dePillis2009 - Mathematical model creation for cancer chemo-immunotherapy
Model Identifier
BIOMD0000000779
Short description
This is an updated version of a previous model that described the dynamics of cancer treatment, with descriptions of tumour cell numbers, specific and non-specific immune cells (NK, CD8+ T cells and other lymphocytes) with inclusion of chemo- and immunotherapy. This model incorporates new data to provide an improved and more comprehensive model, with specific emphasis on better descriptions of IL-2 dynamics.
Format
SBML
(L2V4)
Related Publication
- Mathematical model creation for cancer chemo-immunotherapy
- de Pillis, L., Fister, K.R., Gu, W., Collins, C., Daub, M., Gross, D., Moore, J., Preskill, B.
- Computational and Mathematical Methods in Medicine , 9/ 2009 , Volume 10 , Issue 3 , pages: 165-184 , DOI: 10.1080/17486700802216301
- Department of Mathematics, Harvey Mudd College, Claremont, CA, United States
- One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841-862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8+T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8+T-cell infusion) as treatment modalities. Despite the overall success of the aforementioned model, the problem of illustrating the effects of IL-2 on a growing tumour remains open. In this paper, we update the model of de Pillis et al. and then carefully identify appropriate values for the parameters of the new model according to recent empirical data. We determine new NK and tumour antigen-activated CD8+T-cell count equilibrium values; we complete IL-2 dynamics; and we modify the model in de Pillis et al. to allow for endogenous IL-2 production, IL-2-stimulated NK cell proliferation and IL-2-dependent CD8+T-cell self-regulations. Finally, we show that the potential patient-specific efficacy of immunotherapy may be dependent on experimentally determinable parameters.
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
is (2 statements)
hasProperty (3 statements)
isDescribedBy (1 statement)
hasProperty (3 statements)
Mathematical Modelling Ontology
Ordinary differential equation model
NCIt Interleukin Therapy
NCIt Chemotherapy
NCIt Interleukin Therapy
NCIt Chemotherapy
isDescribedBy (1 statement)
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
Name | Description | Size | Actions |
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Model files |
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dePillis2009.xml | SBML L2V4 Representation of dePillis2009 - Mathematical model creation for cancer chemo-immunotherapy | 101.62 KB | Preview | Download |
Additional files |
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dePillis2009.cps | COPASI file of dePillis2009 - Mathematical model creation for cancer chemo-immunotherapy | 151.71 KB | Preview | Download |
dePillis2009.sedml | SED-ML file of dePillis2009 - Mathematical model creation for cancer chemo-immunotherapy | 4.15 KB | Preview | Download |
- Model originally submitted by : Johannes Meyer
- Submitted: Aug 5, 2019 3:28:45 PM
- Last Modified: Aug 5, 2019 3:28:45 PM
Revisions
Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
Species | Initial Concentration/Amount |
---|---|
T Tumour Cells Neoplastic Cell |
1.0E7 item |
L CD8 T Cells CD8-Positive T-Lymphocyte |
526800.0 item |
I IL 2 Interleukin-2 |
1073.0 item |
N Natural Killer Cells natural killer cell |
2.5E8 item |
Reactions
Reactions | Rate | Parameters |
---|---|---|
T_Tumour_Cells => ; N_Natural_Killer_Cells | compartment*c*N_Natural_Killer_Cells*T_Tumour_Cells | c = 2.9077E-13 |
=> L_CD8_T_Cells; T_Tumour_Cells | compartment*j*T_Tumour_Cells*L_CD8_T_Cells/(k+T_Tumour_Cells) | j = 0.01245; k = 2.019E7 |
L_CD8_T_Cells => ; M_Chemotherapy_Drug | compartment*K_L*(1-exp((-1)*delta_L*M_Chemotherapy_Drug))*L_CD8_T_Cells | K_L = 0.0486; delta_L = 1.8328 |
=> I_IL_2 | compartment*v_I | v_I = 0.0 |
T_Tumour_Cells => ; M_Chemotherapy_Drug | compartment*K_T*(1-exp((-1)*delta_T*M_Chemotherapy_Drug))*T_Tumour_Cells | K_T = 0.9; delta_T = 1.8328 |
N_Natural_Killer_Cells => ; M_Chemotherapy_Drug | compartment*K_N*(1-exp((-1)*delta_N*M_Chemotherapy_Drug))*N_Natural_Killer_Cells | K_N = 0.0675; delta_N = 1.8328 |
=> L_CD8_T_Cells; N_Natural_Killer_Cells, T_Tumour_Cells | compartment*r_1*N_Natural_Killer_Cells*T_Tumour_Cells | r_1 = 2.9077E-11 |
I_IL_2 => | compartment*mu_I*I_IL_2 | mu_I = 11.7427 |
=> N_Natural_Killer_Cells; I_IL_2 | compartment*p_N*N_Natural_Killer_Cells*I_IL_2/(g_N+I_IL_2) | g_N = 250360.0; p_N = 0.068 |
=> L_CD8_T_Cells; I_IL_2 | compartment*p_I*L_CD8_T_Cells*I_IL_2/(g_I+I_IL_2) | p_I = 2.971; g_I = 2503.6 |
Curator's comment:
(added: 05 Aug 2019, 15:28:29, updated: 05 Aug 2019, 15:28:29)
(added: 05 Aug 2019, 15:28:29, updated: 05 Aug 2019, 15:28:29)
Reproduced plot of Figure 1 in the original publication.
Model simulated and plot produced using COPASI 4.24 (Build 197).