1
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Potentiating antibiotic efficacy via perturbation of non-essential gene expression. Commun Biol 2021; 4:1267. [PMID: 34741116 PMCID: PMC8571399 DOI: 10.1038/s42003-021-02783-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 09/21/2021] [Indexed: 02/06/2023] Open
Abstract
Proliferation of multidrug-resistant (MDR) bacteria poses a threat to human health, requiring new strategies. Here we propose using fitness neutral gene expression perturbations to potentiate antibiotics. We systematically explored 270 gene knockout-antibiotic combinations in Escherichia coli, identifying 90 synergistic interactions. Identified gene targets were subsequently tested for antibiotic synergy on the transcriptomic level via multiplexed CRISPR-dCas9 and showed successful sensitization of E. coli without a separate fitness cost. These fitness neutral gene perturbations worked as co-therapies in reducing a Salmonella enterica intracellular infection in HeLa. Finally, these results informed the design of four antisense peptide nucleic acid (PNA) co-therapies, csgD, fnr, recA and acrA, against four MDR, clinically isolated bacteria. PNA combined with sub-minimal inhibitory concentrations of trimethoprim against two isolates of Klebsiella pneumoniae and E. coli showed three cases of re-sensitization with minimal fitness impacts. Our results highlight a promising approach for extending the utility of current antibiotics.
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2
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Bystritskaya E, Chernysheva N, Stenkova A, Guzev K, Rakin A, Isaeva M. Differential Expression of Yersinia pseudotuberculosis General Porin Genes during Short- and Long-Term Antibiotic Stresses. Molecules 2021; 26:3956. [PMID: 34203552 PMCID: PMC8272246 DOI: 10.3390/molecules26133956] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Revised: 06/21/2021] [Accepted: 06/23/2021] [Indexed: 11/25/2022] Open
Abstract
Here, we investigated general porin regulation in Yersinia pseudotuberculosis 488, the causative agent of Far Eastern scarlet-like fever, in response to sublethal concentrations of antibiotics. We chose four antibiotics of different classes and measured gene expression using qRT-PCR and GFP reporter systems. Our data showed temporal regulation of the general porin genes ompF and ompC caused by antibiotic stress. The porin transcription initially decreased, providing early defensive response of the bacterium, while it returned to that of the untreated cells on prolonged antibiotic exposure. Unlike the major porin genes, the transcription of the alternative porin genes ompX and lamB was increased. Moreover, a short-term ompR- and marA-mediated porin regulation was observed. The main finding was a phenotypic heterogeneity of Y. pseudotuberculosis population manifested in variable porin gene expression under carbenicillin exposure. This may offer adaptive fitness advantages for a particular bacterial subpopulation.
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Affiliation(s)
- Evgeniya Bystritskaya
- G.B. Elyakov Pacific Institute of Bioorganic Chemistry, Far Eastern Branch, Russian Academy of Sciences, 159, Pr. 100 Let Vladivostoku, 690022 Vladivostok, Russia; (E.B.); (N.C.); (K.G.)
| | - Nadezhda Chernysheva
- G.B. Elyakov Pacific Institute of Bioorganic Chemistry, Far Eastern Branch, Russian Academy of Sciences, 159, Pr. 100 Let Vladivostoku, 690022 Vladivostok, Russia; (E.B.); (N.C.); (K.G.)
| | - Anna Stenkova
- School of Biomedicine, Far Eastern Federal University, 8 Sukhanova St., 690090 Vladivostok, Russia;
| | - Konstantin Guzev
- G.B. Elyakov Pacific Institute of Bioorganic Chemistry, Far Eastern Branch, Russian Academy of Sciences, 159, Pr. 100 Let Vladivostoku, 690022 Vladivostok, Russia; (E.B.); (N.C.); (K.G.)
| | - Alexander Rakin
- Friedrich-Loeffler-Institut, Federal Research Institute for Animal Health, Institute for Bacterial Infections and Zoonoses, Naumburger Str. 96a, D-07743 Jena, Germany;
| | - Marina Isaeva
- G.B. Elyakov Pacific Institute of Bioorganic Chemistry, Far Eastern Branch, Russian Academy of Sciences, 159, Pr. 100 Let Vladivostoku, 690022 Vladivostok, Russia; (E.B.); (N.C.); (K.G.)
