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Forouzannia F, Shahrezaei V, Kohandel M. The impact of random microenvironmental fluctuations on tumor control probability. J Theor Biol 2020; 509:110494. [PMID: 32979339 DOI: 10.1016/j.jtbi.2020.110494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2020] [Revised: 08/27/2020] [Accepted: 09/12/2020] [Indexed: 11/25/2022]
Abstract
The tumor control probability (TCP) is a metric used to calculate the probability of controlling or eradicating tumors through radiotherapy. Cancer cells vary in their response to radiation, and although many factors are involved, the tumor microenvironment is a crucial one that determines radiation efficacy. The tumor microenvironment plays a significant role in cancer initiation and propagation, as well as in treatment outcome. We have developed stochastic formulations to study the impact of arbitrary microenvironmental fluctuations on TCP and extinction probability (EP), which is defined as the probability of cancer cells removal in the absence of treatment. Since the derivation of analytical solutions are not possible for complicated cases, we employ a modified Gillespie algorithm to analyze TCP and EP, considering the random variations in cellular proliferation and death rates. Our results show that increasing the standard deviation in kinetic rates initially enhances the probability of tumor eradication. However, if the EP does not reach a probability of 1, the increase in the standard deviation subsequently has a negative impact on probability of cancer cells removal, decreasing the EP over time. The greatest effect on EP has been observed when both birth and death rates are being randomly modified and are anticorrelated. In addition, similar results are observed for TCP, where radiotherapy is included, indicating that increasing the standard deviation in kinetic rates at first enhances the probability of tumor eradication. But, it has a negative impact on treatment effectiveness if the TCP does not reach a probability of 1.
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Affiliation(s)
- Farinaz Forouzannia
- Department of Applied Mathematics, University of Waterloo, Waterloo, Canada.
| | - Vahid Shahrezaei
- Department of Mathematics, Imperial College London, South Kensington Campus, London, UK
| | - Mohammad Kohandel
- Department of Applied Mathematics, University of Waterloo, Waterloo, Canada.
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Farhang-Sardroodi S, Darooneh AH, Nikbakht M, Komarova NL, Kohandel M. The effect of spatial randomness on the average fixation time of mutants. PLoS Comput Biol 2017; 13:e1005864. [PMID: 29176825 PMCID: PMC5720826 DOI: 10.1371/journal.pcbi.1005864] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Revised: 12/07/2017] [Accepted: 10/26/2017] [Indexed: 12/03/2022] Open
Abstract
The mean conditional fixation time of a mutant is an important measure of stochastic population dynamics, widely studied in ecology and evolution. Here, we investigate the effect of spatial randomness on the mean conditional fixation time of mutants in a constant population of cells, N. Specifically, we assume that fitness values of wild type cells and mutants at different locations come from given probability distributions and do not change in time. We study spatial arrangements of cells on regular graphs with different degrees, from the circle to the complete graph, and vary assumptions on the fitness probability distributions. Some examples include: identical probability distributions for wild types and mutants; cases when only one of the cell types has random fitness values while the other has deterministic fitness; and cases where the mutants are advantaged or disadvantaged. Using analytical calculations and stochastic numerical simulations, we find that randomness has a strong impact on fixation time. In the case of complete graphs, randomness accelerates mutant fixation for all population sizes, and in the case of circular graphs, randomness delays mutant fixation for N larger than a threshold value (for small values of N, different behaviors are observed depending on the fitness distribution functions). These results emphasize fundamental differences in population dynamics under different assumptions on cell connectedness. They are explained by the existence of randomly occurring “dead zones” that can significantly delay fixation on networks with low connectivity; and by the existence of randomly occurring “lucky zones” that can facilitate fixation on networks of high connectivity. Results for death-birth and birth-death formulations of the Moran process, as well as for the (haploid) Wright Fisher model are presented. We study the influence of randomness on evolutionary dynamics, assuming that a newly arising mutant may experience a different set of environments compared to the wild type. We calculate the mean conditional fixation time of the mutant under different assumptions on spatial interactions, and show that randomness has a strong impact on the fixation time. In particular, it delays the fixation of mutants on 1D circles and accelerates it on complete graphs (the so called mass action, or complete mixing, model). This result holds for advantageous, disadvantageous, and neutral (on average) mutants. The reason for this pattern is quite intuitive: in a rigid, 1D structure, randomness can by chance put a “roadblock” and disrupt mutant spread, causing significant delay. In higher dimensions, there are many ways for a mutant to spread, and it is difficult to block all of them by chance; on the other hand, randomness can enhance fixation by providing an “easier” path. The effects of a random environment are important in biological models such as bacterial growth or cancer initiation/progression.
