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Cosgrove J, Alden K, Stein JV, Coles MC, Timmis J. Simulating CXCR5 Dynamics in Complex Tissue Microenvironments. Front Immunol 2021; 12:703088. [PMID: 34557191 PMCID: PMC8452942 DOI: 10.3389/fimmu.2021.703088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 08/16/2021] [Indexed: 11/25/2022] Open
Abstract
To effectively navigate complex tissue microenvironments, immune cells sense molecular concentration gradients using G-protein coupled receptors. However, due to the complexity of receptor activity, and the multimodal nature of chemokine gradients in vivo, chemokine receptor activity in situ is poorly understood. To address this issue, we apply a modelling and simulation approach that permits analysis of the spatiotemporal dynamics of CXCR5 expression within an in silico B-follicle with single-cell resolution. Using this approach, we show that that in silico B-cell scanning is robust to changes in receptor numbers and changes in individual kinetic rates of receptor activity, but sensitive to global perturbations where multiple parameters are altered simultaneously. Through multi-objective optimization analysis we find that the rapid modulation of CXCR5 activity through receptor binding, desensitization and recycling is required for optimal antigen scanning rates. From these analyses we predict that chemokine receptor signaling dynamics regulate migration in complex tissue microenvironments to a greater extent than the total numbers of receptors on the cell surface.
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Affiliation(s)
- Jason Cosgrove
- Department of Electronic Engineering, University of York, York, United Kingdom.,Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Laboratoire Physico Chimie Curie, Paris, France
| | - Kieran Alden
- Department of Electronic Engineering, University of York, York, United Kingdom
| | - Jens V Stein
- Department of Oncology, Microbiology and Immunology, University of Fribourg, Fribourg, Switzerland
| | - Mark C Coles
- Kennedy Institute of Rheumatology at the University of Oxford, Oxford, United Kingdom
| | - Jon Timmis
- School of Computer Science, University of Sunderland, Sunderland, United Kingdom
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2
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Leroy-Lerêtre M, Dimarco G, Cazales M, Boizeau ML, Ducommun B, Lobjois V, Degond P. Are Tumor Cell Lineages Solely Shaped by Mechanical Forces? Bull Math Biol 2017; 79:2356-2393. [PMID: 28852950 PMCID: PMC5597711 DOI: 10.1007/s11538-017-0333-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2017] [Accepted: 08/08/2017] [Indexed: 12/19/2022]
Abstract
This paper investigates cell proliferation dynamics in small tumor cell aggregates using an individual-based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM model is based on the hypothesis that cells are incompressible objects that grow in size and divide once a threshold size is reached, and that newly born cell adhere to the existing cell cluster. We performed comparisons between the simulation model and experimental data by using several statistical indicators. The results suggest that the emergence of particular morphologies can be explained by simple mechanical interactions.
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Affiliation(s)
- Mathieu Leroy-Lerêtre
- Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS, UPS, Toulouse, France.,ITAV-USR3505, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Giacomo Dimarco
- Department of Mathematics and Computer Science, University of Ferrara, Ferrara, Italy
| | - Martine Cazales
- ITAV-USR3505, Université de Toulouse, CNRS, UPS, Toulouse, France
| | | | - Bernard Ducommun
- ITAV-USR3505, Université de Toulouse, CNRS, UPS, Toulouse, France.,CHU Toulouse, Toulouse, France
| | - Valérie Lobjois
- ITAV-USR3505, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre Degond
- Department of Mathematics, Imperial College London, London, UK.
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Kempf H, Bleicher M, Meyer-Hermann M. Spatio-Temporal Dynamics of Hypoxia during Radiotherapy. PLoS One 2015; 10:e0133357. [PMID: 26273841 PMCID: PMC4537194 DOI: 10.1371/journal.pone.0133357] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2015] [Accepted: 06/26/2015] [Indexed: 12/27/2022] Open
Abstract
Tumour hypoxia plays a pivotal role in cancer therapy for most therapeutic approaches from radiotherapy to immunotherapy. The detailed and accurate knowledge of the oxygen distribution in a tumour is necessary in order to determine the right treatment strategy. Still, due to the limited spatial and temporal resolution of imaging methods as well as lacking fundamental understanding of internal oxygenation dynamics in tumours, the precise oxygen distribution map is rarely available for treatment planing. We employ an agent-based in silico tumour spheroid model in order to study the complex, localized and fast oxygen dynamics in tumour micro-regions which are induced by radiotherapy. A lattice-free, 3D, agent-based approach for cell representation is coupled with a high-resolution diffusion solver that includes a tissue density-dependent diffusion coefficient. This allows us to assess the space- and time-resolved reoxygenation response of a small subvolume of tumour tissue in response to radiotherapy. In response to irradiation the tumour nodule exhibits characteristic reoxygenation and re-depletion dynamics which we resolve with high spatio-temporal resolution. The reoxygenation follows specific timings, which should be respected in treatment in order to maximise the use of the oxygen enhancement effects. Oxygen dynamics within the tumour create windows of opportunity for the use of adjuvant chemotherapeutica and hypoxia-activated drugs. Overall, we show that by using modelling it is possible to follow the oxygenation dynamics beyond common resolution limits and predict beneficial strategies for therapy and in vitro verification. Models of cell cycle and oxygen dynamics in tumours should in the future be combined with imaging techniques, to allow for a systematic experimental study of possible improved schedules and to ultimately extend the reach of oxygenation monitoring available in clinical treatment.
