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- W3048587850 abstract "•A general model links cell size-homeostasis statistics to cell-cycle mechanisms•Many cell-cycle mechanisms that appear plausible cannot maintain cell size•Mechanisms that enact adder behavior may also result in highly robust size control•Cell-cycle features can play unintuitive roles in size-homeostasis behaviors High-throughput imaging has led to an explosion of observations about cell-size homeostasis across the kingdoms of life. Among bacteria, “adder” behavior—in which a constant size increment appears to be added during each cell cycle—is ubiquitous, while various eukaryotes show other size-homeostasis behaviors. Since interactions between cell-cycle progression and growth ultimately determine such behaviors, we developed a general model of cell-cycle regulation. Our analyses reveal a range of scenarios that are plausible but fail to regulate cell size, indicating that mechanisms of cell-cycle regulation are stringently limited by size-control requirements, and possibly why certain cell-cycle features are strongly conserved. Cell-cycle features can play unintuitive roles in altering size-homeostasis behaviors: noisy regulator production can enhance adder behavior, while Whi5-like inhibitor dilutors respond sensitively to perturbations to G2/M control and noisy G1/S checkpoints. Our model thus provides holistic insights into the mechanistic implications of size-homeostasis experimental measurements. High-throughput imaging has led to an explosion of observations about cell-size homeostasis across the kingdoms of life. Among bacteria, “adder” behavior—in which a constant size increment appears to be added during each cell cycle—is ubiquitous, while various eukaryotes show other size-homeostasis behaviors. Since interactions between cell-cycle progression and growth ultimately determine such behaviors, we developed a general model of cell-cycle regulation. Our analyses reveal a range of scenarios that are plausible but fail to regulate cell size, indicating that mechanisms of cell-cycle regulation are stringently limited by size-control requirements, and possibly why certain cell-cycle features are strongly conserved. Cell-cycle features can play unintuitive roles in altering size-homeostasis behaviors: noisy regulator production can enhance adder behavior, while Whi5-like inhibitor dilutors respond sensitively to perturbations to G2/M control and noisy G1/S checkpoints. Our model thus provides holistic insights into the mechanistic implications of size-homeostasis experimental measurements. A fundamental question in biology is how cells regulate cell-cycle progression, which is intimately tied to myriad processes such as cell-size determination (Schmoller et al., 2015Schmoller K.M. Turner J.J. Kõivomägi M. Skotheim J.M. Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size.Nature. 2015; 526: 268-272Crossref PubMed Scopus (177) Google Scholar), drug sensitivity (Shi et al., 2017Shi H. Colavin A. Bigos M. Tropini C. Monds R.D. Huang K.C. Deep phenotypic mapping of bacterial cytoskeletal mutants reveals physiological robustness to cell size.Curr. Biol. 2017; 27: 3419-3429.e4Abstract Full Text Full Text PDF PubMed Scopus (43) Google Scholar), and transcription (Padovan-Merhar et al., 2015Padovan-Merhar O. Nair G.P. Biaesch A.G. Mayer A. Scarfone S. Foley S.W. Wu A.R. Churchman L.S. Singh A. Raj A. Single mammalian cells compensate for differences in cellular volume and DNA copy number through independent global transcriptional mechanisms.Mol. Cell. 2015; 58: 339-352Abstract Full Text Full Text PDF PubMed Scopus (260) Google Scholar). In all organisms, cell-cycle control must be coupled to growth to ensure a fixed average size in steady-state