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Loman TE, Ma Y, Ilin V, Gowda S, Korsbo N, Yewale N, Rackauckas C, Isaacson SA. Catalyst: Fast and flexible modeling of reaction networks. PLoS Comput Biol 2023; 19:e1011530. [PMID: 37851697 PMCID: PMC10584191 DOI: 10.1371/journal.pcbi.1011530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2023] [Accepted: 09/19/2023] [Indexed: 10/20/2023] Open
Abstract
We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst's broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.
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Affiliation(s)
- Torkel E. Loman
- Sainsbury Laboratory, University of Cambridge, Cambridge, United Kingdom
- Computer Science and AI Laboratory (CSAIL), Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Yingbo Ma
- JuliaHub, Cambridge, Massachusetts, United States of America
| | - Vasily Ilin
- Department of Mathematics, University of Washington, Seattle, Washington, United States of America
| | - Shashi Gowda
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Niklas Korsbo
- Pumas-AI, Baltimore, Maryland, United States of America
| | - Nikhil Yewale
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India
| | - Chris Rackauckas
- Computer Science and AI Laboratory (CSAIL), Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
- JuliaHub, Cambridge, Massachusetts, United States of America
- Pumas-AI, Baltimore, Maryland, United States of America
| | - Samuel A. Isaacson
- Department of Mathematics and Statistics, Boston University, Boston, Massachusetts, United States of America
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2
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Loman TE, Locke JCW. The σB alternative sigma factor circuit modulates noise to generate different types of pulsing dynamics. PLoS Comput Biol 2023; 19:e1011265. [PMID: 37540712 PMCID: PMC10431680 DOI: 10.1371/journal.pcbi.1011265] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Revised: 08/16/2023] [Accepted: 06/12/2023] [Indexed: 08/06/2023] Open
Abstract
Single-cell approaches are revealing a high degree of heterogeneity, or noise, in gene expression in isogenic bacteria. How gene circuits modulate this noise in gene expression to generate robust output dynamics is unclear. Here we use the Bacillus subtilis alternative sigma factor σB as a model system for understanding the role of noise in generating circuit output dynamics. σB controls the general stress response in B. subtilis and is activated by a range of energy and environmental stresses. Recent single-cell studies have revealed that the circuit can generate two distinct outputs, stochastic pulsing and a single pulse response, but the conditions under which each response is generated are under debate. We implement a stochastic mathematical model of the σB circuit to investigate this and find that the system's core circuit can generate both response types. This is despite one response (stochastic pulsing) being stochastic in nature, and the other (single response pulse) being deterministic. We demonstrate that the main determinant for whichever response is generated is the degree with which the input pathway activates the core circuit, although the noise properties of the input pathway also biases the system towards one or the other type of output. Thus, our work shows how stochastic modelling can reveal the mechanisms behind non-intuitive gene circuit output dynamics.
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Affiliation(s)
- Torkel E. Loman
- Sainsbury Laboratory, University of Cambridge, Cambridge, United Kingdom
| | - James C. W. Locke
- Sainsbury Laboratory, University of Cambridge, Cambridge, United Kingdom
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Virmani R, Pradhan P, Joshi J, Wang AL, Joshi HC, Sajid A, Singh A, Sharma V, Kundu B, Blankenberg D, Molle V, Singh Y, Arora G. Phosphorylation-mediated regulation of the Bacillus anthracis phosphoglycerate mutase by the Ser/Thr protein kinase PrkC. Biochem Biophys Res Commun 2023; 665:88-97. [PMID: 37149987 DOI: 10.1016/j.bbrc.2023.04.039] [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: 03/19/2023] [Accepted: 04/15/2023] [Indexed: 05/09/2023]
Abstract
Bacillus anthracis Ser/Thr protein kinase PrkC is necessary for phenotypic memory and spore germination, and the loss of PrkC-dependent phosphorylation events affect the spore development. During sporulation, Bacillus sp. can store 3-Phosphoglycerate (3-PGA) that will be required at the onset of germination when ATP will be necessary. The Phosphoglycerate mutase (Pgm) catalyzes the isomerization of 2-PGA and 3-PGA and is important for spore germination as a key metabolic enzyme that maintains 3-PGA pool at later events. Therefore, regulation of Pgm is important for an efficient spore germination process and metabolic switching. While the increased expression of Pgm in B. anthracis decreases spore germination efficiency, it remains unexplored if PrkC could directly influence Pgm activity. Here, we report the phosphorylation and regulation of Pgm by PrkC and its impact on Pgm stability and catalytic activity. Mass spectrometry revealed Pgm phosphorylation on seven threonine residues. In silico mutational analysis highlighted the role of Thr459 residue towards metal and substrate binding. Altogether, we demonstrated that PrkC-mediated Pgm phosphorylation negatively regulates its activity that is essential to maintain Pgm in its apo-like isoform before germination. This study advances the role of Pgm regulation that represents an important switch for B. anthracis resumption of metabolism and spore germination.