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Affiliation(s)
- Harald Kempf
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig, Germany
- Frankfurt Institute for Advanced Studies, Frankfurt, Germany
| | - Marcus Bleicher
- Frankfurt Institute for Advanced Studies, Frankfurt, Germany
| | - Michael Meyer-Hermann
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig, Germany
- Institute for Biochemistry, Biotechnology and Bioinformatics, Technische Universität Braunschweig, Braunschweig, Germany
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Kim M, Reed D, Rejniak KA. The formation of tight tumor clusters affects the efficacy of cell cycle inhibitors: a hybrid model study. J Theor Biol 2014; 352:31-50. [PMID: 24607745 DOI: 10.1016/j.jtbi.2014.02.027] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2013] [Revised: 02/18/2014] [Accepted: 02/24/2014] [Indexed: 11/24/2022]
Abstract
Cyclin-dependent kinases (CDKs) are vital in regulating cell cycle progression, and, thus, in highly proliferating tumor cells CDK inhibitors are gaining interest as potential anticancer agents. Clonogenic assay experiments are frequently used to determine drug efficacy against the survival and proliferation of cancer cells. While the anticancer mechanisms of drugs are usually described at the intracellular single-cell level, the experimental measurements are sampled from the entire cancer cell population. This approach may lead to discrepancies between the experimental observations and theoretical explanations of anticipated drug mechanisms. To determine how individual cell responses to drugs that inhibit CDKs affect the growth of cancer cell populations, we developed a spatially explicit hybrid agent-based model. In this model, each cell is equipped with internal cell cycle regulation mechanisms, but it is also able to interact physically with its neighbors. We model cell cycle progression, focusing on the G1 and G2/M cell cycle checkpoints, as well as on related essential components, such as CDK1, CDK2, cell size, and DNA damage. We present detailed studies of how the emergent properties (e.g., cluster formation) of an entire cell population depend on altered physical and physiological parameters. We analyze the effects of CDK1 and CKD2 inhibitors on population growth, time-dependent changes in cell cycle distributions, and the dynamic evolution of spatial cell patterns. We show that cell cycle inhibitors that cause cell arrest at different cell cycle phases are not necessarily synergistically super-additive. Finally, we demonstrate that the physical aspects of cell population growth, such as the formation of tight cell clusters versus dispersed colonies, alter the efficacy of cell cycle inhibitors, both in 2D and 3D simulations. This finding may have implications for interpreting the treatment efficacy results of in vitro experiments, in which treatment is applied before the cells can grow to produce clusters, especially because in vivo tumors, in contrast, form large masses before they are detected and treated.
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Affiliation(s)
- Munju Kim
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA.
| | - Damon Reed
- Sarcoma Program, Chemical Biology and Molecular Medicine, Adolescent and Young Adult Oncology Program, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Katarzyna A Rejniak
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA; Department of Oncologic Sciences, College of Medicine, University of South Florida, Tampa, FL, USA.
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Beyer A, Eberhard R, Piterman N, Hengartner MO, Hajnal A, Fisher J. A dynamic physical model of cell migration, differentiation and apoptosis in Caenorhabditis elegans. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2012; 736:211-33. [PMID: 22161331 DOI: 10.1007/978-1-4419-7210-1_12] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
The germ line of the nematode C. elegans provides a paradigm to study essential developmental concepts like stem cell differentiation and apoptosis. Here, we have created a computational model encompassing these developmental landmarks and the resulting movement of germ cells along the gonadal tube. We have used a technique based on molecular dynamics (MD) to model the physical movement of cells solely based on the force that arises from dividing cells. This novel way of using MD to drive the model enables calibration of simulation and experimental time. Based on this calibration, the analysis of our model shows that it is in accordance with experimental observations. In addition, the model provides insights into kinetics of molecular pathways within individual cells as well as into physical aspects like the cell density along the germ line and in local neighbourhoods of individual germ cells. In the future, the presented model can be used to test hypotheses about diverse aspects of development like stem cell division or programmed cell death. An iterative process of evolving this model and experimental testing in the model system C. elegans will provide new insights into key developmental aspects.