conditions. Experimentally measurable size-homeostasis behaviors are determined by interactions between cell-cycle control and growth. Single-cell lineage tracking and cell-cycle reporters have yielded many size-homeostasis measurements across bacteria, yeast, mammalian cells, and plant cells. Among bacteria (Campos et al., 2014Campos M. Surovtsev I.V. Kato S. Paintdakhi A. Beltran B. Ebmeier S.E. Jacobs-Wagner C. A constant size extension drives bacterial cell size homeostasis.Cell. 2014; 159: 1433-1446Abstract Full Text Full Text PDF PubMed Scopus (265) Google Scholar; Taheri-Araghi et al., 2015Taheri-Araghi S. Bradde S. Sauls J.T. Hill N.S. Levin P.A. Paulsson J. Vergassola M. Jun S. Cell-size control and homeostasis in bacteria.Curr. Biol. 2015; 25: 385-391Abstract Full Text Full Text PDF PubMed Scopus (388) Google Scholar; Wallden et al., 2016Wallden M. Fange D. Lundius E.G. Baltekin Ö. Elf J. The synchronization of replication and division cycles in individual E. coli cells.Cell. 2016; 166: 729-739Abstract Full Text Full Text PDF PubMed Scopus (177) Google Scholar; Willis and Huang, 2017Willis L. Huang K.C. Sizing up the bacterial cell cycle.Nat. Rev. Microbiol. 2017; 15: 606-620Crossref PubMed Scopus (85) Google Scholar) and an archaeon (Eun et al., 2018Eun Y.-J. Ho P.-Y. Kim M. LaRussa S. Robert L. Renner L.D. Schmid A. Garner E. Amir A. Archaeal cells share common size control with bacteria despite noisier growth and division.Nat. Microbiol. 2018; 3: 148-154Crossref PubMed Scopus (47) Google Scholar), a common theme has emerged: cells appear to regulate their size via an “adder” behavior in which a fixed volume (size) is added between birth and division. Eukaryotic budding yeast and mammalian cells can deviate from adder behavior over the G1 and S/G2 cell-cycle stages while maintaining apparent adder or near-adder behavior between birth and division (Cadart et al., 2018Cadart C. Monnier S. Grilli J. Sáez P.J. Srivastava N. Attia R. Terriac E. Baum B. Cosentino-Lagomarsino M. Piel M. Size control in mammalian cells involves modulation of both growth rate and cell cycle duration.Nat. Commun. 2018; 9: 3275Crossref PubMed Scopus (98) Google Scholar; Chandler-Brown et al., 2017Chandler-Brown D. Schmoller K.M. Winetraub Y. Skotheim J.M. The adder phenomenon emerges from independent control of pre- and post-start phases of the budding yeast cell cycle.Curr. Biol. 2017; 27: 2774-2783.e3Abstract Full Text Full Text PDF PubMed Scopus (47) Google Scholar; Di Talia et al., 2007Di Talia S. Skotheim J.M. Bean J.M. Siggia E.D. Cross F.R. The effects of molecular noise and size control on variability in the budding yeast cell cycle.Nature. 2007; 448: 947-951Crossref PubMed Scopus (345) Google Scholar; Schmoller et al., 2015Schmoller K.M. Turner J.J. Kõivomägi M. Skotheim J.M. Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size.Nature. 2015; 526: 268-272Crossref PubMed Scopus (177) Google Scholar), with the smallest mammalian cells switching to approximately “sizer” behavior, with no correlation between birth and division sizes (Varsano et al., 2017Varsano G. Wang Y. Wu M. Probing Mammalian Cell Size Homeostasis by Channel-Assisted Cell Reshaping.Cell Rep. 2017; 20: 397-410Abstract Full Text Full Text PDF PubMed Scopus (43) Google Scholar). Similarly, small fission yeast cells exhibit sizer behavior at division, while large fission yeast cells show apparent near-adder behavior (Facchetti et al., 2019Facchetti G. Knapp B. Flor-Parra I. Chang F. Howard M. Reprogramming cdr2-dependent geometry-based cell size control in fission yeast.Curr. Biol. 2019; 29: 350-358.e4Abstract Full Text Full Text PDF PubMed Scopus (36) Google Scholar; Fantes, 1977Fantes P.A. Control of cell size and cycle time in Schizosaccharomyces pombe.J. Cell Sci. 1977; 24: 51-67PubMed Google Scholar; Pan et al., 2014Pan K.Z. Saunders T.E. Flor-Parra I. Howard M. Chang F. Cortical regulation of cell size by a sizer cdr2p.eLife. 