Sumana2018 - Mathematical modeling of cancer-immune system, considering the role of antibodies.
Model Identifier
BIOMD0000000885
Short description
Mathematical modeling of cancer-immune system, considering the role of antibodies. Ghosh S1, Banerjee S2. Author information 1 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttaranchal, 247667, India. 2 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttaranchal, 247667, India. sandofma@iitr.ac.in. Abstract A mathematical model for the quantitative analysis of cancer-immune interaction, considering the role of antibodies has been proposed in this paper. The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells (Ivano et al. in J Clin Investig 119(8):2143-2159, 2009). The existence of transcritical bifurcation, which has been proved using Sotomayor theorem, provides strong biological implications. Through numerical simulations, it has been illustrated that under certain therapy (like monoclonal antibody therapy), which is capable of altering the parameters of the system, cancer-free state can be obtained. KEYWORDS: Antibodies; B cells; Cancer cells; Global stability; Plasma cells; Transcritical bifurcation
Format
SBML
(L2V4)
Related Publication
- Mathematical modeling of cancer-immune system, considering the role of antibodies.
- Ghosh S, Banerjee S
- Theory in biosciences = Theorie in den Biowissenschaften , 4/ 2018 , Volume 137 , Issue 1 , pages: 67-78 , PubMed ID: 29572780
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttaranchal, 247667, India.
- A mathematical model for the quantitative analysis of cancer-immune interaction, considering the role of antibodies has been proposed in this paper. The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells (Ivano et al. in J Clin Investig 119(8):2143-2159, 2009). The existence of transcritical bifurcation, which has been proved using Sotomayor theorem, provides strong biological implications. Through numerical simulations, it has been illustrated that under certain therapy (like monoclonal antibody therapy), which is capable of altering the parameters of the system, cancer-free state can be obtained.
Contributors
Submitter of the first revision: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Mohammad Umer Sharif Shohan
Metadata information
hasInstance (3 statements)
hasTaxon (1 statement)
hasProperty (2 statements)
hasTaxon (1 statement)
hasProperty (2 statements)
Curation status
Curated
Tags
Connected external resources
Name | Description | Size | Actions |
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Model files |
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Sumana2018.xml | SBML L2V4 representation of Sumana2018 - Mathematical modeling of cancer–immune system, considering the role of antibodies | 36.76 KB | Preview | Download |
Additional files |
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Sumana2018.cps | COPASI version 4.24 (Build 197) Sumana2018 - Mathematical modeling of cancer–immune system, considering the role of antibodies | 67.02 KB | Preview | Download |
Sumana2018.sedml | SEDML L1V2 Sumana2018 - Mathematical modeling of cancer–immune system, considering the role of antibodies | 3.13 KB | Preview | Download |
- Model originally submitted by : Mohammad Umer Sharif Shohan
- Submitted: Dec 9, 2019 5:11:31 PM
- Last Modified: Dec 9, 2019 5:11:31 PM
Revisions
Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
Species | Initial Concentration/Amount |
---|---|
T 6754 |
1.0E8 mmol |
P Plasma |
1000000.0 mmol |
A | 1.5E8 mmol |
B | 90000.0 mmol |
Reactions
Reactions | Rate | Parameters |
---|---|---|
=> T | compartment*r*T*(1-T/k_2) | r = 0.431; k_2 = 9.8E8 |
P => | compartment*mu_1*P | mu_1 = 0.01 |
=> P; B | compartment*b*(1-u)*B | u = 0.1; b = 0.01 |
A => | compartment*mu_2*A | mu_2 = 6.884 |
=> A; B, P | compartment*(r_1*B+r_2*P) | r_1 = 100.0; r_2 = 1000.0 |
T => ; A | compartment*beta_1*A*T | beta_1 = 3.0218E7 |
B => | compartment*b*(1-u)*B | u = 0.1; b = 0.01 |
=> B | compartment*a*u*B*(1-B/k_1) | a = 0.1; k_1 = 1000000.0; u = 0.1 |
Curator's comment:
(added: 09 Dec 2019, 17:11:20, updated: 09 Dec 2019, 17:11:20)
(added: 09 Dec 2019, 17:11:20, updated: 09 Dec 2019, 17:11:20)
The model has been curated using COPASI 4.24 (Build 197) and the figure 5 (a,b,c) has been generated using COPASI.
From the top- left -> number of B cell,
bottom-left -> number of Antibody and
right -> number of plasma cell