Dong2014  Mathematical modeling on helper t cells in a tumor immune system
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: 5572 , DOI: 10.3934/dcdsb.2014.19.55
 School of Science and Technology, Shizuoka University, 351 Johoku, Nakaku, Hamamatsushi 4328561, 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
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer
Metadata information
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hasProperty (2 statements)
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isDerivedFrom (1 statement)
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Curation status
Curated
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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  SEDML 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
 Submitted on: Dec 18, 2019 12:08:55 PM
 Submitted by: Johannes Meyer
 With comment: Automatically added model identifier BIOMD0000000783

Version: 2
 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 of this model will only be shown to the submitter and their collaborators.
Legends
: Variable used inside SBML models
: 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*(1beta*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)
(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).