A Cayley tree immune network model with antibody dynamics |
| |
Authors: | Russell W Anderson Avidan U Neumann Alan S Perelson |
| |
Institution: | (1) Theoretical Biology and Biophysics, Los Alamos National Laboratory, 87545 Los Alamos, NM, U.S.A.;(2) Santa Fe Institute, 1660 Old Pecos Trail, 87501 Santa Fe, NM, U.S.A.;(3) Theoretical Biology and Biophysics, Los Alamos National Laboratory, 87545 Los Alamos, NM, U.S.A. |
| |
Abstract: | A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analysed. As in
models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin
or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters.
As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend
on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied,
localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation
attractors. For a given set of parameters percolation and chaotic attractors can coexist with localized attractors, and thus
there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percolation
and chaotic attractors. Stable limit cycles, which are frequent in the two-clone antibody B cell (AB) model, are only observed
in highly connected networks. Also found in highly connected networks are localized chaotic attractors. As in experiments
by Lundkvistet al. (1989.Proc. natn. Acad. Sci. U.S.A.
86, 5074–5078), injection ofAb
1 antibodies into a system operating in the chaotic regime can cause a cessation of fluctuations ofAb
1 andAb
2 antibodies, a phenomenon already observed in the two-clone AB model. Interestingly, chaotic fluctuations continue at higher
levels of the tree, a phenomenon observed by Lundkvistet al. but not accounted for previously. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|