Dong2014 - Mathematical modeling on helper t cells in a tumor immune system

  public model
Model Identifier
BIOMD0000000783
Short description 
This model gives a mathematical description of the interactions between tumor cells, cytotoxic T lymphocytes and helper T cells (HTCs) within the tumor microenvironment, with emphasis on the role played by HTCs. The effects and dynamics of adoptive cell immunotherapy and HTC recruitment are also specifically discussed.
Format
SBML (L2V4)
Related Publication
  • Mathematical modeling on helper t cells in a tumor immune system
  • Dong, Y., Miyazaki, R., Takeuchi, Y.
  • Discrete and Continuous Dynamical Systems - Series B , 1/ 2014 , Volume 19 , Issue 1 , pages: 55-72 , DOI: 10.3934/dcdsb.2014.19.55
  • School of Science and Technology, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu-shi 432-8561, Japan
  • Activation of CD8+ cytotoxic T lymphocytes (CTLs) is naturally regarded as a major antitumor mechanism of the immune system. In contrast, CD4+ T cells are commonly classified as helper T cells (HTCs) on the basis of their roles in providing help to the generation and maintenance of effective CD8+ cytotoxic and memory T cells. In order to get a better insight on the role of HTCs in a tumor immune system, we incorporate the third population of HTCs into a previous two dimensional ordinary differential equations (ODEs) model. Further we introduce the adoptive cellular immunotherapy (ACI) as the treatment to boost the immune system to fight against tumors. Compared tumor cells (TCs) and effector cells (ECs), the recruitment of HTCs changes the dynamics of the system substantially, by the effects through particular parameters, i.e., the activation rate of ECs by HTCs, π (scaled as π), and the HTCs stimulation rate by the presence of identified tumor antigens, k2 (scaled as υ2). We describe the stability regions of the interior equilibria É (no treatment case) and E+ (treatment case) in the scaled (π,υ2) parameter space respectively. Both π and υ2 can destabilize É and E+ and cause Hopf bifurcations. Our results show that HTCs might play a crucial role in the long term periodic oscillation behaviors of tumor immune system interactions. They also show that TCs may be eradicated from the patient's body under the ACI treatment.
Contributors
Submitter of the first revision: Johannes Meyer
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer

Metadata information

is (2 statements)
BioModels Database MODEL1908080001
BioModels Database BIOMD0000000783

isDerivedFrom (1 statement)
PubMed 8186756

hasProperty (2 statements)
Mathematical Modelling Ontology Ordinary differential equation model
NCIt Adoptive Immunotherapy

isDescribedBy (1 statement)
Curation status
Curated
Modelling approach(es)
ordinary differential equation model
Tags
Immuno-oncology

Connected external resources

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Model files
Dong2014.xml SBML L2V4 Representation of Dong2014 - Mathematical modeling on helper t cells in a tumor immune system 33.50 KB Preview | Download

Additional files
Dong2014.cps COPASI file of Dong2014 - Mathematical modeling on helper t cells in a tumor immune system 57.82 KB Preview | Download
Dong2014.sedml SED-ML file of Dong2014 - Mathematical modeling on helper t cells in a tumor immune system 3.00 KB Preview | Download

  • Model originally submitted by : Johannes Meyer
  • Submitted: Aug 8, 2019 3:54:30 PM
  • Last Modified: Dec 18, 2019 12:08:55 PM
Revisions
  • Version: 4 public model Download this version
    • Submitted on: Dec 18, 2019 12:08:55 PM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000783
  • Version: 2 public model Download this version
    • Submitted on: Aug 8, 2019 3:54:30 PM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000783

(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions unpublished model revision of this model will only be shown to the submitter and their collaborators.

Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
z Helper T Cells

helper T cell 		1.0 item
y Effector Cells

Effector Immune Cell 		1.0 item
x Tumor Cells

neoplastic cell 		1.0 item
Reactions
Reactions Rate Parameters
z_Helper_T_Cells => compartment*delta_2*z_Helper_T_Cells delta_2 = 0.055
=> z_Helper_T_Cells compartment*sigma_2 sigma_2 = 0.38
=> y_Effector_Cells; x_Tumor_Cells compartment*omega_1*x_Tumor_Cells*y_Effector_Cells omega_1 = 0.04
=> z_Helper_T_Cells; x_Tumor_Cells compartment*omega_2*x_Tumor_Cells*z_Helper_T_Cells omega_2 = 0.002
y_Effector_Cells => compartment*delta_1*y_Effector_Cells delta_1 = 0.3743
=> y_Effector_Cells; z_Helper_T_Cells compartment*rho*y_Effector_Cells*z_Helper_T_Cells rho = 0.01
=> x_Tumor_Cells compartment*alpha*x_Tumor_Cells*(1-beta*x_Tumor_Cells) beta = 0.002; alpha = 1.636
x_Tumor_Cells => ; y_Effector_Cells compartment*x_Tumor_Cells*y_Effector_Cells []
Curator's comment:
(added: 08 Aug 2019, 15:54:19, updated: 08 Aug 2019, 15:54:19)
Reproduced plot of Figure 3 in the original publication. Initial conditions were x(0) = y(0) = z(0) = 1. Model simulated and plot produced using Copasi 4.24 (Build 197).