1
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Rajasekhar P, Carbone SE, Johnston ST, Nowell CJ, Wiklendt L, Crampin EJ, She Y, DiCello JJ, Saito A, Sorensen L, Nguyen T, Lee KM, Hamilton JA, King SK, Eriksson EM, Spencer NJ, Gulbransen BD, Veldhuis NA, Poole DP. TRPV4 is expressed by enteric glia and muscularis macrophages of the colon but does not play a prominent role in colonic motility. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.01.09.574831. [PMID: 38260314 PMCID: PMC10802399 DOI: 10.1101/2024.01.09.574831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/24/2024]
Abstract
Background Mechanosensation is an important trigger of physiological processes in the gastrointestinal tract. Aberrant responses to mechanical input are associated with digestive disorders, including visceral hypersensitivity. Transient Receptor Potential Vanilloid 4 (TRPV4) is a mechanosensory ion channel with proposed roles in visceral afferent signaling, intestinal inflammation, and gut motility. While TRPV4 is a potential therapeutic target for digestive disease, current mechanistic understanding of how TRPV4 may influence gut function is limited by inconsistent reports of TRPV4 expression and distribution. Methods In this study we profiled functional expression of TRPV4 using Ca2+ imaging of wholemount preparations of the mouse, monkey, and human intestine in combination with immunofluorescent labeling for established cellular markers. The involvement of TRPV4 in colonic motility was assessed in vitro using videomapping and contraction assays. Results The TRPV4 agonist GSK1016790A evoked Ca2+ signaling in muscularis macrophages, enteric glia, and endothelial cells. TRPV4 specificity was confirmed using TRPV4 KO mouse tissue or antagonist pre-treatment. Calcium responses were not detected in other cell types required for neuromuscular signaling including enteric neurons, interstitial cells of Cajal, PDGFRα+ cells, and intestinal smooth muscle. TRPV4 activation led to rapid Ca2+ responses by a subpopulation of glial cells, followed by sustained Ca2+ signaling throughout the enteric glial network. Propagation of these waves was suppressed by inhibition of gap junctions or Ca2+ release from intracellular stores. Coordinated glial signaling in response to GSK1016790A was also disrupted in acute TNBS colitis. The involvement of TRPV4 in the initiation and propagation of colonic motility patterns was examined in vitro. Conclusions We reveal a previously unappreciated role for TRPV4 in the initiation of distension-evoked colonic motility. These observations provide new insights into the functional role of TRPV4 activation in the gut, with important implications for how TRPV4 may influence critical processes including inflammatory signaling and motility.
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Affiliation(s)
- Pradeep Rajasekhar
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
- Centre for Dynamic Imaging, WEHI, Parkville, VIC 3052, Australia
- Department of Medical Biology, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Simona E Carbone
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
| | - Stuart T Johnston
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Cameron J Nowell
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
| | - Lukasz Wiklendt
- College of Medicine & Public Health, Flinders Health and Medical Research Institute, Flinders University, Bedford Park, SA, Australia
| | - Edmund J Crampin
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Yinghan She
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
| | - Jesse J DiCello
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
| | - Ayame Saito
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
| | - Luke Sorensen
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
| | - Thanh Nguyen
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
| | - Kevin Mc Lee
- Department of Medicine, The University of Melbourne, Royal Melbourne Hospital, Parkville, VIC 3010, Australia
| | - John A Hamilton
- Department of Medicine, The University of Melbourne, Royal Melbourne Hospital, Parkville, VIC 3010, Australia
| | - Sebastian K King
- Department of Paediatric Surgery, The Royal Children's Hospital, Parkville, VIC 3052, Australia
- Surgical Research, Murdoch Children's Research Institute, Parkville, VIC 3052, Australia
- Department of Paediatrics, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Emily M Eriksson
- Population Health and Immunity, WEHI, Parkville, VIC 3052, Australia
- Department of Medical Biology, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Nick J Spencer
