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Sanders S, Joshi K, Levin PA, Iyer-Biswas S. Beyond the average: An updated framework for understanding the relationship between cell growth, DNA replication, and division in a bacterial system. PLoS Genet 2023; 19:e1010505. [PMID: 36602967 DOI: 10.1371/journal.pgen.1010505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Our understanding of the bacterial cell cycle is framed largely by population-based experiments that focus on the behavior of idealized average cells. Most famously, the contributions of Cooper and Helmstetter help to contextualize the phenomenon of overlapping replication cycles observed in rapidly growing bacteria. Despite the undeniable value of these approaches, their necessary reliance on the behavior of idealized average cells masks the stochasticity inherent in single-cell growth and physiology and limits their mechanistic value. To bridge this gap, we propose an updated and agnostic framework, informed by extant single-cell data, that quantitatively accounts for stochastic variations in single-cell dynamics and the impact of medium composition on cell growth and cell cycle progression. In this framework, stochastic timers sensitive to medium composition impact the relationship between cell cycle events, accounting for observed differences in the relationship between cell cycle events in slow- and fast-growing cells. We conclude with a roadmap for potential application of this framework to longstanding open questions in the bacterial cell cycle field.
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Affiliation(s)
- Sara Sanders
- Department of Biology, Washington University in St. Louis, St. Louis, Missouri, United States of America
| | - Kunaal Joshi
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, United States of America
| | - Petra Anne Levin
- Department of Biology, Washington University in St. Louis, St. Louis, Missouri, United States of America
| | - Srividya Iyer-Biswas
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, United States of America
- Santa Fe Institute, Santa Fe, New Mexico, United States of America
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2
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Berger M, Wolde PRT. Robust replication initiation from coupled homeostatic mechanisms. Nat Commun 2022; 13:6556. [PMID: 36344507 PMCID: PMC9640692 DOI: 10.1038/s41467-022-33886-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Accepted: 10/05/2022] [Indexed: 11/09/2022] Open
Abstract
The bacterium Escherichia coli initiates replication once per cell cycle at a precise volume per origin and adds an on average constant volume between successive initiation events, independent of the initiation size. Yet, a molecular model that can explain these observations has been lacking. Experiments indicate that E. coli controls replication initiation via titration and activation of the initiator protein DnaA. Here, we study by mathematical modelling how these two mechanisms interact to generate robust replication-initiation cycles. We first show that a mechanism solely based on titration generates stable replication cycles at low growth rates, but inevitably causes premature reinitiation events at higher growth rates. In this regime, the DnaA activation switch becomes essential for stable replication initiation. Conversely, while the activation switch alone yields robust rhythms at high growth rates, titration can strongly enhance the stability of the switch at low growth rates. Our analysis thus predicts that both mechanisms together drive robust replication cycles at all growth rates. In addition, it reveals how an origin-density sensor yields adder correlations.
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Affiliation(s)
- Mareike Berger
- grid.417889.b0000 0004 0646 2441Biochemical Networks Group, Department of Information in Matter, AMOLF, 1098 XG Amsterdam, The Netherlands
| | - Pieter Rein ten Wolde
- grid.417889.b0000 0004 0646 2441Biochemical Networks Group, Department of Information in Matter, AMOLF, 1098 XG Amsterdam, The Netherlands
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3
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Pandey PP, Singh H, Jain S. Exponential trajectories, cell size fluctuations, and the adder property in bacteria follow from simple chemical dynamics and division control. Phys Rev E 2021; 101:062406. [PMID: 32688579 DOI: 10.1103/physreve.101.062406] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2019] [Accepted: 04/03/2020] [Indexed: 02/03/2023]
Abstract
Experiments on steady-state bacterial cultures have uncovered several quantitative regularities at the system level. These include, first, the exponential growth of cell size with time and the balanced growth of intracellular chemicals between cell birth and division, which are puzzling given the nonlinear and decentralized chemical dynamics in the cell. We model a cell as a set of chemical populations undergoing nonlinear mass action kinetics in a container whose volume is a linear function of the chemical populations. This turns out to be a special class of dynamical systems that generically has attractors in which all populations grow exponentially with time at the same rate. This explains exponential balanced growth of bacterial cells without invoking any regulatory mechanisms and suggests that this could be a robust property of protocells as well. Second, we consider the hypothesis that cells commit themselves to division when a certain internal chemical population reaches a threshold of N molecules. We show that this hypothesis leads to a simple explanation of some of the variability observed across cells in a bacterial culture. In particular, it reproduces the adder property of cell size fluctuations observed recently in E. coli; the observed correlations among interdivision time, birth volume, and added volume in a generation; and the observed scale of the fluctuations (CV ≈ 10-30%) when N is between 10 and 100. Third, upon including a suitable regulatory mechanism that optimizes the growth rate of the cell, the model reproduces the observed bacterial growth laws including the dependence of the growth rate and ribosomal protein fraction on the medium. Thus, the models provide a framework for unifying diverse aspects of bacterial growth physiology under one roof. They also suggest new questions for experimental and theoretical enquiry.
