1
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Vedel S, Košmrlj A, Nunns H, Trusina A. Synergistic and antagonistic effects of deterministic and stochastic cell-cell variations. Phys Rev E 2024; 109:054404. [PMID: 38907460 DOI: 10.1103/physreve.109.054404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 04/05/2024] [Indexed: 06/24/2024]
Abstract
By diversifying, cells in a clonal population can together overcome the limits of individuals. Diversity in single-cell growth rates allows the population to survive environmental stresses, such as antibiotics, and grow faster than the undiversified population. These functional cell-cell variations can arise stochastically, from noise in biochemical reactions, or deterministically, by asymmetrically distributing damaged components. While each of the mechanisms is well understood, the effect of the combined mechanisms is unclear. To evaluate the contribution of the deterministic component we developed a mathematical model by mapping the growing population to the Ising model. To analyze the combined effects of stochastic and deterministic contributions we introduced the analytical results of the Ising-mapping into an Euler-Lotka framework. Model results, confirmed by simulations and experimental data, show that deterministic cell-cell variations increase near-linearly with stress. As a consequence, we predict that the gain in population doubling time from cell-cell variations is primarily stochastic at low stress but may cross over to deterministic at higher stresses. Furthermore, we find that while the deterministic component minimizes population damage, stochastic variations antagonize this effect. Together our results may help identifying stress-tolerant pathogenic cells and thus inspire novel antibiotic strategies.
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Affiliation(s)
- Søren Vedel
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
- Center for Models of Life, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Andrej Košmrlj
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
| | - Harry Nunns
- Center for Models of Life, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
- Division of Biology and Biological Engineering, California Institute of Technology, 1200 E. California Boulevard, Pasadena, California 91125, USA
| | - Ala Trusina
- Center for Models of Life, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
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2
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Nieto C, Täuber S, Blöbaum L, Vahdat Z, Grünberger A, Singh A. Coupling Cell Size Regulation and Proliferation Dynamics of C. glutamicum Reveals Cell Division Based on Surface Area. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.12.26.573217. [PMID: 38234762 PMCID: PMC10793411 DOI: 10.1101/2023.12.26.573217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Single cells actively coordinate growth and division to regulate their size, yet how this size homeostasis at the single-cell level propagates over multiple generations to impact clonal expansion remains fundamentally unexplored. Classical timer models for cell proliferation (where the duration of the cell cycle is an independent variable) predict that the stochastic variation in colony size will increase monotonically over time. In stark contrast, implementing size control according to adder strategy (where on average a fixed size added from cell birth to division) leads to colony size variations that eventually decay to zero. While these results assume a fixed size of the colony-initiating progenitor cell, further analysis reveals that the magnitude of the intercolony variation in population number is sensitive to heterogeneity in the initial cell size. We validate these predictions by tracking the growth of isogenic microcolonies of Corynebacterium glutamicum in microfluidic chambers. Approximating their cell shape to a capsule, we observe that the degree of random variability in cell size is different depending on whether the cell size is quantified as per length, surface area, or volume, but size control remains an adder regardless of these size metrics. A comparison of the observed variability in the colony population with the predictions suggests that proliferation matches better with a cell division based on the cell surface. In summary, our integrated mathematical-experimental approach bridges the paradigms of single-cell size regulation and clonal expansion at the population levels. This innovative approach provides elucidation of the mechanisms of size homeostasis from the stochastic dynamics of colony size for rod-shaped microbes.
