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Abstract
An enduring mystery of development is how its timing is controlled, particularly for development after birth, where timing is highly flexible and depends on environmental conditions, such as food availability and diet. We followed timing of cell- and organism-level events in individual Caenorhabditis elegans larvae developing from hatching to adulthood, uncovering widespread variations in event timing, both between isogenic individuals in the same environment and when changing conditions and genotypes. However, in almost all cases, we found that events occurred at the same time, when time was rescaled by the duration of development measured in each individual. This observation of “temporal scaling” poses strong constraints on models to explain timing of larval development. It is essential that correct temporal order of cellular events is maintained during animal development. During postembryonic development, the rate of development depends on external conditions, such as food availability, diet, and temperature. How timing of cellular events is impacted when the rate of development is changed at the organism level is not known. We used a unique time-lapse microscopy approach to simultaneously measure timing of oscillatory gene expression, hypodermal stem cell divisions, and cuticle shedding in individual Caenorhabditis elegans larvae, as they developed from hatching to adulthood. This revealed strong variability in timing between isogenic individuals under the same conditions. However, this variability obeyed “temporal scaling,” meaning that events occurred at the same time when measured relative to the total duration of development in each individual. We also observed pervasive changes in timing when temperature, diet, or genotype were varied, but with larval development divided in “epochs” that differed in how event timing was impacted. Yet, these variations in timing were still explained by temporal scaling when time was rescaled by the duration of the respective epochs in each individual. Surprisingly, timing obeyed temporal scaling even in mutants lacking lin-42/Period, presumed a core regulator of timing of larval development, that exhibited strongly delayed, heterogeneous timing. However, shifting conditions middevelopment perturbed temporal scaling and changed event order in a highly condition-specific manner, indicating that a complex machinery is responsible for temporal scaling under constant conditions.
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2
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Razavi M, Saberi Fathi SM, Tuszynski JA. The Effect of the Protein Synthesis Entropy Reduction on the Cell Size Regulation and Division Size of Unicellular Organisms. ENTROPY 2022; 24:e24010094. [PMID: 35052120 PMCID: PMC8775074 DOI: 10.3390/e24010094] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Revised: 12/04/2021] [Accepted: 12/28/2021] [Indexed: 12/14/2022]
Abstract
The underlying mechanism determining the size of a particular cell is one of the fundamental unknowns in cell biology. Here, using a new approach that could be used for most of unicellular species, we show that the protein synthesis and cell size are interconnected biophysically and that protein synthesis may be the chief mechanism in establishing size limitations of unicellular organisms. This result is obtained based on the free energy balance equation of protein synthesis and the second law of thermodynamics. Our calculations show that protein synthesis involves a considerable amount of entropy reduction due to polymerization of amino acids depending on the cytoplasmic volume of the cell. The amount of entropy reduction will increase with cell growth and eventually makes the free energy variations of the protein synthesis positive (that is, forbidden thermodynamically). Within the limits of the second law of thermodynamics we propose a framework to estimate the optimal cell size at division.
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Affiliation(s)
- Mohammad Razavi
- Department of Physics, Faculty of Science, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran;
| | - Seyed Majid Saberi Fathi
- Department of Physics, Faculty of Science, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran;
- Correspondence:
| | - Jack Adam Tuszynski
- Department of Oncology, University of Alberta, Edmonton, AB T6G 1Z2, Canada;
- Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
- Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Torino, Italy
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3
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The Ethanologenic Bacterium Zymomonas mobilis Divides Asymmetrically and Exhibits Heterogeneity in DNA Content. Appl Environ Microbiol 2021; 87:AEM.02441-20. [PMID: 33452021 DOI: 10.1128/aem.02441-20] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 12/23/2020] [Indexed: 02/04/2023] Open
Abstract
The alphaproteobacterium Zymomonas mobilis exhibits extreme ethanologenic physiology, making this species a promising biofuel producer. Numerous studies have investigated its biology relevant to industrial applications and mostly at the population level. However, the organization of single cells in this industrially important polyploid species has been largely uncharacterized. In the present study, we characterized basic cellular behavior of Z. mobilis strain Zm6 under anaerobic conditions at the single-cell level. We observed that growing Z. mobilis cells often divided at a nonmidcell position, which contributed to variant cell size at birth. However, the cell size variance was regulated by a modulation of cell cycle span, mediated by a correlation of bacterial tubulin homologue FtsZ ring accumulation with cell growth. The Z. mobilis culture also exhibited heterogeneous cellular DNA content among individual cells, which might have been caused by asynchronous replication of chromosome that was not coordinated with cell growth. Furthermore, slightly angled divisions might have resulted in temporary curvatures of attached Z. mobilis cells. Overall, the present study uncovers a novel bacterial cell organization in Z. mobilis IMPORTANCE With increasing environmental concerns about the use of fossil fuels, development of a sustainable biofuel production platform has been attracting significant public attention. Ethanologenic Z. mobilis species are endowed with an efficient ethanol fermentation capacity that surpasses, in several respects, that of baker's yeast (Saccharomyces cerevisiae), the most-used microorganism for ethanol production. For development of a Z. mobilis culture-based biorefinery, an investigation of its uncharacterized cell biology is important, because bacterial cellular organization and metabolism are closely associated with each other in a single cell compartment. In addition, the current work demonstrates that the polyploid bacterium Z. mobilis exhibits a distinctive mode of bacterial cell organization, likely reflecting its unique metabolism that does not prioritize incorporation of nutrients for cell growth. Thus, another significant result of this work is to advance our general understanding in the diversity of bacterial cell architecture.