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Affiliation(s)
- Parth Pratim Pandey
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Harshant Singh
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Sanjay Jain
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.,Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
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4
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Zhang Q, Zhang Z, Shi H. Cell Size Is Coordinated with Cell Cycle by Regulating Initiator Protein DnaA in E. coli. Biophys J 2020; 119:2537-2557. [PMID: 33189684 DOI: 10.1016/j.bpj.2020.10.034] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 09/22/2020] [Accepted: 10/16/2020] [Indexed: 10/23/2022] Open
Abstract
Sixty years ago, bacterial cell size was found to be an exponential function of growth rate. Fifty years ago, a more general relationship was proposed, in which cell mass was equal to the initiation mass multiplied by 2 to the power of the ratio of the total time of C and D periods to the doubling time. This relationship has recently been experimentally confirmed by perturbing doubling time, C period, D period, or initiation mass. However, the underlying molecular mechanism remains unclear. Here, we developed a theoretical model for initiator protein DnaA mediating DNA replication initiation in Escherichia coli. We introduced an initiation probability function for competitive binding of DnaA-ATP and DnaA-ADP at oriC. We established a kinetic description of regulatory processes (e.g., expression regulation, titration, inactivation, and reactivation) of DnaA. Cell size as a spatial constraint also participates in the regulation of DnaA. By simulating DnaA kinetics, we obtained a regular DnaA oscillation coordinated with cell cycle and a converged cell size that matches replication initiation frequency to the growth rate. The relationship between the simulated cell size and growth rate, C period, D period, or initiation mass reproduces experimental results. The model also predicts how DnaA number and initiation mass vary with perturbation parameters, comparable with experimental data. The results suggest that 1) when growth rate, C period, or D period changes, the regulation of DnaA determines the invariance of initiation mass; 2) ppGpp inhibition of replication initiation may be important for the growth rate independence of initiation mass because three possible mechanisms therein produce different DnaA dynamics, which is experimentally verifiable; and 3) perturbation of some DnaA regulatory process causes a changing initiation mass or even an abnormal cell cycle. This study may provide clues for concerted control of cell size and cell cycle in synthetic biology.
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Affiliation(s)
- Qing Zhang
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.
| | - Zhichao Zhang
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China
| | - Hualin Shi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
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5
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Rao P, Rozgaja TA, Alqahtani A, Grimwade JE, Leonard AC. Low Affinity DnaA-ATP Recognition Sites in E. coli oriC Make Non-equivalent and Growth Rate-Dependent Contributions to the Regulated Timing of Chromosome Replication. Front Microbiol 2018; 9:1673. [PMID: 30093890 PMCID: PMC6070618 DOI: 10.3389/fmicb.2018.01673] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Accepted: 07/04/2018] [Indexed: 11/13/2022] Open
Abstract
Although the mechanisms that precisely time initiation of chromosome replication in bacteria remain unclear, most clock models are based on accumulation of the active initiator protein, DnaA-ATP. During each cell division cycle, sufficient DnaA-ATP must become available to interact with a distinct set of low affinity recognition sites in the unique chromosomal replication origin, oriC, and assemble the pre-replicative complex (orisome) that unwinds origin DNA and helps load the replicative helicase. The low affinity oriC-DnaA-ATP interactions are required for the orisome's mechanical functions, and may also play a role in timing of new rounds of DNA synthesis. To further examine this possibility, we constructed chromosomal oriCs with equal preference for DnaA-ADP or DnaA-ATP at one or more low affinity recognition sites, thereby lowering the DnaA-ATP requirement for orisome assembly, and measured the effect of the mutations on cell cycle timing of DNA synthesis. Under slow growth conditions, mutation of any one of the six low affinity DnaA-ATP sites in chromosomal oriC resulted in initiation earlier in the cell cycle, but the shift was not equivalent for every recognition site. Mutation of τ2 caused a greater change in initiation age, suggesting its occupation by DnaA-ATP is a temporal bottleneck during orisome assembly. In contrast, during rapid growth, all origins with a single mutated site displayed wild-type initiation timing. Based on these observations, we propose that E. coli uses two different, DnaA-ATP-dependent initiation timing mechanisms; a slow growth timer that is directly coupled to individual site occupation, and a fast growth timer comprising DnaA-ATP and additional factors that regulate DnaA access to oriC. Analysis of origins with paired mutated sites suggests that Fis is an important component of the fast growth timing mechanism.
