1
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Wang T, Weiss A, Aqeel A, Wu F, Lopatkin AJ, David LA, You L. Horizontal gene transfer enables programmable gene stability in synthetic microbiota. Nat Chem Biol 2022; 18:1245-1252. [PMID: 36050493 PMCID: PMC10018779 DOI: 10.1038/s41589-022-01114-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 07/15/2022] [Indexed: 11/09/2022]
Abstract
The functions of many microbial communities exhibit remarkable stability despite fluctuations in the compositions of these communities. To date, a mechanistic understanding of this function-composition decoupling is lacking. Statistical mechanisms have been commonly hypothesized to explain such decoupling. Here, we proposed that dynamic mechanisms, mediated by horizontal gene transfer (HGT), also enable the independence of functions from the compositions of microbial communities. We combined theoretical analysis with numerical simulations to illustrate that HGT rates can determine the stability of gene abundance in microbial communities. We further validated these predictions using engineered microbial consortia of different complexities transferring one or more than a dozen clinically isolated plasmids, as well as through the reanalysis of data from the literature. Our results demonstrate a generalizable strategy to program the gene stability of microbial communities.
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Affiliation(s)
- Teng Wang
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
| | - Andrea Weiss
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
| | - Ammara Aqeel
- Department of Molecular Genetics and Microbiology, Duke University School of Medicine, Durham, NC, USA
| | - Feilun Wu
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
| | - Allison J Lopatkin
- Department of Chemical Engineering, University of Rochester, Rochester, NY, USA
| | - Lawrence A David
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
- Department of Molecular Genetics and Microbiology, Duke University School of Medicine, Durham, NC, USA
- Center for Genomic and Computational Biology, Duke University, Durham, NC, USA
| | - Lingchong You
- Department of Biomedical Engineering, Duke University, Durham, NC, USA.
- Department of Molecular Genetics and Microbiology, Duke University School of Medicine, Durham, NC, USA.
- Center for Genomic and Computational Biology, Duke University, Durham, NC, USA.
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2
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Yin H, Liu S, Wen X. Optimal transition paths of phenotypic switching in a non-Markovian self-regulation gene expression. Phys Rev E 2021; 103:022409. [PMID: 33736096 DOI: 10.1103/physreve.103.022409] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2020] [Accepted: 01/06/2021] [Indexed: 11/07/2022]
Abstract
Gene expression is a complex biochemical process involving multiple reaction steps, creating molecular memory because the probability of waiting time between consecutive reaction steps no longer follows exponential distributions. What effect the molecular memory has on metastable states in gene expression remains not fully understood. Here, we study transition paths of switching between bistable states for a non-Markovian model of gene expression equipped with a self-regulation. Employing the large deviation theory for this model, we analyze the optimal transition paths of switching between bistable states in gene expression, interestingly finding that dynamic behaviors in gene expression along the optimal transition paths significantly depend on the molecular memory. Moreover, we discover that the molecular memory can prolong the time of switching between bistable states in gene expression along the optimal transition paths. Our results imply that the molecular memory may be an unneglectable factor to affect switching between metastable states in gene expression.
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Affiliation(s)
- Hongwei Yin
- School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221111, People's Republic of China.,School of Science, Nanchang University, Nanchang 330031, People's Republic of China
| | - Shuqin Liu
- School of Science, Nanchang University, Nanchang 330031, People's Republic of China
| | - Xiaoqing Wen
- School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221111, People's Republic of China.,School of Science, Nanchang University, Nanchang 330031, People's Republic of China
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3
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Temporal encoding of bacterial identity and traits in growth dynamics. Proc Natl Acad Sci U S A 2020; 117:20202-20210. [PMID: 32747578 DOI: 10.1073/pnas.2008807117] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In biology, it is often critical to determine the identity of an organism and phenotypic traits of interest. Whole-genome sequencing can be useful for this but has limited power for trait prediction. However, we can take advantage of the inherent information content of phenotypes to bypass these limitations. We demonstrate, in clinical and environmental bacterial isolates, that growth dynamics in standardized conditions can differentiate between genotypes, even among strains from the same species. We find that for pairs of isolates, there is little correlation between genetic distance, according to phylogenetic analysis, and phenotypic distance, as determined by growth dynamics. This absence of correlation underscores the challenge in using genomics to infer phenotypes and vice versa. Bypassing this complexity, we show that growth dynamics alone can robustly predict antibiotic responses. These findings are a foundation for a method to identify traits not easily traced to a genetic mechanism.
