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. 2019 Apr:310:31-49.
doi: 10.1016/j.mbs.2019.02.002. Epub 2019 Feb 14.

Local immunodeficiency: Minimal networks and stability

Leonid Bunimovich  1 , Longmei Shu  2
Affiliations

Local immunodeficiency: Minimal networks and stability

Leonid Bunimovich et al. Math Biosci. 2019 Apr.

Abstract

Some basic aspects of the recently discovered phenomenon of local immunodeficiency (Skums et al. [1]) generated by antigenic cooperation in cross-immunoreactivity (CR) networks are investigated. We prove that local immunodeficiency (LI) that is stable under perturbations already occurs in very small networks and under general conditions on their parameters. Therefore our results are applicable not only to Hepatitis C where CR networks are known to be large (Skums et al. [1]), but also to other diseases with CR. A major necessary feature of such networks is the non-homogeneity of their topology. It is also shown that one can construct larger CR networks with stable LI by using small networks with stable LI as their building blocks. Our results imply that stable LI occurs in networks with quite general topology. In particular, the scale-free property of a CR network, assumed in Skums et al. [1], is not required.

Keywords: Cross-immunoreactivity network; Local immunodeficiency; Minimal stable network.

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Figures

Figure 1:
Figure 1:
size 2 CRN
Figure 2:
Figure 2:
chain-branch CRN
Figure 3:
Figure 3:
branch-cycle CRN
Figure 4:
Figure 4:
size 5 CRN
Figure A.5:
Figure A.5:
size 2 CRN (symmetric)
Figure B.6:
Figure B.6:
3-cycle CRN
Figure D.7:
Figure D.7:
size 4 CRN
See this image and copyright information in PMC

References

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