A Mathematical Model on Germinal Center Kinetics and Termination
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model runs in COR and OpenCell with no errors. The units have been checked and they are consistent. The CellML model can replicate the shapes of the graphs of all of the figures in the paper but the scale does not always match those in the paper.
Model Structure
ABSTRACT: We devise a mathematical model to study germinal center (GC) kinetics. Earlier models for GC kinetics are extended by explicitly modeling 1) the cell division history of centroblasts, 2) the Ag uptake by centrocytes, and 3) T cell dynamics. Allowing for T cell kinetics and T-B cell interactions, we study the role of GC T cells in GC kinetics, GC termination, and B cell selection. We find that GC T cells play a major role in GC formation, but that the maintenance of established GC reactions requires very few T cells only. The results therefore suggest that the termination of a GC reaction is largely caused by lack of Ag on the follicular dendritic cells and is hardly influenced by Th cells. Ag consumption by centrocytes is the major factor determining the decay rate of the antigenic stimulus during a GC reaction. Investigating the effect of the Ag dose on GC kinetics, we find that both the total size of the GC and its duration are hardly influenced by the initial amount of Ag. In the model this is due to a buffering effect by competition for limited T cell help and/or competition between proliferating centroblasts.
The original paper reference is cited below:
A Mathematical Model on Germinal Center Kinetics and Termination, Can Kesmir and Rob J. De Boer, 1999, The Journal of Immunology, 163, 2463-2469. PubMed ID: 10452981
cell diagram
The model GC reaction.
B0
centroblast 0 divisions
B1
centroblast 1 division
B2
centroblast 2 divisions
B3
centroblast 3 divisions
B4
centroblast 4 divisions
B5
centroblast 5 divisions
B6
centroblast 6 divisions
B7
centroblast 7 divisions
B8
centroblast 8 divisions
B9
centroblast 9 divisions
B10
centroblast 10 divisions
C
centrocyte
C_star
Ag-bound centrocyte
M
memory or Ab forming cell compartment
A
FDC
T
T cells
CA
centrocyte-FDC complex
CT_star
rescued centrocyte-T cell complex
alpha_B
density dependent expansion term
alpha_T
density dependent expansion term
germinal centre kinetics
immunology
2003-12-04
The University of Auckland
Auckland Bioengineering Institute
A Mathematical Model on Germinal Center Kinetics and Termination
163
2463
2469
Catherine Lloyd
Rob
De Boer
J
c.lloyd@auckland.ac.nz
The University of Auckland, Auckland Bioengineering Institute
1999-09-01
This is the CellML description of Kesmir and De Boer's 1999 mathematical model on germinal centre kinetics and termination.
Can
Kesmir
The Journal of Immunology
Catherine
Lloyd
May
10452981
keyword
Kesmir and De Boer's 1999 mathematical model on germinal centre kinetics and termination.