1
|
Postek W, Staśkiewicz K, Lilja E, Wacław B. Substrate geometry affects population dynamics in a bacterial biofilm. Proc Natl Acad Sci U S A 2024; 121:e2315361121. [PMID: 38621130 PMCID: PMC11047097 DOI: 10.1073/pnas.2315361121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 03/11/2024] [Indexed: 04/17/2024] Open
Abstract
Biofilms inhabit a range of environments, such as dental plaques or soil micropores, often characterized by noneven surfaces. However, the impact of surface irregularities on the population dynamics of biofilms remains elusive, as most experiments are conducted on flat surfaces. Here, we show that the shape of the surface on which a biofilm grows influences genetic drift and selection within the biofilm. We culture Escherichia coli biofilms in microwells with a corrugated bottom surface and observe the emergence of clonal sectors whose size corresponds to that of the corrugations, despite no physical barrier separating different areas of the biofilm. The sectors are remarkably stable and do not invade each other; we attribute this stability to the characteristics of the velocity field within the biofilm, which hinders mixing and clonal expansion. A microscopically detailed computer model fully reproduces these findings and highlights the role of mechanical interactions such as adhesion and friction in microbial evolution. The model also predicts clonal expansion to be limited even for clones with a significant growth advantage-a finding which we confirm experimentally using a mixture of antibiotic-sensitive and antibiotic-resistant mutants in the presence of sublethal concentrations of the antibiotic rifampicin. The strong suppression of selection contrasts sharply with the behavior seen in range expansion experiments in bacterial colonies grown on agar. Our results show that biofilm population dynamics can be affected by patterning the surface and demonstrate how a better understanding of the physics of bacterial growth can be used to control microbial evolution.
Collapse
Affiliation(s)
- Witold Postek
- Dioscuri Centre for Physics and Chemistry of Bacteria, Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa01-224, Poland
- Broad Institute of Massachusetts Institute of Technology and Harvard, Cambridge, MA02142
| | - Klaudia Staśkiewicz
- Dioscuri Centre for Physics and Chemistry of Bacteria, Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa01-224, Poland
| | - Elin Lilja
- Dioscuri Centre for Physics and Chemistry of Bacteria, Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa01-224, Poland
| | - Bartłomiej Wacław
- Dioscuri Centre for Physics and Chemistry of Bacteria, Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa01-224, Poland
- School of Physics and Astronomy, The University of Edinburgh, EdinburghEH9 3FD, United Kingdom
| |
Collapse
|
2
|
Plummer A, Adkins C, Louf JF, Košmrlj A, Datta SS. Obstructed swelling and fracture of hydrogels. SOFT MATTER 2024; 20:1425-1437. [PMID: 38252539 DOI: 10.1039/d3sm01470c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/24/2024]
Abstract
Obstructions influence the growth and expansion of bodies in a wide range of settings-but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system accessible to experiments, simulations, and theory: hydrogels swelling around fixed cylindrical obstacles with varying geometries. When the obstacles are large and widely-spaced, hydrogels swell around them and remain intact. In contrast, our experiments reveal that when the obstacles are narrow and closely-spaced, hydrogels fracture as they swell. We use finite element simulations to map the magnitude and spatial distribution of stresses that build up during swelling at equilibrium in a 2D model, providing a route toward predicting when this phenomenon of self-fracturing is likely to arise. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we also develop a theoretical framework for understanding how the maximum principal tensile and compressive stresses that develop during swelling are controlled by obstacle geometry and material parameters. These results thus help to shed light on the mechanical principles underlying growth/expansion in environments with obstructions.
Collapse
Affiliation(s)
- Abigail Plummer
- Princeton Center for Complex Materials, Princeton University, Princeton, NJ 08540, USA
| | - Caroline Adkins
- Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Jean-François Louf
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA.
- Department of Chemical Engineering, Auburn University, Auburn, AL 36849, USA
| | - Andrej Košmrlj
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA.