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Affiliation(s)
- César Nieto
- Department of Electrical and Computing Engineering, University of Delaware. Newark, DE 19716, USA
| | - Sarah Täuber
- CeBiTec, Bielefeld University. Bielefeld, Germany
- Multiscale Bioengineering, Technical Faculty, Bielefeld University. Bielefeld, Germany
| | - Luisa Blöbaum
- CeBiTec, Bielefeld University. Bielefeld, Germany
- Multiscale Bioengineering, Technical Faculty, Bielefeld University. Bielefeld, Germany
| | - Zahra Vahdat
- Department of Electrical and Computing Engineering, University of Delaware. Newark, DE 19716, USA
| | - Alexander Grünberger
- CeBiTec, Bielefeld University. Bielefeld, Germany
- Multiscale Bioengineering, Technical Faculty, Bielefeld University. Bielefeld, Germany
- Institute of Process Engineering in Life Sciences: Microsystems in Bioprocess Engineering, Karlsruhe Institute of Technology. Karlsruhe, Germany
| | - Abhyudai Singh
- Department of Electrical and Computing Engineering, University of Delaware. Newark, DE 19716, USA
- Center for Bioinformatics and Computational Biology, University of Delaware, Newark, DE 19716 USA
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3
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Fischer SC, Schardt S, Lilao-Garzón J, Muñoz-Descalzo S. The salt-and-pepper pattern in mouse blastocysts is compatible with signaling beyond the nearest neighbors. iScience 2023; 26:108106. [PMID: 37915595 PMCID: PMC10616410 DOI: 10.1016/j.isci.2023.108106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Revised: 08/03/2023] [Accepted: 09/26/2023] [Indexed: 11/03/2023] Open
Abstract
Embryos develop in a concerted sequence of spatiotemporal arrangements of cells. In the preimplantation mouse embryo, the distribution of the cells in the inner cell mass evolves from a salt-and-pepper pattern to spatial segregation of two distinct cell types. The exact properties of the salt-and-pepper pattern have not been analyzed so far. We investigate the spatiotemporal distribution of NANOG- and GATA6-expressing cells in the ICM of the mouse blastocysts with quantitative three-dimensional single-cell-based neighborhood analyses. A combination of spatial statistics and agent-based modeling reveals that the cell fate distribution follows a local clustering pattern. Using ordinary differential equations modeling, we show that this pattern can be established by a distance-based signaling mechanism enabling cells to integrate information from the whole inner cell mass into their cell fate decision. Our work highlights the importance of longer-range signaling to ensure coordinated decisions in groups of cells to successfully build embryos.
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Affiliation(s)
- Sabine C. Fischer
- Julius-Maximilians-Universität Würzburg, Faculty of Biology, Center for Computational and Theoretical Biology, Klara-Oppenheimer-Weg 32, Campus Hubland Nord, 97074 Würzburg, Germany
| | - Simon Schardt
- Julius-Maximilians-Universität Würzburg, Faculty of Biology, Center for Computational and Theoretical Biology, Klara-Oppenheimer-Weg 32, Campus Hubland Nord, 97074 Würzburg, Germany
| | - Joaquín Lilao-Garzón
- Instituto Universitario de Investigaciones Biomédicas y Sanitarias (IUIBS), Universidad Las Palmas de Gran Canaria (ULPGC), Paseo Blas Cabrera Felipe "Físico" 17, Las Palmas de Gran Canaria 35016, Spain
| | - Silvia Muñoz-Descalzo
- Instituto Universitario de Investigaciones Biomédicas y Sanitarias (IUIBS), Universidad Las Palmas de Gran Canaria (ULPGC), Paseo Blas Cabrera Felipe "Físico" 17, Las Palmas de Gran Canaria 35016, Spain
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4
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Wehrens M, Krah LHJ, Towbin BD, Hermsen R, Tans SJ. The interplay between metabolic stochasticity and cAMP-CRP regulation in single E. coli cells. Cell Rep 2023; 42:113284. [PMID: 37864793 DOI: 10.1016/j.celrep.2023.113284] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Revised: 07/17/2023] [Accepted: 09/29/2023] [Indexed: 10/23/2023] Open
Abstract
The inherent stochasticity of metabolism raises a critical question for understanding homeostasis: are cellular processes regulated in response to internal fluctuations? Here, we show that, in E. coli cells under constant external conditions, catabolic enzyme expression continuously responds to metabolic fluctuations. The underlying regulatory feedback is enabled by the cyclic AMP (cAMP) and cAMP receptor protein (CRP) system, which controls catabolic enzyme expression based on metabolite concentrations. Using single-cell microscopy, genetic constructs in which this feedback is disabled, and mathematical modeling, we show how fluctuations circulate through the metabolic and genetic network at sub-cell-cycle timescales. Modeling identifies four noise propagation modes, including one specific to CRP regulation. Together, these modes correctly predict noise circulation at perturbed cAMP levels. The cAMP-CRP system may thus have evolved to control internal metabolic fluctuations in addition to external growth conditions. We conjecture that second messengers may more broadly function to achieve cellular homeostasis.