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4
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Serbanescu D, Ojkic N, Banerjee S. Nutrient-Dependent Trade-Offs between Ribosomes and Division Protein Synthesis Control Bacterial Cell Size and Growth. Cell Rep 2020; 32:108183. [DOI: 10.1016/j.celrep.2020.108183] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Revised: 06/24/2020] [Accepted: 09/01/2020] [Indexed: 01/06/2023] Open
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5
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Huang T, Yuan H, Fan L, Moregen M. H-NS, IHF, and DnaA lead to changes in nucleoid organizations, replication initiation, and cell division. J Basic Microbiol 2019; 60:136-148. [PMID: 32011760 DOI: 10.1002/jobm.201900497] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 10/08/2019] [Accepted: 10/18/2019] [Indexed: 12/29/2022]
Abstract
Histone-like nucleoid-structuring protein (H-NS) and integration host factor (IHF) are major nucleoid-associated proteins, and DnaA, a replication initiator, may also be related with nucleoid compaction. It has been shown that protein-dependent DNA compaction is related with many aspects of bacterial physiology, including transcription, DNA replication, and site-specific recombination. However, the mechanism of bacterial physiology resulting from nucleoid compaction remains unknown. Here, we show that H-NS is important for correct nucleoid compaction in a medium-independent manner. H-NS-mediated nucleoid compaction is not required for correct cell division, but the latter is dependent on H-NS in rich medium. Further, it is found that the IHFα-mediated nucleoid compaction is needed for correct cell division, and the effect is dependent on medium. Also, we show that the effects of H-NS and IHF on nucleoid compaction are cumulative. Interestingly, DnaA also plays an important role in nucleoid compaction, and the effect of DnaA on nucleoid compaction appears to be related to cell division in a medium-dependent manner. The results presented here suggest that scrambled initiation of replication, improper cell division, and slow growth is likely associated with disturbances in nucleoid organization directly or indirectly.
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Affiliation(s)
- Tingting Huang
- State Key Laboratory of Reproductive Regulation and Breeding of Grassland Livestock, School of Life Sciences, Inner Mongolia University, Hohhot, China.,Daban No. 1 Middle School, Chifeng, China
| | - Hong Yuan
- State Key Laboratory of Reproductive Regulation and Breeding of Grassland Livestock, School of Life Sciences, Inner Mongolia University, Hohhot, China.,Basic Medical College, Inner Mongolia Medical University, Hohhot, China
| | - Lifei Fan
- State Key Laboratory of Reproductive Regulation and Breeding of Grassland Livestock, School of Life Sciences, Inner Mongolia University, Hohhot, China
| | - Morigen Moregen
- State Key Laboratory of Reproductive Regulation and Breeding of Grassland Livestock, School of Life Sciences, Inner Mongolia University, Hohhot, China
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6
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Wen K, Huang L, Wang Q, Yu J. Modulation of first-passage time for gene expression via asymmetric cell division. INT J BIOMATH 2019. [DOI: 10.1142/s1793524519500529] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
How to balance the size of exponentially growing cells has always been a focus of biologists. Recent experiments have uncovered that the cell is divided into two daughter cells only when the level of time-keeper protein reaches a fixed threshold and cell division in prokaryote is not completely symmetric. The timing of cell division is essentially random because gene expression is stochastic, but cells seen to manage to have precise timing of cell division events. Although the inter-cellular variability of gene expression has attracted much attention, the randomness of event timing has been rarely studied. In our analysis, the timing of cell division is formulated as the first-passage time (denoted by FPT) for time-keeper protein’s level to cross a critical threshold firstly, we derive exact analytical formulae for the mean and noise of FPT based on stochastic gene expression model with asymmetric cell division. The results of numerical simulation show that the regulatory factors (division rate, newborn cell size, exponential growth rate and threshold) have significant influence on the mean and noise of FPT. We also show that both the increase of division rate and newborn cell size could reduce the mean of FPT and increase the noise of FPT, the larger the exponential growth rate is, the smaller the mean and noise of FPT will be; and the larger the threshold value is, the higher the mean of FPT is and the lower the noise is. In addition, compared with symmetric division, asymmetric division can reduce the mean of FPT and improve the noise of FPT. In summary, our results provide insight into the relationship between regulatory factors and FPT and reveal that asymmetric division is an effective mechanism to shorten the mean of FPT.