- Princeton Materials Institute, Princeton University, Princeton, NJ 08544, USA
| | - Sujit S Datta
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA.
| |
Collapse
|
3
|
Tunstall T, Rogers T, Möbius W. Assisted percolation of slow-spreading mutants in heterogeneous environments. Phys Rev E 2023; 108:044401. [PMID: 37978675 DOI: 10.1103/physreve.108.044401] [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: 03/06/2023] [Accepted: 08/11/2023] [Indexed: 11/19/2023]
Abstract
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This evolutionary dynamic is of practical importance when seeking to prevent the emergence of damaging traits. We show that a subcritical slow-spreading mutant can attain dominance even when the density of patches is below their percolation threshold and predict this transition using geometrical arguments. This work demonstrates a phenomenon of "assisted percolation", where one subcritical process assists another to achieve supercriticality.
Collapse
Affiliation(s)
- Thomas Tunstall
- Living Systems Institute, Faculty of Health and Life Sciences, University of Exeter, Exeter, EX4 4QD, United Kingdom
- Physics and Astronomy, Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QL, United Kingdom
| | - Tim Rogers
- Center for Networks and Collective Behaviour, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
| | - Wolfram Möbius
- Living Systems Institute, Faculty of Health and Life Sciences, University of Exeter, Exeter, EX4 4QD, United Kingdom
- Physics and Astronomy, Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QL, United Kingdom
| |
Collapse
|
4
|
Li LH, Kardar M. Specialization at an expanding front. Phys Rev E 2023; 108:L032402. [PMID: 37849149 DOI: 10.1103/physreve.108.l032402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Accepted: 08/11/2023] [Indexed: 10/19/2023]
Abstract
As a population grows, spreading to new environments may favor specialization. In this paper, we introduce and explore a model for specialization at the front of a colony expanding synchronously into new territory. We show through numerical simulations that, by gaining fitness through accumulating mutations, progeny of the initial seed population can differentiate into distinct specialists. With competition and selection limited to the growth front, the emerging specialists first segregate into sectors, which then expand to dominate the entire population. We quantify the scaling of the fixation time with the size of the population and observe different behaviors corresponding to distinct universality classes: unbounded and bounded gains in fitness lead to superdiffusive (z=3/2) and diffusive (z=2) stochastic wanderings of the sector boundaries, respectively.
Collapse
Affiliation(s)
- Lauren H Li
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
5
|
Golden A, Dukovski I, Segrè D, Korolev KS. Growth instabilities shape morphology and genetic diversity of microbial colonies. Phys Biol 2022; 19:10.1088/1478-3975/ac8514. [PMID: 35901792 PMCID: PMC11209841 DOI: 10.1088/1478-3975/ac8514] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 07/28/2022] [Indexed: 11/11/2022]
Abstract
Cellular populations assume an incredible variety of shapes ranging from circular molds to irregular tumors. While we understand many of the mechanisms responsible for these spatial patterns, little is known about how the shape of a population influences its ecology and evolution. Here, we investigate this relationship in the context of microbial colonies grown on hard agar plates. This a well-studied system that exhibits a transition from smooth circular disks to more irregular and rugged shapes as either the nutrient concentration or cellular motility is decreased. Starting from a mechanistic model of colony growth, we identify two dimensionless quantities that determine how morphology and genetic diversity of the population depend on the model parameters. Our simulations further reveal that population dynamics cannot be accurately described by the commonly-used surface growth models. Instead, one has to explicitly account for the emergent growth instabilities and demographic fluctuations. Overall, our work links together environmental conditions, colony morphology, and evolution. This link is essential for a rational design of concrete, biophysical perturbations to steer evolution in the desired direction.