- College of Medicine & Public Health, Flinders Health and Medical Research Institute, Flinders University, Bedford Park, SA, Australia
| | | | - Nicholas A Veldhuis
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
| | - Daniel P Poole
- Drug Discovery Biology, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, VIC 3052, Australia
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2
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Hoppe MM, Jaynes P, Shuangyi F, Peng Y, Sridhar S, Hoang PM, Liu CX, De Mel S, Poon L, Chan EHL, Lee J, Ong CK, Tang T, Lim ST, Nagarajan C, Grigoropoulos NF, Tan SY, Hue SSS, Chang ST, Chuang SS, Li S, Khoury JD, Choi H, Harris C, Bottos A, Gay LJ, Runge HF, Moutsopoulos I, Mohorianu I, Hodson DJ, Farinha P, Mottok A, Scott DW, Pitt JJ, Chen J, Kumar G, Kannan K, Chng WJ, Chee YL, Ng SB, Tripodo C, Jeyasekharan AD. Patterns of Oncogene Coexpression at Single-Cell Resolution Influence Survival in Lymphoma. Cancer Discov 2023; 13:1144-1163. [PMID: 37071673 PMCID: PMC10157367 DOI: 10.1158/2159-8290.cd-22-0998] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Revised: 12/29/2022] [Accepted: 02/13/2023] [Indexed: 04/19/2023]
Abstract
Cancers often overexpress multiple clinically relevant oncogenes, but it is not known if combinations of oncogenes in cellular subpopulations within a cancer influence clinical outcomes. Using quantitative multispectral imaging of the prognostically relevant oncogenes MYC, BCL2, and BCL6 in diffuse large B-cell lymphoma (DLBCL), we show that the percentage of cells with a unique combination MYC+BCL2+BCL6- (M+2+6-) consistently predicts survival across four independent cohorts (n = 449), an effect not observed with other combinations including M+2+6+. We show that the M+2+6- percentage can be mathematically derived from quantitative measurements of the individual oncogenes and correlates with survival in IHC (n = 316) and gene expression (n = 2,521) datasets. Comparative bulk/single-cell transcriptomic analyses of DLBCL samples and MYC/BCL2/BCL6-transformed primary B cells identify molecular features, including cyclin D2 and PI3K/AKT as candidate regulators of M+2+6- unfavorable biology. Similar analyses evaluating oncogenic combinations at single-cell resolution in other cancers may facilitate an understanding of cancer evolution and therapy resistance. SIGNIFICANCE Using single-cell-resolved multiplexed imaging, we show that selected subpopulations of cells expressing specific combinations of oncogenes influence clinical outcomes in lymphoma. We describe a probabilistic metric for the estimation of cellular oncogenic coexpression from IHC or bulk transcriptomes, with possible implications for prognostication and therapeutic target discovery in cancer. This article is highlighted in the In This Issue feature, p. 1027.
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Affiliation(s)
- Michal Marek Hoppe
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
| | - Patrick Jaynes
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
| | - Fan Shuangyi
- Department of Pathology, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Yanfen Peng
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
| | - Shruti Sridhar
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
| | - Phuong Mai Hoang
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
| | - Clementine Xin Liu
- Department of Haematology-Oncology, National University Health System, Singapore, Singapore
| | - Sanjay De Mel
- Department of Haematology-Oncology, National University Health System, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Limei Poon
- Department of Haematology-Oncology, National University Health System, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Esther Hian Li Chan
- Department of Haematology-Oncology, National University Health System, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Joanne Lee
- Department of Haematology-Oncology, National University Health System, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Choon Kiat Ong
- Division of Cellular and Molecular Research, National Cancer Centre Singapore, Singapore, Singapore
| | - Tiffany Tang
- Division of Medical Oncology, National Cancer Centre Singapore, Singapore, Singapore
| | - Soon Thye Lim
- Division of Medical Oncology, National Cancer Centre Singapore, Singapore, Singapore
| | | | | | - Soo-Yong Tan
- Department of Pathology, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Susan Swee-Shan Hue
- Department of Pathology, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Sheng-Tsung Chang