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Affiliation(s)
- Martijn Wehrens
- AMOLF, 1098 XG Amsterdam, the Netherlands; Hubrecht Institute, Royal Netherlands Academy of Arts and Sciences (KNAW) and University Medical Center, 3584 CT Utrecht, the Netherlands
| | - Laurens H J Krah
- Theoretical Biology Group, Biology Department, Utrecht University, 3584 CH Utrecht, the Netherlands; Centre for Complex Systems Studies, Utrecht University, 3584 CE Utrecht, the Netherlands
| | - Benjamin D Towbin
- Institute of Cell Biology, University of Bern, 3012 Bern, Switzerland
| | - Rutger Hermsen
- Theoretical Biology Group, Biology Department, Utrecht University, 3584 CH Utrecht, the Netherlands; Centre for Complex Systems Studies, Utrecht University, 3584 CE Utrecht, the Netherlands
| | - Sander J Tans
- AMOLF, 1098 XG Amsterdam, the Netherlands; Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2629 HZ Delft, the Netherlands.
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5
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Jafarpour F, Levien E, Amir A. Evolutionary dynamics in non-Markovian models of microbial populations. Phys Rev E 2023; 108:034402. [PMID: 37849168 DOI: 10.1103/physreve.108.034402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 06/07/2023] [Indexed: 10/19/2023]
Abstract
In the past decade, great strides have been made to quantify the dynamics of single-cell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of single-cell growth and division influence evolutionary dynamics. This requires us to connect processes on the single-cell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the single-cell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarse-grained so that the forces of natural selection and genetic drift can be expressed in terms of the long-term fitness? We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the single-cell dynamics affect the fate of a new mutant independently from how they affect the long-term growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multispecies generalization of the Euler-Lotka equation.
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Affiliation(s)
- Farshid Jafarpour
- Institute for Theoretical Physics, Utrecht University, 3584 CC Utrecht, The Netherlands
| | - Ethan Levien
- Mathematics Department, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Ariel Amir
- Department of Complex Systems, Faculty of Physics, The Weizmann Institute of Science, Rehovot 7610001, Israel
- John A. Paulson, School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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6
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Daniels M, van Vliet S, Ackermann M. Changes in interactions over ecological time scales influence single-cell growth dynamics in a metabolically coupled marine microbial community. THE ISME JOURNAL 2023; 17:406-416. [PMID: 36611102 PMCID: PMC9938273 DOI: 10.1038/s41396-022-01312-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/03/2022] [Accepted: 08/23/2022] [Indexed: 01/09/2023]
Abstract
Microbial communities thrive in almost all habitats on earth. Within these communities, cells interact through the release and uptake of metabolites. These interactions can have synergistic or antagonistic effects on individual community members. The collective metabolic activity of microbial communities leads to changes in their local environment. As the environment changes over time, the nature of the interactions between cells can change. We currently lack understanding of how such dynamic feedbacks affect the growth dynamics of individual microbes and of the community as a whole. Here we study how interactions mediated by the exchange of metabolites through the environment change over time within a simple marine microbial community. We used a microfluidic-based approach that allows us to disentangle the effect cells have on their environment from how they respond to their environment. We found that the interactions between two species-a degrader of chitin and a cross-feeder that consumes metabolic by-products-changes dynamically over time as cells modify their environment. Cells initially interact positively and then start to compete at later stages of growth. Our results demonstrate that interactions between microorganisms are not static and depend on the state of the environment, emphasizing the importance of disentangling how modifications of the environment affects species interactions. This experimental approach can shed new light on how interspecies interactions scale up to community level processes in natural environments.
