School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA.
Math Biosci. 2019 Apr;310:31-49. doi: 10.1016/j.mbs.2019.02.002. Epub 2019 Feb 14.
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.
本文研究了最近发现的局部免疫缺陷现象的一些基本方面，该现象是由交叉免疫反应（CR）网络中的抗原合作产生的（Skums 等人，[1]）。我们证明，在非常小的网络中以及在其参数的一般条件下，已经存在稳定的局部免疫缺陷（LI）。因此，我们的结果不仅适用于已知 CR 网络较大的丙型肝炎（Skums 等人，[1]），也适用于其他具有 CR 的疾病。这种网络的一个主要必要特征是其拓扑结构的非均匀性。研究还表明，可以通过使用具有稳定 LI 的小网络作为构建块来构建具有稳定 LI 的更大的 CR 网络。我们的研究结果表明，稳定的 LI 存在于具有相当一般拓扑结构的网络中。特别是，Skums 等人假设的 CR 网络的无标度特性并不需要。