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Affiliation(s)
- Kunwen Wen
- School of Mathematics, Jiaying University, Meizhou 514015, P. R. China
| | - Lifang Huang
- School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China
| | - Qi Wang
- Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, P. R. China
| | - Jianshe Yu
- Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, P. R. China
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7
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Ivanov IN, Vítová M, Bišová K. Growth and the cell cycle in green algae dividing by multiple fission. Folia Microbiol (Praha) 2019; 64:663-672. [PMID: 31347103 DOI: 10.1007/s12223-019-00741-z] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Accepted: 07/15/2019] [Indexed: 11/24/2022]
Abstract
Most cells divide into two daughter cells; however, some green algae can have different division patterns in which a single mother cell can sometimes give rise to up to thousands of daughter cells. Although such cell cycle patterns can be very complex, they are governed by the same general concepts as the most common binary fission. Moreover, cell cycle progression appears to be connected with size, since cells need to ensure that their size after division will not drop below the limit required for survival. Although the exact mechanism that lets cells measure cell size remains largely unknown, there have been several prominent hypotheses that try to explain it.
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Affiliation(s)
- Ivan Nedyalkov Ivanov
- Institute of Microbiology, Centre Algatech, Laboratory of Cell Cycles of Algae, Opatovický mlýn, Czech Academy of Sciences, 379 81, Třeboň, Czech Republic.,Faculty of Science, University of South Bohemia, Branišovská 1760, 370 05, České Budějovice, Czech Republic
| | - Milada Vítová
- Institute of Microbiology, Centre Algatech, Laboratory of Cell Cycles of Algae, Opatovický mlýn, Czech Academy of Sciences, 379 81, Třeboň, Czech Republic
| | - Kateřina Bišová
- Institute of Microbiology, Centre Algatech, Laboratory of Cell Cycles of Algae, Opatovický mlýn, Czech Academy of Sciences, 379 81, Třeboň, Czech Republic.
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Lag Phase Is a Dynamic, Organized, Adaptive, and Evolvable Period That Prepares Bacteria for Cell Division. J Bacteriol 2019; 201:JB.00697-18. [PMID: 30642990 DOI: 10.1128/jb.00697-18] [Citation(s) in RCA: 121] [Impact Index Per Article: 24.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
Lag is a temporary period of nonreplication seen in bacteria that are introduced to new media. Despite latency being described by Müller in 1895, only recently have we gained insights into the cellular processes characterizing lag phase. This review covers literature to date on the transcriptomic, proteomic, metabolomic, physiological, biochemical, and evolutionary features of prokaryotic lag. Though lag is commonly described as a preparative phase that allows bacteria to harvest nutrients and adapt to new environments, the implications of recent studies indicate that a refinement of this view is well deserved. As shown, lag is a dynamic, organized, adaptive, and evolvable process that protects bacteria from threats, promotes reproductive fitness, and is broadly relevant to the study of bacterial evolution, host-pathogen interactions, antibiotic tolerance, environmental biology, molecular microbiology, and food safety.
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9
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Björklund M. Cell size homeostasis: Metabolic control of growth and cell division. BIOCHIMICA ET BIOPHYSICA ACTA-MOLECULAR CELL RESEARCH 2018; 1866:409-417. [PMID: 30315834 DOI: 10.1016/j.bbamcr.2018.10.002] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Revised: 09/25/2018] [Accepted: 10/03/2018] [Indexed: 12/14/2022]
Abstract
Joint regulation of growth rate and cell division rate determines cell size. Here we discuss how animal cells achieve cell size homeostasis potentially involving multiple signaling pathways converging at metabolic regulation of growth rate and cell cycle progression. While several models have been developed to explain cell size control, comparison of the two predominant models shows that size homeostasis is dependent on the ability to adjust cellular growth rate based on cell size. Consequently, maintenance of size homeostasis requires that larger cells can grow slower than small cells in relative terms. We review recent experimental evidence showing that such size adjustment occurs primarily at or immediately before the G1/S transition of the cell cycle. We further propose that bidirectional feedback between growth rate and size results in cell size sensing and discuss potential mechanisms how this may be accomplished.
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Affiliation(s)
- Mikael Björklund
- Zhejiang University-University of Edinburgh (ZJU-UoE) Institute, Zhejiang University School of Medicine, International Campus, 718 East Haizhou Rd., Haining, Zhejiang 314400, PR China.
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10
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A Markovian Approach towards Bacterial Size Control and Homeostasis in Anomalous Growth Processes. Sci Rep 2018; 8:9612. [PMID: 29942025 PMCID: PMC6018433 DOI: 10.1038/s41598-018-27748-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2017] [Accepted: 06/04/2018] [Indexed: 11/26/2022] Open
Abstract
Regardless of the progress achieved during recent years, the mechanisms coupling growth and division to attain cell size homeostasis in bacterial populations are still not well understood. In particular, there is a gap of knowledge about the mechanisms controlling anomalous growth events that are ubiquitous even in wild-type phenotypes. Thus, when cells exceed the doubling size the divisome dynamics sets a characteristic length scale that suggests a sizer property. Yet, it has been recently shown that the size at birth and the size increment still satisfy an adder-like correlation. Herein we propose a Markov chain model, that we complement with computational and experimental approaches, to clarify this issue. In this context, we show that classifying cells as a function of the characteristic size set by the divisome dynamics provides a compelling framework to understand size convergence, growth, and division at the large length scale, including the adaptation to, and rescue from, filamentation processes. Our results reveal the independence of size homeostasis on the division pattern of long cells and help to reconcile sizer concepts at the single cell level with an adder-like behavior at a population level.