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Affiliation(s)
- Michael Daniels
- Department of Environmental Systems Sciences, Microbial Systems Ecology Group, Institute of Biogeochemistry and Pollutant Dynamics, ETH-Zurich, Zurich, Switzerland. .,Department of Environmental Microbiology, Eawag: Swiss Federal Institute of Aquatic Sciences, Duebendorf, Switzerland. .,Interdisciplinary PhD Program Systems Biology, ETH-Zurich and University of Zurich, Zurich, Switzerland.
| | - Simon van Vliet
- grid.6612.30000 0004 1937 0642Biozentrum, University of Basel, Basel, Switzerland
| | - Martin Ackermann
- grid.5801.c0000 0001 2156 2780Department of Environmental Systems Sciences, Microbial Systems Ecology Group, Institute of Biogeochemistry and Pollutant Dynamics, ETH-Zurich, Zurich, Switzerland ,Department of Environmental Microbiology, Eawag: Swiss Federal Institute of Aquatic Sciences, Duebendorf, Switzerland
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7
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Genthon A. Analytical cell size distribution: lineage-population bias and parameter inference. J R Soc Interface 2022; 19:20220405. [PMID: 36416039 PMCID: PMC9682439 DOI: 10.1098/rsif.2022.0405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Accepted: 11/01/2022] [Indexed: 11/25/2023] Open
Abstract
We derive analytical steady-state cell size distributions for size-controlled cells in single-lineage experiments, such as the mother machine, which are fundamentally different from batch cultures where populations of cells grow freely. For exponential single-cell growth, characterizing most bacteria, the lineage-population bias is obtained explicitly. In addition, if volume is evenly split between the daughter cells at division, we show that cells are on average smaller in populations than in lineages. For more general power-law growth rates and deterministic volume partitioning, both symmetric and asymmetric, we derive the exact lineage distribution. This solution is in good agreement with Escherichia coli mother machine data and can be used to infer cell cycle parameters such as the strength of the size control and the asymmetry of the division. When introducing stochastic volume partitioning, we derive the large-size and small-size tails of the lineage distribution and show that the lineage-population bias only depends on the single-cell growth rate. These asymptotic behaviours are extended to the adder model of cell size control. When considering noisy single-cell growth rate, we derive the large-size lineage and population distributions. Finally, we show that introducing noise, either on the volume partitioning or on the single-cell growth rate, can cancel the lineage-population bias.
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Affiliation(s)
- Arthur Genthon
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
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8
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Nieto C, Vargas-García C, Pedraza JM. Continuous rate modeling of bacterial stochastic size dynamics. Phys Rev E 2021; 104:044415. [PMID: 34781449 DOI: 10.1103/physreve.104.044415] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2021] [Accepted: 10/06/2021] [Indexed: 12/26/2022]
Abstract
Bacterial division is an inherently stochastic process with effects on fluctuations of protein concentration and phenotype variability. Current modeling tools for the stochastic short-term cell-size dynamics are scarce and mainly phenomenological. Here we present a general theoretical approach based on the Chapman-Kolmogorov equation incorporating continuous growth and division events as jump processes. This approach allows us to include different division strategies, noisy growth, and noisy cell splitting. Considering bacteria synchronized from their last division, we predict oscillations in both the central moments of the size distribution and its autocorrelation function. These oscillations, barely discussed in past studies, can arise as a consequence of the discrete time displacement invariance of the system with a period of one doubling time, and they do not disappear when including stochasticity on either division times or size heterogeneity on the starting population but only after inclusion of noise in either growth rate or septum position. This result illustrates the usefulness of having a solid mathematical description that explicitly incorporates the inherent stochasticity in various biological processes, both to understand the process in detail and to evaluate the effect of various sources of variability when creating simplified descriptions.