Collapse
Affiliation(s)
- Alexander Golden
- Department of Physics, Graduate Program in Bioinformatics, and Biological Design Center, Boston University, Boston, MA 02215, United States of America
| | - Ilija Dukovski
- Graduate Program in Bioinformatics, and Biological Design Center, Boston University, Boston, MA 02215, United States of America
| | - Daniel Segrè
- Department of Physics, Department of Biology, Department of Biomedical Engineering, Graduate Program in Bioinformatics, and Biological Design Center, Boston University, Boston, MA 02215, United States of America
| | - Kirill S Korolev
- Department of Physics, Graduate Program in Bioinformatics, and Biological Design Center, Boston University, Boston, MA 02215, United States of America
| |
Collapse
|
6
|
Rare and localized events stabilize microbial community composition and patterns of spatial self-organization in a fluctuating environment. THE ISME JOURNAL 2022; 16:1453-1463. [PMID: 35079136 PMCID: PMC9038690 DOI: 10.1038/s41396-022-01189-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Revised: 12/19/2021] [Accepted: 01/06/2022] [Indexed: 01/07/2023]
Abstract
Spatial self-organization is a hallmark of surface-associated microbial communities that is governed by local environmental conditions and further modified by interspecific interactions. Here, we hypothesize that spatial patterns of microbial cell-types can stabilize the composition of cross-feeding microbial communities under fluctuating environmental conditions. We tested this hypothesis by studying the growth and spatial self-organization of microbial co-cultures consisting of two metabolically interacting strains of the bacterium Pseudomonas stutzeri. We inoculated the co-cultures onto agar surfaces and allowed them to expand (i.e. range expansion) while fluctuating environmental conditions that alter the dependency between the two strains. We alternated between anoxic conditions that induce a mutualistic interaction and oxic conditions that induce a competitive interaction. We observed co-occurrence of both strains in rare and highly localized clusters (referred to as “spatial jackpot events”) that persist during environmental fluctuations. To resolve the underlying mechanisms for the emergence of spatial jackpot events, we used a mechanistic agent-based mathematical model that resolves growth and dispersal at the scale relevant to individual cells. While co-culture composition varied with the strength of the mutualistic interaction and across environmental fluctuations, the model provides insights into the formation of spatially resolved substrate landscapes with localized niches that support the co-occurrence of the two strains and secure co-culture function. This study highlights that in addition to spatial patterns that emerge in response to environmental fluctuations, localized spatial jackpot events ensure persistence of strains across dynamic conditions.
Collapse
|
7
|
Möbius W, Tesser F, Alards KMJ, Benzi R, Nelson DR, Toschi F. The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions. J R Soc Interface 2021; 18:20210579. [PMID: 34665975 PMCID: PMC8526172 DOI: 10.1098/rsif.2021.0579] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here, we study the influence of finite-sized individual inhomogeneities and their collective effect on front speed if randomly placed in a two-dimensional habitat. We use an individual-based model to investigate the front dynamics for a region in which dispersal or growth of individuals is reduced to zero (obstacles) or increased above the background (hotspots), respectively. In a regime where front dynamics is determined by a local front speed only, a principle of least time can be employed to predict front speed and shape. The resulting analytical solutions motivate an event-based algorithm illustrating the effects of several obstacles or hotspots. We finally apply the principle of least time to large heterogeneous environments by solving the Eikonal equation numerically. Obstacles lead to a slow-down that is dominated by the number density and width of obstacles, but not by their precise shape. Hotspots result in a speed-up, which we characterize as function of hotspot strength and density. Our findings emphasize the importance of taking the dimensionality of the environment into account.