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Affiliation(s)
| | | | | | - Natalia L. Komarova
- Department of Mathematics, University of California Irvine, Irvine, California, United States of America
- * E-mail: (NLK); (MK)
| | - Mohammad Kohandel
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- * E-mail: (NLK); (MK)
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Bacterial-Chromatin Structural Proteins Regulate the Bimodal Expression of the Locus of Enterocyte Effacement (LEE) Pathogenicity Island in Enteropathogenic Escherichia coli. mBio 2017; 8:mBio.00773-17. [PMID: 28790204 PMCID: PMC5550750 DOI: 10.1128/mbio.00773-17] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
In enteropathogenic Escherichia coli (EPEC), the locus of enterocyte effacement (LEE) encodes a type 3 secretion system (T3SS) essential for pathogenesis. This pathogenicity island comprises five major operons (LEE1 to LEE5), with the LEE5 operon encoding T3SS effectors involved in the intimate adherence of bacteria to enterocytes. The first operon, LEE1, encodes Ler (LEE-encoded regulator), an H-NS (nucleoid structuring protein) paralog that alleviates the LEE H-NS silencing. We observed that the LEE5 and LEE1 promoters present a bimodal expression pattern, depending on environmental stimuli. One key regulator of bimodal LEE1 and LEE5 expression is ler expression, which fluctuates in response to different growth conditions. Under conditions in vitro considered to be equivalent to nonoptimal conditions for virulence, the opposing regulatory effects of H-NS and Ler can lead to the emergence of two bacterial subpopulations. H-NS and Ler share nucleation binding sites in the LEE5 promoter region, but H-NS binding results in local DNA structural modifications distinct from those generated through Ler binding, at least in vitro. Thus, we show how two nucleoid-binding proteins can contribute to the epigenetic regulation of bacterial virulence and lead to opposing bacterial fates. This finding implicates for the first time bacterial-chromatin structural proteins in the bimodal regulation of gene expression. Gene expression stochasticity is an emerging phenomenon in microbiology. In certain contexts, gene expression stochasticity can shape bacterial epigenetic regulation. In enteropathogenic Escherichia coli (EPEC), the interplay between H-NS (a nucleoid structuring protein) and Ler (an H-NS paralog) is required for bimodal LEE5 and LEE1 expression, leading to the emergence of two bacterial subpopulations (with low and high states of expression). The two proteins share mutual nucleation binding sites in the LEE5 promoter region. In vitro, the binding of H-NS to the LEE5 promoter results in local structural modifications of DNA distinct from those generated through Ler binding. Furthermore, ler expression is a key parameter modulating the variability of the proportions of bacterial subpopulations. Accordingly, modulating the production of Ler into a nonpathogenic E. coli strain reproduces the bimodal expression of LEE5. Finally, this study illustrates how two nucleoid-binding proteins can reshape the epigenetic regulation of bacterial virulence.
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Bury-Moné S, Sclavi B. Stochasticity of gene expression as a motor of epigenetics in bacteria: from individual to collective behaviors. Res Microbiol 2017; 168:503-514. [PMID: 28427910 DOI: 10.1016/j.resmic.2017.03.009] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2016] [Revised: 03/07/2017] [Accepted: 03/28/2017] [Indexed: 01/22/2023]
Abstract
Measuring gene expression at the single cell and single molecule level has recently made possible the quantitative measurement of stochasticity of gene expression. This enables identification of the probable sources and roles of noise. Gene expression noise can result in bacterial population heterogeneity, offering specific advantages for fitness and survival in various environments. This trait is therefore selected during the evolution of the species, and is consequently regulated by a specific genetic network architecture. Examples exist in stress-response mechanisms, as well as in infection and pathogenicity strategies, pointing to advantages for multicellularity of bacterial populations.
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Affiliation(s)
- Stéphanie Bury-Moné
- Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, Université Paris-Sud, Université Paris-Saclay, Orsay, France.
| | - Bianca Sclavi
- LBPA, UMR 8113, CNRS, ENS Paris-Saclay, Université Paris-Saclay, F-94235, Cachan, France.