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Affiliation(s)
- Prassanna Rao
- Department of Biological Sciences, Florida Institute of Technology, Melbourne, FL, United States
| | | | - Abdulaziz Alqahtani
- Department of Biological Sciences, Florida Institute of Technology, Melbourne, FL, United States
| | - Julia E Grimwade
- Department of Biological Sciences, Florida Institute of Technology, Melbourne, FL, United States
| | - Alan C Leonard
- Department of Biological Sciences, Florida Institute of Technology, Melbourne, FL, United States
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Co AD, Lagomarsino MC, Caselle M, Osella M. Stochastic timing in gene expression for simple regulatory strategies. Nucleic Acids Res 2017; 45:1069-1078. [PMID: 28180313 PMCID: PMC5388427 DOI: 10.1093/nar/gkw1235] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2016] [Revised: 11/09/2016] [Accepted: 11/24/2016] [Indexed: 12/15/2022] Open
Abstract
Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potential consequences on biological functions and phenotypes. Here, we consider such ‘timing fluctuations’ and we ask how they can be controlled. Our analytical estimates and simulations show that, for an induced gene, timing variability is minimal if the threshold level of expression is approximately half of the steady-state level. Timing fluctuations can be reduced by increasing the transcription rate, while they are insensitive to the translation rate. In presence of self-regulatory strategies, we show that self-repression reduces timing noise for threshold levels that have to be reached quickly, while self-activation is optimal at long times. These results lay a framework for understanding stochasticity of endogenous systems such as the cell cycle, as well as for the design of synthetic trigger circuits.
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Affiliation(s)
- Alma Dal Co
- Department of Physics and INFN, Università degli Studi di Torino, via P. Giuria 1, Turin, Italy
| | - Marco Cosentino Lagomarsino
- Sorbonne Universités, Université Pierre et Marie Curie, Institut de Biologie Paris Seine, Place Jussieu 4, Paris, France.,UMR 7238 CNRS, Computational and Quantitative Biology, Paris, France.,IFOM, FIRC Institute of Molecular Oncology, Via Adamello 16, Milan, Italy
| | - Michele Caselle
- Department of Physics and INFN, Università degli Studi di Torino, via P. Giuria 1, Turin, Italy
| | - Matteo Osella
- Department of Physics and INFN, Università degli Studi di Torino, via P. Giuria 1, Turin, Italy
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7
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Step by Step, Cell by Cell: Quantification of the Bacterial Cell Cycle. Trends Microbiol 2017; 25:250-256. [DOI: 10.1016/j.tim.2016.12.005] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2016] [Revised: 11/09/2016] [Accepted: 12/12/2016] [Indexed: 11/22/2022]
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Khlebodarova TM, Likhoshvai VA. New evidence of an old problem: The coupling of genome replication to cell growth in bacteria. RUSS J GENET+ 2014. [DOI: 10.1134/s102279541408002x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Likhoshvai VA, Khlebodarova TM. Mathematical modeling of bacterial cell cycle: the problem of coordinating genome replication with cell growth. J Bioinform Comput Biol 2014; 12:1450009. [PMID: 24969747 DOI: 10.1142/s0219720014500097] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we perform an analysis of bacterial cell-cycle models implementing different strategies to coordinately regulate genome replication and cell growth dynamics. It has been shown that the problem of coupling these processes does not depend directly on the dynamics of cell volume expansion, but does depend on the type of cell growth law. Our analysis has distinguished two types of cell growth laws, "exponential" and "linear", each of which may include both exponential and linear patterns of cell growth. If a cell grows following a law of the "exponential" type, including the exponential V(t) = V(0) exp (kt) and linear V(t) = V(0)(1 + kt) dynamic patterns, then the cell encounters the problem of coupling growth rates and replication. It has been demonstrated that to solve the problem, it is sufficient for a cell to have a repressor mechanism to regulate DNA replication initiation. For a cell expanding its volume by a law of the "linear" type, including exponential V(t) = V(0) + V(1) exp (kt) and linear V(t) = V(0) + kt dynamic patterns, the problem of coupling growth rates and replication does not exist. In other words, in the context of the coupling problem, a repressor mechanism to regulate DNA replication, and cell growth laws of the "linear" type displays the attributes of universality. The repressor-type mechanism allows a cell to follow any growth dynamic pattern, while the "linear" type growth law allows a cell to use any mechanism to regulate DNA replication.