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4
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Binary Expression Enhances Reliability of Messaging in Gene Networks. ENTROPY 2020; 22:e22040479. [PMID: 33286254 PMCID: PMC7516962 DOI: 10.3390/e22040479] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Revised: 04/20/2020] [Accepted: 04/20/2020] [Indexed: 01/31/2023]
Abstract
The promoter state of a gene and its expression levels are modulated by the amounts of transcription factors interacting with its regulatory regions. Hence, one may interpret a gene network as a communicating system in which the state of the promoter of a gene (the source) is communicated by the amounts of transcription factors that it expresses (the message) to modulate the state of the promoter and expression levels of another gene (the receptor). The reliability of the gene network dynamics can be quantified by Shannon's entropy of the message and the mutual information between the message and the promoter state. Here we consider a stochastic model for a binary gene and use its exact steady state solutions to calculate the entropy and mutual information. We show that a slow switching promoter with long and equally standing ON and OFF states maximizes the mutual information and reduces entropy. That is a binary gene expression regime generating a high variance message governed by a bimodal probability distribution with peaks of the same height. Our results indicate that Shannon's theory can be a powerful framework for understanding how bursty gene expression conciliates with the striking spatio-temporal precision exhibited in pattern formation of developing organisms.
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5
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Gonzalez-Ayala J, Guo J, Medina A, Roco JMM, Calvo Hernández A. Optimization induced by stability and the role of limited control near a steady state. Phys Rev E 2019; 100:062128. [PMID: 31962470 DOI: 10.1103/physreve.100.062128] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Indexed: 06/10/2023]
Abstract
A relationship between stability and self-optimization is found for weakly dissipative heat devices. The effect of limited control on operation variables around an steady state is such that, after instabilities, the paths toward relaxation are given by trajectories stemming from restitution forces which improve the system thermodynamic performance (power output, efficiency, and entropy generation). Statistics over random trajectories for many cycles shows this behavior as well. Two types of dynamics are analyzed, one where an stability basin appears and another one where the system is globally stable. Under both dynamics there is an induced trend in the control variables space due to stability. In the energetic space this behavior translates into a preference for better thermodynamic states, and thus stability could favor self-optimization under limited control. This is analyzed from the multiobjective optimization perspective. As a result, the statistical behavior of the system is strongly influenced by the Pareto front (the set of points with the best compromise between several objective functions) and the stability basin. Additionally, endoreversible and irreversible behaviors appear as very relevant limits: The first one is an upper bound in energetic performance, connected with the Pareto front, and the second one represents an attractor for the stochastic trajectories.
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Affiliation(s)
- J Gonzalez-Ayala
- Departamento de Física Aplicada, Universidad de Salamanca, 37008 Salamanca, Spain
- Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, 37008 Salamanca, Spain
| | - J Guo
- Departamento de Física Aplicada, Universidad de Salamanca, 37008 Salamanca, Spain
- College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, People's Republic of China
| | - A Medina
- Departamento de Física Aplicada, Universidad de Salamanca, 37008 Salamanca, Spain
- Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, 37008 Salamanca, Spain
| | - J M M Roco
- Departamento de Física Aplicada, Universidad de Salamanca, 37008 Salamanca, Spain
- Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, 37008 Salamanca, Spain
| | - A Calvo Hernández
- Departamento de Física Aplicada, Universidad de Salamanca, 37008 Salamanca, Spain
- Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, 37008 Salamanca, Spain
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6
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Gómez-Schiavon M, Buchler NE. Epigenetic switching as a strategy for quick adaptation while attenuating biochemical noise. PLoS Comput Biol 2019; 15:e1007364. [PMID: 31658246 PMCID: PMC6837633 DOI: 10.1371/journal.pcbi.1007364] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2019] [Revised: 11/07/2019] [Accepted: 08/30/2019] [Indexed: 11/30/2022] Open
Abstract