- Department of Pathology, Chi-Mei Medical Center, Tainan City, Taiwan
| | - Shih-Sung Chuang
- Department of Pathology, Chi-Mei Medical Center, Tainan City, Taiwan
| | - Shaoying Li
- Department of Hematopathology, Division of Pathology and Laboratory Medicine, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Joseph D. Khoury
- Department of Pathology and Microbiology, University of Nebraska Medical Center, Omaha, Nebraska
| | - Hyungwon Choi
- Department of Medicine, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Carl Harris
- F. Hoffmann-La Roche Ltd, Basel, Switzerland
| | | | - Laura J. Gay
- Wellcome MRC Cambridge Stem Cell Institute, Cambridge, United Kingdom
| | | | | | - Irina Mohorianu
- Wellcome MRC Cambridge Stem Cell Institute, Cambridge, United Kingdom
| | - Daniel J. Hodson
- Wellcome MRC Cambridge Stem Cell Institute, Cambridge, United Kingdom
| | | | - Anja Mottok
- BC Cancer Research Centre, Vancouver, Canada
| | | | - Jason J. Pitt
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
- Genome Institute of Singapore, Agency for Science, Technology and Research, Singapore, Singapore
| | - Jinmiao Chen
- Singapore Immunology Network, Agency for Science, Technology and Research, Singapore, Singapore
| | - Gayatri Kumar
- Translational Molecular Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Kasthuri Kannan
- Translational Molecular Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Wee Joo Chng
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
- Department of Medicine, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Yen Lin Chee
- Department of Haematology-Oncology, National University Health System, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Siok-Bian Ng
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
- Department of Pathology, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Claudio Tripodo
- Tumor Immunology Unit, University of Palermo, Palermo, Italy
- IFOM ETS – The AIRC Institute of Molecular Oncology, Milan, Italy
| | - Anand D. Jeyasekharan
- Cancer Science Institute of Singapore, National University of Singapore, Singapore, Singapore
- Department of Haematology-Oncology, National University Health System, Singapore, Singapore
- NUS Centre for Cancer Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
- Department of Medicine, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
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3
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Rosén E, Mangukiya HB, Elfineh L, Stockgard R, Krona C, Gerlee P, Nelander S. Inference of glioblastoma migration and proliferation rates using single time-point images. Commun Biol 2023; 6:402. [PMID: 37055469 PMCID: PMC10102065 DOI: 10.1038/s42003-023-04750-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Accepted: 03/23/2023] [Indexed: 04/15/2023] Open
Abstract
Cancer cell migration is a driving mechanism of invasion in solid malignant tumors. Anti-migratory treatments provide an alternative approach for managing disease progression. However, we currently lack scalable screening methods for identifying novel anti-migratory drugs. To this end, we develop a method that can estimate cell motility from single end-point images in vitro by estimating differences in the spatial distribution of cells and inferring proliferation and diffusion parameters using agent-based modeling and approximate Bayesian computation. To test the power of our method, we use it to investigate drug responses in a collection of 41 patient-derived glioblastoma cell cultures, identifying migration-associated pathways and drugs with potent anti-migratory effects. We validate our method and result in both in silico and in vitro using time-lapse imaging. Our proposed method applies to standard drug screen experiments, with no change needed, and emerges as a scalable approach to screen for anti-migratory drugs.
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Affiliation(s)
- Emil Rosén
- Dept of Immunology, Genetics, and Pathology, Uppsala University, Uppsala, Sweden
| | | | - Ludmila Elfineh
- Dept of Immunology, Genetics, and Pathology, Uppsala University, Uppsala, Sweden
| | - Rebecka Stockgard
- Dept of Immunology, Genetics, and Pathology, Uppsala University, Uppsala, Sweden
| | - Cecilia Krona
- Dept of Immunology, Genetics, and Pathology, Uppsala University, Uppsala, Sweden
| | - Philip Gerlee
- Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden
- Mathematical Sciences, University of Gothenburg, Gothenburg, Sweden
| | - Sven Nelander
- Dept of Immunology, Genetics, and Pathology, Uppsala University, Uppsala, Sweden.