- School of Biomedicine, Far Eastern Federal University, 8 Sukhanova St., 690090 Vladivostok, Russia;
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3
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Abstract
Single-cell sequencing-based methods for profiling gene transcript levels have revealed substantial heterogeneity in expression levels among morphologically indistinguishable cells. This variability has important functional implications for tissue biology and disease states such as cancer. Mapping of epigenomic information such as chromatin accessibility, nucleosome positioning, histone tail modifications and enhancer-promoter interactions in both bulk-cell and single-cell samples has shown that these characteristics of chromatin state contribute to expression or repression of associated genes. Advances in single-cell epigenomic profiling methods are enabling high-resolution mapping of chromatin states in individual cells. Recent studies using these techniques provide evidence that variations in different aspects of chromatin organization collectively define gene expression heterogeneity among otherwise highly similar cells.
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Affiliation(s)
- Benjamin Carter
- Laboratory of Epigenome Biology, Systems Biology Center, NHLBI, NIH, Bethesda, MD, USA.
| | - Keji Zhao
- Laboratory of Epigenome Biology, Systems Biology Center, NHLBI, NIH, Bethesda, MD, USA.
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4
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The effect of spatiotemporal antibiotic inhomogeneities on the evolution of resistance. J Theor Biol 2019; 486:110077. [PMID: 31715181 DOI: 10.1016/j.jtbi.2019.110077] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2019] [Revised: 10/31/2019] [Accepted: 11/09/2019] [Indexed: 12/30/2022]
Abstract
Combating the evolution of widespread antibiotic resistance is one of the most pressing challenges facing modern medicine. Recent research has demonstrated that the evolution of pathogens with high levels of resistance can be accelerated by spatial and temporal inhomogeneities in antibiotic concentration, which frequently arise in patients and the environment. Strategies to predict and counteract the effects of such inhomogeneities will be critical in the fight against resistance. In this paper we develop a mechanistic framework for modelling the adaptive evolution of resistance in the presence of spatiotemporal antibiotic concentrations, which treats the adaptive process as an interaction between two mutually orthogonal forces; the first returns cells to their wild-type state in the absence of antibiotic selection, and the second selects for increased coping ability in the presence of an antibiotic. We apply our model to investigate laboratory adaptation experiments, and then extend it to consider the case in which multiple strategies for resistance undergo competitive evolution.
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5
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Otoupal PB, Chatterjee A. CRISPR Gene Perturbations Provide Insights for Improving Bacterial Biofuel Tolerance. Front Bioeng Biotechnol 2018; 6:122. [PMID: 30234107 PMCID: PMC6131188 DOI: 10.3389/fbioe.2018.00122] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2018] [Accepted: 08/14/2018] [Indexed: 11/13/2022] Open
Abstract
Economically-viable biofuel production is often limited by low levels of microbial tolerance to high biofuel concentrations. Here we demonstrate the first application of deactivated CRISPR perturbations of gene expression to improve Escherichia coli biofuel tolerance. We construct a library of 31 unique CRISPR inhibitions and activations of gene expression in E. coli and explore their impacts on growth during 10 days of exposure to n-butanol and n-hexane. We show that perturbation of metabolism and membrane-related genes induces the greatest impacts on growth in n-butanol, as does perturbation of redox-related genes in n-hexanes. We identify uncharacterized genes yjjZ and yehS with strong potential for improving tolerance to both biofuels. Perturbations demonstrated significant temporal dependencies, suggesting that rationally designing time-sensitive gene circuits can optimize tolerance. We also introduce a sgRNA-specific hyper-mutator phenotype (~2,600-fold increase) into our perturbation strains using error-prone Pol1. We show that despite this change, strains exhibited similar growth phenotypes in n-butanol as before, demonstrating the robustness of CRISPR perturbations during prolonged use. Collectively, these results demonstrate the potential of CRISPR manipulation of gene expression for improving biofuel tolerance and provide constructive starting points for optimization of biofuel producing microorganisms.