Epigenetic switches are bistable, molecular systems built from self-reinforcing feedback loops that can spontaneously switch between heritable phenotypes in the absence of DNA mutation. It has been hypothesized that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation, but the evolutionary trajectories and conditions by which an epigenetic switch can outcompete adaptation through genetic mutation remain unknown. Here, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically through mutation and exhibit epigenetic switching. We evolved these genetic circuits under a fluctuating environment that alternatively selected for low and high protein expression levels. In all tested conditions, the population first evolved by genetic mutation towards a region of genotypes where genetic adaptation can occur faster after each environmental transition. Once in this region, the self-activating genetic circuit can exhibit epigenetic switching, which starts competing with genetic adaptation. We show a trade-off between either minimizing the adaptation time or increasing the robustness of the phenotype to biochemical noise. Epigenetic switching was superior in a fast fluctuating environment because it adapted faster than genetic mutation after an environmental transition, while still attenuating the effect of biochemical noise on the phenotype. Conversely, genetic adaptation was favored in a slowly fluctuating environment because it maximized the phenotypic robustness to biochemical noise during the constant environment between transitions, even if this resulted in slower adaptation. This simple trade-off predicts the conditions and trajectories under which an epigenetic switch evolved to outcompete genetic adaptation, shedding light on possible mechanisms by which bet-hedging strategies might emerge and persist in natural populations. Epigenetic switches regulate cell fate decisions during development in multicellular organisms, but their origin predates multicellularity because they are found in viruses, bacteria, and unicellular eukaryotes. It has been suggested that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation to fluctuating environments. To discern the evolutionary pressures that select for epigenetic switches, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically and exhibit epigenetic switching. Unlike laboratory evolution experiments, this in silico experiment was run many times over a range of evolutionary parameters (population size, selection pressure, mutation step-size, fluctuation frequency) and different model assumptions to uncover statistical regularities in the evolutionary trajectories. Using this computational approach, we could elucidate simple principles that predict the conditions that favor adaptation by epigenetic switching over genetic mutation in a fluctuating environment.
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Affiliation(s)
- Mariana Gómez-Schiavon
- Program in Computational Biology & Bioinformatics, Duke University, Durham, North Carolina, United States of America
- Center for Genomic & Computational Biology, Duke University, Durham, North Carolina, United States of America
- Department of Biology, Duke University, Durham, North Carolina, United States of America
- * E-mail:
| | - Nicolas E. Buchler
- Center for Genomic & Computational Biology, Duke University, Durham, North Carolina, United States of America
- Department of Biology, Duke University, Durham, North Carolina, United States of America
- Department of Physics, Duke University, Durham, North Carolina, United States of America
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7
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Kumar N, Cramer GM, Dahaj SAZ, Sundaram B, Celli JP, Kulkarni RV. Stochastic modeling of phenotypic switching and chemoresistance in cancer cell populations. Sci Rep 2019; 9:10845. [PMID: 31350465 PMCID: PMC6659620 DOI: 10.1038/s41598-019-46926-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2019] [Accepted: 06/26/2019] [Indexed: 02/06/2023] Open
Abstract
Phenotypic heterogeneity in cancer cells is widely observed and is often linked to drug resistance. In several cases, such heterogeneity in drug sensitivity of tumors is driven by stochastic and reversible acquisition of a drug tolerant phenotype by individual cells even in an isogenic population. Accumulating evidence further suggests that cell-fate transitions such as the epithelial to mesenchymal transition (EMT) are associated with drug resistance. In this study, we analyze stochastic models of phenotypic switching to provide a framework for analyzing cell-fate transitions such as EMT as a source of phenotypic variability in drug sensitivity. Motivated by our cell-culture based experimental observations connecting phenotypic switching in EMT and drug resistance, we analyze a coarse-grained model of phenotypic switching between two states in the presence of cytotoxic stress from chemotherapy. We derive analytical results for time-dependent probability distributions that provide insights into the rates of phenotypic switching and characterize initial phenotypic heterogeneity of cancer cells. The results obtained can also shed light on fundamental questions relating to adaptation and selection scenarios in tumor response to cytotoxic therapy.