Collapse
Affiliation(s)
- Wolfram Möbius
- Living Systems Institute, University of Exeter, Exeter, UK.,Physics and Astronomy, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK.,Department of Applied Physics, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.,Department of Physics, Harvard University, Cambridge, MA, USA
| | - Francesca Tesser
- Department of Applied Physics, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.,PMMH, ESPCI Paris-PSL, Paris, France
| | - Kim M J Alards
- Department of Applied Physics, Technische Universiteit Eindhoven, Eindhoven, The Netherlands
| | - Roberto Benzi
- Universitá di Roma 'Tor Vergata' and INFN, Rome, Italy
| | - David R Nelson
- Department of Physics, Harvard University, Cambridge, MA, USA.,Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, USA
| | - Federico Toschi
- Department of Applied Physics, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.,Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Rome, Italy
| |
Collapse
|
8
|
Azimzade Y, Saberi AA. Geometrically regulating evolutionary dynamics in biofilms. Phys Rev E 2021; 103:L050401. [PMID: 34134254 DOI: 10.1103/physreve.103.l050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Accepted: 04/21/2021] [Indexed: 11/07/2022]
Abstract
The theoretical understanding of evolutionary dynamics in spatially structured populations often relies on nonspatial models. Biofilms are among such populations where a more accurate understanding is of theoretical interest and can reveal new solutions to existing challenges. Here, we studied how the geometry of the environment affects the evolutionary dynamics of expanding populations, using the Eden model. Our results show that fluctuations of subpopulations during range expansion in two- and three-dimensional environments are not Brownian. Furthermore, we found that the substrate's geometry interferes with the evolutionary dynamics of populations that grow upon it. Inspired by these findings, we propose a periodically wedged pattern on surfaces prone to develop biofilms. On such patterned surfaces, natural selection becomes less effective and beneficial mutants would have a harder time establishing. Additionally, this modification accelerates genetic drift and leads to less diverse biofilms. Both interventions are highly desired for biofilms.
Collapse
Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
| | - Abbas Ali Saberi
- Department of Physics, University of Tehran, Tehran 14395-547, Iran.,Institut für Theoretische Physik, Universitat zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany
| |
Collapse
|
9
|
Borer B, Ciccarese D, Johnson D, Or D. Spatial organization in microbial range expansion emerges from trophic dependencies and successful lineages. Commun Biol 2020; 3:685. [PMID: 33208809 PMCID: PMC7674409 DOI: 10.1038/s42003-020-01409-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Accepted: 10/09/2020] [Indexed: 12/15/2022] Open
Abstract
Evidence suggests that bacterial community spatial organization affects their ecological function, yet details of the mechanisms that promote spatial patterns remain difficult to resolve experimentally. In contrast to bacterial communities in liquid cultures, surface-attached range expansion fosters genetic segregation of the growing population with preferential access to nutrients and reduced mechanical restrictions for cells at the expanding periphery. Here we elucidate how localized conditions in cross-feeding bacterial communities shape community spatial organization. We combine experiments with an individual based mathematical model to resolve how trophic dependencies affect localized growth rates and nucleate successful cell lineages. The model tracks individual cell lineages and attributes these with trophic dependencies that promote counterintuitive reproductive advantages and result in lasting influences on the community structure, and potentially, on its functioning. We examine persistence of lucky lineages in structured habitats where expansion is interrupted by physical obstacles to gain insights into patterns in porous domains.
Collapse
Affiliation(s)
- Benedict Borer
- Department of Environmental Systems Science, ETH Zürich, 8092, Zürich, Switzerland.
| | - Davide Ciccarese
- Department of Environmental Systems Science, ETH Zürich, 8092, Zürich, Switzerland
- Department of Environmental Microbiology, Swiss Federal Institute of Aquatic Science and Technology (Eawag), 8600, Dübendorf, Switzerland
| | - David Johnson
- Department of Environmental Microbiology, Swiss Federal Institute of Aquatic Science and Technology (Eawag), 8600, Dübendorf, Switzerland
| | - Dani Or
- Department of Environmental Systems Science, ETH Zürich, 8092, Zürich, Switzerland
| |
Collapse
|
10
|
Ciccarese D, Zuidema A, Merlo V, Johnson DR. Interaction-dependent effects of surface structure on microbial spatial self-organization. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190246. [PMID: 32200742 DOI: 10.1098/rstb.2019.0246] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Surface-attached microbial communities consist of different cell types that, at least to some degree, organize themselves non-randomly across space (referred to as spatial self-organization). While spatial self-organization can have important effects on the functioning, ecology and evolution of communities, the underlying determinants of spatial self-organization remain unclear. Here, we hypothesize that the presence of physical objects across a surface can have important effects on spatial self-organization. Using pairs of isogenic strains of Pseudomonas stutzeri, we performed range expansion experiments in the absence or presence of physical objects and quantified the effects on spatial self-organization. We demonstrate that physical objects create local deformities along the expansion frontier, and these deformities increase in magnitude during range expansion. The deformities affect the densities of interspecific boundaries and diversity along the expansion frontier, and thus affect spatial self-organization, but the effects are interaction-dependent. For competitive interactions that promote sectorized patterns of spatial self-organization, physical objects increase the density of interspecific boundaries and diversity. By contrast, for cross-feeding interactions that promote dendritic patterns, they decrease the density of interspecific boundaries and diversity. These qualitatively different outcomes are probably caused by fundamental differences in the orientations of the interspecific boundaries. Thus, in order to predict the effects of physical objects on spatial self-organization, information is needed regarding the interactions present within a community and the general geometric shapes of spatial self-organization that emerge from those interactions. This article is part of the theme issue 'Conceptual challenges in microbial community ecology'.