2014; 3: e02040Crossref PubMed Scopus (78) Google Scholar). By contrast, the stem cells of Arabidopsis thaliana exhibit intermediate adder-sizer behavior (Willis et al., 2016Willis L. Refahi Y. Wightman R. Landrein B. Teles J. Huang K.C. Meyerowitz E.M. Jönsson H. Cell size and growth regulation in the Arabidopsis thaliana apical stem cell niche.Proc. Natl. Acad. Sci. USA. 2016; 113: E8238-E8246Crossref PubMed Scopus (106) Google Scholar). Here, “apparent” size-homeostasis behavior corresponds to the value of the fitted slope between size at the start versus size at the end of the cycle, which does not necessarily imply an underlying mechanism that measures a specific aspect of size. Despite the recent explosion of size-homeostasis measurements, there is a lack of clarity as to the implications of these similarities and differences for mechanisms of cell-cycle control and its coupling to growth. Furthermore, how the necessity for size homeostasis limits mechanisms of cell-cycle control is not understood. Seminal studies have revealed how cell-cycle progression is coupled to growth in several model organisms. In budding yeast, the G1/S inhibitor Whi5 is produced throughout S/G2/M and then diluted by growth during G1 to trigger G1/S at a threshold minimum concentration (Schmoller et al., 2015Schmoller K.M. Turner J.J. Kõivomägi M. Skotheim J.M. Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size.Nature. 2015; 526: 268-272Crossref PubMed Scopus (177) Google Scholar). Mathematical models showed that for budding yeast-like proliferation dynamics, this “inhibitor dilutor” G1/S regulation imparts adder behavior between birth and division (Chandler-Brown et al., 2017Chandler-Brown D. Schmoller K.M. Winetraub Y. Skotheim J.M. The adder phenomenon emerges from independent control of pre- and post-start phases of the budding yeast cell cycle.Curr. Biol. 2017; 27: 2774-2783.e3Abstract Full Text Full Text PDF PubMed Scopus (47) Google Scholar; Heldt et al., 2018Heldt F.S. Lunstone R. Tyson J.J. Novák B. Dilution and titration of cell-cycle regulators may control cell size in budding yeast.PLOS Comput. Biol. 2018; 14: e1006548Crossref PubMed Scopus (27) Google Scholar; Soifer et al., 2016Soifer I. Robert L. Amir A. Single-cell analysis of growth in budding yeast and bacteria reveals a common size regulation strategy.Curr. Biol. 2016; 26: 356-361Abstract Full Text Full Text PDF PubMed Scopus (103) Google Scholar). Whi5 has functional homologs in mammals (Rb) and plants (RBR1), suggesting that an inhibitor-dilutor mechanism may regulate G1/S. In the bacterium Escherichia coli, the division protein FtsZ is a “master regulator” of division, with newly synthesized FtsZ accumulating at midcell proportionally with cell growth to trigger division at a total intracellular threshold level (Sekar et al., 2018Sekar K. Rusconi R. Sauls J.T. Fuhrer T. Noor E. Nguyen J. Fernandez V.I. Buffing M.F. Berney M. Jun S. et al.Synthesis and degradation of FtsZ quantitatively predict the first cell division in starved bacteria.Mol. Syst. Biol. 2018; 14: e8623Crossref PubMed Scopus (27) Google Scholar; Si et al., 2019Si F. Le Treut G. Sauls J.T. Vadia S. Levin P.A. Jun S. Mechanistic origin of cell-size control and homeostasis in bacteria.Curr. Biol. 2019; 29: 1760-1770.e7Abstract Full Text Full Text PDF PubMed Scopus (89) Google Scholar), a mechanism that recapitulates the observed adder behavior. Similarly, active ATP-bound DnaA, which accumulates at the origins of replication in many bacteria, causes adder behavior between consecutive G1/Ss and between consecutive divisions in the following scenario: (1) it is produced