Bose2011 - Noise-assisted interactions of tumor and immune cells

  public model
Model Identifier
BIOMD0000000894
Short description 
Noise-assisted interactions of tumor and immune cells.
Bose T1, Trimper S.
Author information

1
    Institute of Physics, Martin-Luther-University, D-06099 Halle, Germany. thomas.bose@physik.uni-halle.de

Abstract

We consider a three-state model comprising tumor cells, effector cells, and tumor-detecting cells under the influence of noises. It is demonstrated that inevitable stochastic forces existing in all three cell species are able to suppress tumor cell growth completely. Whereas the deterministic model does not reveal a stable tumor-free state, the auto-correlated noise combined with cross-correlation functions can either lead to tumor-dormant states, tumor progression, as well as to an elimination of tumor cells. The auto-correlation function exhibits a finite correlation time τ, while the cross-correlation functions shows a white-noise behavior. The evolution of each of the three kinds of cells leads to a multiplicative noise coupling. The model is investigated by means of a multivariate Fokker-Planck equation for small τ. The different behavior of the system is, above all, determined by the variation of the correlation time and the strength of the cross-correlation between tumor and tumor-detecting cells. The theoretical model is based on a biological background discussed in detail, and the results are tested using realistic parameters from experimental observations.
Format
SBML (L2V4)
Related Publication
  • Noise-assisted interactions of tumor and immune cells.
  • Bose T, Trimper S
  • Physical review. E, Statistical, nonlinear, and soft matter physics , 8/ 2011 , Volume 84 , Issue 2 Pt 1 , pages: 021927 , PubMed ID: 21929038
  • Institute of Physics, Martin-Luther-University, D-06099 Halle, Germany. thomas.bose@physik.uni-halle.de
  • We consider a three-state model comprising tumor cells, effector cells, and tumor-detecting cells under the influence of noises. It is demonstrated that inevitable stochastic forces existing in all three cell species are able to suppress tumor cell growth completely. Whereas the deterministic model does not reveal a stable tumor-free state, the auto-correlated noise combined with cross-correlation functions can either lead to tumor-dormant states, tumor progression, as well as to an elimination of tumor cells. The auto-correlation function exhibits a finite correlation time τ, while the cross-correlation functions shows a white-noise behavior. The evolution of each of the three kinds of cells leads to a multiplicative noise coupling. The model is investigated by means of a multivariate Fokker-Planck equation for small τ. The different behavior of the system is, above all, determined by the variation of the correlation time and the strength of the cross-correlation between tumor and tumor-detecting cells. The theoretical model is based on a biological background discussed in detail, and the results are tested using realistic parameters from experimental observations.
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

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

Connected external resources

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Model files
Bose2011.xml SBML L2V4 representation of Bose2011 - Noise-assisted interactions of tumor and immune cells. 34.95 KB Preview | Download

Additional files
Bose2011.cps COPASI version 4.24 (Build 197) Bose2011 - Noise-assisted interactions of tumor and immune cells. 59.88 KB Preview | Download
Bose2011.sedml SEDML L1V2 Bose2011 - Noise-assisted interactions of tumor and immune cells. 2.65 KB Preview | Download

  • Model originally submitted by : Mohammad Umer Sharif Shohan
  • Submitted: Dec 16, 2019 11:23:53 AM
  • Last Modified: Jan 2, 2020 10:46:23 AM
Revisions
  • Version: 3 public model Download this version
    • Submitted on: Jan 2, 2020 10:46:23 AM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: SBML edited to add isDerivedFrom
  • Version: 2 public model Download this version
    • Submitted on: Dec 16, 2019 11:23:53 AM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000894

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Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
z

Lymphocyte 		0.0 mmol
x

Neoplastic Cell 		1.0E-6 mmol
y

Effector Immune Cell 		0.01 mmol
Reactions
Reactions Rate Parameters
z => compartment*(mu-(R*(1+Dx*tau)+Dx*(1+0.5*Dz*tau)))*z R = 1.0; Dz = 1.2; Dx = 2.1; tau = 0.3; mu = 20.0
=> x; z compartment*((1+R*(1-Dx*tau)+0.5*Dx*Dz*tau)*x+Dx*(1+R*tau)*z) R = 1.0; Dz = 1.2; Dx = 2.1; tau = 0.3
x => ; y compartment*(x*x+x*y) []
=> y; z compartment*y*z []
y => compartment*(p-Dy)*y Dy = 0.01; p = 0.06
=> z; x compartment*(R*(1-Dx*tau)+Dx*Dz*tau)*x R = 1.0; Dz = 1.2; Dx = 2.1; tau = 0.3
Curator's comment:
(added: 16 Dec 2019, 11:23:44, updated: 16 Dec 2019, 11:23:44)
The model has been encoded in COPASI 4.24 (Build 197) and the figure 3a has been reproduced using COPASI There was one parameter missing in the paper that is of y (Effector cell) initial concentration. From the existing paper I tried to do parameter scan and found that the value was 0.01. This produces the exact figure