Collapse
Affiliation(s)
- Davide Ciccarese
- Department of Environmental Systems Science, ETH Zürich, 8092 Zürich, Switzerland.,Department of Environmental Microbiology, Swiss Federal Institute of Aquatic Science and Technology (Eawag), 8600 Dübendorf, Switzerland
| | - Anita Zuidema
- Department of Environmental Systems Science, ETH Zürich, 8092 Zürich, Switzerland.,Department of Environmental Microbiology, Swiss Federal Institute of Aquatic Science and Technology (Eawag), 8600 Dübendorf, Switzerland
| | - Valeria Merlo
- Department of Environmental Systems Science, ETH Zürich, 8092 Zürich, Switzerland.,Department of Environmental Microbiology, Swiss Federal Institute of Aquatic Science and Technology (Eawag), 8600 Dübendorf, Switzerland
| | - David R Johnson
- Department of Environmental Microbiology, Swiss Federal Institute of Aquatic Science and Technology (Eawag), 8600 Dübendorf, Switzerland
| |
Collapse
|
11
|
Segredo-Otero E, Sanjuán R. The role of spatial structure in the evolution of viral innate immunity evasion: A diffusion-reaction cellular automaton model. PLoS Comput Biol 2020; 16:e1007656. [PMID: 32040504 PMCID: PMC7034925 DOI: 10.1371/journal.pcbi.1007656] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Revised: 02/21/2020] [Accepted: 01/14/2020] [Indexed: 12/20/2022] Open
Abstract
Most viruses have evolved strategies for preventing interferon (IFN) secretion and evading innate immunity. Recent work has shown that viral shutdown of IFN secretion can be viewed as a social trait, since the ability of a given virus to evade IFN-mediated immunity depends on the phenotype of neighbor viruses. Following this idea, we investigate the role of spatial structure in the evolution of innate immunity evasion. For this, we model IFN signaling and viral spread using a spatially explicit approximation that combines a diffusion-reaction model and cellular automaton. Our results indicate that the benefits of preventing IFN secretion for a virus are strongly determined by spatial structure through paracrine IFN signaling. Therefore, innate immunity evasion can evolve as a cooperative or even altruistic trait based on indirect fitness effects that IFN shutdown exerts on other members of the viral population. We identify key factors determining whether evasion from IFN-mediated immunity should evolve, such as population bottlenecks occurring during viral transmission, the relative speed of cellular infection and IFN secretion, and the diffusion properties of the medium.
Collapse
Affiliation(s)
- Ernesto Segredo-Otero
- Institute for Integrative Systems Biology (I2SysBio), Consejo Superior de Investigaciones Científicas-Universitat de València, València, Spain
| | - Rafael Sanjuán
- Institute for Integrative Systems Biology (I2SysBio), Consejo Superior de Investigaciones Científicas-Universitat de València, València, Spain
| |
Collapse
|
12
|
Abstract
Bacterial chemotaxis, the directed movement of cells along gradients of chemoattractants, is among the best-characterized subjects in molecular biology1-10, but much less is known about its physiological roles11. It is commonly seen as a starvation response when nutrients run out, or as an escape response from harmful situations12-16. Here we identify an alternative role of chemotaxis by systematically examining the spatiotemporal dynamics of Escherichia coli in soft agar12,17,18. Chemotaxis in nutrient-replete conditions promotes the expansion of bacterial populations into unoccupied territories well before nutrients run out in the current environment. Low levels of chemoattractants act as aroma-like cues in this process, establishing the direction and enhancing the speed of population movement along the self-generated attractant gradients. This process of navigated range expansion spreads faster and yields larger population gains than unguided expansion following the canonical Fisher-Kolmogorov dynamics19,20 and is therefore a general strategy to promote population growth in spatially extended, nutrient-replete environments.