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Davies EV, James CE, Brockhurst MA, Winstanley C. Evolutionary diversification of Pseudomonas aeruginosa in an artificial sputum model. BMC Microbiol 2017; 17:3. [PMID: 28056789 PMCID: PMC5216580 DOI: 10.1186/s12866-016-0916-z] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2016] [Accepted: 12/15/2016] [Indexed: 12/20/2022] Open
Abstract
Background During chronic lung infections of cystic fibrosis patients Pseudomonas aeruginosa populations undergo extensive evolutionary diversification. However, the selective drivers of this evolutionary process are poorly understood. To test the effects of temperate phages on diversification in P. aeruginosa biofilms we experimentally evolved populations of P. aeruginosa for approximately 240 generations in artificial sputum medium with or without a community of three temperate phages. Results Analysis of end-point populations using a suite of phenotypic tests revealed extensive phenotypic diversification within populations, but no significant differences between the populations evolved with or without phages. The most common phenotypic variant observed was loss of all three types of motility (swimming, swarming and twitching) and resistance to all three phages. Despite the absence of selective pressure, some members of the population evolved antibiotic resistance. The frequency of antibiotic resistant isolates varied according to population and the antibiotic tested. However, resistance to ceftazidime and tazobactam-piperacillin was observed more frequently than resistance to other antibiotics, and was associated with higher prevelence of isolates exhibiting a hypermutable phenotype and increased beta-lactamase production. Conclusions We observed considerable within-population phenotypic diversity in P. aeruginosa populations evolving in the artificial sputum medium biofilm model. Replicate populations evolved both in the presence and absence of phages converged upon similar sets of phenotypes. The evolved phenotypes, including antimicrobial resistance, were similar to those observed amongst clinical isolates from cystic fibrosis infections. Electronic supplementary material The online version of this article (doi:10.1186/s12866-016-0916-z) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Emily V Davies
- Institute of Infection and Global Health, University of Liverpool, 8 West Derby Street, Liverpool, L69 7BE, UK
| | - Chloe E James
- Institute of Infection and Global Health, University of Liverpool, 8 West Derby Street, Liverpool, L69 7BE, UK.,School of Environment and Life Sciences, University of Salford, Manchester, M5 4WT, UK
| | | | - Craig Winstanley
- Institute of Infection and Global Health, University of Liverpool, 8 West Derby Street, Liverpool, L69 7BE, UK.
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Steenackers HP, Parijs I, Dubey A, Foster KR, Vanderleyden J. Experimental evolution in biofilm populations. FEMS Microbiol Rev 2016; 40:373-97. [PMID: 26895713 PMCID: PMC4852284 DOI: 10.1093/femsre/fuw002] [Citation(s) in RCA: 95] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 01/21/2016] [Indexed: 12/19/2022] Open
Abstract
Biofilms are a major form of microbial life in which cells form dense surface associated communities that can persist for many generations. The long-life of biofilm communities means that they can be strongly shaped by evolutionary processes. Here, we review the experimental study of evolution in biofilm communities. We first provide an overview of the different experimental models used to study biofilm evolution and their associated advantages and disadvantages. We then illustrate the vast amount of diversification observed during biofilm evolution, and we discuss (i) potential ecological and evolutionary processes behind the observed diversification, (ii) recent insights into the genetics of adaptive diversification, (iii) the striking degree of parallelism between evolution experiments and real-life biofilms and (iv) potential consequences of diversification. In the second part, we discuss the insights provided by evolution experiments in how biofilm growth and structure can promote cooperative phenotypes. Overall, our analysis points to an important role of biofilm diversification and cooperation in bacterial survival and productivity. Deeper understanding of both processes is of key importance to design improved antimicrobial strategies and diagnostic techniques. This review paper provides an overview of (i) the different experimental models used to study biofilm evolution, (ii) the vast amount of diversification observed during biofilm evolution (including potential causes and consequences) and (iii) recent insights in how growth in biofilms can lead to the evolution of cooperative phenotypes.
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Affiliation(s)
- Hans P Steenackers
- Department of Microbial and Molecular Systems, Centre of Microbial and Plant Genetics, KU Leuven, Leuven 3001, Belgium
| | - Ilse Parijs
- Department of Microbial and Molecular Systems, Centre of Microbial and Plant Genetics, KU Leuven, Leuven 3001, Belgium
| | | | - Kevin R Foster
- Department of Zoology, University of Oxford, Oxford OX1 3PS, UK Oxford Centre for Integrative Systems Biology, University of Oxford, Oxford OX1 3QU, UK
| | - Jozef Vanderleyden
- Department of Microbial and Molecular Systems, Centre of Microbial and Plant Genetics, KU Leuven, Leuven 3001, Belgium
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Hansen NCK, Avershina E, Mydland LT, Næsset JA, Austbø D, Moen B, Måge I, Rudi K. High nutrient availability reduces the diversity and stability of the equine caecal microbiota. MICROBIAL ECOLOGY IN HEALTH AND DISEASE 2015; 26:27216. [PMID: 26246403 PMCID: PMC4526772 DOI: 10.3402/mehd.v26.27216] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/08/2015] [Revised: 06/18/2015] [Accepted: 07/03/2015] [Indexed: 11/14/2022]
Abstract
BACKGROUND It is well known that nutrient availability can alter the gut microbiota composition, while the effect on diversity and temporal stability remains largely unknown. METHODS Here we address the equine caecal microbiota temporal stability, diversity, and functionality in response to diets with different levels of nutrient availability. Hay (low and slower nutrient availability) versus a mixture of hay and whole oats (high and more rapid nutrient availability) were used as experimental diets. RESULTS We found major effects on the microbiota despite that the caecal pH was far from sub-clinical acidosis. We found that the low nutrient availability diet was associated with a higher level of both diversity and temporal stability of the caecal microbiota than the high nutrient availability diet. These observations concur with general ecological theories, suggesting a stabilising effect of biological diversity and that high nutrient availability has a destabilising effect through reduced diversity. CONCLUSION Nutrient availability does not only change the composition but also the ecology of the caecal microbiota.
