Institut für Theoretische Physik
Tel: 0049 341 97 32 432
Email: holger.schmidtchen [a] itp.uni-leipzig.de
PGP Key 6AE3 3A5F E12D EB14 6D51 BEBC 6A49 E696 4CBB 6CBC
Research topic of my diploma thesis and the present PhD project is pattern formation in a randomly evolving network model of the B-lymphocyte system. Abstract:
B-Lymphocytes express on their surface receptors (antibodies) of a given specifity (idiotype). Crosslinking these receptors by complementary structures (antigens or other antibodies) stimulates the lymphocyte. Thus a large functional network of interacting lymphocytes, the idiotypic network, emerges. Idiotypic networks conceived by Niels Jerne 40 years ago, experience a renewed interest, e.g. in the context of autoimmune diseases.
In our minimalistic model idiotypes are represented by bitstrings. A node is occupied if a lymphocyte clone of the corresponding idiotype exists at the given moment, otherwise it is empty. An idiotype survives only if it meets enough but not too many complementary structures. The dynamics is driven by the influx of new idiotypes, randomly generated in the bone marrow.
The random evolution leads to networks of highly organized architecture. The vertices can be classified into different groups, which are clearly distinct, e.g. by their mean life time. There are densely connected core groups and peripheral groups of isolated vertices, resembling central and peripheral part of the idiotypic network in biology. We found the building principles of the observed network patterns and propose a description of their architecture, which are easily transferable to other patterns and applicable to different system sizes. We can calculate analytically characteristics previously found in simulations, such as the size of the groups and the number of links between them. Recently, we also achieved an analytical description of dynamical group properties such as the mean life time.
Advisor is Prof. Dr. Ulrich Behn.