Collapse
|
13
|
Cremer J, Melbinger A, Wienand K, Henriquez T, Jung H, Frey E. Cooperation in Microbial Populations: Theory and Experimental Model Systems. J Mol Biol 2019; 431:4599-4644. [PMID: 31634468 DOI: 10.1016/j.jmb.2019.09.023] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2019] [Revised: 09/25/2019] [Accepted: 09/26/2019] [Indexed: 01/07/2023]
Abstract
Cooperative behavior, the costly provision of benefits to others, is common across all domains of life. This review article discusses cooperative behavior in the microbial world, mediated by the exchange of extracellular products called public goods. We focus on model species for which the production of a public good and the related growth disadvantage for the producing cells are well described. To unveil the biological and ecological factors promoting the emergence and stability of cooperative traits we take an interdisciplinary perspective and review insights gained from both mathematical models and well-controlled experimental model systems. Ecologically, we include crucial aspects of the microbial life cycle into our analysis and particularly consider population structures where ensembles of local communities (subpopulations) continuously emerge, grow, and disappear again. Biologically, we explicitly consider the synthesis and regulation of public good production. The discussion of the theoretical approaches includes general evolutionary concepts, population dynamics, and evolutionary game theory. As a specific but generic biological example, we consider populations of Pseudomonas putida and its regulation and use of pyoverdines, iron scavenging molecules, as public goods. The review closes with an overview on cooperation in spatially extended systems and also provides a critical assessment of the insights gained from the experimental and theoretical studies discussed. Current challenges and important new research opportunities are discussed, including the biochemical regulation of public goods, more realistic ecological scenarios resembling native environments, cell-to-cell signaling, and multispecies communities.
Collapse
Affiliation(s)
- J Cremer
- Department of Molecular Immunology and Microbiology, Groningen Biomolecular Sciences and Biotechnology Institute, University of Groningen, 9747 AG Groningen, the Netherlands
| | - A Melbinger
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for Nanoscience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
| | - K Wienand
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for Nanoscience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
| | - T Henriquez
- Microbiology, Department of Biology I, Ludwig-Maximilians-Universität München, Grosshaderner Strasse 2-4, Martinsried, Germany
| | - H Jung
- Microbiology, Department of Biology I, Ludwig-Maximilians-Universität München, Grosshaderner Strasse 2-4, Martinsried, Germany.
| | - E Frey
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for Nanoscience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany.
| |
Collapse
|
14
|
Chu S, Kardar M, Nelson DR, Beller DA. Evolution in range expansions with competition at rough boundaries. J Theor Biol 2019; 478:153-160. [PMID: 31220465 DOI: 10.1016/j.jtbi.2019.06.018] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2019] [Revised: 06/10/2019] [Accepted: 06/17/2019] [Indexed: 11/30/2022]
Abstract
When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic spatial wandering of both genetic lineages and the boundaries between genetically segregated sectors. Laboratory experiments on microbial range expansions have shown that this stochastic wandering, transverse to the front, is superdiffusive due to the front's growing roughness, implying much faster loss of genetic diversity than predicted by simple flat front diffusive models. We study the evolutionary consequences of this superdiffusive wandering using two complementary numerical models of range expansions: the stepping stone model, and a new interpretation of the model of directed paths in random media, in the context of a roughening population front. Through these approaches we compute statistics for the times since common ancestry for pairs of individuals with a given spatial separation at the front, and we explore how environmental heterogeneities can locally suppress these superdiffusive fluctuations.
