Kuznetsov1994 - Nonlinear dynamics of immunogenic tumors

  public model
Model Identifier
BIOMD0000000762
Short description 
This mathematical model describes the response of cytotoxic T lymphocytes to the growth of an immunogenic tumor, with the inclusion on a number of in vivo phenomena, such as the immunostimulation of tumor growth, evasion of immune function by the tumor, and the formation of a tumor "dormant state". Specifically, this model is used to describe the kinetics of growth and regression of the B-cell lymphoma BCL1 in the spleen of mice.
Format
SBML (L2V4)
Related Publication
  • Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis.
  • Kuznetsov VA, Makalkin IA, Taylor MA, Perelson AS
  • Bulletin of mathematical biology , 3/ 1994 , Volume 56 , Issue 2 , pages: 295-321 , PubMed ID: 8186756
  • Laboratory of Mathematical Immunobiophysics, Russian Academy of Sciences, Moscow.
  • We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seen in vivo, including immunostimulation of tumor growth, "sneaking through" of the tumor, and formation of a tumor "dormant state". The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measured in vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.
Contributors
Submitter of the first revision: Johannes Meyer
Submitter of this revision: Johannes Meyer
Modellers: Johannes Meyer

Metadata information

is (2 statements)
BioModels Database MODEL1907230002
BioModels Database BIOMD0000000762

isDescribedBy (1 statement)
PubMed 8186756

isVersionOf (2 statements)
Curation status
Curated
Modelling approach(es)
ordinary differential equation model
Tags
Immuno-oncology

Connected external resources

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Model files
Kuznetsov1994.xml SBML L2V4 Kuznetsov1994 - Nonlinear dynamics of immunogenic tumors 34.28 KB Preview | Download

Additional files
Kuznetsov1994.cps COPASI file of SBML L2V4 Kuznetsov1994 - Nonlinear dynamics of immunogenic tumors 58.17 KB Preview | Download
Kuznetsov1994.sedml SED-ML file of SBML L2V4 Kuznetsov1994 - Nonlinear dynamics of immunogenic tumors 1.70 KB Preview | Download

  • Model originally submitted by : Johannes Meyer
  • Submitted: Jul 26, 2019 9:25:48 AM
  • Last Modified: Jul 26, 2019 9:25:48 AM
Revisions
  • Version: 7 public model Download this version
    • Submitted on: Jul 26, 2019 9:25:48 AM
    • Submitted by: Johannes Meyer
    • With comment: Automatically added model identifier BIOMD0000000762
Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
E

effector T cell 		320000.0 mmol
T

Neoplastic Cell 		5000000.0 mmol
Reactions
Reactions Rate Parameters
E => ; T compartment*m*E*T m = 3.422E-10
T => ; T compartment*a*b*T^2 b = 2.0E-9; a = 0.18
T => ; E compartment*n*E*T n = 1.101E-7
=> E compartment*s s = 13000.0
=> E; E, T compartment*p*E*T/(g+T) p = 0.1245; g = 2.019E7
E => compartment*d*E d = 0.0412
=> T; T compartment*a*T a = 0.18
Curator's comment:
(added: 23 Jul 2019, 13:46:40, updated: 23 Jul 2019, 13:46:40)
Reproduction of Figure 1B in the original publication. Model solved and image produced using COPASI 4.24 (Build 197).