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.