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Affiliation(s)
- Vitaly A Likhoshvai
- Institute of Cytology and Genetics, Siberian Branch, Russian Academy of Sciences, Prospekt Lavrentieva 10, Novosibirsk 630090, Russia , Novosibirsk State University, av. Pirogova 2, Novosibirsk 630090, Russia
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10
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Abstract
The coordination of cell growth and division is a long-standing problem in biology. Focusing on Escherichia coli in steady growth, we quantify cell division control using a stochastic model, by inferring the division rate as a function of the observable parameters from large empirical datasets of dividing cells. We find that (i) cells have mechanisms to control their size, (ii) size control is effected by changes in the doubling time, rather than in the single-cell elongation rate, (iii) the division rate increases steeply with cell size for small cells, and saturates for larger cells. Importantly, (iv) the current size is not the only variable controlling cell division, but the time spent in the cell cycle appears to play a role, and (v) common tests of cell size control may fail when such concerted control is in place. Our analysis illustrates the mechanisms of cell division control in E. coli. The phenomenological framework presented is sufficiently general to be widely applicable and opens the way for rigorous tests of molecular cell-cycle models.
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11
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Temperature-dependence of the DnaA-DNA interaction and its effect on the autoregulation of dnaA expression. Biochem J 2013; 449:333-41. [PMID: 23092251 DOI: 10.1042/bj20120876] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The DnaA protein is a key factor for the regulation of the timing and synchrony of initiation of bacterial DNA replication. The transcription of the dnaA gene in Escherichia coli is regulated by two promoters, dnaAP1 and dnaAP2. The region between these two promoters contains several DnaA-binding sites that have been shown to play an important role in the negative auto-regulation of dnaA expression. The results obtained in the present study using an in vitro and in vivo quantitative analysis of the effect of mutations to the high-affinity DnaA sites reveal an additional effect of positive autoregulation. We investigated the role of transcription autoregulation in the change of dnaA expression as a function of temperature. While negative auto-regulation is lost at dnaAP1, the effects of both positive and negative autoregulation are maintained at the dnaAP2 promoter upon lowering the growth temperature. These observations can be explained by the results obtained in vitro showing a difference in the temperature-dependence of DnaA-ATP binding to its high- and low-affinity sites, resulting in a decrease in DnaA-ATP oligomerization at lower temperatures. The results of the present study underline the importance of the role for autoregulation of gene expression in the cellular adaptation to different growth temperatures.
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Zarei M, Sclavi B, Cosentino Lagomarsino M. Gene silencing and large-scale domain structure of the E. coli genome. MOLECULAR BIOSYSTEMS 2013; 9:758-67. [DOI: 10.1039/c3mb25364c] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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13
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Osella M, Lagomarsino MC. Growth-rate-dependent dynamics of a bacterial genetic oscillator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012726. [PMID: 23410378 DOI: 10.1103/physreve.87.012726] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2012] [Revised: 12/22/2012] [Indexed: 05/26/2023]
Abstract
Gene networks exhibiting oscillatory dynamics are widespread in biology. The minimal regulatory designs giving rise to oscillations have been implemented synthetically and studied by mathematical modeling. However, most of the available analyses generally neglect the coupling of regulatory circuits with the cellular "chassis" in which the circuits are embedded. For example, the intracellular macromolecular composition of fast-growing bacteria changes with growth rate. As a consequence, important parameters of gene expression, such as ribosome concentration or cell volume, are growth-rate dependent, ultimately coupling the dynamics of genetic circuits with cell physiology. This work addresses the effects of growth rate on the dynamics of a paradigmatic example of genetic oscillator, the repressilator. Making use of empirical growth-rate dependencies of parameters in bacteria, we show that the repressilator dynamics can switch between oscillations and convergence to a fixed point depending on the cellular state of growth, and thus on the nutrients it is fed. The physical support of the circuit (type of plasmid or gene positions on the chromosome) also plays an important role in determining the oscillation stability and the growth-rate dependence of period and amplitude. This analysis has potential application in the field of synthetic biology, and suggests that the coupling between endogenous genetic oscillators and cell physiology can have substantial consequences for their functionality.
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Affiliation(s)
- Matteo Osella
- Genomic Physics Group, UMR7238 CNRS Microorganism Genomics, 15, rue de l'École de Médecine, Paris, France.
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