dePillis2008 - Optimal control of mixed immunotherapy and chemotherapy of tumors

  public model
Model Identifier
BIOMD0000000913
Short description
<notes xmlns="http://www.sbml.org/sbml/level2/version4"> <body xmlns="http://www.w3.org/1999/xhtml"> <pre>Optimal control of mixed immunotherapy and chemotherapy of tumors Lisette Depillis, K. R. Fister , W. Gu, Tiffany Head, Kenny Maples, Todd Neal, Anand Murugan and Kenji Kozai Abstract We investigate a mathematical population model of tumor-immune interactions. Thepopulations involved are tumor cells, specific and non-specific immune cells, and con-centrations of therapeutic treatments. We establish the existence of an optimal con-trol for this model and provide necessary conditions for the optimal control triple forsimultaneous application of chemotherapy, tumor infiltrating lymphocyte (TIL) ther-apy, and interleukin-2 (IL-2) treatment. We discuss numerical results for the combina-tion of the chemo-immunotherapy regimens. We find that the qualitative nature of ourresults indicates that chemotherapy is the dominant intervention with TIL interactingin a complementary fashion with the chemotherapy. However, within the optimal con-trol context, the interleukin-2 treatment does not become activated for the estimatedparameter ranges.
Format
SBML (L2V4)
Related Publication
  • Optimal control of mixed immunotherapy and chemotherapy of tumors
  • Lisette Depillis, K. R. Fister , W. Gu, Tiffany Head, Kenny Maples, Todd Neal, Anand Murugan and Kenji Kozai
  • Journal of Biological Systems , 12/ 2008 , Volume 16 , Issue 1 , pages: 51-80 , DOI: 10.1142/S0218339008002435
  • ∗ Department of Mathematics, Harvey Mudd College Claremont, CA 91711, USA † Department of Mathematics, Pomona College Claremont, CA 91711, USA ‡ Department of Mathematics, Murray State University Murray, KY 42071, USA
  • We investigate a mathematical population model of tumor-immune interactions. Thepopulations involved are tumor cells, specific and non-specific immune cells, and con-centrations of therapeutic treatments. We establish the existence of an optimal con-trol for this model and provide necessary conditions for the optimal control triple forsimultaneous application of chemotherapy, tumor infiltrating lymphocyte (TIL) ther-apy, and interleukin-2 (IL-2) treatment. We discuss numerical results for the combina-tion of the chemo-immunotherapy regimens. We find that the qualitative nature of ourresults indicates that chemotherapy is the dominant intervention with TIL interactingin a complementary fashion with the chemotherapy. However, within the optimal con-trol context, the interleukin-2 treatment does not become activated for the estimatedparameter ranges.
Contributors
Submitter of the first revision: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan

Metadata information

isDescribedBy (2 statements)
is (2 statements)
BioModels Database BIOMD0000000913
BioModels Database MODEL2001200003

hasTaxon (1 statement)
Taxonomy Homo sapiens

hasProperty (1 statement)
Mathematical Modelling Ontology Ordinary differential equation model

isDerivedFrom (3 statements)
Mathematical Modelling Ontology Ordinary differential equation model
Taxonomy Homo sapiens
BioModels Database MODEL2001160001

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

Connected external resources

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Model files
dePillis2008.xml SBML L2V4 dePillis2008 - Optimal control of mixed immunotherapy and chemotherapy of tumors 63.58 KB Preview | Download

Additional files
dePillis2008.cps COPASI version 4.24 (Build 197) dePillis2008 - Optimal control of mixed immunotherapy and chemotherapy of tumors 106.13 KB Preview | Download
dePillis2008.sedml SEDML L1V2 dePillis2008 - Optimal control of mixed immunotherapy and chemotherapy of tumors 4.60 KB Preview | Download

  • Model originally submitted by : Mohammad Umer Sharif Shohan
  • Submitted: Jan 20, 2020 4:59:11 PM
  • Last Modified: Jan 21, 2020 9:17:51 AM
Revisions
  • Version: 5 public model Download this version
    • Submitted on: Jan 21, 2020 9:17:51 AM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000913
  • Version: 2 public model Download this version
    • Submitted on: Jan 20, 2020 4:59:11 PM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000913

(*) 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
N

Immune Cell 		500000.0 mmol
C

C120462 		4.17E10 mmol
I

Interleukin-2 		2000.0 mmol
L

cytotoxic T-lymphocyte 		2000.0 mmol
T

neoplasm 		1.0E7 mmol
M

Combination Chemotherapy 		0.0 mmol
Reactions
Reactions Rate Parameters
=> N; T compartment*(alpha_1+g*T^eta/(h+T^eta)*N) alpha_1 = 13000.0; h = 600.0; g = 0.025; eta = 1.0
=> C compartment*alpha_2 alpha_2 = 5.0E8
I => compartment*mu_I*I mu_I = 10.0
L => ; T, M compartment*(m*L+q*L*T+u*L*L+K_L*M*L) K_L = 0.6; q = 3.42E-10; u = 3.0; m = 0.02
=> T compartment*a*T*(1-b*T) a = 0.002; b = 1.02E-9
=> L; C, T, I compartment*(r2*C*T+p_I*L*I/(g_I+I)+V_L) r2 = 3.0E-11; p_I = 0.125; V_L=0.0; g_I = 2.0E7
M => compartment*gamma*M gamma = 0.9
N => ; T, M compartment*(f*N+p*N*T+K_N*M*N) p = 1.0E-7; f = 0.0412; K_N = 0.6
C => ; M compartment*(beta*C+K_C*M*C) beta = 0.012; K_C = 0.6
T => ; N, M compartment*(c1*N*T+D*T+K_T*M*T) D = 6.6666657777779E-7; K_T = 0.8; c1 = 3.23E-7
Curator's comment:
(added: 20 Jan 2020, 16:59:02, updated: 20 Jan 2020, 16:59:02)
The model has been encoded in COPASI 4.24 (Build 197) and figure 1 has been reproduced using COPASI