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Affiliation(s)
- César Nieto
- Department of Physics, Universidad de los Andes, Bogotá 111711, Colombia.,Department of Electrical and Computer Engineering, University of Delaware, Newark, Delaware 19716, USA
| | - César Vargas-García
- Corporacion Colombiana de Investigación Agropecuaria AGROSAVIA, Mosquera 250047, Colombia
| | - Juan M Pedraza
- Department of Physics, Universidad de los Andes, Bogotá 111711, Colombia
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9
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Pigolotti S. Generalized Euler-Lotka equation for correlated cell divisions. Phys Rev E 2021; 103:L060402. [PMID: 34271641 DOI: 10.1103/physreve.103.l060402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 04/27/2021] [Indexed: 11/07/2022]
Abstract
Cell division times in microbial populations display significant fluctuations that impact the population growth rate in a nontrivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by the Euler-Lotka equation, which is a classic result in mathematical biology. However, cell division times can be significantly correlated, due to physical properties of cells that are passed through generations. In this Letter, we derive an equation remarkably similar to the Euler-Lotka equation which is valid in the presence of correlations. Our exact result is based on large deviation theory and does not require particularly strong assumptions on the underlying dynamics. We apply our theory to a phenomenological model of bacterial cell division in E. coli and to experimental data. We find that the discrepancy between the growth rate predicted by the Euler-Lotka equation and our generalized version is relatively small, but large enough to be measurable by our approach.
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Affiliation(s)
- Simone Pigolotti
- Biological Complexity Unit, Okinawa Institute of Science and Technology and Graduate University, Onna, Okinawa 904-0495, Japan
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10
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Barber F, Min J, Murray AW, Amir A. Modeling the impact of single-cell stochasticity and size control on the population growth rate in asymmetrically dividing cells. PLoS Comput Biol 2021; 17:e1009080. [PMID: 34153030 PMCID: PMC8248971 DOI: 10.1371/journal.pcbi.1009080] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Revised: 07/01/2021] [Accepted: 05/14/2021] [Indexed: 11/18/2022] Open
Abstract
Microbial populations show striking diversity in cell growth morphology and lifecycle; however, our understanding of how these factors influence the growth rate of cell populations remains limited. We use theory and simulations to predict the impact of asymmetric cell division, cell size regulation and single-cell stochasticity on the population growth rate. Our model predicts that coarse-grained noise in the single-cell growth rate λ decreases the population growth rate, as previously seen for symmetrically dividing cells. However, for a given noise in λ we find that dividing asymmetrically can enhance the population growth rate for cells with strong size control (between a “sizer” and an “adder”). To reconcile this finding with the abundance of symmetrically dividing organisms in nature, we propose that additional constraints on cell growth and division must be present which are not included in our model, and we explore the effects of selected extensions thereof. Further, we find that within our model, epigenetically inherited generation times may arise due to size control in asymmetrically dividing cells, providing a possible explanation for recent experimental observations in budding yeast. Taken together, our findings provide insight into the complex effects generated by non-canonical growth morphologies. How rapidly a population of single-celled organisms can grow will strongly impact their long-term success. Prior work has shown that many factors impact this population growth rate, including the rate at which single cells grow, random variability between cells, and whether cells regulate their own size. Here we show that cell division asymmetry can also have a strong impact on the population growth rate. We use theory and computer simulations to study the growth rate of cells that divide asymmetrically, producing one smaller cell and one larger cell with each cell division event. We show that variability in how fast single cells grow will still decrease the population growth rate, when asymmetry is moderate or size control is weak, but that cells with strong size control can diminish this decrease by dividing more asymmetrically. We also demonstrate that cell cycle lengths can be positively correlated for closely related cells when they both divide asymmetrically and regulate their size. This counter-intuitive result contrasts with previous findings based on cell size regulation in symmetrically dividing cells that if cells grow for “too long” in one cell cycle, this will be corrected for by reduced growth during a shorter, subsequent cell cycle.
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Affiliation(s)
- Felix Barber
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts, United States of America
- Center for Genomics and Systems Biology, Department of Biology, New York University, New York, New York, United States of America
| | - Jiseon Min
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Andrew W. Murray
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts, United States of America
- FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Ariel Amir
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, United States of America
- * E-mail:
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11
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Mutability of demographic noise in microbial range expansions. ISME JOURNAL 2021; 15:2643-2654. [PMID: 33746203 PMCID: PMC8397776 DOI: 10.1038/s41396-021-00951-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Accepted: 02/24/2021] [Indexed: 11/13/2022]
Abstract
Demographic noise, the change in the composition of a population due to random birth and death events, is an important driving force in evolution because it reduces the efficacy of natural selection. Demographic noise is typically thought to be set by the population size and the environment, but recent experiments with microbial range expansions have revealed substantial strain-level differences in demographic noise under the same growth conditions. Many genetic and phenotypic differences exist between strains; to what extent do single mutations change the strength of demographic noise? To investigate this question, we developed a high-throughput method for measuring demographic noise in colonies without the need for genetic manipulation. By applying this method to 191 randomly-selected single gene deletion strains from the E. coli Keio collection, we find that a typical single gene deletion mutation decreases demographic noise by 8% (maximal decrease: 81%). We find that the strength of demographic noise is an emergent trait at the population level that can be predicted by colony-level traits but not cell-level traits. The observed differences in demographic noise from single gene deletions can increase the establishment probability of beneficial mutations by almost an order of magnitude (compared to in the wild type). Our results show that single mutations can substantially alter adaptation through their effects on demographic noise and suggest that demographic noise can be an evolvable trait of a population.
