Maximum entropy models for antibody diversity

Thierry Mora, Aleksandra M. Walczak, William Bialek, Curtis Gove Callan

Research output: Contribution to journalArticlepeer-review

244 Scopus citations


Recognition of pathogens relies on families of proteins showing great diversity. Here we construct maximum entropy models of the sequence repertoire, building on recent experiments that provide a nearly exhaustive sampling of the IgM sequences in zebrafish. These models are based solely on pairwise correlations between residue positions but correctly capture the higher order statistical properties of the repertoire. By exploiting the interpretation of these models as statistical physics problems, we make several predictions for the collective properties of the sequence ensemble: The distribution of sequences obeys Zipf's law, the repertoire decomposes into several clusters, and there is a massive restriction of diversity because of the correlations. These predictions are completely inconsistent with models in which amino acid substitutions are made independently at each site and are in good agreement with the data. Our results suggest that antibody diversity is not limited by the sequences encoded in the genome and may reflect rapid adaptation to antigenic challenges. This approach should be applicable to the study of the global properties of other protein families.

Original languageEnglish (US)
Pages (from-to)5405-5410
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number12
StatePublished - Mar 23 2010

All Science Journal Classification (ASJC) codes

  • General


  • D regions
  • Immune receptor proteins
  • Statistical models


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