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11
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Abstract
Microbial cells go through repeated cycles of growth and division. These cycles are not perfect: the time and size at division can fluctuate from one cycle to the next. Still, cell size is kept tightly controlled, and fluctuations do not accumulate to large deviations. How this control is implemented in single cells is still not fully understood. We performed experiments that follow individual bacteria in microfluidic traps for hundreds of generations. This enables us to identify distinct individual dynamic properties that are maintained over many cycles of growth and division. Surprisingly, we find that each cell suppresses fluctuations with a different strength; this variability defines an “individual” behavior for each cell, which is inherited along many generations. Microbial growth and division are fundamental processes relevant to many areas of life science. Of particular interest are homeostasis mechanisms, which buffer growth and division from accumulating fluctuations over multiple cycles. These mechanisms operate within single cells, possibly extending over several division cycles. However, all experimental studies to date have relied on measurements pooled from many distinct cells. Here, we disentangle long-term measured traces of individual cells from one another, revealing subtle differences between temporal and pooled statistics. By analyzing correlations along up to hundreds of generations, we find that the parameter describing effective cell size homeostasis strength varies significantly among cells. At the same time, we find an invariant cell size, which acts as an attractor to all individual traces, albeit with different effective attractive forces. Despite the common attractor, each cell maintains a distinct average size over its finite lifetime with suppressed temporal fluctuations around it, and equilibration to the global average size is surprisingly slow (>150 cell cycles). To show a possible source of variable homeostasis strength, we construct a mathematical model relying on intracellular interactions, which integrates measured properties of cell size with those of highly expressed proteins. Effective homeostasis strength is then influenced by interactions and by noise levels and generally varies among cells. A predictable and measurable consequence of variable homeostasis strength appears as distinct oscillatory patterns in cell size and protein content over many generations. We discuss implications of our results to understanding mechanisms controlling division in single cells and their characteristic timescales.
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12
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Huls PG, Vischer NOE, Woldringh CL. Different Amounts of DNA in Newborn Cells of Escherichia coli Preclude a Role for the Chromosome in Size Control According to the "Adder" Model. Front Microbiol 2018; 9:664. [PMID: 29675011 PMCID: PMC5895768 DOI: 10.3389/fmicb.2018.00664] [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: 12/04/2017] [Accepted: 03/21/2018] [Indexed: 11/18/2022] Open
Abstract
According to the recently-revived adder model for cell size control, newborn cells of Escherichia coli will grow and divide after having added a constant size or length, ΔL, irrespective of their size at birth. Assuming exponential elongation, this implies that large newborns will divide earlier than small ones. The molecular basis for the constant size increment is still unknown. As DNA replication and cell growth are coordinated, the constant ΔL could be based on duplication of an equal amount of DNA, ΔG, present in newborn cells. To test this idea, we measured amounts of DNA and lengths of nucleoids in DAPI-stained cells growing in batch culture at slow and fast rates. Deeply-constricted cells were divided in two subpopulations of longer and shorter lengths than average; these were considered to represent large and small prospective daughter cells, respectively. While at slow growth, large and small prospective daughter cells contained similar amounts of DNA, fast growing cells with multiforked replicating chromosomes, showed a significantly higher amount of DNA (20%) in the larger cells. This observation precludes the hypothesis that ΔL is based on the synthesis of a constant ΔG. Growth curves were constructed for siblings generated by asymmetric division and growing according to the adder model. Under the assumption that all cells at the same growth rate exhibit the same time between initiation of DNA replication and cell division (i.e., constant C+D-period), the constructions predict that initiation occurs at different sizes (Li) and that, at fast growth, large newborn cells transiently contain more DNA than small newborns, in accordance with the observations. Because the state of segregation, measured as the distance between separated nucleoids, was found to be more advanced in larger deeply-constricted cells, we propose that in larger newborns nucleoid separation occurs faster and at a shorter length, allowing them to divide earlier. We propose a composite model in which both differential initiation and segregation leads to an adder-like behavior of large and small newborn cells.
