Alvarez2019 - A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity

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Short description
This is a non-linear mathematical model of cancer immunosurveillance that takes into account intratumoral phenotypic heterogeneity, such as differential expression of cell surface receptors and growth factors, according to cell-mediated immune responses. The model describes phenomena that have also been observed in vivo, such as tumor dormancy, cancer immunoediting, and a strong sensitivity to initial conditions.
Format
SBML (L2V4)
Related Publication
  • A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity.
  • Alvarez RF, Barbuto JAM, Venegeroles R
  • Journal of theoretical biology , 6/ 2019 , Volume 471 , pages: 42-50
  • Centro de Ciências Naturais e Humanas, UFABC, Santo André, 09210-170, SP, Brazil. Electronic address: robinson.alvarez@usp.br.
  • Human cancers display intra-tumor heterogeneity in many phenotypic features, such as expression of cell surface receptors, growth, and angiogenic, proliferative, and immunogenic factors, which represent obstacles to a successful immune response. In this paper, we propose a nonlinear mathematical model of cancer immunosurveillance that takes into account some of these features based on cell-mediated immune responses. The model describes phenomena that are seen in vivo, such as tumor dormancy, robustness, immunoselection over tumor heterogeneity (also called "cancer immunoediting") and strong sensitivity to initial conditions in the composition of tumor microenvironment. The results framework has as common element the tumor as an attractor for abnormal cells. Bifurcation analysis give us as tumor attractors fixed-points, limit cycles and chaotic attractors, the latter emerging from period-doubling cascade displaying Feigenbaum's universality. Finally, we simulated both elimination and escape tumor scenarios by means of a stochastic version of the model according to the Doob-Gillespie algorithm.
Contributors
Johannes Meyer

Metadata information

hasProperty
Mathematical Modelling Ontology Ordinary differential equation model
GO:0002418
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Curation status
Curated


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Alvarez2019.xml SBML L2V4 Representation of Alvarez2019 - A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity 62.15 KB Preview | Download

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Alvarez2019.cps COPASI file of Alvarez2019 - A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity 121.43 KB Preview | Download
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  • Model originally submitted by : Johannes Meyer
  • Submitted: Aug 12, 2019 4:18:43 PM
  • Last Modified: Aug 12, 2019 4:18:43 PM
Revisions
  • Version: 2 public model Download this version
    • Submitted on: Aug 12, 2019 4:18:43 PM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000790
Curator's comment:
(added: 12 Aug 2019, 16:18:29, updated: 12 Aug 2019, 16:18:29)
Reproduced plot of Figure 1 in the original publication. Initial conditions are as indicated in the figure caption, with E1(0) = 1.05e7. Model simulated and plot produced using COPASI 4.24 (Build 197).