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Affiliation(s)
- Richa Virmani
- Department of Zoology, University of Delhi, Delhi, 110007, India
| | - Prashant Pradhan
- Kusuma School of Biological Sciences, IIT Delhi, Hauz Khas, New Delhi, 110016, India
| | - Jayadev Joshi
- Genomic Medicine Institute, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, 44195, USA
| | - Avril Luyang Wang
- Department of Molecular Genetics and Microbiology, University of Toronto, Toronto, M5S1A8, Canada
| | | | - Andaleeb Sajid
- Department of Internal Medicine, Yale University School of Medicine, New Haven, CT, 06520, USA
| | - Anoop Singh
- Department of Zoology, University of Delhi, Delhi, 110007, India
| | - Vishal Sharma
- Department of Zoology, University of Delhi, Delhi, 110007, India
| | - Bishwajit Kundu
- Kusuma School of Biological Sciences, IIT Delhi, Hauz Khas, New Delhi, 110016, India
| | - Daniel Blankenberg
- Genomic Medicine Institute, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, 44195, USA
| | - Virginie Molle
- Laboratory of Pathogen Host Interactions, Université de Montpellier, CNRS, UMR, 5235, Montpellier, France
| | - Yogendra Singh
- Department of Zoology, University of Delhi, Delhi, 110007, India.
| | - Gunjan Arora
- Department of Internal Medicine, Yale University School of Medicine, New Haven, CT, 06520, USA.
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Choudhary D, Lagage V, Foster KR, Uphoff S. Phenotypic heterogeneity in the bacterial oxidative stress response is driven by cell-cell interactions. Cell Rep 2023; 42:112168. [PMID: 36848288 PMCID: PMC10935545 DOI: 10.1016/j.celrep.2023.112168] [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: 10/04/2022] [Revised: 12/14/2022] [Accepted: 02/09/2023] [Indexed: 02/27/2023] Open
Abstract
Genetically identical bacterial cells commonly display different phenotypes. This phenotypic heterogeneity is well known for stress responses, where it is often explained as bet hedging against unpredictable environmental threats. Here, we explore phenotypic heterogeneity in a major stress response of Escherichia coli and find it has a fundamentally different basis. We characterize the response of cells exposed to hydrogen peroxide (H2O2) stress in a microfluidic device under constant growth conditions. A machine-learning model reveals that phenotypic heterogeneity arises from a precise and rapid feedback between each cell and its immediate environment. Moreover, we find that the heterogeneity rests upon cell-cell interaction, whereby cells shield each other from H2O2 via their individual stress responses. Our work shows how phenotypic heterogeneity in bacterial stress responses can emerge from short-range cell-cell interactions and result in a collective phenotype that protects a large proportion of the population.
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Affiliation(s)
- Divya Choudhary
- Department of Biochemistry, University of Oxford, Oxford, UK
| | | | - Kevin R Foster
- Department of Biochemistry, University of Oxford, Oxford, UK; Department of Biology, University of Oxford, Oxford, UK
| | - Stephan Uphoff
- Department of Biochemistry, University of Oxford, Oxford, UK.
