Characterisation of the Idiotypic Immune Network Through Persistent Entropy

  • Matteo RuccoEmail author
  • Filippo Castiglione
  • Emanuela Merelli
  • Marco Pettini
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


In the present work we intend to investigate how to detect the behaviour of the immune system reaction to an external stimulus in terms of phase transitions. The immune model considered follows Jerne’s idiotypic network theory. We considered two graph complexity measures—the connectivity entropy and the approximate von Neumann entropy—and one entropy for topological spaces, the so-called persistent entropy. The simplicial complex is obtained enriching the graph structure of the weighted idiotypic network, and it is formally analyzed by persistent homology and persistent entropy. We obtained numerical evidences that approximate von Neumann entropy and persistent entropy detect the activation of the immune system. In addition, persistent entropy allows also to identify the antibodies involved in the immune memory.


Topological data analysis Idiotypic network Complex networks Graph entropy Persistent entropy Approximate von Neumann entropy Information theory 



We acknowledge the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme (FP7) for Research of the European Commission, under the FP7 FET-Proactive Call 8—DyMCS, Grant Agreement TOPDRIM, number FP7-ICT-318121.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Matteo Rucco
    • 1
    Email author
  • Filippo Castiglione
    • 2
  • Emanuela Merelli
    • 1
  • Marco Pettini
    • 3
  1. 1.School of Science and TechnologyUniversity of CamerinoCamerinoItaly
  2. 2.Institute for Applied Mathematics (IAC) CNRRomeItaly
  3. 3.Centre de Physique ThéoriqueAix-Marseille UniversityMarseilleFrance

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