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Affiliation(s)
- Peter G Huls
- Faculty of Science, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, Netherlands
| | - Norbert O E Vischer
- Bacterial Cell Biology, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, Netherlands
| | - Conrad L Woldringh
- Bacterial Cell Biology, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, Netherlands
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13
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Wehrens M, Ershov D, Rozendaal R, Walker N, Schultz D, Kishony R, Levin PA, Tans SJ. Size Laws and Division Ring Dynamics in Filamentous Escherichia coli cells. Curr Biol 2018; 28:972-979.e5. [PMID: 29502951 DOI: 10.1016/j.cub.2018.02.006] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2017] [Revised: 12/07/2017] [Accepted: 02/05/2018] [Indexed: 10/17/2022]
Abstract
Our understanding of bacterial cell size control is based mainly on stress-free growth conditions in the laboratory [1-10]. In the real world, however, bacteria are routinely faced with stresses that produce long filamentous cell morphologies [11-28]. Escherichia coli is observed to filament in response to DNA damage [22-25], antibiotic treatment [11-14, 28], host immune systems [15, 16], temperature [17], starvation [20], and more [18, 19, 21], conditions which are relevant to clinical settings and food preservation [26]. This shape plasticity is considered a survival strategy [27]. Size control in this regime remains largely unexplored. Here we report that E. coli cells use a dynamic size ruler to determine division locations combined with an adder-like mechanism to trigger divisions. As filamentous cells increase in size due to growth, or decrease in size due to divisions, its multiple Fts division rings abruptly reorganize to remain one characteristic cell length away from the cell pole and two such length units away from each other. These rules can be explained by spatiotemporal oscillations of Min proteins. Upon removal of filamentation stress, the cells undergo a sequence of division events, randomly at one of the possible division sites, on average after the time required to grow one characteristic cell size. These results indicate that E. coli cells continuously keep track of absolute length to control size, suggest a wider relevance for the adder principle beyond the control of normally sized cells, and provide a new perspective on the function of the Fts and Min systems.
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Affiliation(s)
| | - Dmitry Ershov
- AMOLF, Science Park 104, 1098 XG Amsterdam, the Netherlands
| | | | - Noreen Walker
- AMOLF, Science Park 104, 1098 XG Amsterdam, the Netherlands
| | - Daniel Schultz
- Department of Biology, Technion-Israel Institute of Technology, Haifa 32000, Israel; Department of Systems Biology, Harvard Medical School, Boston MA 02138, USA
| | - Roy Kishony
- Department of Biology, Technion-Israel Institute of Technology, Haifa 32000, Israel; Department of Systems Biology, Harvard Medical School, Boston MA 02138, USA
| | - Petra Anne Levin
- Department of Biology, Washington University, One Brookings Drive, St. Louis, MO, USA
| | - Sander J Tans
- AMOLF, Science Park 104, 1098 XG Amsterdam, the Netherlands; Bionanoscience Department, Delft University of Technology, Van der Maasweg 9, 2629 HZ Delft, the Netherlands.
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14
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Barber F, Ho PY, Murray AW, Amir A. Details Matter: Noise and Model Structure Set the Relationship between Cell Size and Cell Cycle Timing. Front Cell Dev Biol 2017; 5:92. [PMID: 29164112 PMCID: PMC5675860 DOI: 10.3389/fcell.2017.00092] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2017] [Accepted: 10/05/2017] [Indexed: 12/31/2022] Open
Abstract
Organisms across all domains of life regulate the size of their cells. However, the means by which this is done is poorly understood. We study two abstracted “molecular” models for size regulation: inhibitor dilution and initiator accumulation. We apply the models to two settings: bacteria like Escherichia coli, that grow fully before they set a division plane and divide into two equally sized cells, and cells that form a bud early in the cell division cycle, confine new growth to that bud, and divide at the connection between that bud and the mother cell, like the budding yeast Saccharomyces cerevisiae. In budding cells, delaying cell division until buds reach the same size as their mother leads to very weak size control, with average cell size and standard deviation of cell size increasing over time and saturating up to 100-fold higher than those values for cells that divide when the bud is still substantially smaller than its mother. In budding yeast, both inhibitor dilution or initiator accumulation models are consistent with the observation that the daughters of diploid cells add a constant volume before they divide. This “adder” behavior has also been observed in bacteria. We find that in bacteria an inhibitor dilution model produces adder correlations that are not robust to noise in the timing of DNA replication initiation or in the timing from initiation of DNA replication to cell division (the C+D period). In contrast, in bacteria an initiator accumulation model yields robust adder correlations in the regime where noise in the timing of DNA replication initiation is much greater than noise in the C + D period, as reported previously (Ho and Amir, 2015). In bacteria, division into two equally sized cells does not broaden the size distribution.