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Steward KF, Refai M, Dyer WE, Copié V, Lachowiec J, Bothner B. Acute stress reduces population-level metabolic and proteomic variation. BMC Bioinformatics 2023; 24:87. [PMID: 36882728 PMCID: PMC9993721 DOI: 10.1186/s12859-023-05185-4] [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: 04/18/2022] [Accepted: 02/14/2023] [Indexed: 03/09/2023] Open
Abstract
BACKGROUND Variation in omics data due to intrinsic biological stochasticity is often viewed as a challenging and undesirable feature of complex systems analyses. In fact, numerous statistical methods are utilized to minimize the variation among biological replicates. RESULTS We demonstrate that the common statistics relative standard deviation (RSD) and coefficient of variation (CV), which are often used for quality control or part of a larger pipeline in omics analyses, can also be used as a metric of a physiological stress response. Using an approach we term Replicate Variation Analysis (RVA), we demonstrate that acute physiological stress leads to feature-wide canalization of CV profiles of metabolomes and proteomes across biological replicates. Canalization is the repression of variation between replicates, which increases phenotypic similarity. Multiple in-house mass spectrometry omics datasets in addition to publicly available data were analyzed to assess changes in CV profiles in plants, animals, and microorganisms. In addition, proteomics data sets were evaluated utilizing RVA to identify functionality of reduced CV proteins. CONCLUSIONS RVA provides a foundation for understanding omics level shifts that occur in response to cellular stress. This approach to data analysis helps characterize stress response and recovery, and could be deployed to detect populations under stress, monitor health status, and conduct environmental monitoring.
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Affiliation(s)
- Katherine F Steward
- Department of Chemistry and Biochemistry, Montana State University, Bozeman, MT, 59717, USA
| | - Mohammed Refai
- Department of Chemistry and Biochemistry, Montana State University, Bozeman, MT, 59717, USA
| | - William E Dyer
- Department of Chemistry and Biochemistry, Montana State University, Bozeman, MT, 59717, USA.,Department of Plant Sciences and Plant Pathology, Montana State University, Bozeman, USA
| | - Valérie Copié
- Department of Chemistry and Biochemistry, Montana State University, Bozeman, MT, 59717, USA.,Thermal Biology Institute, Montana State University, Bozeman, USA
| | - Jennifer Lachowiec
- Department of Plant Sciences and Plant Pathology, Montana State University, Bozeman, USA
| | - Brian Bothner
- Department of Chemistry and Biochemistry, Montana State University, Bozeman, MT, 59717, USA. .,Thermal Biology Institute, Montana State University, Bozeman, USA.
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Dorman CJ. Variable DNA topology is an epigenetic generator of physiological heterogeneity in bacterial populations. Mol Microbiol 2023; 119:19-28. [PMID: 36565252 PMCID: PMC10108321 DOI: 10.1111/mmi.15014] [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: 10/28/2022] [Revised: 11/25/2022] [Accepted: 12/06/2022] [Indexed: 12/25/2022]
Abstract
Transcription is a noisy and stochastic process that produces sibling-to-sibling variations in physiology across a population of genetically identical cells. This pattern of diversity reflects, in part, the burst-like nature of transcription. Transcription bursting has many causes and a failure to remove the supercoils that accumulate in DNA during transcription elongation is an important contributor. Positive supercoiling of the DNA ahead of the transcription elongation complex can result in RNA polymerase stalling if this DNA topological roadblock is not removed. The relaxation of these positive supercoils is performed by the ATP-dependent type II topoisomerases DNA gyrase and topoisomerase IV. Interference with the action of these topoisomerases involving, inter alia, topoisomerase poisons, fluctuations in the [ATP]/[ADP] ratio, and/or the intervention of nucleoid-associated proteins with GapR-like or YejK-like activities, may have consequences for the smooth operation of the transcriptional machinery. Antibiotic-tolerant (but not resistant) persister cells are among the phenotypic outliers that may emerge. However, interference with type II topoisomerase activity can have much broader consequences, making it an important epigenetic driver of physiological diversity in the bacterial population.
