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

  public model
Model Identifier
BIOMD0000000790
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 , PubMed ID: 30930063
  • 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
Submitter of the first revision: Johannes Meyer
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer

Metadata information

is (2 statements)
BioModels Database BIOMD0000000790
BioModels Database MODEL1908120003

isDescribedBy (1 statement)
PubMed 30930063

hasProperty (2 statements)
Mathematical Modelling Ontology Ordinary differential equation model
Gene Ontology immune response to tumor cell

Curation status
Curated
Modelling approach(es)
ordinary differential equation model
Tags
Immuno-oncology

Connected external resources

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Model files
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

Additional files
Alvarez2019.cps COPASI file of Alvarez2019 - A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity 121.43 KB Preview | Download
Alvarez2019.sedml SED-ML file of Alvarez2019 - A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity 1.75 KB Preview | Download

  • 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
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
E 2 Adaptive

T cell 		0.0 item
T 1

neoplastic cell 		8.0E7 item
T 2

neoplastic cell 		2.0E7 item
E 1 Innate

natural killer cell ; innate lymphoid cell 		1.05E7 item
Reactions
Reactions Rate Parameters
E_2_Adaptive => compartment*d_3*E_2_Adaptive d_3 = 0.02
T_1 => ; T_2 compartment*nu*T_1*T_2 nu = 1.101E-9
=> T_2 compartment*a*p*T_2*(1-b*T_2) b = 2.0E-9; a = 0.514; p = 0.35
E_2_Adaptive => ; T_1 compartment*d_2*T_1*E_2_Adaptive d_2 = 3.42E-10
E_1_Innate => ; T_1, T_2 compartment*c_3*(T_1+T_2)*E_1_Innate c_3 = 3.422E-10
=> E_2_Adaptive; T_1, E_1_Innate compartment*d_1*T_1*E_1_Innate d_1 = 1.1E-7
T_2 => ; E_1_Innate compartment*mu*q*E_1_Innate*T_2 q = 1.0; mu = 1.101E-7
E_1_Innate => compartment*c_2*E_1_Innate c_2 = 0.0412
T_2 => ; T_1 compartment*r*nu*T_1*T_2 nu = 1.101E-9; r = 1.5
=> E_1_Innate compartment*c_1 c_1 = 13000.0
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).