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4
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Bull JA, Byrne HM. Quantification of spatial and phenotypic heterogeneity in an agent-based model of tumour-macrophage interactions. PLoS Comput Biol 2023; 19:e1010994. [PMID: 36972297 PMCID: PMC10079237 DOI: 10.1371/journal.pcbi.1010994] [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: 09/14/2022] [Revised: 04/06/2023] [Accepted: 03/04/2023] [Indexed: 03/29/2023] Open
Abstract
We introduce a new spatial statistic, the weighted pair correlation function (wPCF). The wPCF extends the existing pair correlation function (PCF) and cross-PCF to describe spatial relationships between points marked with combinations of discrete and continuous labels. We validate its use through application to a new agent-based model (ABM) which simulates interactions between macrophages and tumour cells. These interactions are influenced by the spatial positions of the cells and by macrophage phenotype, a continuous variable that ranges from anti-tumour to pro-tumour. By varying model parameters that regulate macrophage phenotype, we show that the ABM exhibits behaviours which resemble the 'three Es of cancer immunoediting': Equilibrium, Escape, and Elimination. We use the wPCF to analyse synthetic images generated by the ABM. We show that the wPCF generates a 'human readable' statistical summary of where macrophages with different phenotypes are located relative to both blood vessels and tumour cells. We also define a distinct 'PCF signature' that characterises each of the three Es of immunoediting, by combining wPCF measurements with the cross-PCF describing interactions between vessels and tumour cells. By applying dimension reduction techniques to this signature, we identify its key features and train a support vector machine classifier to distinguish between simulation outputs based on their PCF signature. This proof-of-concept study shows how multiple spatial statistics can be combined to analyse the complex spatial features that the ABM generates, and to partition them into interpretable groups. The intricate spatial features produced by the ABM are similar to those generated by state-of-the-art multiplex imaging techniques which distinguish the spatial distribution and intensity of multiple biomarkers in biological tissue regions. Applying methods such as the wPCF to multiplex imaging data would exploit the continuous variation in biomarker intensities and generate more detailed characterisation of the spatial and phenotypic heterogeneity in tissue samples.
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Affiliation(s)
- Joshua A. Bull
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Helen M. Byrne
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
- Ludwig Institute for Cancer Research, Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
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5
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Hutchinson LG, Grimm O. Integrating digital pathology and mathematical modelling to predict spatial biomarker dynamics in cancer immunotherapy. NPJ Digit Med 2022; 5:92. [PMID: 35821064 PMCID: PMC9276679 DOI: 10.1038/s41746-022-00636-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Accepted: 06/24/2022] [Indexed: 11/26/2022] Open
Abstract
In oncology clinical trials, on-treatment biopsy samples are taken to confirm the mode of action of new molecules, among other reasons. Yet, the time point of sample collection is typically scheduled according to 'Expert Best Guess'. We have developed an approach integrating digital pathology and mathematical modelling to provide clinical teams with quantitative information to support this decision. Using digitised biopsies from an ongoing clinical trial as the input to an agent-based mathematical model, we have quantitatively optimised and validated the model demonstrating that it accurately recapitulates observed biopsy samples. Furthermore, the validated model can be used to predict the dynamics of simulated biopsies, with applications from protocol design for phase 1–2 studies to the conception of combination therapies, to personalised healthcare.
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Affiliation(s)
- L G Hutchinson
- Roche Pharma Research and Early Development, Pharmaceutical Sciences, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd, Grenzacherstrasse 124, 4070, Basel, Switzerland.
| | - O Grimm
- Roche Pharma Research and Early Development, Pharmaceutical Sciences, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd, Grenzacherstrasse 124, 4070, Basel, Switzerland
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6
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Parra ER. Methods to Determine and Analyze the Cellular Spatial Distribution Extracted From Multiplex Immunofluorescence Data to Understand the Tumor Microenvironment. Front Mol Biosci 2021; 8:668340. [PMID: 34179080 PMCID: PMC8226163 DOI: 10.3389/fmolb.2021.668340] [Citation(s) in RCA: 29] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 06/02/2021] [Indexed: 12/13/2022] Open
Abstract
Image analysis using multiplex immunofluorescence (mIF) to detect different proteins in a single tissue section has revolutionized immunohistochemical methods in recent years. With mIF, individual cell phenotypes, as well as different cell subpopulations and even rare cell populations, can be identified with extraordinary fidelity according to the expression of antibodies in an mIF panel. This technology therefore has an important role in translational oncology studies and probably will be incorporated in the clinic. The expression of different biomarkers of interest can be examined at the tissue or individual cell level using mIF, providing information about cell phenotypes, distribution of cells, and cell biological processes in tumor samples. At present, the main challenge in spatial analysis is choosing the most appropriate method for extracting meaningful information about cell distribution from mIF images for analysis. Thus, knowing how the spatial interaction between cells in the tumor encodes clinical information is important. Exploratory analysis of the location of the cell phenotypes using point patterns of distribution is used to calculate metrics summarizing the distances at which cells are processed and the interpretation of those distances. Various methods can be used to analyze cellular distribution in an mIF image, and several mathematical functions can be applied to identify the most elemental relationships between the spatial analysis of cells in the image and established patterns of cellular distribution in tumor samples. The aim of this review is to describe the characteristics of mIF image analysis at different levels, including spatial distribution of cell populations and cellular distribution patterns, that can increase understanding of the tumor microenvironment.
