Maximum entropy models for antibody diversity

By Thierry Mora, Aleksandra M. Walczak, William Bialek, C. Callan. 2009

327 citations recorded by the source corpus.

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.

Subfields: Genetics, Molecular Biology

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Citations in the corpus

Protein 3D Structure Computed from Evolutionary Sequence Variation (2011, neutral): “optimization problem are of the form [11,45,49]:”
Dissecting the Specificity of Protein-Protein Interaction in Bacterial Two-Component Signaling: Orphans and Crosstalks (2011, background): “The idea of disentangling direct from indirect correlations was observed to be successful also in single protein domains [18,19].”
Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners (2014, neutral): “Proposed initially more than a decade ago [21,22], it was not until very recently that the first successful MaxEnt approaches to the study of co-evolution were published [8,23].”
Are Biological Systems Poised at Criticality? (2010, methodology): “A translation invariant maximum entropy model of non-aligned sequences correctly predicts amino acid frequencies at absolute positions [33].”
Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity (2016, unknown): “Rep-Seq data allow for a detailed description of the sequences distribution based on Maximum Entropy (MaxEnt) modeling of repertoires, as it has been proven in the case of zebra-fish Abs [7] and human T cell receptors [8, 9].”
Colloquium: Criticality and dynamical scaling in living systems (2017, background): “…retinal neural populations (Schneidman et al., 2006; Tkačik et al., 2014, 2013, 2015) to flocks of birds (Bialek et al., 2012) and the immune system (Mora et al., 2010), for which excellent empirical data sets are available– have parameter values sitting close to the edge of a phase transition,…”
Inferring interaction partners from protein sequences (2016, background): “[22] Mora T, Walczak AM, Bialek W, Callan CG (2010) Maximum entropy models for antibody diversity.”
Generation and analyses of human synthetic antibody libraries and their application for protein microarrays. (2016, background): “Since natural repertoires have been proofread by the immune system these tend to exhibit high functional diversity but, at the same time, these have been shown to contain many highfrequency clones and to be genetically constrained (Winter and Milstein, 1991; Mora et al., 2010; Jiang et al., 2011).”
Inverse statistical problems: from the inverse Ising problem to data science (2017, methodology): “This principle has been invoked in neural modelling [196], protein structure determination [239], and DNA sequence analysis [153].”