial susceptibility to ribosome-targeting antibiotics, Mol. Syst. Biol. 11, 796 (2015).
- X. Dai, M. Zhu, M. Warren, R. Balakrishnan, V. Patsalo, H. Okano, J. R. Williamson, K. Fredrick, Y.-P. Wang, and T. Hwa, Reduction of translating ribosomes enables Escherichia coli to maintain elongation rates during slow growth, Nat. Microbiol. 2, 16231 (2016).
- D. W. Erickson, S. J. Schink, V. Patsalo, J. R. Williamson, U. Gerland, and T. Hwa, A global resource allocation strategy governs growth transition kinetics of Escherichia coli, Nature (London) 551, 119 (2017).
- C. Wu, M. Mori, M. Abele, A. Banaei-Esfahani, Z. Zhang, H. Okano, R. Aebersold, C. Ludwig, and T. Hwa, Enzyme expression kinetics by Escherichia coli during transition from rich to minimal media depends on proteome reserves, Nat. Microbiol. 8, 347 (2023).
- M. Basan, S. Hui, H. Okano, Z. Zhang, Y. Shen, J. R Williamson, and T. Hwa, Overflow metabolism in Escherichia coli results from efficient proteome allocation, Nature (London) 528, 99 (2015).
- M. Mori, C. Cheng, B. R. Taylor, H. Okano, and T. Hwa, Functional decomposition of metabolism allows a system-level quantification of fluxes and protein allocation towards specific metabolic functions, Nat. Commun. 14, 4161 (2023).
- M. Scott, S. Klumpp, E. M. Mateescu, and T. Hwa, Emergence of robust growth laws from optimal regulation of ribosome synthesis, Mol. Syst. Biol. 10, 747 (2014).
- X.-P. Hu and M. J. Lercher, An optimal growth law for RNA composition and its partial implementation through ribosomal and tRNA gene locations in bacterial genomes, PLoS Genet. 17, e1009939 (2021).
- Y. K. Kohanim, D. Levi, G. Jona, B. D. Towbin, A. Bren, and U. Alon, A bacterial growth law out of steady state, Cell Rep. 23, 2891 (2018).
- A. Bren, Y. Hart, E. Dekel, D. Koster, and U. Alon, The last generation of bacterial growth in limiting nutrient, BMC Syst. Biol. 7, 27 (2013).
- M. Kafri, E. Metzl-Raz, F. Jonas, and N. Barkai, Rethinking cell growth models, FEMS Yeast Research 16, fow081 (2016).
- E. Metzl-Raz, M. Kafri, G. Yaakov, I. Soifer, Y. Gurvich, and N. Barkai, Principles of cellular resource allocation revealed by condition-dependent proteome profiling, Elife 6, e28034 (2017).
- J. Xia, B. J. Sánchez, Y. Chen, K. Campbell, S. Kasvandik, and J. Nielsen, Proteome allocations change linearly with the specific growth rate of Saccharomyces cerevisiae under glucose limitation, Nat. Commun. 13, 2819 (2022).
- M. Mori, V. Patsalo, C. Euler, J. R. Williamson, and M. Scott, Proteome partitioning constraints in long-term laboratory evolution, Nat. Commun. 15, 4087 (2024).
- M. Zhu, M. Mori, T. Hwa, and X. Dai, Distantly related bacteria share a rigid proteome allocation strategy with flexible enzyme kinetics, Proc. Natl. Acad. Sci. USA 122, e2427091122 (2025).
- T. V. Karpinets, D. J. Greenwood, C. E. Sams, and J. T. Ammons, RNA:protein ratio of the unicellular organism as a characteristic of phosphorous and nitrogen stoichiometry and of the cellular requirement of ribosomes for protein synthesis, BMC Biol. 4, 30 (2006).
- R. E. Ecker and M. Schaechter, Ribosome content and the rate of growth of Salmonella typhimurium, Biochim. Biophys. Acta (BBA) 76, 275 (1963).
- R. J. Harvey and A. L. Koch, How partially inhibitory concentrations of chloramphenicol affect the growth of Escherichia coli, Antimicrob. Agents Chemother. 18, 323 (1980).
- R. Balakrishnan, M. Mori, I. Segota, Z. Zhang, R. Aebersold, C. Ludwig, and T. Hwa, Principles of gene regulation quantitatively connect DNA to RNA and proteins in bacteria, Science 378, eabk2066 (2022).
- F. Ceroni, A. Boo, S. Furini, T. E. Gorochowski, O. Borkowski, Y. N. Ladak, A. R. Awan, C. Gilbert, G.-B. Stan, and T. Ellis, Burden-driven feedback control of gene expression, Nat. Methods 15, 387 (2018).
- A. Ripamonti, M. Lacassin, R. Droghetti, G. Bokinsky, and M. C. Lagomarsino, Transcriptional competition biases the effects of second messengers in E. coli, bioRxiv (2025).
- A. Campbell, Synchronization of cell division, Bacteriol. Rev. 21, 263 (1957).
- H. E. Kubitschek, W. W. Baldwin, S. J. Schroeter, and R. Graetzer, Independence of buoyant cell density and growth rate in Escherichia coli, J. Bacteriol. 158, 296 (1984).
- D. Serbanescu, N. Ojkic, and S. Banerjee, Nutrient-dependent trade-offs between ribosomes and division protein synthesis control bacterial cell size and growth, Cell Rep. 32, 108183 (2020).
- D. Reyes-González, H. De Luna-Valenciano, J. Utrilla, M. Sieber, R. Peña-Miller, and A. Fuentes-Hernández, Dynamic proteome allocation regulates the profile of interaction of auxotrophic bacterial consortia, R. Soc. Open Sci. 9, 212008 (2022).
- A. Mukherjee, Y.-F. Chang, Y. Huang, N. C. Benites, L. Ammar, J. Ealy, M. Polk, and M. Basan, Plasticity of growth laws tunes resource allocation strategies in bacteria, PLoS Comput. Biol. 20, e1011735 (2024).
- P. P. Dennis and H. Bremer, Differential rate of ribosomal protein synthesis in Escherichia coli B/r, J. Mol. Biol. 84, 407 (1974).
- J. R. Warner and C. Gorenstein, Yeast has a true stringent response, Nature (London) 275, 338 (1978).
- C. You, H. Okano, S. Hui, Z. Zhang, M. Kim, C. W. Gunderson, Y.-P. Wang, P. Lenz, D. Yan, and T. Hwa, Coordination of bacterial proteome with metabolism by cyclic AMP, Nature (London) 500, 301 (2013).
- H. Bremer and P. P. Dennis, Modulation of chemical composition and other parameters of the cell at different exponential growth rates, EcoSal Plus 3 (2008).
- O. Maaløe, Biological regulation and development, in Biological Regulation and Development, edited by R. F. Goldberger (Plenum Press, New York, NY, 1979), pp. 487–542.
- E. Bosdriesz, D. Molenaar, B. Teusink, and F. J Bruggeman, How fast-growing bacteria robustly tune their ribosome concentration to approximate growth-rate maximization, FEBS J. 282, 2029 (2015).
- A. Roy, D. Goberman, and R. Pugatch, A unifying autocatalytic network-based framework for bacterial growth laws, Proc. Natl. Acad. Sci. USA 118, e2107829118 (2021).