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Affiliation(s)
- Peter B Otoupal
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO, United States
| | - Anushree Chatterjee
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO, United States.,BioFrontiers Institute, University of Colorado at Boulder, Boulder, CO, United States
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6
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Otoupal PB, Cordell WT, Bachu V, Sitton MJ, Chatterjee A. Multiplexed deactivated CRISPR-Cas9 gene expression perturbations deter bacterial adaptation by inducing negative epistasis. Commun Biol 2018; 1:129. [PMID: 30272008 PMCID: PMC6123780 DOI: 10.1038/s42003-018-0135-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Accepted: 08/08/2018] [Indexed: 12/21/2022] Open
Abstract
The ever-increasing threat of multi-drug resistant bacteria, a shrinking antibiotic pipeline, and the innate ability of microorganisms to adapt necessitates long-term strategies to slow the evolution of antibiotic resistance. Here we develop an approach, dubbed Controlled Hindrance of Adaptation of OrganismS or CHAOS, involving induction of epistasis between gene perturbations to deter adaption. We construct a combinatorial library of multiplexed, deactivated CRISPR-Cas9 devices to systematically perturb gene expression in Escherichia coli. While individual perturbations improved fitness during antibiotic exposure, multiplexed perturbations caused large fitness loss in a significant epistatic fashion. Strains exhibiting epistasis adapted significantly more slowly over three to fourteen days, and loss in adaptive potential was shown to be sustainable. Finally, we show that multiplexed peptide nucleic acids increase the antibiotic susceptibility of clinically isolated Carbapenem-resistant E. coli in an epistatic fashion. Together, these results suggest a new therapeutic strategy for restricting the evolution of antibiotic resistance. Peter Otoupal et al. present CHAOS, an approach for preventing the development of antibiotic resistance in E. coli through CRISPR-Cas9-based perturbation of gene expression. They show that multiplexed perturbations decrease fitness of clinically-isolated Carbapenem-resistant E. coli upon antibiotic exposure.
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Affiliation(s)
- Peter B Otoupal
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO, 80303, USA
| | - William T Cordell
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO, 80303, USA
| | - Vismaya Bachu
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO, 80303, USA
| | - Madeleine J Sitton
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO, 80303, USA
| | - Anushree Chatterjee
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO, 80303, USA. .,BioFrontiers Institute, University of Colorado at Boulder, Boulder, CO, 80303, USA.
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7
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Ríos P, Rocha C, Castro W, Vidal M, Canal E, Bernal M, Reynolds ND, Tilley DH, Simons MP. Extensively drug-resistant (XDR) Pseudomonas aeruginosa identified in Lima, Peru co-expressing a VIM-2 metallo-β-lactamase, OXA-1 β-lactamase and GES-1 extended-spectrum β-lactamase. JMM Case Rep 2018; 5:e005154. [PMID: 30275958 PMCID: PMC6159545 DOI: 10.1099/jmmcr.0.005154] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2018] [Accepted: 05/23/2018] [Indexed: 11/18/2022] Open
Abstract
Introduction Pseudomonas aeruginosa has the ability to acquire plasmids and other mobile genetic elements that confer resistance to antibiotics. Bacterial genes encoding different β-lactamases (bla), such as metallo-β-lactamases (MBLs) and extended-spectrum β-lactamases (ESBL), can confer resistance to multiple classes of β-lactam antibiotics. Case presentation An 83 year old female was admitted in 2012 to the Peruvian Naval Hospital, Centro Médico Naval 'Cirujano Mayor Santiago Távara' (CEMENA), in Lima, Peru. A midstream urine sample was collected and sent to the local CEMENA laboratory for routine urine culture. P. aeruginosa was isolated and initial antibiotic susceptibility testing showed it to be sensitive to imipenem. The clinicians started a course of meropenem, but the patient did not improve. After 5 days, a second urine culture was performed and a P. aeruginosa was isolated again, but this time the strain showed resistance to imipenem. The treatment course was changed to fosfomycin and the patient improved. Phenotypic and molecular laboratory testing to characterize the antibiotic resistance were performed, demonstrating the presence of both MBL and ESBL genes. Conclusion To our knowledge, this is the first report of a P. aeruginosa XDR clinical isolate that co-expresses an MBL (VIM-2), OXA-1 beta-lactamase and the ESBL (GES-1) in Peru. It is also the first report of a VIM carbapenemase in Peru.