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Affiliation(s)
- Niraj Kumar
- Department of Physics, University of Massachusetts Boston, Boston, MA, 02125, USA
| | - Gwendolyn M Cramer
- Department of Physics, University of Massachusetts Boston, Boston, MA, 02125, USA.,Department of Radiation Oncology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA
| | - Seyed Alireza Zamani Dahaj
- Department of Physics, University of Massachusetts Boston, Boston, MA, 02125, USA.,School of Physics, Georgia Institute of Technology, Atlanta, GA, 30332, USA
| | - Bala Sundaram
- Department of Physics, University of Massachusetts Boston, Boston, MA, 02125, USA
| | - Jonathan P Celli
- Department of Physics, University of Massachusetts Boston, Boston, MA, 02125, USA
| | - Rahul V Kulkarni
- Department of Physics, University of Massachusetts Boston, Boston, MA, 02125, USA.
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8
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Menn D, Sochor P, Goetz H, Tian XJ, Wang X. Intracellular Noise Level Determines Ratio Control Strategy Confined by Speed-Accuracy Trade-off. ACS Synth Biol 2019; 8:1352-1360. [PMID: 31083890 DOI: 10.1021/acssynbio.9b00030] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Robust and precise ratio control of heterogeneous phenotypes within an isogenic population is an essential task, especially in the development and differentiation of a large number of cells such as bacteria, sensory receptors, and blood cells. However, the mechanisms of such ratio control are poorly understood. Here, we employ experimental and mathematical techniques to understand the combined effects of signal induction and gene expression stochasticity on phenotypic multimodality. We identify two strategies to control phenotypic ratios from an initially homogeneous population, suitable roughly to high-noise and low-noise intracellular environments, and we show that both can be used to generate precise fractional differentiation. In noisy gene expression contexts, such as those found in bacteria, induction within the circuit's bistable region is enough to cause noise-induced bimodality within a feasible time frame. However, in less noisy contexts, such as tightly controlled eukaryotic systems, spontaneous state transitions are rare and hence bimodality needs to be induced with a controlled pulse of induction that falls outside the bistable region. Finally, we show that noise levels, system response time, and ratio tuning accuracy impose trade-offs and limitations on both ratio control strategies, which guide the selection of strategy alternatives.
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Affiliation(s)
- David Menn
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85281, United States
| | - Patrick Sochor
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85281, United States
| | - Hanah Goetz
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85281, United States
| | - Xiao-Jun Tian
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85281, United States
| | - Xiao Wang
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85281, United States
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9
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Charlebois DA, Balázsi G. Modeling cell population dynamics. In Silico Biol 2019; 13:21-39. [PMID: 30562900 PMCID: PMC6598210 DOI: 10.3233/isb-180470] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Revised: 09/13/2018] [Accepted: 10/16/2018] [Indexed: 12/27/2022]
Abstract
Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.
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Affiliation(s)
- Daniel A. Charlebois
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, NY, USA
- Department of Physics, University of Alberta, Edmonton, AB, Canada
| | - Gábor Balázsi
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, NY, USA
- Department of Biomedical Engineering, Stony Brook University, NY, USA
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10
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Abstract
Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.
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Affiliation(s)
- Daniel A Charlebois
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, NY, USA.,Department of Physics, University of Alberta, Edmonton, AB, Canada
| | - Gábor Balázsi
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, NY, USA.,Department of Biomedical Engineering, Stony Brook University, NY, USA
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11
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The emergence of metabolic heterogeneity and diverse growth responses in isogenic bacterial cells. ISME JOURNAL 2018; 12:1199-1209. [PMID: 29335635 DOI: 10.1038/s41396-017-0036-2] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Revised: 11/28/2017] [Accepted: 12/03/2017] [Indexed: 11/08/2022]
Abstract
Microorganisms adapt to frequent environmental changes through population diversification. Previous studies demonstrated phenotypic diversity in a clonal population and its important effects on microbial ecology. However, the dynamic changes of phenotypic composition have rarely been characterized. Also, cellular variations and environmental factors responsible for phenotypic diversity remain poorly understood. Here, we studied phenotypic diversity driven by metabolic heterogeneity. We characterized metabolic activities and growth kinetics of starved Escherichia coli cells subject to nutrient upshift at single-cell resolution. We observed three subpopulations with distinct metabolic activities and growth phenotypes. One subpopulation was metabolically active and immediately grew upon nutrient upshift. One subpopulation was metabolically inactive and non-viable. The other subpopulation was metabolically partially active, and did not grow upon nutrient upshift. The ratio of these subpopulations changed dynamically during starvation. A long-term observation of cells with partial metabolic activities indicated that their metabolism was later spontaneously restored, leading to growth recovery. Further investigations showed that oxidative stress can induce the emergence of a subpopulation with partial metabolic activities. Our findings reveal the emergence of metabolic heterogeneity and associated dynamic changes in phenotypic composition. In addition, the results shed new light on microbial dormancy, which has important implications in microbial ecology and biomedicine.