- L. Calabrese, L. Ciandrini, and M. C. Lagomarsino, How total mRNA influences cell growth, Proc. Natl. Acad. Sci. USA 121, e2400679121 (2024).
- G.-W. Li, D. Burkhardt, C. Gross, and J. S. Weissman, Quantifying absolute protein synthesis rates reveals principles underlying allocation of cellular resources, Cell 157, 624 (2014).
- J. C. Taggart and G.-W. Li, Production of protein-complex components is stoichiometric and lacks general feedback regulation in eukaryotes, Cell Syst. 7, 580, (2018).
- Q. Zhang, E. Brambilla, R. Li, H. Shi, M. C. Lagomarsino, and B. Sclavi, A decrease in transcription capacity limits growth rate upon translation inhibition, mSystems, 5, e00575 (2020).
- M. Panlilio, J. Grilli, G. Tallarico, I. Iuliani, B. Sclavi, P. Cicuta, and M. C. Lagomarsino, Threshold accumulation of a constitutive protein explains E. coli cell-division behavior in nutrient upshifts, Proc. Natl. Acad. Sci. USA 118, e2016391118 (2021).
- I. Iuliani, G. Mbemba, M. C. Lagomarsino, and B. Sclavi, Direct single-cell observation of a key Escherichia coli cell-cycle oscillator, Sci. Adv. 10, eado5398 (2024).
- R. Schleif, Control of production of ribosomal protein, J. Mol. Biol. 27, 41 (1967).
- P. P. Dennis and H. Bremer, Macromolecular composition during steady-state growth of Escherichia coli B/r, J. Bacteriol. 119, 270 (1974).
- G. Churchward, H. Bremer, and R. Young, Macromolecular composition of bacteria, J. Theor. Biol. 94, 651 (1982).
- R. Hermsen, H. Okano, C. You, N. Werner, and T. Hwa, A growth-rate composition formula for the growth of E. coli on co-utilized carbon substrates, Mol. Syst. Biol. 11, 801 (2015).
- R. Droghetti, P. Fuchs, I. Iuliani, V. Firmano, G. Tallarico, L. Calabrese, J. Grilli, B. Sclavi, L. Ciandrini, and M. C. Lagomarsino, Incoherent feedback from coupled amino acids and ribosome pools generates damped oscillations in growing E. coli, Nat. Commun. 16, 3063 (2025).
- M. Mori, S. Schink, D. W. Erickson, U. Gerland, and T. Hwa, Quantifying the benefit of a proteome reserve in fluctuating environments, Nat. Commun. 8, 1225 (2017).
- X. Dai and M. Zhu, Coupling of ribosome synthesis and translational capacity with cell growth, Trends Biochem. Sci. 45, 681 (2020).
- L. Calabrese, J. Grilli, M. Osella, C. P. Kempes, M. C. Lagomarsino, and L. Ciandrini, Protein degradation sets the fraction of active ribosomes at vanishing growth, PLoS Comput. Biol. 18, e1010059 (2022).
- V. Cherkasov, T. Grousl, P. Theer, Y. Vainshtein, C. Gläßer, C. Mongis, G. Kramer, G. Stoecklin, M. Knop, A. Mogk, and B. Bukau, Systemic control of protein synthesis through sequestration of translation and ribosome biogenesis factors during severe heat stress, FEBS Lett. 589, 3654 (2015).
- O. Gemin, M. Gluc, H. Rosa, M. Purdy, M. Niemann, Y. Peskova, S. Mattei, and A. Jomaa, Ribosomes hibernate on mitochondria during cellular stress, Nat. Commun. 15, 8666 (2024).
- C. Wu, R. Balakrishnan, N. Braniff, M. Mori, G. Manzanarez, Z. Zhang, and T. Hwa, Cellular perception of growth rate and the mechanistic origin of bacterial growth law, Proc. Natl. Acad. Sci. USA 119, e2201585119 (2022).
- O. Borkowski, A. Goelzer, M. Schaffer, M. Calabre, U. Mäder, S. Aymerich, M. Jules, and V. Fromion, Translation elicits a growth rate-dependent, genome-wide, differential protein production in Bacillus subtilis, Mol. Syst. Biol. 12, MSB156608 (2016).
- Q. Wang and J. Lin, Heterogeneous recruitment abilities to RNA polymerases generate nonlinear scaling of gene expression with cell volume, Nat. Commun. 12, 6852 (2021).
- H. M. Salis, E. A. Mirsky, and C. A. Voigt, Automated design of synthetic ribosome binding sites to control protein expression, Nat. Biotechnol. 27, 946 (2009).
- P. Greulich, L. Ciandrini, R. J. Allen, and M. C. Romano, Mixed population of competing totally asymmetric simple exclusion processes with a shared reservoir of particles, Phys. Rev. E 85, 011142 (2012).
- C. T. MacDonald, J. H. Gibbs, and A. C. Pipkin, Kinetics of biopolymerization on nucleic acid templates, Biopolymers 6, 1 (1968).
- C. T. MacDonald and J. H. Gibbs, Concerning the kinetics of polypeptide synthesis on polyribosomes, Biopolymers 7, 707 (1969).
- T. Chou, K. Mallick, and R. K. P. Zia, Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport, Rep. Prog. Phys. 74, 116601 (2011).
- J. Szavits-Nossan, L. Ciandrini, and M. C. Romano, Deciphering mRNA sequence determinants of protein production rate, Phys. Rev. Lett. 120, 128101 (2018).
- L. B. Shaw, R. K. Zia, and K. H. Lee, Totally asymmetric exclusion process with extended objects: A model for protein synthesis, Phys. Rev. E 68, 021910 (2003).
- R. Milo, R. Phillips, and N. Orme, Cell Biology by the Numbers (Taylor & Francis Group, New York, 2016).
- B. Kavčič, G. Tkačik, and T. Bollenbach, Mechanisms of drug interactions between translation-inhibiting antibiotics, Nat. Commun. 11, 4013 (2020).
- J. Keisers, L. V. Dal Zovo, N. Kern, and L. Ciandrini, Biologically relevant finite-size effects in a driven lattice gas with particle pausing and dynamical defects, arXiv:2406.16569.
- J. Keisers, N. Kern, and L. Ciandrini, Paused in translation: A model for the transcript length-dependent impact of ribosome-targeting antibiotics, arXiv:2507.19395.
- M. Metelev, E. Lundin, I. L. Volkov, A. H. Gynnå, J. Elf, and M. Johansson, Direct measurements of mRNA translation kinetics in living cells, Nat. Commun. 13, 1852 (2022).
- J. Mäkelä, A. Papagiannakis, W.-H. Lin, M. C. Lanz, S. Glenn, M. Swaffer, G. K. Marinov, J. M. Skotheim, and C. Jacobs-Wagner, Genome concentration limits cell growth and modulates proteome composition in Escherichia coli, eLife, 13, RP97465 (2024).
- G. E. Neurohr, R. L. Terry, J. Lengefeld, M. Bonney, G. P. Brittingham, F. Moretto, T. P. Miettinen, L. P. Vaites, L. M. Soares, J. A. Paulo, J. W. Harper, S. Buratowski, S. Manalis, F. J. van Werven, L. J. Holt, and A. Amon, Excessive cell growth causes cytoplasm dilution and contributes to senescence, Cell 176, 1083 (2019).
