A statistical mechanics approach to autopoietic immune networks

Abstract

The aim of this work is to try to bridge over theoretical immunology and disordered statistical mechanics. Our long term hope is to contribute to the development of a quantitative theoretical immunology from which practical applications may stem. In order to make theoretical immunology appealing to the statistical physicist audience we are going to work out a research article which, from one side, may hopefully act as a benchmark for future improvements and developments, from the other side, it is written in a very pedagogical way both from a theoretical physics viewpoint as well as from the theoretical immunology one. Furthermore, we have chosen to test our model describing a wide range of features of the adaptive immune response in only a paper: this has been necessary in order to emphasize the benefit available when using disordered statistical mechanics as a tool for the investigation. However, as a consequence, each section is not at all exhaustive and would deserve deep investigation: for the sake of completeness, we restricted details in the analysis of each feature with the aim of introducing a self-consistent model.

22 pages, 14 figure

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• The high temperature region of the Viana-Bray diluted spin glass model
• The mean field Ising model trough interpolating techniques
• Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
• Criticality in diluted ferromagnet
• Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs
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Cited by in corpus (15)

• Equilibrium statistical mechanics of bipartite spin systems
• Immune networks: multi-tasking capabilities near saturation
• A thermodynamical perspective of immune capabilities
• Free energy and complexity of spherical bipartite models
• A Hebbian approach to complex network generation
• Mean field bipartite spin models treated with mechanical techniques
• Parallel processing in immune networks
• Percolation on correlated random networks
• Replica symmetry breaking in multi-species Sherrington-Kirkpatrick model
• Interpolating the Sherrington-Kirkpatrick replica trick
• Organization and evolution of synthetic idiotypic networks
• First-passage phenomena in hierarchical networks
• Equilibrium statistical mechanics on correlated random graphs
• Randomly Evolving Idiotypic Networks: Structural Properties and Architecture
• Multi-body quenched disordered $XY$ and $p$-clock models on random graphs