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Affiliation(s)
- Edwin Roger Parra
- Department of Translational Molecular Pathology, The University of Texas MD Anderson Cancer Center, Houston, TX, United States
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7
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Hywood JD, Rice G, Pageon SV, Read MN, Biro M. Detection and characterization of chemotaxis without cell tracking. J R Soc Interface 2021; 18:20200879. [PMID: 33715400 PMCID: PMC8086846 DOI: 10.1098/rsif.2020.0879] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 02/15/2021] [Indexed: 02/06/2023] Open
Abstract
Swarming has been observed in various biological systems from collective animal movements to immune cells. In the cellular context, swarming is driven by the secretion of chemotactic factors. Despite the critical role of chemotactic swarming, few methods to robustly identify and quantify this phenomenon exist. Here, we present a novel method for the analysis of time series of positional data generated from realizations of agent-based processes. We convert the positional data for each individual time point to a function measuring agent aggregation around a given area of interest, hence generating a functional time series. The functional time series, and a more easily visualized swarming metric of agent aggregation derived from these functions, provide useful information regarding the evolution of the underlying process over time. We extend our method to build upon the modelling of collective motility using drift-diffusion partial differential equations (PDEs). Using a functional linear model, we are able to use the functional time series to estimate the drift and diffusivity terms associated with the underlying PDE. By producing an accurate estimate for the drift coefficient, we can infer the strength and range of attraction or repulsion exerted on agents, as in chemotaxis. Our approach relies solely on using agent positional data. The spatial distribution of diffusing chemokines is not required, nor do individual agents need to be tracked over time. We demonstrate our approach using random walk simulations of chemotaxis and experiments investigating cytotoxic T cells interacting with tumouroids.
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Affiliation(s)
- Jack D. Hywood
- Sydney Medical School, The University of Sydney, Sydney, Australia
| | - Gregory Rice
- Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
| | - Sophie V. Pageon
- EMBL Australia, Single Molecule Science node, School of Medical Sciences, University of New South Wales, Sydney, Australia
| | - Mark N. Read
- School of Computer Science & Charles Perkins Centre, University of Sydney, Sydney, Australia
| | - Maté Biro
- EMBL Australia, Single Molecule Science node, School of Medical Sciences, University of New South Wales, Sydney, Australia
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8
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De Oliveira AL, Binder BJ. Discrete Manhattan and Chebyshev pair correlation functions in k dimensions. Phys Rev E 2020; 102:012130. [PMID: 32795028 DOI: 10.1103/physreve.102.012130] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2020] [Accepted: 06/24/2020] [Indexed: 12/22/2022]
Abstract
Pair correlation functions provide a summary statistic which quantifies the amount of spatial correlation between objects in a spatial domain. While pair correlation functions are commonly used to quantify continuous-space point processes, the on-lattice discrete case is less studied. Recent work has brought attention to the discrete case, wherein on-lattice pair correlation functions are formed by normalizing empirical pair distances against the probability distribution of random pair distances in a lattice with Manhattan and Chebyshev metrics. These distance distributions are typically derived on an ad hoc basis as required for specific applications. Here we present a generalized approach to deriving the probability distributions of pair distances in a lattice with discrete Manhattan and Chebyshev metrics, extending the Manhattan and Chebyshev pair correlation functions to lattices in k dimensions. We also quantify the variability of the Manhattan and Chebyshev pair correlation functions, which is important to understanding the reliability and confidence of the statistic.