- M. Kafri, E. Metzl-Raz, G. Jona, and N. Barkai, The cost of protein production, Cell Rep. 14, 22 (2016).
- M. P. Swaffer, G. K. Marinov, H. Zheng, L. F. Valenzuela, C. Y. Tsui, A. W. Jones, J. Greenwood, A. Kundaje, W. J. Greenleaf, R. Reyes-Lamothe, and J. M. Skotheim, RNA polymerase II dynamics and mRNA stability feedback scale mRNA amounts with cell size, Cell 186, 5254 (2023).
- J. Lin and A. Amir, Homeostasis of protein and mRNA concentrations in growing cells, Nat. Commun. 9, 4496 (2018).
- H. Chen, K. Shiroguchi, H. Ge, and X. S. Xie, Genome-wide study of mRNA degradation and transcript elongation in Escherichia coli, Mol. Syst. Biol. 11, 781 (2015).
- J. S. Edwards, R. U. Ibarra, and B. O. Palsson, In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data, Nat. Biotechnol. 19, 125 (2001).
- V. Chubukov, L. Gerosa, K. Kochanowski, and U. Sauer, Coordination of microbial metabolism, Nat. Rev. Microbiol. 12, 327 (2014).
- S. Goyal, J. Yuan, T. Chen, J. D. Rabinowitz, and N. S. Wingreen, Achieving optimal growth through product feedback inhibition in metabolism, PLoS Comput. Biol. 6, e1000802 (2010).
- The Economic Cell Collective, Economic Principles in Cell Biology (2025), https://doi.org/10.5281/zenodo.8156386.
- R. Balakrishnan, R. T. de Silva, T. Hwa, and J. Cremer, Suboptimal resource allocation in changing environments constrains response and growth in bacteria, Mol. Syst. Biol. 17, MSB202110597 (2021).
- T. W. Lo, H. J. Choi, D. Huang, and P. A. Wiggins, Noise robustness and metabolic load determine the principles of central dogma regulation, Sci. Adv. 10, eado3095 (2024).
- H. Bremer, Parameters affecting the rate of synthesis of ribosomes and RNA polymerase in bacteria, J. Theor. Biol. 53, 115 (1975).
- S. Kostinski and S. Reuveni, Ribosome composition maximizes cellular growth rates in E. coli, Phys. Rev. Lett. 125, 028103 (2020).
- S. Kostinski and S. Reuveni, Growth laws and invariants from ribosome biogenesis in lower eukarya, Phys. Rev. Res. 3, 013020 (2021).
- S. Gottesman and M. R. Maurizi, Regulation by proteolysis: Energy-dependent proteases and their targets, Microbiol. Rev. 56, 592 (1992).
- A. L. Goldberg, Degradation of abnormal proteins in Escherichia coli, Proc. Natl. Acad. Sci. USA 69, 422 (1972).
- A. L. Goldberg, Protein degradation and protection against misfolded or damaged proteins, Nature (London) 426, 895 (2003).
- S. Dukan, A. Farewell, M. Ballesteros, F. Taddei, M. Radman, and T. Nyström, Protein oxidation in response to increased transcriptional or translational errors, Proc. Natl. Acad. Sci. USA 97, 5746 (2000).
- S. Manohar, S. Jacob, J. Wang, K. A. Wiechecki, H. W. L. Koh, V. Simões, H. Choi, C. Vogel, and G. M. Silva, Polyubiquitin chains linked by lysine residue 48 (K48) selectively target oxidized proteinsin vivo, Antioxidants Redox Signaling 31, 1133 (2019).
- R. M. Vabulas, and F. U. Hartl, Protein synthesis upon acute nutrient restriction relies on proteasome function, Science 310, 1960 (2005).
- K. C. Stein and J. Frydman, The stop-and-go traffic regulating protein biogenesis: How translation kinetics controls proteostasis, J. Biol. Chem. 294, 2076 (2019).
- M. Hochstrasser, Ubiquitin, proteasomes, and the regulation of intracellular protein degradation, Curr. Opin. Cell Biol. 7, 215 (1995).
- H. Nakatogawa, K. Suzuki, Y. Kamada, and Y. Ohsumi, Dynamics and diversity in autophagy mechanisms: Lessons from yeast, Nat. Rev. Mol. Cell Biol. 10, 458 (2009).
- J. Onodera and Y. Ohsumi, Autophagy is required for maintenance of amino acid levels and protein synthesis under nitrogen starvation, J. Biol. Chem. 280, 31582 (2005).
- A. Adachi, M. Koizumi, and Y. Ohsumi, Autophagy induction under carbon starvation conditions is negatively regulated by carbon catabolite repression, J. Biol. Chem. 292, 19905 (2017).
- Arthur L. Koch, The Adaptive Responses of Escherichia coli to a Feast and Famine Existence (Elsevier, Amsterdam, 1971), pp. 147–217.
- S. H.-J. Li, Z. Li, J. O. Park, C. G. King, J. D. Rabinowitz, N. S. Wingreen, and Z. Gitai, Escherichia coli translation strategies differ across carbon, nitrogen and phosphorus limitation conditions, Nat. Microbiol. 3, 939 (2018).
- S. Gottesman, Proteases and their targets in Escherichia coli, Annu. Rev. Genet. 30, 465 (1996).
- A. L. Goldberg and J. F. Dice, Intracellular protein degradation in mammalian and bacterial cells, Annu. Rev. Biochem. 43, 835 (1974).
- M. R. Maurizi, Proteases and protein degradation in Escherichia coli, Experientia 48, 178 (1992).
- A. Maitra and K. A. Dill, Bacterial growth laws reflect the evolutionary importance of energy efficiency, Proc. Natl. Acad. Sci. USA 112, 406 (2014).
- M. Santra, D. W. Farrell, and K. A. Dill, Bacterial proteostasis balances energy and chaperone utilization efficiently, Proc. Natl. Acad. Sci. USA 114, E2654 (2017).
- K. Nath and A. L. Koch, Protein degradation in Escherichia coli. I. Measurement of rapidly and slowly decaying components, J. Biol. Chem. 245, 2889 (1970).
- M. J. Pine, Regulation of intracellular proteolysis in Escherichia coli, J. Bacteriol. 115, 107 (1973).
- R. D. Mosteller, R. V. Goldstein, and K. R. Nishimoto, Metabolism of individual proteins in exponentially growing Escherichia coli, J. Biol. Chem. 255, 2524 (1980).
- R. Christiano, N. Nagaraj, F. Fröhlich, and T. C. Walther, Global proteome turnover analyses of the yeasts S. cerevisiae and S. pombe, Cell Rep. 9, 1959 (2014).
- M. M. -Perez, and J. Villén, Determinants and regulation of protein turnover in yeast, Cell Syst. 5, 283 (2017).
- L. Calabrese, M. Cosentino Lagomarsino, and L. Ciandrini, Survey of protein degradation rates across growth conditions in E. coli and S. cerevisiae, Mendeley Data, V1 (2021), doi:10.17632/85pxpdsx38.1.
