Perelson1993 - HIVinfection_CD4Tcells_ModelA

  public model
Model Identifier
BIOMD0000000874
Short description

This a model from the article:
Dynamics of HIV infection of CD4+ T cells.
Perelson AS, Kirschner DE, De Boer R. Math Biosci 1993 Mar;114(1):81-125 8096155 ,
Abstract:
We examine a model for the interaction of HIV with CD4+ T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. Using this model we show that many of the puzzling quantitative features of HIV infection can be explained simply. We also consider effects of AZT on viral growth and T-cell population dynamics. The model exhibits two steady states, an uninfected state in which no virus is present and an endemically infected state, in which virus and infected T cells are present. We show that if N, the number of infectious virions produced per actively infected T cell, is less a critical value, Ncrit, then the uninfected state is the only steady state in the nonnegative orthant, and this state is stable. For N > Ncrit, the uninfected state is unstable, and the endemically infected state can be either stable, or unstable and surrounded by a stable limit cycle. Using numerical bifurcation techniques we map out the parameter regimes of these various behaviors. oscillatory behavior seems to lie outside the region of biologically realistic parameter values. When the endemically infected state is stable, it is characterized by a reduced number of T cells compared with the uninfected state. Thus T-cell depletion occurs through the establishment of a new steady state. The dynamics of the establishment of this new steady state are examined both numerically and via the quasi-steady-state approximation. We develop approximations for the dynamics at early times in which the free virus rapidly binds to T cells, during an intermediate time scale in which the virus grows exponentially, and a third time scale on which viral growth slows and the endemically infected steady state is approached. Using the quasi-steady-state approximation the model can be simplified to two ordinary differential equations the summarize much of the dynamical behavior. We compute the level of T cells in the endemically infected state and show how that level varies with the parameters in the model. The model predicts that different viral strains, characterized by generating differing numbers of infective virions within infected T cells, can cause different amounts of T-cell depletion and generate depletion at different rates. Two versions of the model are studied. In one the source of T cells from precursors is constant, whereas in the other the source of T cells decreases with viral load, mimicking the infection and killing of T-cell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Perelson AS, Kirschner DE, De Boer R. (1993) - version=1.0
The original CellML model was created by:
Ethan Choi
mcho099@aucklanduni.ac.nz
The University of Auckland

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2011 The BioModels.net Team.
To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

In summary, you are entitled to use this encoded model in absolutely any manner you deem suitable, verbatim, or with modification, alone or embedded it in a larger context, redistribute it, commercially or not, in a restricted way or not..

To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

Format
SBML (L2V4)
Related Publication
  • Dynamics of HIV infection of CD4+ T cells.
  • Perelson AS, Kirschner DE, De Boer R
  • Mathematical biosciences , 3/ 1993 , Volume 114 , pages: 81-125 , PubMed ID: 8096155
  • Theoretical Division, Los Alamos National Laboratory, New Mexico.
  • We examine a model for the interaction of HIV with CD4+ T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. Using this model we show that many of the puzzling quantitative features of HIV infection can be explained simply. We also consider effects of AZT on viral growth and T-cell population dynamics. The model exhibits two steady states, an uninfected state in which no virus is present and an endemically infected state, in which virus and infected T cells are present. We show that if N, the number of infectious virions produced per actively infected T cell, is less a critical value, Ncrit, then the uninfected state is the only steady state in the nonnegative orthant, and this state is stable. For N > Ncrit, the uninfected state is unstable, and the endemically infected state can be either stable, or unstable and surrounded by a stable limit cycle. Using numerical bifurcation techniques we map out the parameter regimes of these various behaviors. oscillatory behavior seems to lie outside the region of biologically realistic parameter values. When the endemically infected state is stable, it is characterized by a reduced number of T cells compared with the uninfected state. Thus T-cell depletion occurs through the establishment of a new steady state. The dynamics of the establishment of this new steady state are examined both numerically and via the quasi-steady-state approximation. We develop approximations for the dynamics at early times in which the free virus rapidly binds to T cells, during an intermediate time scale in which the virus grows exponentially, and a third time scale on which viral growth slows and the endemically infected steady state is approached. Using the quasi-steady-state approximation the model can be simplified to two ordinary differential equations the summarize much of the dynamical behavior. We compute the level of T cells in the endemically infected state and show how that level varies with the parameters in the model. The model predicts that different viral strains, characterized by generating differing numbers of infective virions within infected T cells, can cause different amounts of T-cell depletion and generate depletion at different rates. Two versions of the model are studied. In one the source of T cells from precursors is constant, whereas in the other the source of T cells decreases with viral load, mimicking the infection and killing of T-cell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)
Contributors
Submitter of the first revision: Camille Laibe
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Camille Laibe, Mohammad Umer Sharif Shohan