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Affiliation(s)
- Felix Barber
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, United States
| | - Po-Yi Ho
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, United States
| | - Andrew W Murray
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, United States.,FAS Center for Systems Biology, Harvard University, Cambridge, MA, United States
| | - Ariel Amir
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, United States
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15
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Modi S, Vargas-Garcia CA, Ghusinga KR, Singh A. Analysis of Noise Mechanisms in Cell-Size Control. Biophys J 2017; 112:2408-2418. [PMID: 28591613 DOI: 10.1016/j.bpj.2017.04.050] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2016] [Revised: 03/27/2017] [Accepted: 04/24/2017] [Indexed: 11/15/2022] Open
Abstract
At the single-cell level, noise arises from multiple sources, such as inherent stochasticity of biomolecular processes, random partitioning of resources at division, and fluctuations in cellular growth rates. How these diverse noise mechanisms combine to drive variations in cell size within an isoclonal population is not well understood. Here, we investigate the contributions of different noise sources in well-known paradigms of cell-size control, such as adder (division occurs after adding a fixed size from birth), sizer (division occurs after reaching a size threshold), and timer (division occurs after a fixed time from birth). Analysis reveals that variation in cell size is most sensitive to errors in partitioning of volume among daughter cells, and not surprisingly, this process is well regulated among microbes. Moreover, depending on the dominant noise mechanism, different size-control strategies (or a combination of them) provide efficient buffering of size variations. We further explore mixer models of size control, where a timer phase precedes/follows an adder, as has been proposed in Caulobacter crescentus. Although mixing a timer and an adder can sometimes attenuate size variations, it invariably leads to higher-order moments growing unboundedly over time. This results in a power-law distribution for the cell size, with an exponent that depends inversely on the noise in the timer phase. Consistent with theory, we find evidence of power-law statistics in the tail of C. crescentus cell-size distribution, although there is a discrepancy between the observed power-law exponent and that predicted from the noise parameters. The discrepancy, however, is removed after data reveal that the size added by individual newborns in the adder phase itself exhibits power-law statistics. Taken together, this study provides key insights into the role of noise mechanisms in size homeostasis, and suggests an inextricable link between timer-based models of size control and heavy-tailed cell-size distributions.
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Affiliation(s)
- Saurabh Modi
- Department of Biomedical Engineering, University of Delaware, Newark, Delaware
| | | | - Khem Raj Ghusinga
- Department of Electrical and Computer Engineering, University of Delaware, Newark, Delaware
| | - Abhyudai Singh
- Department of Biomedical Engineering, University of Delaware, Newark, Delaware; Department of Electrical and Computer Engineering, University of Delaware, Newark, Delaware; Department of Mathematical Sciences, University of Delaware, Newark, Delaware.
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17
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Furse S, Jakubec M, Rise F, Williams HE, Rees CED, Halskau Ø. Evidence that Listeria innocua modulates its membrane's stored curvature elastic stress, but not fluidity, through the cell cycle. Sci Rep 2017; 7:8012. [PMID: 28808346 PMCID: PMC5556093 DOI: 10.1038/s41598-017-06855-z] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2017] [Accepted: 06/20/2017] [Indexed: 01/22/2023] Open
Abstract
This paper reports that the abundances of endogenous cardiolipin and phosphatidylethanolamine halve during elongation of the Gram-positive bacterium Listeria innocua. The lyotropic phase behaviour of model lipid systems that describe these modulations in lipid composition indicate that the average stored curvature elastic stress of the membrane is reduced on elongation of the cell, while the fluidity appears to be maintained. These findings suggest that phospholipid metabolism is linked to the cell cycle and that changes in membrane composition can facilitate passage to the succeding stage of the cell cycle. This therefore suggests a means by which bacteria can manage the physical properties of their membranes through the cell cycle.
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Affiliation(s)
- Samuel Furse
- Department of Molecular Biology, University of Bergen, Thormøhlensgate 55, NO-5006, Bergen, Norway
| | - Martin Jakubec
- Department of Molecular Biology, University of Bergen, Thormøhlensgate 55, NO-5006, Bergen, Norway
| | - Frode Rise
- Department of Chemistry, University of Oslo, P. O. Box 1033, Blindern, NO-0315, Oslo, Norway
| | - Huw E Williams
- Centre for Biomolecular Sciences, University of Nottingham, University Park, NG7 2RD, Nottingham, United Kingdom
| | - Catherine E D Rees
- School of Biosciences, University of Nottingham, Sutton Bonington Campus, LE12 5RD, Nottinghamshire, United Kingdom
| | - Øyvind Halskau
- Department of Molecular Biology, University of Bergen, Thormøhlensgate 55, NO-5006, Bergen, Norway.
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18
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du Lac M, Scarpelli AH, Younger AKD, Bates DG, Leonard JN. Predicting the Dynamics and Heterogeneity of Genomic DNA Content within Bacterial Populations across Variable Growth Regimes. ACS Synth Biol 2017; 6:1131-1139. [PMID: 27689718 DOI: 10.1021/acssynbio.5b00217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
For many applications in microbial synthetic biology, optimizing a desired function requires careful tuning of the degree to which various genes are expressed. One challenge for predicting such effects or interpreting typical characterization experiments is that in bacteria such as E. coli, genome copy number varies widely across different phases and rates of growth, which also impacts how and when genes are expressed from different loci. While such phenomena are relatively well-understood at a mechanistic level, our quantitative understanding of such processes is essentially limited to ideal exponential growth. In contrast, common experimental phenomena such as growth on heterogeneous media, metabolic adaptation, and oxygen restriction all cause substantial deviations from ideal exponential growth, particularly as cultures approach the higher densities at which industrial biomanufacturing and even routine screening experiments are conducted. To meet the need for predicting and explaining how gene dosage impacts cellular functions outside of exponential growth, we here report a novel modeling strategy that leverages agent-based simulation and high performance computing to robustly predict the dynamics and heterogeneity of genomic DNA content within bacterial populations across variable growth regimes. We show that by feeding routine experimental data, such as optical density time series, into our heterogeneous multiphasic growth simulator, we can predict genomic DNA distributions over a range of nonexponential growth conditions. This modeling strategy provides an important advance in the ability of synthetic biologists to evaluate the role of genomic DNA content and heterogeneity in affecting the performance of existing or engineered microbial functions.
