Fassoni2019 - Oncogenesis encompassing mutations and genetic instability
Model Identifier
BIOMD0000000807
Short description
This model describes the multistep process that transform a normal cell and its descendants into a malignant tumour by considering three populations: normal, premalignant and cancer cells. Created by COPASI 4.24(Build 197)
Abstract:
Tumorigenesis has been described as a multistep process, where each step is associated with a genetic alteration, in the direction to progressively transform a normal cell and its descendants into a malignant tumour. Into this work, we propose a mathematical model for cancer onset and development, considering three populations: normal, premalignant and cancer cells. The model takes into account three hallmarks of cancer: self-sufficiency on growth signals, insensibility to anti-growth signals and evading apoptosis. By using a nonlinear expression to describe the mutation from premalignant to cancer cells, the model includes genetic instability as an enabling characteristic of tumour progression. Mathematical analysis was performed in detail. Results indicate that apoptosis and tissue repair system are the first barriers against tumour progression. One of these mechanisms must be corrupted for cancer to develop from a single mutant cell. The results also show that the presence of aggressive cancer cells opens way to survival of less adapted premalignant cells. Numerical simulations were performed with parameter values based on experimental data of breast cancer, and the necessary time taken for cancer to reach a detectable size from a single mutant cell was estimated with respect to some parameters. We find that the rates of apoptosis and mutations have a large influence on the pace of tumour progression and on the time it takes to become clinically detectable.
Format
SBML
(L3V1)
Related Publication
-
Modeling dynamics for oncogenesis encompassing mutations and genetic instability.
- Fassoni AC, Yang HM
- Mathematical medicine and biology : a journal of the IMA , 6/ 2019 , Volume 36 , Issue 2 , pages: 241-267 , PubMed ID: 29947770
- Instituto de Matemática e Computação, UNIFEI, Itajubá, Minas Gerais, Brazil.
- Tumorigenesis has been described as a multistep process, where each step is associated with a genetic alteration, in the direction to progressively transform a normal cell and its descendants into a malignant tumour. Into this work, we propose a mathematical model for cancer onset and development, considering three populations: normal, premalignant and cancer cells. The model takes into account three hallmarks of cancer: self-sufficiency on growth signals, insensibility to anti-growth signals and evading apoptosis. By using a nonlinear expression to describe the mutation from premalignant to cancer cells, the model includes genetic instability as an enabling characteristic of tumour progression. Mathematical analysis was performed in detail. Results indicate that apoptosis and tissue repair system are the first barriers against tumour progression. One of these mechanisms must be corrupted for cancer to develop from a single mutant cell. The results also show that the presence of aggressive cancer cells opens way to survival of less adapted premalignant cells. Numerical simulations were performed with parameter values based on experimental data of breast cancer, and the necessary time taken for cancer to reach a detectable size from a single mutant cell was estimated with respect to some parameters. We find that the rates of apoptosis and mutations have a large influence on the pace of tumour progression and on the time it takes to become clinically detectable.
Contributors
Submitter of the first revision: Szeyi Ng
Submitter of this revision: Szeyi Ng
Modellers: Szeyi Ng
Submitter of this revision: Szeyi Ng
Modellers: Szeyi Ng
Metadata information
is (2 statements)
isDescribedBy (1 statement)
hasProperty (6 statements)
isDescribedBy (1 statement)
hasProperty (6 statements)
Mathematical Modelling Ontology
Ordinary differential equation model
NCIt Tumorigenesis
NCIt Breast Cancer Model
NCIt Genetic
NCIt Mutation Abnormality
NCIt Tumorigenesis
NCIt Breast Cancer Model
NCIt Genetic
NCIt Mutation Abnormality
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
SBGN view in Newt Editor
| Name | Description | Size | Actions |
|---|---|---|---|
Model files |
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| model.xml | SBML L3V1 file for the model | 97.00 KB | Preview | Download |
Additional files |
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| Fassoni2019 - 5A.sedml | Sedml L1V2 file producing figure 5A | 7.28 KB | Preview | Download |
| Fassoni2019 - Oncogenesis encompassing mutations and genetic instability.cps | COPASI 4.24 (Build 197) file for the model | 112.14 KB | Preview | Download |
| Figure 5.png | PNG plot of the model simulation Fig.5 | 95.69 KB | Preview | Download |
- Model originally submitted by : Szeyi Ng
- Submitted: Sep 5, 2019 2:29:47 PM
- Last Modified: Oct 2, 2019 2:19:07 PM
Revisions
-
Version: 6
- Submitted on: Oct 2, 2019 2:19:07 PM
- Submitted by: Szeyi Ng
- With comment: Model revised without commit message
-
Version: 5
- Submitted on: Sep 11, 2019 2:44:15 PM
- Submitted by: Szeyi Ng
- With comment: Edited model metadata online.