Metadata information

is (2 statements)
BioModels Database MODEL1006230079
BioModels Database MODEL1006230079

isDescribedBy (1 statement)
PubMed 8096155

hasTaxon (1 statement)
Taxonomy Homo sapiens

isVersionOf (2 statements)
Experimental Factor Ontology HIV infection
Gene Ontology viral entry into host cell

occursIn (1 statement)
Brenda Tissue Ontology helper T-lymphocyte


Curation status
Curated

Connected external resources

Name Description Size Actions

Model files

Perelson1993.xml SBML L2V4 representation of Perelson1993_HIVinfection_CD4Tcells_ModelA 43.16 KB Preview | Download

Additional files

MODEL1006230079-biopax2.owl Auto-generated BioPAX (Level 2) 1.06 KB Preview | Download
MODEL1006230079-biopax3.owl Auto-generated BioPAX (Level 3) 2.02 KB Preview | Download
MODEL1006230079.m Auto-generated Octave file 2.94 KB Preview | Download
MODEL1006230079.pdf Auto-generated PDF file 141.14 KB Preview | Download
MODEL1006230079.png Auto-generated Reaction graph (PNG) 5.04 KB Preview | Download
MODEL1006230079.sci Auto-generated Scilab file 200.00 Bytes Preview | Download
MODEL1006230079.svg Auto-generated Reaction graph (SVG) 851.00 Bytes Preview | Download
MODEL1006230079.vcml Auto-generated VCML file 900.00 Bytes Preview | Download
MODEL1006230079.xpp Auto-generated XPP file 1.79 KB Preview | Download
MODEL1006230079_url.xml old xml file 13.57 KB Preview | Download
MODEL1006230079_urn.xml Auto-generated SBML file with URNs 14.19 KB Preview | Download
Perelson1993.cps COPASI version 4.24 (Build 197) representation of Perelson1993_HIVinfection_CD4Tcells_ModelA 74.03 KB Preview | Download
Perelson1993.sedml SEDML L1V2 representation of Perelson1993_HIVinfection_CD4Tcells_ModelA 3.70 KB Preview | Download

  • Model originally submitted by : Camille Laibe
  • Submitted: Jun 23, 2010 10:12:28 AM
  • Last Modified: Nov 25, 2019 2:10:39 PM
Revisions
  • Version: 5 public model Download this version
    • Submitted on: Nov 25, 2019 2:10:39 PM
    • Submitted by: Mohammad Umer Sharif Shohan
    • With comment: Automatically added model identifier BIOMD0000000874
  • Version: 2 public model Download this version
    • Submitted on: Jun 25, 2010 2:37:31 PM
    • Submitted by: Camille Laibe
    • With comment: Current version of Perelson1993_HIVinfection_CD4Tcells_ModelA
  • Version: 1 public model Download this version
    • Submitted on: Jun 23, 2010 10:12:28 AM
    • Submitted by: Camille Laibe
    • With comment: Original import of Perelson1993_HIVinfection_CD4Tcells_ModelA

(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions unpublished model revision of this model will only be shown to the submitter and their collaborators.

Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
T 1

P01730
0.0 mol
T

P01730
1000.0 mol
T 2

P01730
0.0 mol
V 0.001 mol
Reactions
Reactions Rate Parameters
=> T_1; V, T COMpartment*k_1*V*T k_1 = 2.4E-5
=> T COMpartment*(s+r*T) s = 10.0; r = 0.03
T_1 => COMpartment*(mu_T*T_1+k_2*T_1) mu_T = 0.02; k_2 = 0.003
T => ; V, T_1, T_2 COMpartment*(mu_T*T+k_1*V*T+r*T*(T+T_1+T_2)/T_max) k_1 = 2.4E-5; mu_T = 0.02; T_max = 1500.0; r = 0.03
=> T_2; T_1 COMpartment*k_2*T_1 k_2 = 0.003
T_2 => COMpartment*mu_b*T_2 mu_b = 0.24
=> V; T_2 COMpartment*N*mu_b*T_2 N = 1000.0; mu_b = 0.24
V => ; T COMpartment*(k_1*V*T+mu_V*V) k_1 = 2.4E-5; mu_V = 2.4
Curator's comment:
(added: 25 Nov 2019, 14:09:21, updated: 25 Nov 2019, 14:09:21)
The model has been curated using COPASI 4.24 (Build 197) and the Figure 2 (top right and bottom left) has been generated using ggplot package in R. The figures are exact match to the publication figure