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Affiliation(s)
- Paul Ríos
- U.S. Naval Medical Research Unit No.6 (NAMRU-6), Lima, Perú
| | - Claudio Rocha
- U.S. Naval Medical Research Unit No.6 (NAMRU-6), Lima, Perú
| | - William Castro
- Centro Médico Naval "Cirujano Mayor Santiago Távara (CEMENA)", Lima, Perú
| | - Maria Vidal
- Centro Médico Naval "Cirujano Mayor Santiago Távara (CEMENA)", Lima, Perú
| | - Enrique Canal
- U.S. Naval Medical Research Unit No.6 (NAMRU-6), Lima, Perú
| | - Manuela Bernal
- U.S. Naval Medical Research Unit No.6 (NAMRU-6), Lima, Perú
| | | | | | - Mark P Simons
- U.S. Naval Medical Research Unit No.6 (NAMRU-6), Lima, Perú
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8
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Aunins TR, Erickson KE, Prasad N, Levy SE, Jones A, Shrestha S, Mastracchio R, Stodieck L, Klaus D, Zea L, Chatterjee A. Spaceflight Modifies Escherichia coli Gene Expression in Response to Antibiotic Exposure and Reveals Role of Oxidative Stress Response. Front Microbiol 2018; 9:310. [PMID: 29615983 PMCID: PMC5865062 DOI: 10.3389/fmicb.2018.00310] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2017] [Accepted: 02/09/2018] [Indexed: 11/13/2022] Open
Abstract
Bacteria grown in space experiments under microgravity conditions have been found to undergo unique physiological responses, ranging from modified cell morphology and growth dynamics to a putative increased tolerance to antibiotics. A common theory for this behavior is the loss of gravity-driven convection processes in the orbital environment, resulting in both reduction of extracellular nutrient availability and the accumulation of bacterial byproducts near the cell. To further characterize the responses, this study investigated the transcriptomic response of Escherichia coli to both microgravity and antibiotic concentration. E. coli was grown aboard International Space Station in the presence of increasing concentrations of the antibiotic gentamicin with identical ground controls conducted on Earth. Here we show that within 49 h of being cultured, E. coli adapted to grow at higher antibiotic concentrations in space compared to Earth, and demonstrated consistent changes in expression of 63 genes in response to an increase in drug concentration in both environments, including specific responses related to oxidative stress and starvation response. Additionally, we find 50 stress-response genes upregulated in response to the microgravity when compared directly to the equivalent concentration in the ground control. We conclude that the increased antibiotic tolerance in microgravity may be attributed not only to diminished transport processes, but also to a resultant antibiotic cross-resistance response conferred by an overlapping effect of stress response genes. Our data suggest that direct stresses of nutrient starvation and acid-shock conveyed by the microgravity environment can incidentally upregulate stress response pathways related to antibiotic stress and in doing so contribute to the increased antibiotic stress tolerance observed for bacteria in space experiments. These results provide insights into the ability of bacteria to adapt under extreme stress conditions and potential strategies to prevent antimicrobial-resistance in space and on Earth.
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Affiliation(s)
- Thomas R Aunins
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO, United States
| | - Keesha E Erickson
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO, United States
| | - Nripesh Prasad
- Genomic Services Laboratory, HudsonAlpha Institute for Biotechnology, Huntsville, AL, United States
| | - Shawn E Levy
- Genomic Services Laboratory, HudsonAlpha Institute for Biotechnology, Huntsville, AL, United States
| | - Angela Jones
- Genomic Services Laboratory, HudsonAlpha Institute for Biotechnology, Huntsville, AL, United States
| | - Shristi Shrestha
- Genomic Services Laboratory, HudsonAlpha Institute for Biotechnology, Huntsville, AL, United States.,Department of Biological Sciences, The University of Alabama in Huntsville, Huntsville, AL, United States
| | - Rick Mastracchio
- Astronaut Office, Johnson Space Center, National Aeronautics and Space Administration, Washington, DC, United States
| | - Louis Stodieck
- BioServe Space Technologies, Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO, United States
| | - David Klaus
- Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO, United States
| | - Luis Zea
- BioServe Space Technologies, Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO, United States
| | - Anushree Chatterjee
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO, United States.,BioFrontiers Institute, University of Colorado Boulder, Boulder, CO, United States
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9
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Transcriptome-Level Signatures in Gene Expression and Gene Expression Variability during Bacterial Adaptive Evolution. mSphere 2017; 2:mSphere00009-17. [PMID: 28217741 PMCID: PMC5311112 DOI: 10.1128/msphere.00009-17] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2017] [Accepted: 01/23/2017] [Indexed: 01/22/2023] Open
Abstract
