Robertson-Tessi M 2012 A model of tumor Immune interaction

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Short description

Its a mathematical model presenting the interaction between a growing tumor and immune system. Model involves tumor cells, dendritic cell, helper Tcells, regulatory Tcells, effector cells and certain cytokines (e.g. TGFbeta, IL10, IL2 ) produced by these cells. It represent a dynamic regulation of tumor production/killing by different immune cells and cytokines.

Related Publication
  • A mathematical model of tumor-immune interactions.
  • Robertson-Tessi M, El-Kareh A, Goriely A
  • Journal of theoretical biology , 2/ 2012 , Volume 294 , pages: 56-73 , PubMed ID: 22051568
  • Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721, United States.
  • A mathematical model of the interactions between a growing tumor and the immune system is presented. The equations and parameters of the model are based on experimental and clinical results from published studies. The model includes the primary cell populations involved in effector T-cell mediated tumor killing: regulatory T cells, helper T cells, and dendritic cells. A key feature is the inclusion of multiple mechanisms of immunosuppression through the main cytokines and growth factors mediating the interactions between the cell populations. Decreased access of effector cells to the tumor interior with increasing tumor size is accounted for. The model is applied to tumors with different growth rates and antigenicities to gauge the relative importance of various immunosuppressive mechanisms. The most important factors leading to tumor escape are TGF-β-induced immunosuppression, conversion of helper T cells into regulatory T cells, and the limitation of immune cell access to the full tumor at large tumor sizes. The results suggest that for a given tumor growth rate, there is an optimal antigenicity maximizing the response of the immune system. Further increases in antigenicity result in increased immunosuppression, and therefore a decrease in tumor killing rate. This result may have implications for immunotherapies which modulate the effective antigenicity. Simulation of dendritic cell therapy with the model suggests that for some tumors, there is an optimal dose of transfused dendritic cells.
Submitter of the first revision: Krishna Kumar Tiwari
Submitter of this revision: Krishna Kumar Tiwari
Modellers: Krishna Kumar Tiwari

Metadata information

is (2 statements)
BioModels Database MODEL1901250001
BioModels Database BIOMD0000000731

isDescribedBy (1 statement)
PubMed 22051568

hasTaxon (1 statement)
Taxonomy Homo sapiens

hasProperty (10 statements)
hasPart (1 statement)
isPropertyOf (1 statement)
Mathematical Modelling Ontology Ordinary differential equation model

Curation status


Connected external resources

SBGN view in Newt Editor

Name Description Size Actions

Model files

22051568_Tessi.xml SBML Level2 version4 149.97 KB Preview | Download

Additional files

22051568_Tessi.cps COPASI 4.24 (build196) file 178.90 KB Preview | Download
22051568_Tessi.sedml SEDML file 1.01 KB Preview | Download

  • Model originally submitted by : Krishna Kumar Tiwari
  • Submitted: Jan 29, 2019 3:00:35 PM
  • Last Modified: Jan 29, 2019 3:00:35 PM
  • Version: 5 public model Download this version
    • Submitted on: Jan 29, 2019 3:00:35 PM
    • Submitted by: Krishna Kumar Tiwari
    • With comment: Automatically added model identifier BIOMD0000000731
: Variable used inside SBML models

Species Initial Concentration/Amount
func CD4 HTC

helper T-lymphocyte
0.0 mmol
func TRegs

regulatory T-lymphocyte
0.0 mmol

empty set
1.0 mmol

empty set
1.0 mmol

0.0 mmol

Transforming growth factor beta-1
0.0 mmol
Reactions Rate Parameters
Pool => func_CD4_HTC; sl_CD4_HTC, IL2, TGFb MISC*alpha4*sl_CD4_HTC*IL2/((1+TGFb/S2)*(C1+IL2)) alpha4 = 1.9 1/ms; C1 = 0.3 pg/l; S2 = 2.9 pg/l
func_CD4_HTC => func_TRegs; TGFb, func_CD4_HTC MISC*alpha7*func_CD4_HTC*TGFb/(S3+TGFb) S3 = 1.7 pg/l; alpha7 = 0.022 1/ms
IL10 => Sink MISC*IL10/t1 t1 = 0.05 ks
Pool => sl_CD8_ETC; Me, M, l_DC MISC*alpha1*Me/(1+k4*M/l_DC) k4 = 0.33 1; alpha1 = 23.0 1/ms
Pool => sl_CD4_HTC; Mh, M, ul_DC, l_DC MISC*alpha3*Mh/(1+k4*M/(ul_DC+l_DC)) alpha3 = 9.9 1/ms; k4 = 0.33 1
Tumorcells => Sink; func_CD8_ETC, func_TRegs, TGFb MISC*r0*Tx/(1+k2*Tx/func_CD8_ETC)*1/((1+k3*func_TRegs/func_CD8_ETC)*(1+TGFb/S1)) Tx = 0.999999666666889; k3 = 11.0 1; S1 = 3.5 pg/l; k2 = 1.2 1; r0 = 0.9 1/ms
Pool => IL2; sl_CD4_HTC, TGFb, IL10 MISC*pc*sl_CD4_HTC/((1+TGFb/S4)*(1+IL10/I2)) pc = 1.7E-5; S4 = 0.9 pg/l; I2 = 0.75 pg/l
Pool => TGFb; func_TRegs, Tumorcells MISC*(p1*func_TRegs+p2*Tx) Tx = 0.999999666666889; p2 = 1.1E-7; p1 = 1.8E-8
Curator's comment:
(added: 25 Jan 2019, 11:45:24, updated: 25 Jan 2019, 11:45:24)
Figure 6c and 7c are reproduced (trends and y axis level) exactly as per literature (using Global quantity "alpha"= 0.0000631, "gamma" = 333 for figure 6a/6c and using Global quantity "alpha"= 10, "gamma" = 574 for figure 7a/7c). Figure 6a and 7a is matching in terms of trend but y axis level are slightly different from published literature. Model is created using COPASI Version 2.43 (Build 194). Data exported from Copasi and graph is created using open office calc.