Collapse
Affiliation(s)
- Sherry Chu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - David R Nelson
- Department of Physics, Department of Molecular and Cellular Biology and School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - Daniel A Beller
- Department of Physics, University of California, Merced, CA 95343, USA.
| |
Collapse
|
15
|
Gralka M, Hallatschek O. Environmental heterogeneity can tip the population genetics of range expansions. eLife 2019; 8:e44359. [PMID: 30977724 PMCID: PMC6513619 DOI: 10.7554/elife.44359] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Accepted: 04/11/2019] [Indexed: 12/12/2022] Open
Abstract
The population genetics of most range expansions is thought to be shaped by the competition between Darwinian selection and random genetic drift at the range margins. Here, we show that the evolutionary dynamics during range expansions is highly sensitive to additional fluctuations induced by environmental heterogeneities. Tracking mutant clones with a tunable fitness effect in bacterial colonies grown on randomly patterned surfaces we found that environmental heterogeneity can dramatically reduce the efficacy of selection. Time-lapse microscopy and computer simulations suggest that this effect arises generically from a local 'pinning' of the expansion front, whereby stretches of the front are slowed down on a length scale that depends on the structure of the environmental heterogeneity. This pinning focuses the range expansion into a small number of 'lucky' individuals with access to expansion paths, altering the neutral evolutionary dynamics and increasing the importance of chance relative to selection.
Collapse
Affiliation(s)
- Matti Gralka
- Department of PhysicsUniversity of California, BerkeleyBerkeleyUnited States
| | - Oskar Hallatschek
- Department of PhysicsUniversity of California, BerkeleyBerkeleyUnited States
- Department of Integrative BiologyUniversity of California, BerkeleyBerkeleyUnited States
| |
Collapse
|
16
|
Allen RJ, Waclaw B. Bacterial growth: a statistical physicist's guide. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:016601. [PMID: 30270850 PMCID: PMC6330087 DOI: 10.1088/1361-6633/aae546] [Citation(s) in RCA: 51] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
Bacterial growth presents many beautiful phenomena that pose new theoretical challenges to statistical physicists, and are also amenable to laboratory experimentation. This review provides some of the essential biological background, discusses recent applications of statistical physics in this field, and highlights the potential for future research.
Collapse
Affiliation(s)
- Rosalind J Allen
- School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | | |
Collapse
|
17
|
Weinstein BT, Lavrentovich MO, Möbius W, Murray AW, Nelson DR. Genetic drift and selection in many-allele range expansions. PLoS Comput Biol 2017; 13:e1005866. [PMID: 29194439 PMCID: PMC5728587 DOI: 10.1371/journal.pcbi.1005866] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2017] [Revised: 12/13/2017] [Accepted: 11/01/2017] [Indexed: 12/15/2022] Open
Abstract
We experimentally and numerically investigate the evolutionary dynamics of four competing strains of E. coli with differing expansion velocities in radially expanding colonies. We compare experimental measurements of the average fraction, correlation functions between strains, and the relative rates of genetic domain wall annihilations and coalescences to simulations modeling the population as a one-dimensional ring of annihilating and coalescing random walkers with deterministic biases due to selection. The simulations reveal that the evolutionary dynamics can be collapsed onto master curves governed by three essential parameters: (1) an expansion length beyond which selection dominates over genetic drift; (2) a characteristic angular correlation describing the size of genetic domains; and (3) a dimensionless constant quantifying the interplay between a colony’s curvature at the frontier and its selection length scale. We measure these parameters with a new technique that precisely measures small selective differences between spatially competing strains and show that our simulations accurately predict the dynamics without additional fitting. Our results suggest that the random walk model can act as a useful predictive tool for describing the evolutionary dynamics of range expansions composed of an arbitrary number of genotypes with different fitnesses. Population expansions occur naturally during the spread of invasive species and have played a role in our evolutionary history when humans migrated out of Africa. We use a colony of non-motile bacteria expanding into unoccupied, nutrient-rich territory on an agar plate as a model system to explore how an expanding population’s spatial structure impacts its evolutionary dynamics. Spatial structure is present in expanding microbial colonies because daughter cells migrate only a small distance away from their mothers each generation. Generally, the constituents of expansions occurring in nature and in the lab have different genetic compositions (genotypes, or alleles if a single gene differs), each instilling different fitnesses, which compete to proliferate at the frontier. Here, we show that a random-walk model can accurately predict the dynamics of four expanding strains of E. coli with different fitnesses; each strain represents a competing allele. Our results can be extended to describe any number of competing genotypes with different fitnesses in a naturally occurring expansion as long as the underlying motility of the organisms does not cause our model to break down. Our model can also be used to precisely measure small selective differences between spatially competing genotypes in controlled laboratory settings.