- C. Kraft, A. Deplazes, M. Sohrmann, and M. Peter, Mature ribosomes are selectively degraded upon starvation by an autophagy pathway requiring the UBP3p/BRE5p ubiquitin protease, Nat. Cell Biol. 10, 602 (2008).
- P. Sabatier, M. Lechner, U. H. Guzmán, C. M. Beusch, X. Zeng, L. Wang, F. Izaguirre, A. Seth, O. Gritsenko, S. Rodin, K.-H. Grinnemo, Z. Ye, and J. V. Olsen, Global analysis of protein turnover dynamics in single cells, Cell 188, 2433 (2025).
- B. Schwanhäusser, D. Busse, N. Li, G. Dittmar, J. Schuchhardt, J. Wolf, W. Chen, and M. Selbach, Global quantification of mammalian gene expression control, Nature (London) 473, 337 (2011).
- H. An and J. W. Harper, Systematic analysis of ribophagy in human cells reveals bystander flux during selective autophagy, Nat. Cell Biol. 20, 135 (2018).
- C. P. Kempes, L. Wang, J. P. Amend, J. Doyle, and T. Hoehler, Evolutionary tradeoffs in cellular composition across diverse bacteria, ISME J. 10, 2145 (2016).
- C. P Kempes, P. M. van Bodegom, D. Wolpert, E. Libby, J. Amend, and T. Hoehler, Drivers of bacterial maintenance and minimal energy requirements, Front. Microbiol. 8, 31 (2017) .
- C. Soubrier, E. Foxall, L. Ciandrini, and K. D. Duc, Optimal control of ribosome population for gene expression under periodic nutrient intake, J. R. Soc. Interface 21, 20230652 (2024).
- I. Shachrai, A. Zaslaver, U. Alon, and E. Dekel, Cost of unneeded proteins in E. coli is reduced after several generations in exponential growth, Mol. Cell 38, 758 (2010).
- U. Łapińska, G. Glover, P. Capilla-Lasheras, A. J. Young, and S. Pagliara, Bacterial ageing in the absence of external stressors, Philos. Trans. R. Soc. B 374, 20180442 (2019).
- E. V. Rusilowicz-Jones, S. Urbé, and M. J. Clague, Protein degradation on the global scale, Mol. Cell 82, 1414 (2022).
- A. Y. Weiße, D. A. Oyarzún, V. Danos, and P. S. Swain, Mechanistic links between cellular trade-offs, gene expression, and growth, Proc. Natl. Acad. Sci. USA 112, E1038 (2015).
- A. I. May, M. Prescott, and Y. Ohsumi, Autophagy facilitates adaptation of budding yeast to respiratory growth by recycling serine for one-carbon metabolism, Nat. Commun. 11, 5052 (2020).
- G. Micali, A. M Hockenberry, A. D. Co, and M. Ackermann, Minorities drive growth resumption in cross-feeding microbial communities, Proc. Natl. Acad. Sci. USA 120, e2301398120 (2023).
- K. Potrykus and M. Cashel, (p)ppGpp: still magical? Annu. Rev. Microbiol. 62, 35 (2008).
- M. Zhu and X. Dai, Shaping of microbial phenotypes by trade-offs, Nat. Commun. 15, 4238 (2024).
- M. Cashel and J. Gallant, Two compounds implicated in the function of the RC gene of Escherichia coli, Nature (London) 221, 838 (1969).
- M. Zhu, Y. Pan, and X. Dai, (p)ppGpp: The magic governor of bacterial growth economy, Curr. Genet. 65, 1121 (2019).
- A. G. Marr, Growth rate of Escherichia coli, Microbiol. Rev. 55, 316 (1991).
- X. Zhang, P. Dennis, M. Ehrenberg, and H. Bremer, Kinetic properties of RRN promoters in Escherichia coli, Biochimie 84, 981 (2002).
- G. C. Atkinson, T. Tenson, and V. Hauryliuk, The RelA/SpoT homolog (RSH) superfamily: Distribution and functional evolution of ppgpp synthetases and hydrolases across the tree of life, PLoS One 6, e23479 (2011).
- T. M. Wendrich, G. Blaha, D. N. Wilson, M. A. Marahiel, and K. H. Nierhaus, Dissection of the mechanism for the stringent factor RelA, Mol. Cell 10, 779 (2002).
- L. U. Magnusson, A. Farewell, and T. Nyström, ppGpp: A global regulator in Escherichia coli, Trends Microbiol. 13, 236 (2005).
- D. J. Ferullo and S. T. Lovett, The stringent response and cell cycle arrest in Escherichia coli, PLoS Genet. 4, e1000300 (2008).
- J. A. Kraemer, A. G. Sanderlin, and M. T. Laub, The stringent response inhibits DNA replication initiation in E. coli by modulating supercoiling of oriC, mBio 10, e01330 (2019).
- S. Ronneau and R. Hallez, Make and break the alarmone: Regulation of (p)ppGpp synthetase/hydrolase enzymes in bacteria, FEMS Microbiol. Rev. 43, 389 (2019).
- M. R. Paule, Transcription of ribosomal RNA genes by eukaryotic RNA polymerase I, Molecular Biology Intelligence Unit (Landes Bioscience, 1998).
- R. J. White, RNA Polymerase III Transcription (Springer, Berlin, Heidelberg, 1998).
- M. R. Paule and R. J. White, Survey and summary transcription by RNA polymerases I and III, Nucl. Acids Res. 28, 1283 (2000).
- C. M. Moehle and A. G. Hinnebusch, Association of binding sites with stringent control of ribosomal protein gene transcription in Saccharomyces cerevisiae, Mol. Cell. Biol. 11, 2723 (1991).
- Y. J. Joo, J.-H. Kim, U.-B. Kang, M.-H. Yu, and J. Kim, Gcn4p-mediated transcriptional repression of ribosomal protein genes under amino-acid starvation: Gcn4p-mediated transcriptional repression of RP genes, EMBO J. 30, 859 (2010).
- A. González, and M. N. Hall, Nutrient sensing and TOR signaling in yeast and mammals, EMBO J. 36, 397 (2017).
- D. E. Martin, A. Soulard, and M. N. Hall, Tor regulates ribosomal protein gene expression via PKA and the forkhead transcription factor FHL1, Cell 119, 969 (2004).
- H. Hu and X. Li, Transcriptional regulation in eukaryotic ribosomal protein genes, Genomics 90, 421 (2007).
- C. Mayer, J. Zhao, Xuejun Yuan, and Ingrid Grummt, mTOR-dependent activation of the transcription factor TIF-IA links rRNA synthesis to nutrient availability, Genes Dev. 18, 423 (2004).
- A. A. Mestre, P. Zhou, and J.-T. Chi, Metazoan stringent-like response mediated by MESH1 phenotypic conservation via distinct mechanisms, Comput. Struct. Biotechnol. J. 20, 2680 (2022).
- K. Inoki and K.-L. Guan, Complexity of the TOR signaling network, Trends Cell Biol. 16, 206 (2006).
- C. De Virgilio and R. Loewith, The TOR network from yeast to man, Int. J. Biochem. Cell Biol. 38, 1476 (2006).