proportionally with growth; (2) it triggers replication initiation (G1/S) at a threshold level per origin and is then inactivated; and (3) a fixed time or added-size increment elapses between G1/S and division (Amir, 2014Amir A. Cell size regulation in bacteria.Phys. Rev. Lett. 2014; 112: 208102Crossref Scopus (184) Google Scholar; Barber et al., 2017Barber F. Ho P.Y. Murray A.W. Amir A. Details matter: noise and model structure set the relationship between cell size and cell cycle timing.Front. Cell Dev. Biol. 2017; 5: 92Crossref PubMed Scopus (16) Google Scholar; Ho and Amir, 2015Ho P.-Y. Amir A. Simultaneous regulation of cell size and chromosome replication in bacteria.Front. Microbiol. 2015; 6: 662Crossref PubMed Scopus (60) Google Scholar; Logsdon et al., 2017Logsdon M.M. Ho P.Y. Papavinasasundaram K. Richardson K. Cokol M. Sassetti C.M. Amir A. Aldridge B.B. A parallel adder coordinates mycobacterial cell-cycle progression and cell-size homeostasis in the context of asymmetric growth and organization.Curr. Biol. 2017; 27: 3367-3374.e7Abstract Full Text Full Text PDF PubMed Scopus (38) Google Scholar). In fast-growing E. coli, experimental data support this scenario (Si et al., 2019Si F. Le Treut G. Sauls J.T. Vadia S. Levin P.A. Jun S. Mechanistic origin of cell-size control and homeostasis in bacteria.Curr. Biol. 2019; 29: 1760-1770.e7Abstract Full Text Full Text PDF PubMed Scopus (89) Google Scholar), although there is a conflicting report regarding the role of DnaA in replication initiation (Flåtten et al., 2015Flåtten I. Fossum-Raunehaug S. Taipale R. Martinsen S. Skarstad K. The DnaA protein is not the limiting factor for initiation of replication in Escherichia coli.PLoS Genet. 2015; 11e1005276Crossref PubMed Scopus (30) Google Scholar; Willis and Huang, 2017Willis L. Huang K.C. Sizing up the bacterial cell cycle.Nat. Rev. Microbiol. 2017; 15: 606-620Crossref PubMed Scopus (85) Google Scholar). Furthermore, DnaA-mediated G1/S followed by a fixed time interval and FtsZ-mediated division may operate simultaneously in fast growth conditions, with the slower process triggering cell division (Micali et al., 2018aMicali G. Grilli J. Marchi J. Osella M. Cosentino Lagomarsino M. Dissecting the control mechanisms for DNA replication and cell division in E. coli.Cell Rep. 2018; 25: 761-771.e4Abstract Full Text Full Text PDF PubMed Scopus (24) Google Scholar, Micali et al., 2018bMicali G. Grilli J. Osella M. Lagomarsino M.C. Concurrent processes set E. coli cell division.Sci. Adv. 2018; 4: eaau3324Crossref PubMed Scopus (26) Google Scholar; Si et al., 2019Si F. Le Treut G. Sauls J.T. Vadia S. Levin P.A. Jun S. Mechanistic origin of cell-size control and homeostasis in bacteria.Curr. Biol. 2019; 29: 1760-1770.e7Abstract Full Text Full Text PDF PubMed Scopus (89) Google Scholar). DnaA and FtsZ are broadly conserved among bacteria but details of their dynamics are unknown and therefore are a priori expected to vary across the domain; the extent to which the requirement for size homeostasis limits their dynamics is also unknown. Master regulators also control cell-cycle checkpoint progression in eukaryotes: the broadly conserved cyclin-dependent kinase 1 (CDK1)-cyclin (Harashima et al., 2013Harashima H. Dissmeyer N. Schnittger A. Cell cycle control across the eukaryotic kingdom.Trends Cell Biol. 2013; 23: 345-356Abstract Full Text Full Text PDF PubMed Scopus (254) Google Scholar) accumulates during growth to trigger G1/S and then G2/M at successive threshold activity levels in engineered fission yeast (Coudreuse and Nurse, 2010Coudreuse D. Nurse P. Driving the cell cycle with a minimal CDK control network.Nature. 