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Affiliation(s)
- Melchior du Lac
- Warwick
Integrative Synthetic Biology Centre, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | | | | | - Declan G. Bates
- Warwick
Integrative Synthetic Biology Centre, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
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19
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Zheng XY, O'Shea EK. Cyanobacteria Maintain Constant Protein Concentration despite Genome Copy-Number Variation. Cell Rep 2017; 19:497-504. [PMID: 28423314 DOI: 10.1016/j.celrep.2017.03.067] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Revised: 03/22/2017] [Accepted: 03/23/2017] [Indexed: 11/25/2022] Open
Abstract
The cyanobacterium Synechococcus elongatus PCC 7942 has multiple copies of its single chromosome, and the copy number varies in individual cells, providing an ideal system to study the effect of genome copy-number variation on cell size and gene expression. Using single-cell fluorescence imaging, we found that protein concentration remained constant across individual cells regardless of genome copy number. Cell volume and the total protein amount from a single gene were both positively, linearly correlated with genome copy number, suggesting that changes in cell volume play an important role in buffering genome copy-number variance. This study provides a quantitative examination of gene expression regulation in cells with variable genome copies and sheds light on the compensation mechanisms for variance in genome copy number.
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Affiliation(s)
- Xiao-Yu Zheng
- Howard Hughes Medical Institute, Harvard University Faculty of Arts and Sciences Center for Systems Biology, Harvard University, Cambridge, MA 02138, USA; Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138, USA
| | - Erin K O'Shea
- Howard Hughes Medical Institute, Harvard University Faculty of Arts and Sciences Center for Systems Biology, Harvard University, Cambridge, MA 02138, USA; Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138, USA; Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA.
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20
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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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21
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A mechanistic stochastic framework for regulating bacterial cell division. Sci Rep 2016; 6:30229. [PMID: 27456660 PMCID: PMC4960620 DOI: 10.1038/srep30229] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2016] [Accepted: 06/29/2016] [Indexed: 12/20/2022] Open
Abstract
How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells add a fixed size (volume) from birth to division, irrespective of their size at birth. To mechanistically explain the adder principle, we consider a timekeeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that the noise in division timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distribution of the added volume when scaled by its mean becomes invariant of the growth rate. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for controlling size.
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22
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Marantan A, Amir A. Stochastic modeling of cell growth with symmetric or asymmetric division. Phys Rev E 2016; 94:012405. [PMID: 27575162 DOI: 10.1103/physreve.94.012405] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2016] [Indexed: 11/07/2022]
Abstract
We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.
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Affiliation(s)
- Andrew Marantan
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ariel Amir
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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23
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Adder and a coarse-grained approach to cell size homeostasis in bacteria. Curr Opin Cell Biol 2016; 38:38-44. [PMID: 26901290 DOI: 10.1016/j.ceb.2016.02.004] [Citation(s) in RCA: 73] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Revised: 01/14/2016] [Accepted: 02/03/2016] [Indexed: 12/29/2022]
Abstract
Cell size control and homeostasis is a long-standing subject in biology. Recent experimental work provides extensive evidence for a simple, quantitative size homeostasis principle coined adder (as opposed to sizer or timer). The adder principle provides unexpected insights into how bacteria maintain their size without employing a feedback mechanism. We review the genesis of adder and recent cell size homeostasis study on evolutionarily divergent bacterial organisms and beyond. We propose new coarse-grained approaches to understand the underlying mechanisms of cell size control at the whole cell level.
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24
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Fievet A, Ducret A, Mignot T, Valette O, Robert L, Pardoux R, Dolla AR, Aubert C. Single-Cell Analysis of Growth and Cell Division of the Anaerobe Desulfovibrio vulgaris Hildenborough. Front Microbiol 2015; 6:1378. [PMID: 26696987 PMCID: PMC4672049 DOI: 10.3389/fmicb.2015.01378] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Accepted: 11/20/2015] [Indexed: 01/08/2023] Open
Abstract
Recent years have seen significant progress in understanding basic bacterial cell cycle properties such as cell growth and cell division. While characterization and regulation of bacterial cell cycle is quite well-documented in the case of fast growing aerobic model organisms, no data has been so far reported for anaerobic bacteria. This lack of information in anaerobic microorganisms can mainly be explained by the absence of molecular and cellular tools such as single cell microscopy and fluorescent probes usable for anaerobes and essential to study cellular events and/or subcellular localization of the actors involved in cell cycle. In this study, single-cell microscopy has been adapted to study for the first time, in real time, the cell cycle of a bacterial anaerobe, Desulfovibrio vulgaris Hildenborough (DvH). This single-cell analysis provides mechanistic insights into the cell division cycle of DvH, which seems to be governed by the recently discussed so-called incremental model that generates remarkably homogeneous cell sizes. Furthermore, cell division was reversibly blocked during oxygen exposure. This may constitute a strategy for anaerobic cells to cope with transient exposure to oxygen that they may encounter in their natural environment, thereby contributing to their aerotolerance. This study lays the foundation for the first molecular, single-cell assay that will address factors that cannot otherwise be resolved in bulk assays and that will allow visualization of a wide range of molecular mechanisms within living anaerobic cells.