- S. Wullschleger, R. Loewith, and M. N. Hall, TOR signaling in growth and metabolism, Cell 124, 471 (2006).
- A. G. Hinnebusch, Translational regulation of GCN4 and the general amino acid control of yeast, Annu. Rev. Microbiol. 59, 407 (2005).
- M. Zhu and X. Dai, Growth suppression by altered (p)ppGpp levels results from non-optimal resource allocation in Escherichia coli, Nucl. Acids Res. 47, 4684 (2019).
- H. Mu, F. Han, Q. Wang, Y. Wang, X. Dai, and M. Zhu, Recent functional insights into the magic role of (p)ppGpp in growth control, Comput. Struct. Biotechnol. J. 21, 168 (2023).
- M. Zhu, H. Mu, and X. Dai, Integrated control of bacterial growth and stress response by (p)ppGpp in Escherichia coli: A seesaw fashion, iScience, 27, 108818 (2024).
- K. Kochanowski, H. Okano, V. Patsalo, J. Williamson, U. Sauer, and T. Hwa, Global coordination of metabolic pathways in Escherichia coli by active and passive regulation, Mol. Syst. Biol. 17, e10064 (2021).
- E. Kussell, Phenotypic diversity, population growth, and information in fluctuating environments, Science 309, 2075 (2005).
- E. Biselli, S. J. Schink, and U. Gerland, Slower growth of Escherichia coli leads to longer survival in carbon starvation due to a decrease in the maintenance rate, Mol. Syst. Biol. 16, e9478 (2020).
- R. Droghetti, Z. Gough, H. Seyed-Allaei, S. J. Schink, and U. Gerland, Gradual entry into carbon starvation decreases the death rate of Escherichia coli, bioRxiv (2024).
- M. Basan, T. Honda, D. Christodoulou, M. Hörl, Y.-F. Chang, E. Leoncini, A. Mukherjee, H. Okano, B. R. Taylor, J. M. Silverman, C. Sanchez, J. R. Williamson, J. Paulsson, T. Hwa, and U. Sauer, A universal trade-off between growth and lag in fluctuating environments, Nature (London) 584, 470 (2020).
- N. Giordano, F. Mairet, J.-L. Gouzé, J. Geiselmann, and H. de Jong, Dynamical allocation of cellular resources as an optimal control problem: Novel insights into microbial growth strategies, PLoS Comput. Biol. 12, e1004802 (2016).
- J. Lin and A. Amir, Disentangling intrinsic and extrinsic gene expression noise in growing cells, Phys. Rev. Lett. 126, 078101 (2021).
- J. Monod, The growth of bacterial cultures, Annu. Rev. Microbiol. 3, 371 (1949).
- T. Gervais, B. Kscheschinski, M. Mell, N. Goepfert, E. van Nimwegen, and T. Julou, E. coli prepares for starvation by dramatically remodeling its proteome in the first hours after loss of nutrients, bioRxiv (2024).
- T. Julou, T. Gervais, D. de Groot, and E. van Nimwegen, Growth rate controls the sensitivity of gene regulatory circuits, Sci Adv. 11, eadu9279 (2025).
- A. Murugan, K. Husain, M. J. Rust, C. Hepler, J. Bass, J. M. J. Pietsch, P. S. Swain, S. G. Jena, J. E. Toettcher, A. K. Chakraborty, K. G. Sprenger, T. Mora, A. M. Walczak, O. Rivoire, S. Wang, K. B. Wood, A. Skanata, E. Kussell, R. Ranganathan, H.-Y. Shih, et al., Roadmap on biology in time varying environments, Phys. Biol. 18, 041502 (2021).
- O. Fridman, A. Goldberg, I. Ronin, N. Shoresh, and N. Q. Balaban, Optimization of lag time underlies antibiotic tolerance in evolved bacterial populations, Nature (London) 513, 418 (2014).
- A. P. Gasch, P. T. Spellman, C. M. Kao, O. Carmel-Harel, M. B. Eisen, G. Storz, D. Botstein, and P. O. Brown, Genomic expression programs in the response of yeast cells to environmental changes, Mol. Biol. Cell 11, 4241 (2000).
- M. Ronen and D. Botstein, Transcriptional response of steady-state yeast cultures to transient perturbations in carbon source, Proc. Natl. Acad. Sci. USA 103, 389 (2005).
- M. J. Brauer, C. Huttenhower, E. M. Airoldi, R. Rosenstein, J. C. Matese, D. Gresham, V. M. Boer, O. G. Troyanskaya, and D. Botstein, Coordination of growth rate, cell cycle, stress response, and metabolic activity in yeast, Mol. Biol. Cell 19, 352 (2008).
- C. Cadart, L. Venkova, P. Recho, M. C. Lagomarsino, and M. Piel, The physics of cell-size regulation across timescales, Nat. Phys. 15, 993 (2019).
- J. van den Berg, A. J. Boersma, and B. Poolman, Microorganisms maintain crowding homeostasis, Nat. Rev. Microbiol. 15, 309 (2017).
- G. E. Neurohr and A. Amon, Relevance and regulation of cell density, Trends Cell Biol. 30, 213 (2020).
- P. D. Odermatt, T. P. Miettinen, J. Lemière, J. H. Kang, E. Bostan, S. R. Manalis, K. C. Huang, and F. Chang, Variations of intracellular density during the cell cycle arise from tip-growth regulation in fission yeast, eLife 10, e64901 (2021).
- J. Fu, Q. Ni, Y. Wu, A. Gupta, Z. Ge, H. Yang, Y. Afrida, I. Barman, and S. X. Sun, Cells prioritize the regulation of cell mass density, Sci. Adv. 11, eadv9759 (2024).
- N. Srivastava, L. Calabrese, C. N. Plancke, R. Rollin, L. Venkova, K. Havas, M. C. Lagomarsino, and M. Piel, A dual homeostatic regulation of dry mass and volume defines a target density in proliferating mammalian cells, bioRxiv (2025).
- T. Y. Pang and M. J. Lercher, Optimal density of bacterial cells, PLoS Comput. Biol. 19, e1011177 (2023).
- X. Dai, M. Zhu, M. Warren, R. Balakrishnan, H. Okano, J. Williamson, K. Fredrick, and T. Hwa, Slowdown of translational elongation in Escherichia coli under hyperosmotic stress, mBio 9, e02375 (2018).
- M. Delarue, G. P. Brittingham, S. Pfeffer, I. V. Surovtsev, S. Pinglay, K. J. Kennedy, M. Schaffer, J. I. Gutierrez, D. Sang, G. Poterewicz, J. K. Chung, J. M. Plitzko, J. T. Groves, C. Jacobs-Wagner, B. D. Engel, and L. J. Holt, mTORC1 controls phase separation and the biophysical properties of the cytoplasm by tuning crowding, Cell 174, 338 (2018).
- M. B. Ginzberg, R. Kafri, and M. Kirschner, On being the right (cell) size, Science 348, 1245075 (2015).
- R. Rollin, J.-F. Joanny, and Pierre Sens, Physical basis of the cell size scaling laws, eLife, 12, e82490 (2023).
- D. C. Tosteson and J. F. Hoffman, Regulation of cell volume by active cation transport in high and low potassium sheep red cells, J. Gen. Physiol. 44, 169 (1960).