2010; 468: 1074-1079Crossref PubMed Scopus (282) Google Scholar). The CDK1-cyclin regulatory network is complex, but data indicate that it may result in a simple scaling relating active CDK1-cyclin accumulation to cell size (Keifenheim et al., 2017Keifenheim D. Sun X.M. D’Souza E. Ohira M.J. Magner M. Mayhew M.B. Marguerat S. Rhind N. Size-dependent expression of the mitotic activator Cdc25 suggests a mechanism of size control in fission yeast.Curr. Biol. 2017; 27: 1491-1497.e4Abstract Full Text Full Text PDF PubMed Scopus (49) Google Scholar; Patterson et al., 2019Patterson J.O. Rees P. Nurse P. Noisy cell-size correlated expression of Cyclin B drives probabilistic cell-size homeostasis in fission yeast.Curr. Biol. 2019; 29: 1379-1386.e4Abstract Full Text Full Text PDF PubMed Scopus (27) Google Scholar). Note that previous models focused on particular organisms with specific cell-cycle and growth regimes, and thus they did not provide a comprehensive framework connecting proliferation dynamics to size-homeostasis measurements, or they did not consider the mechanism(s) coupling growth and cell-cycle progression and therefore lacked predictive power for how genetic perturbations would affect size-homeostasis behavior. In this study, we sought to develop a theoretical framework to address two major outstanding questions: how does the requirement for cell-size homeostasis limit cell-cycle regulator dynamics and mechanisms of cell-cycle checkpoint progression, and what are the implications of size-homeostasis experimental measurements for the mechanisms of cell-cycle regulation? We developed a general model of cell proliferation and used it to predict the size-homeostasis behaviors produced by a wide range of cell-cycle control mechanisms. Instances of the model focus on cells with two phases partitioned by the major eukaryotic cell-cycle checkpoints (G1/S and G2/M, assuming that G2/M and division are coincident) and on two rate-limiting mechanisms of irreversible checkpoint progression: master regulators like CDK1-cyclin or FtsZ/DnaA that accumulate to threshold activity levels and Whi5-like inhibitor dilutors. The assumed G1 and S/G2/M phases mean that the model applies to organisms with two clearly delineated phases and not to bacteria in fast growth conditions with multiple replication forks or to fission yeast in which cytokinesis between daughter cells occurs after the initiation of DNA replication. We systematically identified plausible cell-cycle control scenarios that nevertheless fail to regulate cell size and are thus impossible. We determined how growth, noise origins, cell-cycle checkpoint criteria, and cell-cycle regulator dynamics differentially affect size homeostasis measurements and how additional size-homeostasis measurements may discriminate among underlying mechanisms that cause robust deviation from adder, as observed in A. thaliana. This framework and the insights it provides should be broadly useful for interpreting, motivating, and understanding the constraints on cell-size homeostasis measurements across all organisms. Our model considers two types of checkpoint regulators in the cell cycle (Figure 1A). In the first type, a master regulator (e.g., CDK1-cyclin in a minimal model of fission yeast; Coudreuse and Nurse, 2010Coudreuse D. Nurse P. Driving the cell cycle with a minimal CDK control network.Nature. 2010; 468: 1074-1079Crossref PubMed Scopus (282) Google Scholar) accumulates from zero and triggers G1/S or G2/M progression at a fixed intracellular threshold density within a cellular region that increases with cell size (S) as ∼SλT (Figure 1A), when it is immediately degraded to zero. In the second type of checkpoint regulator, an inhibitor dilutor (e.g., Whi5 in budding yeast; Schmoller et al., 2015Schmoller K.M. Turner J.J. Kõivomägi M. Skotheim J.M. Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size.Nature. 