Sumana2018 - Mathematical modeling of cancer-immune system, considering the role of antibodies.

  public model
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

Metadata information

hasInstance (3 statements)
hasTaxon (1 statement)
Taxonomy Homo sapiens

hasProperty (2 statements)
Curation status
Curated
Tags
Immuno-oncology

Connected external resources

SBGN view in Newt Editor

Name Description Size Actions

Model files
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
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
  • Version: 2 public model Download this version
    • Submitted on: Dec 9, 2019 5:11:31 PM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000885
Legends
: 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)
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