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Affiliation(s)
| | - Benjamin J Binder
- School of Mathematical Sciences, University of Adelaide, Adelaide 5005, Australia
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9
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Owen JP, Kelsh RN, Yates CA. A quantitative modelling approach to zebrafish pigment pattern formation. eLife 2020; 9:52998. [PMID: 32716296 PMCID: PMC7384860 DOI: 10.7554/elife.52998] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2019] [Accepted: 06/21/2020] [Indexed: 12/14/2022] Open
Abstract
Pattern formation is a key aspect of development. Adult zebrafish exhibit a striking striped pattern generated through the self-organisation of three different chromatophores. Numerous investigations have revealed a multitude of individual cell-cell interactions important for this self-organisation, but it has remained unclear whether these known biological rules were sufficient to explain pattern formation. To test this, we present an individual-based mathematical model incorporating all the important cell-types and known interactions. The model qualitatively and quantitatively reproduces wild type and mutant pigment pattern development. We use it to resolve a number of outstanding biological uncertainties, including the roles of domain growth and the initial iridophore stripe, and to generate hypotheses about the functions of leopard. We conclude that our rule-set is sufficient to recapitulate wild-type and mutant patterns. Our work now leads the way for further in silico exploration of the developmental and evolutionary implications of this pigment patterning system.
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Affiliation(s)
- Jennifer P Owen
- Department of Biology and Biochemistry and Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, United Kingdom
| | - Robert N Kelsh
- Department of Biology and Biochemistry and Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, United Kingdom
| | - Christian A Yates
- Department of Biology and Biochemistry and Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, United Kingdom
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10
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Zhang S, Chong A, Hughes BD. Persistent exclusion processes: Inertia, drift, mixing, and correlation. Phys Rev E 2019; 100:042415. [PMID: 31770998 DOI: 10.1103/physreve.100.042415] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Indexed: 12/16/2022]
Abstract
In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple walkers with motion persistence and spatial exclusion in one and two dimensions, and use a mean-field approximation to investigate relevant population-level partial differential equations in the continuum limit. We show that this model of a persistent exclusion process is in general well described by a nonlinear diffusion equation. With reference to results presented in the current literature, our results reveal that the nonlinearity arises from the combination of motion persistence and volume exclusion, with linearity in terms of the canonical diffusion or heat equation being recovered in either the case of persistence without spatial exclusion, or spatial exclusion without persistence. We generalize our results to include systems of multiple species of interacting, motion-persistent walkers, as well as to incorporate a global drift in addition to persistence. These models are shown to be governed approximately by systems of nonlinear advection-diffusion equations. By comparing the prediction of the mean-field approximation to stochastic simulation results, we assess the performance of our results. Finally, we also address the problem of inferring the presence of persistence from simulation results, with a view to application to experimental cell-imaging data.
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Affiliation(s)
- Stephen Zhang
- School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
| | - Aaron Chong
- School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
| | - Barry D Hughes
- School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
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11
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Johnston ST, Crampin EJ. Corrected pair correlation functions for environments with obstacles. Phys Rev E 2019; 99:032124. [PMID: 30999485 DOI: 10.1103/physreve.99.032124] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Indexed: 01/30/2023]
Abstract
Environments with immobile obstacles or void regions that inhibit and alter the motion of individuals within that environment are ubiquitous. Correlation in the location of individuals within such environments arises as a combination of the mechanisms governing individual behavior and the heterogeneous structure of the environment. Measures of spatial structure and correlation have been successfully implemented to elucidate the roles of the mechanisms underpinning the behavior of individuals. In particular, the pair correlation function has been used across biology, ecology, and physics to obtain quantitative insight into a variety of processes. However, naively applying standard pair correlation functions in the presence of obstacles may fail to detect correlation, or suggest false correlations, due to a reliance on a distance metric that does not account for obstacles. To overcome this problem, here we present an analytic expression for calculating a corrected pair correlation function for lattice-based domains containing obstacles. We demonstrate that this obstacle pair correlation function is necessary for isolating the correlation associated with the behavior of individuals, rather than the structure of the environment. Using simulations that mimic cell migration and proliferation we demonstrate that the obstacle pair correlation function recovers the short-range correlation known to be present in this process, independent of the heterogeneous structure of the environment. Further, we show that the analytic calculation of the obstacle pair correlation function derived here is significantly faster to implement than the corresponding numerical approach.
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Affiliation(s)
- Stuart T Johnston
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia.,ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Melbourne School of Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
| | - Edmund J Crampin
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia.,ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Melbourne School of Engineering, University of Melbourne, Parkville, Victoria 3010, Australia.,School of Medicine, Faculty of Medicine Dentistry and Health Sciences, University of Melbourne, Parkville, Victoria 3010, Australia
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