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Affiliation(s)
- Antje Beyer
- Department of Genetics, University of Cambridge, Cambridge, UK.
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Geris L, Van Liedekerke P, Smeets B, Tijskens E, Ramon H. A cell based modelling framework for skeletal tissue engineering applications. J Biomech 2010; 43:887-92. [DOI: 10.1016/j.jbiomech.2009.11.010] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2009] [Revised: 11/06/2009] [Accepted: 11/07/2009] [Indexed: 11/16/2022]
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7
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Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics. Bull Math Biol 2010; 72:1696-731. [DOI: 10.1007/s11538-009-9498-3] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2009] [Accepted: 12/10/2009] [Indexed: 01/11/2023]
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Beyer T, Meyer-Hermann M. Multiscale modeling of cell mechanics and tissue organization. ACTA ACUST UNITED AC 2009; 28:38-45. [PMID: 19349250 DOI: 10.1109/memb.2009.931790] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Nowadays, experimental biology gathers a large number of molecular and genetic data to understand the processes in living systems. Many of these data are evaluated on the level of cells, resulting in a changed phenotype of cells. Tools are required to translate the information on the cellular scale to the whole tissue, where multiple interacting cell types are involved. Agent-based modeling allows the investigation of properties emerging from the collective behavior of individual units. A typical agent in biology is a single cell that transports information from the intracellular level to larger scales. Mainly, two scales are relevant: changes in the dynamics of the cell, e.g. surface properties, and secreted molecules that can have effects at a distance larger than the cell diameter.
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Affiliation(s)
- Tilo Beyer
- Institute of Molecular and Clinical Immunology Medical Faculty, Ottovon-Guericke-University, Magdeburg, Germany.
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Beyer T, Meyer-Hermann M. Cell transmembrane receptors determine tissue pattern stability. PHYSICAL REVIEW LETTERS 2008; 101:148102. [PMID: 18851578 DOI: 10.1103/physrevlett.101.148102] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2007] [Indexed: 05/26/2023]
Abstract
The analysis of biological systems requires mathematical tools that represent their complexity from the molecular scale up to the tissue level. The formation of cell aggregates by chemotaxis is investigated using Delaunay object dynamics. It is found that when cells migrate fast such that the chemokine distribution is far from equilibrium, the details of the chemokine receptor dynamics can induce an internalization driven instability of cell aggregates. The instability occurs in a parameter regime relevant for lymphoid tissue and is similar to ectopic lymphoid structures.
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Affiliation(s)
- Tilo Beyer
- Institute for Molecular and Clinical Immunology, Medical Faculty, Otto-von-Guericke-University, Leipziger Str. 44, 39120 Magdeburg, Germany.
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Galle J, Hoffmann M, Aust G. From single cells to tissue architecture-a bottom-up approach to modelling the spatio-temporal organisation of complex multi-cellular systems. J Math Biol 2008; 58:261-83. [PMID: 18386011 DOI: 10.1007/s00285-008-0172-4] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2007] [Revised: 02/21/2008] [Indexed: 10/22/2022]
Abstract
Collective phenomena in multi-cellular assemblies can be approached on different levels of complexity. Here, we discuss a number of mathematical models which consider the dynamics of each individual cell, so-called agent-based or individual-based models (IBMs). As a special feature, these models allow to account for intracellular decision processes which are triggered by biomechanical cell-cell or cell-matrix interactions. We discuss their impact on the growth and homeostasis of multi-cellular systems as simulated by lattice-free models. Our results demonstrate that cell polarisation subsequent to cell-cell contact formation can be a source of stability in epithelial monolayers. Stroma contact-dependent regulation of tumour cell proliferation and migration is shown to result in invasion dynamics in accordance with the migrating cancer stem cell hypothesis. However, we demonstrate that different regulation mechanisms can equally well comply with present experimental results. Thus, we suggest a panel of experimental studies for the in-depth validation of the model assumptions.
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Affiliation(s)
- J Galle
- Interdisciplinary Center for Bioinformatics, University Leipzig, Leipzig, Germany.
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11
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Beyer T, Meyer-Hermann M. Mechanisms of organogenesis of primary lymphoid follicles. Int Immunol 2008; 20:615-23. [DOI: 10.1093/intimm/dxn020] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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12
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Meyer-Hermann M. Delaunay-Object-Dynamics: Cell Mechanics with a 3D Kinetic and Dynamic Weighted Delaunay-Triangulation. Curr Top Dev Biol 2008; 81:373-99. [DOI: 10.1016/s0070-2153(07)81013-1] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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