Randomly Evolving Idiotypic Networks: Structural Properties and Architecture

TL;DR

This paper models the idiotypic network of B-lymphocytes as a dynamic, evolving graph with nodes representing lymphocyte populations, revealing how complex organized patterns emerge from simple rules and parameters.

Contribution

It introduces a minimalistic, dynamic model of B-lymphocyte networks that analytically explains the emergence of organized patterns and their structural properties.

Findings

Networks evolve into organized patterns with distinct node groups

Analytical formulas for group sizes and link counts are derived

Patterns observed in simulations match analytical predictions

Abstract

We consider a minimalistic dynamic model of the idiotypic network of B-lymphocytes. A network node represents a population of B-lymphocytes of the same specificity (idiotype), which is encoded by a bitstring. The links of the network connect nodes with complementary and nearly complementary bitstrings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists, otherwise it is empty. There is a continuous influx of new B-lymphocytes of random idiotype from the bone marrow. B-lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors, unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which allow to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.