2015; 526: 268-272Crossref PubMed Scopus (177) Google Scholar) accumulates during one phase and is diluted in the subsequent phase, triggering progression at a minimum threshold density with no subsequent degradation. The region of regulator accumulation grows in proportion to size if λT = 1 (as do most nuclei), or is independent of size if λT = 0 (as for genomic loci), or scales with surface area or midcell perimeter if λT ≈ 2/3 or 1/3, respectively (as in A. thaliana apical stem cells; Willis et al., 2016Willis L. Refahi Y. Wightman R. Landrein B. Teles J. Huang K.C. Meyerowitz E.M. Jönsson H. Cell size and growth regulation in the Arabidopsis thaliana apical stem cell niche.Proc. Natl. Acad. Sci. USA. 2016; 113: E8238-E8246Crossref PubMed Scopus (106) Google Scholar). Master regulators can accumulate through either G1 or S/G2/M, as is common for cyclins in eukaryotes, or through both G1 and S/G2/M, as for CDK1-cyclin in engineered fission yeast (Coudreuse and Nurse, 2010Coudreuse D. Nurse P. Driving the cell cycle with a minimal CDK control network.Nature. 2010; 468: 1074-1079Crossref PubMed Scopus (282) Google Scholar; Hochegger et al., 2008Hochegger H. Takeda S. Hunt T. Cyclin-dependent kinases and cell-cycle transitions: does one fit all?.Nat. Rev. Mol. Cell Biol. 2008; 9: 910-916Crossref PubMed Scopus (383) Google Scholar) and FtsZ/DnaA in slow-growing bacteria, assuming that FtsZ/DnaA operate similarly at fast (Si et al., 2019Si F. Le Treut G. Sauls J.T. Vadia S. Levin P.A. Jun S. Mechanistic origin of cell-size control and homeostasis in bacteria.Curr. Biol. 2019; 29: 1760-1770.e7Abstract Full Text Full Text PDF PubMed Scopus (89) Google Scholar) and slow growth rates. Regulator production rates (dC/dt) can be cell-size dependent and may differ between phases according todCdt=κphaseSλc,phasewhere C is the number of proteins and λc, phase, κphase dictate size dependence and production rate, respectively (Figure 1A). The majority of proteins are thought to be maintained at constant concentrations during steady-state growth and thus are produced at a fixed rate that is proportional to cell size in exponentially growing cells (λc, phase = 1) (Newman et al., 2006Newman J.R. Ghaemmaghami S. Ihmels J. Breslow D.K. Noble M. DeRisi J.L. Weissman J.S. Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise.Nature. 2006; 441: 840-846Crossref PubMed Scopus (1161) Google Scholar; Padovan-Merhar et al., 2015Padovan-Merhar O. Nair G.P. Biaesch A.G. Mayer A. Scarfone S. Foley S.W. Wu A.R. Churchman L.S. Singh A. Raj A. Single mammalian cells compensate for differences in cellular volume and DNA copy number through independent global transcriptional mechanisms.Mol. Cell. 2015; 58: 339-352Abstract Full Text Full Text PDF PubMed Scopus (260) Google Scholar; Schmoller and Skotheim, 2015Schmoller K.M. Skotheim J.M. The biosynthetic basis of cell size control.Trends Cell Biol. 2015; 25: 793-802Abstract Full Text Full Text PDF PubMed Scopus (80) Google Scholar), while Whi5 is produced independently of size through S/G2/M in budding yeast (λc, S/G2/M = 0) (Schmoller et al., 2015Schmoller K.M. Turner J.J. Kõivomägi M. Skotheim J.M. Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size.Nature. 