- A. R. Kay, How cells can control their size by pumping ions, Front. Cell Dev. Biol. 5, 41 (2017).
- J. Rodenburg, M. Dijkstra, and R. van Roij, Van'tHoff's law for active suspensions: the role of the solvent chemical potential, Soft Matter 13, 8957 (2017).
- L. Galera-Laporta, C. J. Comerci, J. Garcia-Ojalvo, and G. M. Süel, Ionobiology: The functional dynamics of the intracellular metallome, with lessons from bacteria, Cell Syst. 12, 497 (2021).
- G. Terradot, E. Krasnopeeva, P. S. Swain, and T. Pilizota, Escherichia coli maintains pH via the membrane potential, PRX Life 2, 043015 (2024).
- R. D. Requião, L. Fernandes, H. J. A. de Souza, S. Rossetto, T. Domitrovic, and F. L. Palhano, Protein charge distribution in proteomes and its impact on translation, PLoS Comput. Biol. 13, e1005549 (2017).
- C. A. Smith, Physiology of the bacterial cell. A molecular approach: By F. C. Neidhardt, J. L. Ingraham, and M. Schaechter. Pp. 507. Sinauer Associates, Sunderland, MA. 1990.43.95, Biochem. Educ. 20, 124 (1992).
- E. R. Rojas and K. C. Huang, Regulation of microbial growth by turgor pressure, Curr. Opin. Microbiol. 42, 62 (2018).
- L. M. Siqveland and S. M. Skjaeveland, Derivations of the Young-Laplace equation, Capillarity 4, 23 (2021).
- L. Venkova, A. S. Vishen, S. Lembo, N. Srivastava, B. Duchamp, A. Ruppel, A. Williart, S. Vassilopoulos, A. Deslys, J. Manuel Garcia Arcos, A. Diz-Muñoz, M. Balland, J.-F. Joanny, D. Cuvelier, P. Sens, and M. Piel, A mechano-osmotic feedback couples cell volume to the rate of cell deformation, eLife, 11, e72381 (2022).
- E. R. Oldewurtel, Y. Kitahara, and S. van Teeffelen, Robust surface-to-mass coupling and turgor-dependent cell width determine bacterial dry-mass density, Proc. Natl. Acad. Sci. USA 118, e416118 (2021).
- A. Terhorst, A. Sandikci, C. A. Whittaker, T. Szórádi, L. J. Holt, G. E. Neurohr, and A. Amon, The environmental stress response regulates ribosome content in cell cycle-arrested S. cerevisiae, Front. Cell Dev. Biol. 11, 1118766 (2023).
- N. Nordholt, J. H. van Heerden, and F. J. Bruggeman, Biphasic cell-size and growth-rate homeostasis by single Bacillus subtilis cells, Curr. Biol. 30, 2238 (2020).
- P. Kar, S. Tiruvadi-Krishnan, J. Männik, J. Männik, and A. Amir, Distinguishing different modes of growth using single-cell data, eLife, 10, e72565 (2021).
- J. J. B. Messelink, F. Meyer, M. Bramkamp, and C. P. Broedersz, Single-cell growth inference of Corynebacterium glutamicum reveals asymptotically linear growth, eLife 10, e70106 (2021).
- Y. Chen, J.-H. Huang, C. Phong, and J. E. Ferrell, Jr., Viscosity-dependent control of protein synthesis and degradation, Nat. Commun. 15, 2149 (2024).
- M. Basan, A. Mukherjee, Y. Huang, S. Oh, C. Sanchez, Y.-F. Chang, X. Liu, G. A. Bradshaw, N. C. Benites, J. Paulsson, M. W. Kirschner, Y. Sung, and J. Elgeti, Homeostasis of cytoplasmic crowding by cell wall fluidization and ribosomal counterions, https://www.biorxiv.org/content/10.1101/2023.08.31.555748v6.full.pdf
- R. Buda, Y. Liu, J. Yang, S. Hegde, K. Stevenson, F. Bai, and T. Pilizota, Dynamics of Escherichia coli's passive response to a sudden decrease in external osmolarity, Proc. Natl. Acad. Sci. USA 113, E5838 (2016).
- D. Deviri and S. A. Safran, Balance of osmotic pressures determines the nuclear-to-cytoplasmic volume ratio of the cell, Proc. Natl. Acad. Sci. USA 119, e2118301119 (2022).
- F. A. Pennacchio, A. Poli, F. M. Pramotton, S. Lavore, I. Rancati, M. Cinquanta, D. Vorselen, E. Prina, O. M. Romano, A. Ferrari, M. Piel, M. C. Lagomarsino, and P. Maiuri, N2FXm, a method for joint nuclear and cytoplasmic volume measurements, unravels the osmo-mechanical regulation of nuclear volume in mammalian cells, Nat. Commun. 15, 1070, (2024).
- A. Biswas, O. Muñoz, K. Kim, C. Hoege, B. M. Lorton, R. Nikolay, M. L. Kraushar, D. Shechter, J. Guck, V. Zaburdaev, and S. Reber, Conserved nucleocytoplasmic density homeostasis drives cellular organization across eukaryotes, Nat. Commun. 16, 7597 (2025).
- S. Klumpp, M. Scott, S. Pedersen, and T. Hwa, Molecular crowding limits translation and cell growth, Proc. Natl. Acad. Sci. USA 110, 16754 (2013).
- B. Alric, C. Formosa-Dague, E. Dague, L. J. Holt, and M. Delarue, Macromolecular crowding limits growth under pressure, Nat. Phys. 18, 411 (2022).
- K. A. Dill, K. Ghosh, and J. D. Schmit, Physical limits of cells and proteomes, Proc. Natl. Acad. Sci. USA 108, 17876 (2011).
- P. Kaldis, Quo vadis cell growth and division? Front. Cell Dev. Biol. 4, 95 (2016).
- J. Männik, C. L. Woldringh, and A. Zaritsky, Editorial: The bacterial cell: Coupling between growth, nucleoid replication, cell division, and shape Front. Microbiol. 7, 116 (2016).
- F. Bertaux, S. Marguerat, and V. Shahrezaei, Division rate, cell size and proteome allocation: Impact on gene expression noise and implications for the dynamics of genetic circuits, R. Soc. Open Sci. 5, 172234 (2018).
- J. M. Skotheim, Cell growth and cell cycle control, Mol. Biol. Cell 24, 678 (2013).
- I. Fishov, A. Zaritsky, and N. B. Grover, On microbial states of growth, Mol. Microbiol. 15, 789 (1995).
- M. Laplante and D. M. Sabatini, mTOR signaling in growth control and disease, Cell 149, 274 (2012).
- J. I. Øvrebø, Y. Ma, and B. A. Edgar, Cell growth and the cell cycle: New insights about persistent questions, BioEssays 44, 2200150 (2022).
- F. Bertaux, J. von Kügelgen, S. Marguerat, and V. Shahrezaei, A bacterial size law revealed by a coarse-grained model of cell physiology, PLoS Comput. Biol. 16, e1008245 (2020).
- P. P. Pandey, H. Singh, and S. Jain, Exponential trajectories, cell size fluctuations, and the adder property in bacteria follow from simple chemical dynamics and division control, Phys. Rev. E 101, 062406 (2020).