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Affiliation(s)
- Anouchka Fievet
- Centre National de la Recherche Scientifique, Laboratoire de Chimie Bactérienne UMR 7283, Aix Marseille Université Marseille, France
| | - Adrien Ducret
- Centre National de la Recherche Scientifique, Laboratoire de Chimie Bactérienne UMR 7283, Aix Marseille Université Marseille, France
| | - Tâm Mignot
- Centre National de la Recherche Scientifique, Laboratoire de Chimie Bactérienne UMR 7283, Aix Marseille Université Marseille, France
| | - Odile Valette
- Centre National de la Recherche Scientifique, Laboratoire de Chimie Bactérienne UMR 7283, Aix Marseille Université Marseille, France
| | - Lydia Robert
- INRA, UMR1319 Micalis Jouy-en-Josas, France ; AgroParisTech, UMR Micalis Jouy-en-Josas, France
| | - Romain Pardoux
- Centre National de la Recherche Scientifique, Laboratoire de Chimie Bactérienne UMR 7283, Aix Marseille Université Marseille, France
| | - Alain R Dolla
- Centre National de la Recherche Scientifique, Laboratoire de Chimie Bactérienne UMR 7283, Aix Marseille Université Marseille, France
| | - Corinne Aubert
- Centre National de la Recherche Scientifique, Laboratoire de Chimie Bactérienne UMR 7283, Aix Marseille Université Marseille, France
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25
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Schmoller KM, Skotheim JM. The Biosynthetic Basis of Cell Size Control. Trends Cell Biol 2015; 25:793-802. [PMID: 26573465 DOI: 10.1016/j.tcb.2015.10.006] [Citation(s) in RCA: 87] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Revised: 10/12/2015] [Accepted: 10/12/2015] [Indexed: 11/16/2022]
Abstract
Cell size is an important physiological trait that sets the scale of all biosynthetic processes. Although physiological studies have revealed that cells actively regulate their size, the molecular mechanisms underlying this regulation have remained unclear. Here we review recent progress in identifying the molecular mechanisms of cell size control. We focus on budding yeast, where cell growth dilutes a cell cycle inhibitor to couple growth and division. We discuss a new model for size control based on the titration of activator and inhibitor molecules whose synthesis rates are differentially dependent on cell size.
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Affiliation(s)
- Kurt M Schmoller
- Department of Biology, Stanford University, Stanford, CA 94305, USA
| | - Jan M Skotheim
- Department of Biology, Stanford University, Stanford, CA 94305, USA.
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26
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Zaritsky A, Woldringh CL. Chromosome replication, cell growth, division and shape: a personal perspective. Front Microbiol 2015; 6:756. [PMID: 26284044 PMCID: PMC4522554 DOI: 10.3389/fmicb.2015.00756] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Accepted: 07/10/2015] [Indexed: 11/13/2022] Open
Abstract
The origins of Molecular Biology and Bacterial Physiology are reviewed, from our personal standpoints, emphasizing the coupling between bacterial growth, chromosome replication and cell division, dimensions and shape. Current knowledge is discussed with historical perspective, summarizing past and present achievements and enlightening ideas for future studies. An interactive simulation program of the bacterial cell division cycle (BCD), described as "The Central Dogma in Bacteriology," is briefly represented. The coupled process of transcription/translation of genes encoding membrane proteins and insertion into the membrane (so-called transertion) is invoked as the functional relationship between the only two unique macromolecules in the cell, DNA and peptidoglycan embodying the nucleoid and the sacculus respectively. We envision that the total amount of DNA associated with the replication terminus, so called "nucleoid complexity," is directly related to cell size and shape through the transertion process. Accordingly, the primary signal for cell division transmitted by DNA dynamics (replication, transcription and segregation) to the peptidoglycan biosynthetic machinery is of a physico-chemical nature, e.g., stress in the plasma membrane, relieving nucleoid occlusion in the cell's center hence enabling the divisome to assemble and function between segregated daughter nucleoids.
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Affiliation(s)
- Arieh Zaritsky
- Faculty of Natural Sciences, Ben-Gurion University of the Negev, Be’er-Sheva, Israel
| | - Conrad L. Woldringh
- Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, Netherlands
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