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12
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Jia C, Singh A, Grima R. Cell size distribution of lineage data: analytic results and parameter inference. iScience 2021; 24:102220. [PMID: 33748708 PMCID: PMC7961097 DOI: 10.1016/j.isci.2021.102220] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Revised: 01/29/2021] [Accepted: 02/17/2021] [Indexed: 01/06/2023] Open
Abstract
Recent advances in single-cell technologies have enabled time-resolved measurements of the cell size over several cell cycles. These data encode information on how cells correct size aberrations so that they do not grow abnormally large or small. Here, we formulate a piecewise deterministic Markov model describing the evolution of the cell size over many generations, for all three cell size homeostasis strategies (timer, sizer, and adder). The model is solved to obtain an analytical expression for the non-Gaussian cell size distribution in a cell lineage; the theory is used to understand how the shape of the distribution is influenced by the parameters controlling the dynamics of the cell cycle and by the choice of cell tracking protocol. The theoretical cell size distribution is found to provide an excellent match to the experimental cell size distribution of E. coli lineage data collected under various growth conditions.
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Affiliation(s)
- Chen Jia
- Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, China
| | - Abhyudai Singh
- Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, EH9 3JH, UK
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13
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Levien E, GrandPre T, Amir A. Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations. PHYSICAL REVIEW LETTERS 2020; 125:048102. [PMID: 32794821 DOI: 10.1103/physrevlett.125.048102] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 06/18/2020] [Indexed: 06/11/2023]
Abstract
In exponentially proliferating populations of microbes, the population doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population's growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a population's growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a nonmonotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.
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Affiliation(s)
- Ethan Levien
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, Harvard 02138, USA
| | - Trevor GrandPre
- Department of Physics, University of California, Berkeley, California, Berkeley 94720, USA
| | - Ariel Amir
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, Harvard 02138, USA
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14
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Blitvić N, Fernandez VI. Aging a little: On the optimality of limited senescence in Escherichia coli. J Theor Biol 2020; 502:110331. [PMID: 32439456 DOI: 10.1016/j.jtbi.2020.110331] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Revised: 04/04/2020] [Accepted: 05/11/2020] [Indexed: 12/31/2022]
Abstract
Recent studies have shown that even in the absence of extrinsic stress, the morphologically symmetrically dividing model bacteria Escherichia coli do not generate offspring with equal reproductive fitness. Instead, daughter cells exhibit asymmetric division times that converge to two distinct growth states. This represents a limited senescence/rejuvenation process derived from asymmetric division that is stable for hundreds of generations. It remains unclear why the bacteria do not continue the senescence beyond this asymptote. Although there are inherent fitness benefits for heterogeneity in population growth rates, the two growth equilibria are surprisingly similar, differing by a few percent. In this work we derive an explicit model for the growth of a bacterial population with two growth equilibria, based on a generalized Fibonacci recurrence, in order to quantify the fitness benefit of a limited senescence process and examine costs associated with asymmetry that could generate the observed behavior. We find that a simple saturating effect of asymmetric partitioning of subcellular components is sufficient to explain why two distinct but similar growth states may be optimal while providing evolutionarily significant growth advantages.
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Affiliation(s)
- Natasha Blitvić
- Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YW, United Kingdom.
| | - Vicente I Fernandez
- Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, 8093 Zürich, Switzerland.
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