- M. ElGamel and A. Mugler, Effects of molecular noise on cell size control, Phys. Rev. Lett. 132, 098403 (2024).
- S. Xie, M. Swaffer, and J. M. Skotheim, Eukaryotic cell size control and its relation to biosynthesis and senescence, Annu. Rev. Cell Dev. Biol. 38, 291 (2022).
- L. K. Harris, and J. A. Theriot, Relative rates of surface and volume synthesis set bacterial cell size, Cell 165, 1479 (2016).
- A. Amir, Cell size regulation in bacteria, Phys. Rev. Lett. 112, 208102 (2014).
- M. Osella, E. Nugent, and M. C. Lagomarsino, Concerted control of Escherichia coli cell division, Proc. Natl. Acad. Sci. USA 111, 3431 (2014).
- J. Grilli, C. Cadart, G. Micali, M. Osella, and M. C. Lagomarsino, The empirical fluctuation pattern of E. coli division control, Front. Microbiol. 9, 1541 (2018).
- G. Micali, J. Grilli, J. Marchi, M. Osella, and M. C. Lagomarsino, Dissecting the control mechanisms for DNA replication and cell division in E. coli, Cell Rep. 25, 761 (2018).
- G. Micali, J. Grilli, M. Osella, and M. Cosentino Lagomarsino, Concurrent processes set E. coli cell division, Sci. Adv. 4, eaau3324 (2018).
- H. Zheng, Y. Bai, M. Jiang, T. A. Tokuyasu, X. Huang, F. Zhong, Y. Wu, X. Fu, N. Kleckner, T. Hwa, and C. Liu, General quantitative relations linking cell growth and the cell cycle in Escherichia coli, Nat. Microbiol. 5, 995 (2020).
- S. Taheri-Araghi, S. Bradde, J. T. Sauls, N. S. Hill, P. A. Levin, J. Paulsson, M. Vergassola, and S. Jun, Cell-size control and homeostasis in bacteria, Curr. Biol. 25, 385 (2015).
- P. A Fantes, W. D. Grant, R. H. Pritchard, P. E. Sudbery, and A. E. Wheals, The regulation of cell size and the control of mitosis, J. Theor. Biol. 50, 213 (1975).
- J. M. Mahaffy, and J. W. Zyskind, A model for the initiation of replication in Escherichia coli, J. Theor. Biol. 140, 453 (1989).
- W. D. Donachie and G. W. Blakely, Coupling the initiation of chromosome replication to cell size in Escherichia coli, Curr. Opin. Microbiol. 6, 146 (2003).
- M. Basan, M. Zhu, X. Dai, M. Warren, D. Sévin, Y.-P. Wang, and T. Hwa, Inflating bacterial cells by increased protein synthesis, Mol. Syst. Biol. 11, MSB156178 (2015).
- F. Si, G. Le Treut, J. T. Sauls, S. Vadia, P. A. Levin, and S. Jun, Mechanistic origin of cell-size control and homeostasis in bacteria, Curr. Biol. 29, 1760 (2019).
- N. Ojkic, D. Serbanescu, and S. Banerjee, Surface-to-volume scaling and aspect ratio preservation in rod-shaped bacteria, eLife 8, e47033 (2019).
- J. Männik, P. Kar, C. Amarasinghe, A. Amir, and J. Männik, Determining the rate-limiting processes for cell division in Escherichia coli, Nat. Commun. 15, 9948 (2024).
- G. Witz, E. van Nimwegen, and T. Julou, Initiation of chromosome replication controls both division and replication cycles in E. coli through a double-adder mechanism, eLife 8, e48063 (2019).
- C. Nieto, C. A. Vargas-García, and A. Singh, A generalized adder for cell size homeostasis: Effects on stochastic clonal proliferation, Biophys. J. 124, 1376 (2025).
- L. Susman, M. Kohram, H. Vashistha, J. T Nechleba, H. Salman, and N. Brenner, Individuality and slow dynamics in bacterial growth homeostasis, Proc. Natl. Acad. Sci. USA 115, E5679 (2018).
- A. Pavlou, E. Cinquemani, C. Pinel, N. Giordano, V. M.-G. Mathilde, I. Mihalcescu, J. Geiselmann, and H. de Jong, Single-cell data reveal heterogeneity of investment in ribosomes across a bacterial population, Nat. Commun. 16, 285 (2025).
- D. J. Kiviet, P. Nghe, N. Walker, S. Boulineau, V. Sunderlikova, and S. J. Tans, Stochasticity of metabolism and growth at the single-cell level, Nature (London) 514, 376 (2014).
- J. Grilli, M. Osella, A. S. Kennard, and M. C. Lagomarsino, Relevant parameters in models of cell division control, Phys. Rev. E 95, 032411 (2017).
- M. Wallden, D. Fange, E. G. Lundius, Ö. Baltekin, and J. Elf, The synchronization of replication and division cycles in individual E. coli cells, Cell 166, 729 (2016).
- C. Nieto, J. Arias-Castro, C. Sánchez, C. Vargas-García, and J. M. Pedraza, Unification of cell division control strategies through continuous rate models, Phys. Rev. E 101, 022401 (2020).
- C. Nieto, C. A. Vargas-García, J. M. Pedraza, and A. Singh, Mechanisms of cell size regulation in slow-growing Escherichia coli cells: Discriminating models beyond the adder, npj Syst. Biol. Appl. 10, 61 (2024).
- A. Colin, G. Micali, L. Faure, M. C. Lagomarsino, and S. van Teeffelen, Two different cell-cycle processes determine the timing of cell division in Escherichia coli, eLife 10, e67495 (2021).
- W. D. Donachie, Relationship between cell size and time of initiation of DNA replication, Nature (London) 219, 1077 (1968).
- S. Cooper, The origins and meaning of the Schaechter-Maaloe-Kjeldgaard experiments, Microbiology 139, 1117 (1993).
- H. Zheng, P.-Y. Ho, M. Jiang, B. Tang, W. Liu, D. Li, X. Yu, N. E. Kleckner, A. Amir, and C. Liu, Interrogating the Escherichia coli cell cycle by cell dimension perturbations, Proc. Natl. Acad. Sci. USA 113, 15000 (2016).
- F. Si, D. Li, S. E. Cox, J. T. Sauls, O. Azizi, C. Sou, A. B. Schwartz, M. J. Erickstad, Y. Jun, X. Li, and S. Jun, Invariance of initiation mass and predictability of cell size in Escherichia coli, Curr. Biol. 27, 1278 (2017).
- S. Tiruvadi-Krishnan, J. Männik, P. Kar, J. Lin, A. Amir, and J. Männik, Coupling between DNA replication, segregation, and the onset of constriction in Escherichia coli, Cell Rep. 38, 110539 (2022).
- S. Bakshi, E. Leoncini, C. Baker, S. J. Cañas-Duarte, B. Okumus, and J. Paulsson, Tracking bacterial lineages in complex and dynamic environments with applications for growth control and persistence, Nat. Microbiol. 6, 783 (2021).
- I. Soifer, L. Robert, and A. Amir, Single-cell analysis of growth in budding yeast and bacteria reveals a common size regulation strategy, Curr. Biol. 26, 356 (2016).
