A bacterial size law revealed by a coarse-grained model of cell physiology

Bertaux, François; Kügelgen, Julius von; Marguerat, Samuel; Shahrezaei, Vahid

doi:10.1101/078998

Cited by 10 publications

(19 citation statements)

References 73 publications

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“…Such a model can explain both adder and sizer principles, where degradation of the protein at cell birth leads to adder, and equal sharing leads to sizer (Deforet et al, 2015; Bertaux et al, 2016). There is also extensive debate regarding the precise point at which the adder principle is applied, with suggestions that it applies solely from birth to division (e.g., Campos et al, 2014), or recent evidence that it applies at the initiation of replication (Ho and Amir, 2015; Taheri-Araghi et al, 2015; Si et al, 2017).…”

Section: Discussionmentioning

confidence: 99%

Mycobacteria Modify Their Cell Size Control under Sub-Optimal Carbon Sources

Priestman

Thomas

Robertson

et al. 2017

Front. Cell Dev. Biol.

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The decision to divide is the most important one that any cell must make. Recent single cell studies suggest that most bacteria follow an “adder” model of cell size control, incorporating a fixed amount of cell wall material before dividing. Mycobacteria, including the causative agent of tuberculosis Mycobacterium tuberculosis, are known to divide asymmetrically resulting in heterogeneity in growth rate, doubling time, and other growth characteristics in daughter cells. The interplay between asymmetric cell division and adder size control has not been extensively investigated. Moreover, the impact of changes in the environment on growth rate and cell size control have not been addressed for mycobacteria. Here, we utilize time-lapse microscopy coupled with microfluidics to track live Mycobacterium smegmatis cells as they grow and divide over multiple generations, under a variety of growth conditions. We demonstrate that, under optimal conditions, M. smegmatis cells robustly follow the adder principle, with constant added length per generation independent of birth size, growth rate, and inherited pole age. However, the nature of the carbon source induces deviations from the adder model in a manner that is dependent on pole age. Understanding how mycobacteria maintain cell size homoeostasis may provide crucial targets for the development of drugs for the treatment of tuberculosis, which remains a leading cause of global mortality.

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Section: Discussionmentioning

confidence: 99%

Mycobacteria Modify Their Cell Size Control under Sub-Optimal Carbon Sources

Priestman

Thomas

Robertson

et al. 2017

Front. Cell Dev. Biol.

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“…Here we take explicitly cell division into account and, for concreteness, use the "adder" model for cell division. We consider an initiator protein I, which accumulates from 0 after cell birth, and triggers the cell division once I reaches the division threshold I c and is then destroyed (or "reset", e.g., after initiation of DNA replication in bacteria, the ATP-bound DnaA is dephosphorylated to the ADP-bound form) [46][47][48]. During a division event, we assume proteins and mRNAs are divided between the two daughter cells following a binomial distribution [49].…”