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Affiliation(s)
- Charles J Dorman
- Department of Microbiology, Moyne Institute of Preventive Medicine, Trinity College Dublin, Dublin 2, Ireland
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Loell K, Wu Y, Staller MV, Cohen B. Activation domains can decouple the mean and noise of gene expression. Cell Rep 2022; 40:111118. [PMID: 35858548 PMCID: PMC9912357 DOI: 10.1016/j.celrep.2022.111118] [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: 09/08/2021] [Revised: 01/18/2022] [Accepted: 06/28/2022] [Indexed: 11/03/2022] Open
Abstract
Regulatory mechanisms set a gene's average level of expression, but a gene's expression constantly fluctuates around that average. These stochastic fluctuations, or expression noise, play a role in cell-fate transitions, bet hedging in microbes, and the development of chemotherapeutic resistance in cancer. An outstanding question is what regulatory mechanisms contribute to noise. Here, we demonstrate that, for a fixed mean level of expression, strong activation domains (ADs) at low abundance produce high expression noise, while weak ADs at high abundance generate lower expression noise. We conclude that differences in noise can be explained by the interplay between a TF's nuclear concentration and the strength of its AD's effect on mean expression, without invoking differences between classes of ADs. These results raise the possibility of engineering gene expression noise independently of mean levels in synthetic biology contexts and provide a potential mechanism for natural selection to tune the noisiness of gene expression.
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Affiliation(s)
- Kaiser Loell
- Department of Genetics, Washington University School of Medicine in St. Louis, St. Louis, MO 63108, USA,The Edison Family Center for Genome Sciences & Systems Biology, Washington University School of Medicine in St. Louis, St. Louis, MO 63108, USA
| | - Yawei Wu
- Department of Genetics, Washington University School of Medicine in St. Louis, St. Louis, MO 63108, USA,The Edison Family Center for Genome Sciences & Systems Biology, Washington University School of Medicine in St. Louis, St. Louis, MO 63108, USA
| | - Max V. Staller
- Center for Computational Biology, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Barak Cohen
- Department of Genetics, Washington University School of Medicine in St. Louis, St. Louis, MO 63108, USA; The Edison Family Center for Genome Sciences & Systems Biology, Washington University School of Medicine in St. Louis, St. Louis, MO 63108, USA.
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Ho TD, Ellermeier CD. Activation of the extracytoplasmic function σ factor σ V by lysozyme in Clostridioides difficile. Curr Opin Microbiol 2022; 65:162-166. [PMID: 34894542 PMCID: PMC8792214 DOI: 10.1016/j.mib.2021.11.008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 11/12/2021] [Accepted: 11/18/2021] [Indexed: 02/03/2023]
Abstract
Clostridioides difficile is naturally resistant to high levels of lysozyme an important component of the innate immune defense system. C. difficile encodes both constitutive as well as inducible lysozyme resistance genes. The inducible lysozyme resistance genes are controlled by an alternative σ factor σV that belongs to the Extracytoplasmic function σ factor family. In the absence of lysozyme, the activity of σV is inhibited by the anti-σ factor RsiV. In the presence of lysozyme RsiV is destroyed via a proteolytic cascade that leads to σV activation and increased lysozyme resistance. This review highlights how activity of σV is controlled.
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Affiliation(s)
- Theresa D. Ho
- Department of Microbiology and Immunology, Carver College of Medicine, University of Iowa, 431 Newton Rd, Iowa City, IA 52242
| | - Craig D. Ellermeier
- Department of Microbiology and Immunology, Carver College of Medicine, University of Iowa, 431 Newton Rd, Iowa City, IA 52242,Graduate Program in Genetics, University of Iowa, Iowa City, IA 52242, USA,Corresponding author: , 319-384-4565
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