-
Version: 3
- Submitted on: Sep 5, 2019 2:44:42 PM
- Submitted by: Szeyi Ng
- With comment: Automatically added model identifier BIOMD0000000807
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Version: 2
- Submitted on: Sep 5, 2019 2:29:47 PM
- Submitted by: Szeyi Ng
- With comment: Edited model metadata online.
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Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
| Species | Initial Concentration/Amount |
|---|---|
| normalized pre cancer cell g Breast Cancer Cell ; Prior |
1.0E-8 mmol |
| normalized cancer cell a Breast Cancer Cell |
0.0 mmol |
| normalized normal cell n Cell ; Healthy |
0.99999999 mmol |
Reactions
| Reactions | Rate | Parameters |
|---|---|---|
| normalized_pre_cancer_cell_g => | compartment*mu_G*normalized_pre_cancer_cell_g | mu_G = 0.01 1/ms |
| normalized_cancer_cell_a => ; normalized_pre_cancer_cell_g | compartment*beta_6*normalized_cancer_cell_a*normalized_pre_cancer_cell_g | beta_6 = 0.0 1/ms |
| => normalized_normal_cell_n | compartment*r_N/K | r_N = 1000000.0 1/ms; K = 1.0E8 |
| normalized_pre_cancer_cell_g => ; normalized_normal_cell_n | compartment*beta_2*K*normalized_normal_cell_n*normalized_pre_cancer_cell_g | beta_2 = 3.5E-10 1/ms; K = 1.0E8 |
| normalized_pre_cancer_cell_g => ; normalized_cancer_cell_a | compartment*beta_5*normalized_cancer_cell_a*normalized_pre_cancer_cell_g | beta_5 = 0.0 1/ms |
| => normalized_pre_cancer_cell_g | compartment*r_G*normalized_pre_cancer_cell_g | r_G = 0.05 1/ms |
| normalized_pre_cancer_cell_g => normalized_cancer_cell_a | compartment*delta*normalized_pre_cancer_cell_g^2/(xi/K+normalized_pre_cancer_cell_g) | delta = 1.0E-5 1/ms; xi = 1000.0 1; K = 1.0E8 |
| normalized_normal_cell_n => ; normalized_cancer_cell_a | compartment*beta_1*K*normalized_normal_cell_n*normalized_cancer_cell_a | beta_1 = 3.5E-10 1/ms; K = 1.0E8 |
| normalized_cancer_cell_a => | compartment*xi_A*normalized_cancer_cell_a | xi_A = 0.006 1/ms |
Curator's comment:
(added: 05 Sep 2019, 14:42:30, updated: 05 Sep 2019, 14:42:30)
(added: 05 Sep 2019, 14:42:30, updated: 05 Sep 2019, 14:42:30)
All the reproduced figures are plotted using COPASI.
Fig 5A with 5A.sedml and model.xml xi_A=0.006 and beta_3=0.35x10^(-9)
Fig 5B with 5B.sedml and model.xml xi_A=0.003 and beta_3=0.35x10^(-9)
Fig 5C with 5C.sedml and model.xml xi_A=0 and beta_3=0.35x10^(-9)
Fig 5D with 5D.sedml and model.xml xi_A=0 and beta_3=0.28x10^(-9)
Professor Fassoni has confirmed us with some parameters used to reproduce the figures:
Because the different orders of magnitude involved( large populations and small parameters), to simulate it, we used the normalized (nondimensional) populations.
So in the figure we plotted, we used :n(t)=N(t)/K, G(t)=G(t)/K, a(t)=A(t)/K and n(t),g(t),a(t) follow the same ODEs of N(t),G(t),A(t) (system 2.4).
We have the following replacements in parameters:
- r_N is replaced by r_N/K
- K_A is replaced by K_A/K
- \xi is replaced by \xi/K
- \beta_i is replaced by \beta_i * K (i=1,2,3)
- the other parameters remain the same
- the initial conditions, which are N(0)=(r_N/\mu_N)-1, G(0)=1, A(0)=0, are replaced by n(0)=N(0)/K, g(0)=G(0)/K, a(0)=A(0)/K
We used the value K=10^8.
Correction for parameter K_A in table 1 of the paper: K_A=10^7