- E. Zatulovskiy, S. Zhang, D. F. Berenson, B. R. Topacio, and J. M. Skotheim, Cell growth dilutes the cell cycle inhibitor RB to trigger cell division, Science 369, 466 (2020).
- S. Xie and J. M. Skotheim, A G1 sizer coordinates growth and division in the mouse epidermis, Curr. Biol. 30, 916 (2020).
- I. Jones, L. Dent, T. Higo, T. Roumeliotis, M. A. Garcia, H. Shree, J. Choudhary, M. Pedersen, and C. Bakal, Characterization of proteome-size scaling by integrative omics reveals mechanisms of proliferation control in cancer, Sci. Adv. 9, eadd0636 (2023).
- Y. Chen, G. Zhao, J. Zahumensky, S. Honey, and B. Futcher, Differential scaling of gene expression with cell size may explain size control in budding yeast, Mol. Cell 78, 359 (2020).
- M. Huelsmann, O. T. Schubert, and M. Ackermann, A framework for understanding collective microbiome metabolism, Nat. Microbiol. 9, 3097 (2024).
- A. V. Narla, T. Hwa, and A. Murugan, Dynamic coexistence driven by physiological transitions in microbial communities, Proc. Natl. Acad. Sci. USA 122, e2405527122 (2025).
- M. D. Bello, H. Lee, A. Goyal, and J. Gore, Resource–diversity relationships in bacterial communities reflect the network structure of microbial metabolism, Nat. Ecol. Evol. 5, 1424 (2021).
- C. I. Abreu, M. D. Bello, C. Bunse, J. Pinhassi, and J. Gore, Warmer temperatures favor slower-growing bacteria in natural marine communities, Sci. Adv. 9, eade8352 (2023).
- K. Faust and J. Raes, Microbial interactions: From networks to models, Nat. Rev. Microbiol. 10, 538 (2012).
- N. W. Smith, P. R. Shorten, E. Altermann, N. C. Roy, and W. C. McNabb, The classification and evolution of bacterial cross-feeding, Front. Ecol. Evol. 7, 153 (2019).
- C. Kost, K. R. Patil, J. Friedman, S. L. Garcia, and M. Ralser, Metabolic exchanges are ubiquitous in natural microbial communities, Nat. Microbiol. 8, 2244 (2023).
- N. I. van den Berg, D. Machado, S. Santos, I. Rocha, J. Chacón, W. Harcombe, S. Mitri, and K. R. Patil, Ecological approaches for predicting emergent properties in microbial communities, Nat. Ecol. Evol. 6, 855 (2022).
- R. MacArthur, Species packing and competitive equilibrium for many species, Theor. Popul. Biol. 1, 1 (1970).
- P. Chesson, Macarthur's consumer-resource model, Theor. Popul. Biol. 37, 26 (1990).
- G. D'Souza, S. Shitut, D. Preussger, G. Yousif, S. Waschina, and C. Kost, Ecology and evolution of metabolic cross-feeding interactions in bacteria, Nat. Prod. Rep. 35, 455 (2018).
- G. D’ Souza and C. Kost, Experimental evolution of metabolic dependency in bacteria, PLoS Genet. 12, e1006364 (2016).
- L. Oña, S. Giri, N. Avermann, M. Kreienbaum, K. M. Thormann, and C. Kost, Obligate cross-feeding expands the metabolic niche of bacteria, Nat. Ecol. Evol. 5, 1224 (2021).
- G. D'Souza, S. Waschina, S. Pande, K. Bohl, C. Kaleta, and C. Kost, Less is more: Selective advantages can explain the prevalent loss of biosynthetic genes in bacteria, Evolution 68, 2559 (2014).
- S. Starke, D. M. M. Harris, J. Zimmermann, S. Schuchardt, M. Oumari, D. Frank, C. Bang, P. Rosenstiel, S. Schreiber, N. Frey, et al., Amino acid auxotrophies in human gut bacteria are linked to higher microbiome diversity and long-term stability ISME J. 17, 2370 (2023).
- H. Okano, R. Hermsen, and T. Hwa, Hierarchical and simultaneous utilization of carbon substrates: Mechanistic insights, physiological roles, and ecological consequences, Curr. Opin. Microbiol. 63, 172 (2021).
- J. J. Morris, R. E. Lenski, and E. R. Zinser, The black queen hypothesis: Evolution of dependencies through adaptive gene loss, mBio 3, e00036-12 (2012).
- R. J. Allen, and B. Waclaw, Bacterial growth: A statistical physicist's guide, Rep. Prog. Phys. 82, 016601 (2018).
- A. Novick and L. Szilard, Description of the chemostat, Science 112, 715 (1950).
- A. D. Co, S. van Vliet, and M. Ackermann, Emergent microscale gradients give rise to metabolic cross-feeding and antibiotic tolerance in clonal bacterial populations, Philos. Trans. R. Soc. B 374, 20190080 (2019).
- A. D. Co, S. van Vliet, D. J. Kiviet, S. Schlegel, and M. Ackermann, Short-range interactions govern the dynamics and functions of microbial communities, Nat. Ecol. Evol. 4, 366 (2020).
- S. van Vliet, A. D. Co, A. R. Winkler, S. Spriewald, B. Stecher, and M. Ackermann, Spatially correlated gene expression in bacterial groups: The role of lineage history, spatial gradients, and cell-cell interactions, Cell Syst. 6, 496 (2018).
- J. B. McKinlay, Are bacteria leaky? Mechanisms of metabolite externalization in bacterial cross-feeding, Annu. Rev. Microbiol. 77, 277 (2023).
- R. Mohmmed Yagb Omer, O. Mazzarisi, M. D. Bello, and J. Grilli, Evolutionary learning of microbial populations in partially predictable environments, arXiv:2508.00527.
- T. Wang, Modeling for microbial communities with cross-feeding and predator-prey interactions, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2021.
- J. Johnke, Y. Cohen, M. de Leeuw, A. Kushmaro, E. Jurkevitch, and A. Chatzinotas, Multiple micro-predators controlling bacterial communities in the environment, Curr. Opin. Biotechnol. 27, 185 (2014).
- P. Guo, C. Li, J. Liu, and B. Chai, Predation has a significant impact on the complexity and stability of microbial food webs in subalpine lakes, Microbiol. Spectr. 11, e0241123 (2023).
- V. Epshtein and E. Nudler, Cooperation between RNA polymerase molecules in transcription elongation, Science 300, 801 (2003).
- M. Patrick, P. P. Dennis, M. Ehrenberg, and H. Bremer, Free RNA polymerase in Escherichia coli, Biochimie 119, 80 (2015).
- R. Baker and C. Yanofsky, Transcription initiation frequency and translational yield for the tryptophan operon of Escherichia coli, J. Mol. Biol. 69, 89 (1972).
- D. B. Newell and E. Tiesinga, The International System of Units (SI): 2019 Edition (2019), https://doi.org/10.6028/NIST.SP.330-2019.
- S. J. Schink, E. Biselli, C. Ammar, and U. Gerland, Death rate of E. coli during starvation is set by maintenance cost and biomass recycling, Cell Syst. 9, 64 (2019).