Randomly Evolving Idiotypic Networks: Analysis of Building Principles
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We investigate a minimalistic model of the idiotypic network of B-lymphocytes where idiotypes are represented by bitstrings encoding the nodes of a network. A node is occupied if a lymphocyte clone of the corresponding idiotype exists at the given moment, otherwise it is empty. There is a continuous influx of B-lymphocytes of randomly (by mutation) generated idiotype from the bone marrow. B-lymphocytes are stimulated to proliferate if its receptors (antibodies) are cross-linked by complementary structures. Unstimulated lymphocytes die. Thus, the links of the network connect nodes encoded by complementary bitstrings allowing for a few mismatches.
The random evolution leads to a network of highly organized architecture depending on only few parameters. The nodes can be classified into different groups with clearly distinct properties. We report on the building principles which allow to calculate analytically characteristics as the size and the number of links between the groups previously found by simulations.
KeywordsPattern Module Shape Space Base Graph Random Evolution Idiotypic Network
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- 1.Burnett, F.M.: The clonal selection theory of acquired immunity. Vanderbuilt Univ. Press, Nashville, TN (1959)Google Scholar
- 2.Jerne, N.K.: Towards a network theory of the immune system. Ann. Inst. Pasteur Immunol. 125C, 373–389 (1974)Google Scholar
- 5.Carneiro, J.: Towards a comprehensive view of the immune system. Ph.D thesis, University of Porto (1997)Google Scholar
- 12.Brede, M., Behn, U.: Patterns in randomly evolving networks: Idiotypic networks. Phys. Rev. E 67, 031920, 1–18 (2003)Google Scholar
- 15.Varela, F.J., Coutinho, A.: Second generation immune networks. Immunology Today 5, 159–166 (1991)Google Scholar
- 16.Stewart, J., Varela, F.J.: Morphogenesis in shape space. Elementary meta-dynamics in a model of the immune system. J. Theor. Biol. 153, 477–498 (1991)Google Scholar
- 18.yEd - JavaTM Graph Editor, v2.3.1_02, http://www.yWorks.com
- 19.Schmidtchen, H.: Architecture of randomly evolving networks. Diploma Thesis, Leipzig University, Leipzig (2006)Google Scholar
- 20.Brede, M.: Random Evolution of Idiotypic Networks: Dynamics and Architecture. Ph.D Thesis, Leipzig University, Leipzig (2003)Google Scholar
- 22.Brede, M., Behn, U.: The architecture of idiotypic networks: percolation and scaling behaviour. Phys. Rev. E 64, 011908, 1–11 (2001)Google Scholar