2015; 526: 268-272Crossref PubMed Scopus (177) Google Scholar). In fission yeast, the activity of CDK1-cyclin may increase with a stronger size dependence (λc, phase > 1) that arises from multiple regulators with cell size-dependent levels (Keifenheim et al., 2017Keifenheim D. Sun X.M. D’Souza E. Ohira M.J. Magner M. Mayhew M.B. Marguerat S. Rhind N. Size-dependent expression of the mitotic activator Cdc25 suggests a mechanism of size control in fission yeast.Curr. Biol. 2017; 27: 1491-1497.e4Abstract Full Text Full Text PDF PubMed Scopus (49) Google Scholar). The ratio of regulator production rates (rS/G2/M = κS/G2/M/κG1) represents two extreme scenarios: either production is limited by gene-copy number, meaning that the production rate doubles in S/G2/M upon gene duplication regardless of ploidy (rS/G2/M = 2) or production is unaffected by gene-copy number (rS/G2/M = 1) because another factor such as ribosome abundance is limiting (Heldt et al., 2018Heldt F.S. Lunstone R. Tyson J.J. Novák B. Dilution and titration of cell-cycle regulators may control cell size in budding yeast.PLOS Comput. Biol. 2018; 14: e1006548Crossref PubMed Scopus (27) Google Scholar; Schmoller and Skotheim, 2015Schmoller K.M. Skotheim J.M. The biosynthetic basis of cell size control.Trends Cell Biol. 2015; 25: 793-802Abstract Full Text Full Text PDF PubMed Scopus (80) Google Scholar; Schmoller et al., 2015Schmoller K.M. Turner J.J. Kõivomägi M. Skotheim J.M. Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size.Nature. 2015; 526: 268-272Crossref PubMed Scopus (177) Google Scholar) (Figure 1A). Proteins are assumed to be stable, which is consistent with the measurements of key regulators, aside from targeted degradation (Hochegger et al., 2008Hochegger H. Takeda S. Hunt T. Cyclin-dependent kinases and cell-cycle transitions: does one fit all?.Nat. Rev. Mol. Cell Biol. 2008; 9: 910-916Crossref PubMed Scopus (383) Google Scholar; Schmoller et al., 2015Schmoller K.M. Turner J.J. Kõivomägi M. Skotheim J.M. Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size.Nature. 2015; 526: 268-272Crossref PubMed Scopus (177) Google Scholar). For G1/S regulators, the regulator persists through cell divisions, and for simplicity we assume that it is inherited in proportion to daughter cell sizes without noise. In our model, cells divide into sisters with size-ratio 1:(σ − 1). Thus, binary fission and asymmetric division are accounted for by σ = 2 and σ ≠ 2, respectively (Figure 1B), and at steady state, cells increase their average birth size by an average factor σ over the cell cycle. The growth rate (dS/dt) can be cell size dependent according todSdt=γSλgWhile many organisms grow exponentially (λg = 1) (Di Talia et al., 2007Di Talia S. Skotheim J.M. Bean J.M. Siggia E.D. Cross F.R. The effects of molecular noise and size control on variability in the budding yeast cell cycle.Nature. 2007; 448: 947-951Crossref PubMed Scopus (345) Google Scholar; Osella et al., 2014Osella M. Nugent E. Cosentino Lagomarsino M. Concerted control of Escherichia coli cell division.Proc. Natl. Acad. Sci. USA. 2014; 111: 3431-3435Crossref PubMed Scopus (122) Google Scholar; Soifer et al., 2016Soifer I. Robert L. Amir A. Single-cell analysis of growth in budding yeast and bacteria reveals a common size regulation strategy.Curr. Biol. 2016; 26: 356-361Abstract Full Text Full Text PDF PubMed Scopus (103) Google Scholar; Taheri-Araghi et al., 2015Taheri-Araghi S. Bradde S. Sauls J.T. Hill N.S. Levin P.A. Paulsson J. Vergassola M. Jun S. Cell-size control and homeostasis in bacteria.Curr. Biol. 2015; 25: 385-391Abstract Full Text Full Text PDF PubMed Scopus (388) Google Scholar; Wang et al., 2010Wang P. Robert L. Pelletier J. Dang W.L. Taddei F. Wright A. Jun S. Robust growth of Escherichia coli.Curr. Biol. 2010; 20: 1099-1103Abstract Full Text Full Text PDF PubMed Scopus (585) Google Scholar; Willis et al., 2016Willis L. Refahi Y. Wightman R. Landrein B. Teles J. Huang K.C. Meyerowitz E.M. Jönsson H. Cell size and growth regulation in the Arabidopsis thaliana apical stem cell niche.Proc. Natl. Acad. Sci. USA. 2016; 113: E8238-E8246Crossref PubMed Scopus (106) Google Scholar), there is some evidence of linear growth in certain regimes (λg = 0) (Lin and Amir, 2018Lin J. Amir A. Homeostasis of protein and mRNA concentrations in growing cells.Nat. Commun. 