Antibiotic-resistant bacteria are an increasingly serious public health concern, as strains emerge that demonstrate resistance to almost all available treatments. One factor that contributes to the crisis is the adaptive ability of bacteria, which exhibit remarkable phenotypic and gene expression heterogeneity in order to gain a survival advantage in damaging environments. This high degree of variability in gene expression across biological populations makes it a challenging task to identify key regulators of bacterial adaptation. Here, we research the regulation of adaptive resistance by investigating transcriptome profiles of Escherichia coli upon adaptation to disparate toxins, including antibiotics and biofuels. We locate potential target genes via conventional gene expression analysis as well as using a new analysis technique examining differential gene expression variability. By investigating trends across the diverse adaptation conditions, we identify a focused set of genes with conserved behavior, including those involved in cell motility, metabolism, membrane structure, and transport, and several genes of unknown function. To validate the biological relevance of the observed changes, we synthetically perturb gene expression using clustered regularly interspaced short palindromic repeat (CRISPR)-dCas9. Manipulation of select genes in combination with antibiotic treatment promotes adaptive resistance as demonstrated by an increased degree of antibiotic tolerance and heterogeneity in MICs. We study the mechanisms by which identified genes influence adaptation and find that select differentially variable genes have the potential to impact metabolic rates, mutation rates, and motility. Overall, this work provides evidence for a complex nongenetic response, encompassing shifts in gene expression and gene expression variability, which underlies adaptive resistance. IMPORTANCE Even initially sensitive bacteria can rapidly thwart antibiotic treatment through stress response processes known as adaptive resistance. Adaptive resistance fosters transient tolerance increases and the emergence of mutations conferring heritable drug resistance. In order to extend the applicable lifetime of new antibiotics, we must seek to hinder the occurrence of bacterial adaptive resistance; however, the regulation of adaptation is difficult to identify due to immense heterogeneity emerging during evolution. This study specifically seeks to generate heterogeneity by adapting bacteria to different stresses and then examines gene expression trends across the disparate populations in order to pinpoint key genes and pathways associated with adaptive resistance. The targets identified here may eventually inform strategies for impeding adaptive resistance and prolonging the effectiveness of antibiotic treatment.
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10
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Otoupal PB, Erickson KE, Escalas-Bordoy A, Chatterjee A. CRISPR Perturbation of Gene Expression Alters Bacterial Fitness under Stress and Reveals Underlying Epistatic Constraints. ACS Synth Biol 2017; 6:94-107. [PMID: 27529436 DOI: 10.1021/acssynbio.6b00050] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
The evolution of antibiotic resistance has engendered an impending global health crisis that necessitates a greater understanding of how resistance emerges. The impact of nongenetic factors and how they influence the evolution of resistance is a largely unexplored area of research. Here we present a novel application of CRISPR-Cas9 technology for investigating how gene expression governs the adaptive pathways available to bacteria during the evolution of resistance. We examine the impact of gene expression changes on bacterial adaptation by constructing a library of deactivated CRISPR-Cas9 synthetic devices to tune the expression of a set of stress-response genes in Escherichia coli. We show that artificially inducing perturbations in gene expression imparts significant synthetic control over fitness and growth during stress exposure. We present evidence that these impacts are reversible; strains with synthetically perturbed gene expression regained wild-type growth phenotypes upon stress removal, while maintaining divergent growth characteristics under stress. Furthermore, we demonstrate a prevailing trend toward negative epistatic interactions when multiple gene perturbations are combined simultaneously, thereby posing an intrinsic constraint on gene expression underlying adaptive trajectories. Together, these results emphasize how CRISPR-Cas9 can be employed to engineer gene expression changes that shape bacterial adaptation, and present a novel approach to synthetically control the evolution of antimicrobial resistance.
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Affiliation(s)
- Peter B. Otoupal
- Department
of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, United States
| | - Keesha E. Erickson
- Department
of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, United States
| | - Antoni Escalas-Bordoy
- Department
of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, United States
| | - Anushree Chatterjee
- Department
of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, United States
- BioFrontiers
Institute, University of Colorado at Boulder, Boulder, Colorado 80309, United States
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11
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Sandoval-Motta S, Aldana M. Adaptive resistance to antibiotics in bacteria: a systems biology perspective. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2016; 8:253-67. [DOI: 10.1002/wsbm.1335] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2015] [Revised: 01/19/2016] [Accepted: 02/02/2016] [Indexed: 12/11/2022]
Affiliation(s)
- Santiago Sandoval-Motta
- Centro de Ciencias de la Complejidad; Universidad Nacional Autónoma de México; Ciudad de México Mexico
| | - Maximino Aldana
- Centro de Ciencias de la Complejidad; Universidad Nacional Autónoma de México; Ciudad de México Mexico
- Instituto de Ciencias Físicas; Universidad Nacional Autónoma de México; Cuernavaca Morelos Mexico
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