Collapse
Affiliation(s)
- Bryan T. Weinstein
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, United States of America
- * E-mail:
| | - Maxim O. Lavrentovich
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Wolfram Möbius
- Living Systems Institute, University of Exeter, Exeter, United Kingdom
- Physics and Astronomy, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom
- Department of Physics, Harvard University, Cambridge, Massachusetts, United States of America
| | - Andrew W. Murray
- FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - David R. Nelson
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, United States of America
- Department of Physics, Harvard University, Cambridge, Massachusetts, United States of America
- FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts, United States of America
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts, United States of America
| |
Collapse
|
18
|
Minors K, Dawes JHP. Invasions Slow Down or Collapse in the Presence of Reactive Boundaries. Bull Math Biol 2017; 79:2197-2214. [PMID: 28766158 PMCID: PMC5597713 DOI: 10.1007/s11538-017-0326-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2016] [Accepted: 07/20/2017] [Indexed: 12/03/2022]
Abstract
Motivated by the propagation of thin bacterial films around planar obstacles, this paper considers the dynamics of travelling wave solutions to the Fisher–KPP equation \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$u_t = u(1-u) + u_{xx} + u_{yy}$$\end{document}ut=u(1-u)+uxx+uyy in a planar strip \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$-\infty< x < \infty $$\end{document}-∞<x<∞, \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$0 \le y \le L$$\end{document}0≤y≤L. We examine the propagation of fronts in the presence of a mixed boundary condition (also referred to as a ‘partially absorbing’ or ‘reactive’ boundary) \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$u_y = \alpha u$$\end{document}uy=αu, with \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\alpha >0$$\end{document}α>0, at \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$y=0$$\end{document}y=0. The presence of boundary conditions of this kind leads to the development of front solutions that propagate in x but contain transverse structure in y. Motivated by the observation that the speed of propagation in the Fisher–KPP equation is determined (for exponentially decaying initial conditions) by the behaviour at the leading edge, we analyse the linearised Fisher–KPP equation in order to estimate the speed of the stable travelling front, a function of the width L and the imposed boundary conditions. For wide strips the speed estimate based on the linearised equation agrees well with the results of numerical simulations. For narrow channels numerical simulations indicate that the stable front propagates more slowly, and for sufficiently small L or sufficiently large \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\alpha $$\end{document}α the front speed falls to zero and the front collapses. The reason for the collapse is the non-existence, far behind the front, of a stable positive equilibrium solution u(x, y). While existence of these equilibrium states can be demonstrated via phase plane arguments, the investigation of stability is similar to calculations of critical patch sizes carried out in similar ecological models.
Collapse
|
19
|
Möbius W, Laan L. Physical and Mathematical Modeling in Experimental Papers. Cell 2016; 163:1577-83. [PMID: 26687351 DOI: 10.1016/j.cell.2015.12.006] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2015] [Indexed: 11/15/2022]
Abstract
An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations.
Collapse
Affiliation(s)
- Wolfram Möbius
- Department of Physics and FAS Center for Systems Biology, Harvard University, Cambridge, MA 02138, USA.
| | - Liedewij Laan
- Department of Bionanoscience, Kavli Institute of Nanoscience, Faculty of Applied Sciences, Delft University of Technology, 2628 CJ Delft, the Netherlands.
| |
Collapse
|