Section: Model Of Stochastic Gene Expressionmentioning

confidence: 99%

Homeostasis of protein and mRNA concentrations in growing cells

Lin

Amir

2018

Preprint

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Many experiments show that the concentrations of protein and mRNA fluctuate but on average are constant in growing cells, independent of the genome copy number. However, models of stochastic gene expression often assume constant gene expression rates that are proportional to the gene copy numbers, which are therefore incompatible with experiments. Here, we construct a minimal gene expression model to fill this gap. We show that (1) because the ribosomes translate all proteins, the concentrations of proteins are regulated in an exponentially growing cell volume; (2) the competition between genes for the RNA polymerases makes the gene expression rate independent of the genome number; (3) the fluctuations in ribosome level and cell density can generate a global extrinsic noise in protein concentrations; (4) correlations between mRNA and protein levels can be quantified.Despite the noisy nature of gene expression [1][2][3][4][5][6], various aspects of single cell dynamics, such as volume growth, are effectively deterministic. Recent single-cell measurements show that the growth of cell volumes is often exponential. These include bacteria [7][8][9][10], budding yeast [10][11][12][13][14] and mammalian cells [10,15]. Moreover, the mRNA and protein numbers are on average proportional to the cell volume throughout the cell cycle [16][17][18][19][20]. Therefore, the homeostasis of mRNA concentration and protein concentration is maintained in an exponentially growing cell volume. The exponential growths of mRNA and protein number indicate dynamical transcription and translation rates proportional to the cell volume, and also independent of the genome copy number. However, current gene expression models often assume a fixed cell volume with constant transcription and translation rates [1,5,[21][22][23], which are proportional to the gene copy number. Therefore, fixed cell volume models fail to reveal how cells keep constant mRNA and protein concentrations as the cell volume grows and the genome is replicated.The homeostasis of protein and mRNA concentrations imply that there must be a regulatory mechanism in place to prevent the accumulation of noise over time and to maintain a bounded distribution of concentrations. The goal of this work is to identify such a mechanism by developing a genome-wide coarse-grained model taking into account explicitly cell volume growth. We will consider an idealized cell in which genes are constitutively expressed for simplicity. The ubiquity of homeostasis suggests that the global machineries of gene expression, RNA polymerases (RNAPs) and ribosomes, should play a central role within the model. Indeed, as we will show later, the exponential growth of cell volume, protein and mRNA number originates from the auto-catalytic nature of ribosomes, the limiting factor in the translational process [24][25][26]. The bounded distributions of concentrations are a result of the fact that ribosomes make all proteins. The independence of the mRNA concentration of the genome copy number is a natural resul...

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“…By incorporating or respecting the Cooper-Helmstetter and Donachie models, a number of theoretical models involving the control of DNA replication initiation have been constructed (e.g. [18,[22][23][24][25][26][27][28][29]). Recent experimental data indicated that the Donachie relation still holds under various perturbations that do not affect nutrient quality, which greatly extends the nutrient growth law [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Coordination betweenE. coliCell Size and Cell Cycle Mediated by DnaA

Zhang

Shi

2020

Preprint

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Sixty years ago, bacterial cell size was found as an exponential function of growth rate. Fifty years ago, a more general relationship was proposed, in which the cell mass was equal to the initiation mass multiplied by the ratio of the total time of the C and D periods to the doubling time. This relationship has recently been experimentally confirmed by perturbing doubling time, C period, D period or the initiation mass. However, the underlying molecular mechanism remains unclear. Here, we developed a mechanistic and kinetic model to describe how the initiator protein DnaA mediates the initiation of DNA replication in E. coli. In the model, we introduced an initiation probability function involving competitive binding of DnaA-ATP (active) and DnaA-ADP (inactive) at replication origin to determine the initiation of replication. In addition, we considered RNAP availability, ppGpp inhibition, DnaA autorepression, DnaA titration by chromosomal sites, hydrolysis of DnaA-ATP along with DNA replication, reactivation of DnaA-ADP and established a kinetic description of these DnaA regulatory processes. We simulated DnaA kinetics and obtained a self-consistent cell size and a regular DnaA oscillation coordinated with the cell cycle at steady state. The relationship between the cell size obtained by the simulation and the growth rate, C period, D period or initiation mass reproduces the results of the experiment. This model also predicts how the number of DnaA and the initiation mass vary with the perturbation parameters (including those reflecting the mutation or interference of DnaA regulatory processes), which is comparable to experimental data. The results suggest that the regulatory mechanisms of DnaA level and activity are associated with the invariance of initiation mass and the cell size general relationship for matching frequencies of replication initiation and cell division. This study may provide clues for concerted control of cell size and cell cycle in synthetic biology. *

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A bacterial size law revealed by a coarse-grained model of cell physiology

Cited by 10 publications

References 73 publications

Mycobacteria Modify Their Cell Size Control under Sub-Optimal Carbon Sources

Mycobacteria Modify Their Cell Size Control under Sub-Optimal Carbon Sources

Homeostasis of protein and mRNA concentrations in growing cells

Coordination betweenE. coliCell Size and Cell Cycle Mediated by DnaA

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