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Affiliation(s)
- Naja C K Hansen
- Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Aas, Norway
| | - Ekaterina Avershina
- Department of Chemistry, Biotechnology and Food Science, Norwegian University of Life Sciences, Aas, Norway
| | - Liv T Mydland
- Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Aas, Norway
| | - Jon A Næsset
- Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Aas, Norway
| | - Dag Austbø
- Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, Aas, Norway
| | - Birgitte Moen
- Nofima, The Norwegian Institute of Food, Fisheries and Aquaculture Research, Aas, Norway
| | - Ingrid Måge
- Nofima, The Norwegian Institute of Food, Fisheries and Aquaculture Research, Aas, Norway
| | - Knut Rudi
- Department of Chemistry, Biotechnology and Food Science, Norwegian University of Life Sciences, Aas, Norway;
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Matias MG, Combe M, Barbera C, Mouquet N. Ecological strategies shape the insurance potential of biodiversity. Front Microbiol 2013; 3:432. [PMID: 23316188 PMCID: PMC3539934 DOI: 10.3389/fmicb.2012.00432] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2012] [Accepted: 12/14/2012] [Indexed: 11/26/2022] Open
Abstract
Biodiversity is thought to provide insurance for ecosystem functioning under heterogeneous environments; however, such insurance potential is under serious threat following unprecedented loss of biodiversity. One of the key mechanism underlying ecological insurance is that niche differentiation allows asynchronous responses to fluctuating environments, although the role of different ecological strategies (e.g., specialists vs. generalists) has yet to be formally evaluated. We present here a simple experimental study that illustrates how different ecological strategies (i.e., generalists vs. specialists) can shape the biodiversity-insurance relationship. We assembled microcosm of generalists and specialist bacteria over a gradient of salinity and found that, bacterial communities made up of generalists were more productive and more stable over time under environmental fluctuations. We discuss our results in context with simple theoretical predictions and propose future directions for biological insurance theory. We argue that beyond species richness itself, it is essential to incorporate the distribution of ecological strategies across relevant environmental gradients as predictors of the insurance potential of biodiversity in natural ecosystems.
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Affiliation(s)
- Miguel G Matias
- Institut des Sciences de l'Evolution, UMR CNRS-UM2 5554, Université Montpellier 2 Montpellier cedex 05, France
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Ishii S, Sadowsky MJ. Escherichia coli in the Environment: Implications for Water Quality and Human Health. Microbes Environ 2012; 23:101-8. [PMID: 21558695 DOI: 10.1264/jsme2.23.101] [Citation(s) in RCA: 268] [Impact Index Per Article: 20.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Escherichia coli is naturally present in the intestinal tracts of warm-blooded animals. Since E. coli is released into the environment through deposition of fecal material, this bacterium is widely used as an indicator of fecal contamination of waterways. Recently, research efforts have been directed towards the identification of potential sources of fecal contamination impacting waterways and beaches. This is often referred to as microbial source tracking. However, recent studies have reported that E. coli can become "naturalized" to soil, sand, sediments, and algae in tropical, subtropical, and temperate environments. This phenomenon raises issues concerning the continued use of this bacterium as an indicator of fecal contamination. In this review, we discuss the relationship between E. coli and fecal pollution and the use of this bacterium as an indicator of fecal contamination in freshwater systems. We also discuss recent studies showing that E. coli can become an active member of natural microbial communities in the environment, and how this bacterium is being used for microbial source tracking. We also discuss the impact of environmentally-"naturalized" E. coli populations on water quality.
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Affiliation(s)
- Satoshi Ishii
- Department of Soil, Water, and Climate, University of Minnesota
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Abstract
Biofilms contain bacterial cells that are in a wide range of physiological states. Within a biofilm population, cells with diverse genotypes and phenotypes that express distinct metabolic pathways, stress responses and other specific biological activities are juxtaposed. The mechanisms that contribute to this genetic and physiological heterogeneity include microscale chemical gradients, adaptation to local environmental conditions, stochastic gene expression and the genotypic variation that occurs through mutation and selection. Here, we discuss the processes that generate chemical gradients in biofilms, the genetic and physiological responses of the bacteria as they adapt to these gradients and the techniques that can be used to visualize and measure the microscale physiological heterogeneities of bacteria in biofilms.
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