2018; 9: 4496Crossref PubMed Scopus (62) Google Scholar). γ sets the average timescale for growth; lnσ/γ is the average cell-cycle duration for exponential growth (Figure 1C). Growth is assumed to be exponential, unless otherwise stated. We consider master regulators or inhibitor dilutors of G1/S or G2/M in combination with various phenomenological controls over S/G2/M or G1, respectively, including sizer (cells reach a critical size), adder (cells add a fixed size increment), or timer (a fixed time period elapses) control. The cell size at the end of the phase (Se, phase) is determined by cell size at the beginning of the phase (Si, phase) according toSe, phase=fphaseSi, phase+(σphase−fphase)μi, phasewhere fphase is the mode of control (fphase = 0, 1, or σphase for sizer, adder, or timer control and exponential growth, respectively; Method Details), σphase > 1 is the average fold-size increase, and μi, phase is the average initial size at steady state (Figure 1D). We refer to phases that follow this size determination rule as independently regulated. The average fraction of the cell cycle spent in G1 at steady state (τ, which equals G1 duration × γ/lnσ for exponential growth) and the mode of division (σ) determine σG1 ≈ στ and σS/G2/M ≈ σ1−τ because σ = σG1 σS/G2/M (approximations are exact for exponential growth; Method Details). Average sizes at birth (μi, G1) and G1/S (μi, S/G2/M) are determined by a combination of parameters governing the average regulator dynamics (λc, phase, κphase) and threshold levels or concentrations, G1 duration (τ), growth type (λg, γ), and division behavior (σ) (Method Details). Cell-size fluctuations emerge from noise in regulator dynamics, noise in the critical regulator density that triggers cell-cycle progression, and noise in sizer/adder/timer mechanisms. The impact of this noise on size homeostasis is encapsulated by just two parameters (ηG1/S and ηG2/S; Method Details) according toηcheckpoint=Noise in the transition's checkpoint mechanismCoefficient of variation CV in G1/S size(Figure 1E). For example, assuming typical values of the G1/S size coefficient of variation (CV) (average/standard deviation) of ∼13% (Cadart et al., 2018Cadart C. Monnier S. Grilli J. Sáez P.J. Srivastava N. Attia R. Terriac E. Baum B. Cosentino-Lagomarsino M. Piel M. Size control in mammalian cells involves modulation of both growth rate and cell cycle duration.Nat. Commun. 2018; 9: 3275Crossref PubMed Scopus (98) Google Scholar; Taheri-Araghi et al., 2015Taheri-Araghi S. Bradde S. Sauls J.T. Hill N.S. Levin P.A. Paulsson J. Vergassola M. Jun S. Cell-size control and homeostasis in bacteria.Curr. Biol. 2015; 25: 385-391Abstract Full Text Full Text PDF PubMed Scopus (388) Google Scholar; Willis et al., 2016Willis L. Refahi Y. Wightman R. Landrein B. Teles J. Huang K.C. Meyerowitz E.M. Jönsson H. Cell size and growth regulation in the Arabidopsis thaliana apical stem cell niche.Proc. Natl. Acad. Sci. USA. 2016; 113: E8238-E8246Crossref PubMed Scopus (106) Google Scholar), a CV of ∼7% in the threshold density of the G1/S checkpoint gives ηG1/S ∼ 0.5, while under S/G2/M timer, adder, or critical size regulation, a CV of ∼7% in the critical duration, increment, or cell size, respectively, gives ηG2/M ∼ 0.5. Thus, ηcheckpoint is" @default.
- W3048587850 created "2020-08-18" @default.
- W3048587850 creator A5010315204 @default.
- W3048587850 creator A5047419115 @default.
- W3048587850 creator A5052019253 @default.
- W3048587850 date "2020-08-01" @default.
- W3048587850 modified "2023-09-23" @default.
- W3048587850 title "Limits and Constraints on Mechanisms of Cell-Cycle Regulation Imposed by Cell Size-Homeostasis Measurements" @default.
- W3048587850 cites W1780666943 @default.
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