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12
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Late-Arriving Signals Contribute Less to Cell-Fate Decisions. Biophys J 2017; 113:2110-2120. [PMID: 29117533 DOI: 10.1016/j.bpj.2017.09.012] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Revised: 08/14/2017] [Accepted: 09/05/2017] [Indexed: 11/24/2022] Open
Abstract
Gene regulatory networks are largely responsible for cellular decision-making. These networks sense diverse external signals and respond by adjusting gene expression, enabling cells to reach environment-dependent decisions crucial for their survival or reproduction. However, information-carrying signals may arrive at variable times. Besides the intrinsic strength of these signals, their arrival time (timing) may also carry information about the environment and can influence cellular decision-making in ways that are poorly understood. For example, it is unclear how the timing of individual phage infections affects the lysis-lysogeny decision of bacteriophage λ despite variable infection times being likely in the wild and even in laboratory conditions. In this work, we combine mathematical modeling with experimentation to address this question. We develop an experimentally testable theory, which reveals that late-infecting phages contribute less to cellular decision-making. This implies that infection delays lower the probability of lysogeny compared to simultaneous infections. Furthermore, we show that infection delays reduce lysogenization by providing insufficient CII for threshold crossing during the critical decision-making period. We find evidence for a cutoff time after which subsequent infections cannot influence the cellular decision. We derive an intuitive formula that approximates the probability of lysogeny for variable infection times by a time-weighted average of probabilities for simultaneous infections. We validate these theoretical predictions experimentally. Similar concepts and simplifying modeling approaches may help elucidate the mechanisms underlying other cellular decisions.
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13
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Ogura M, Wakaiki M, Rubin H, Preciado VM. Delayed bet-hedging resilience strategies under environmental fluctuations. Phys Rev E 2017; 95:052404. [PMID: 28618624 DOI: 10.1103/physreve.95.052404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Indexed: 06/07/2023]
Abstract
Many biological populations, such as bacterial colonies, have developed through evolution a protection mechanism, called bet hedging, to increase their probability of survival under stressful environmental fluctuation. In this context, the concept of preadaptation refers to a common type of bet-hedging protection strategy in which a relatively small number of individuals in a population stochastically switch their phenotypes to a dormant metabolic state in which they increase their probability of survival against potential environmental shocks. Hence, if an environmental shock took place at some point in time, preadapted organisms would be better adapted to survive and proliferate once the shock is over. In many biological populations, the mechanisms of preadaptation and proliferation present delays whose influence in the fitness of the population are not well understood. In this paper, we propose a rigorous mathematical framework to analyze the role of delays in both preadaptation and proliferation mechanisms in the survival of biological populations, with an emphasis on bacterial colonies. Our theoretical framework allows us to analytically quantify the average growth rate of a bet-hedging bacterial colony with stochastically delayed reactions with arbitrary precision. We verify the accuracy of the proposed method by numerical simulations and conclude that the growth rate of a bet-hedging population shows a nontrivial dependency on their preadaptation and proliferation delays. Contrary to the current belief, our results show that faster reactions do not, in general, increase the overall fitness of a biological population.
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Affiliation(s)
- Masaki Ogura
- Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma, Nara 630-0192, Japan
| | - Masashi Wakaiki
- Graduate School of System Informatics, Kobe University, Nada, Kobe, Hyogo 657-8501, Japan
| | - Harvey Rubin
- Department of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Victor M Preciado
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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14
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Sustainable theory of a logistic model - Fisher information approach. Math Biosci 2017; 285:81-91. [DOI: 10.1016/j.mbs.2016.12.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Revised: 12/29/2016] [Accepted: 12/31/2016] [Indexed: 11/22/2022]
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