Antibody-specific model of amino acid substitution for immunological inferences from alignments of antibody sequences.

Antibodies are glycoproteins produced by the immune system as a dynamically adaptive line of defense against invading pathogens. Very elegant and specific mutational mechanisms allow B lymphocytes to produce a large and diversified repertoire of antibodies, which is modified and enhanced throughout all adulthood. One of these mechanisms is somatic hypermutation, which stochastically mutates nucleotides in the antibody genes, forming new sequences with different properties and, eventually, higher affinity and selectivity to the pathogenic target. As somatic hypermutation involves fast mutation of antibody sequences, this process can be described using a Markov substitution model of molecular evolution. Here, using large sets of antibody sequences from mice and humans, we infer an empirical amino acid substitution model AB, which is specific to antibody sequences. Compared with existing general amino acid models, we show that the AB model provides significantly better description for the somatic evolution of mice and human antibody sequences, as demonstrated on large next generation sequencing (NGS) antibody data. General amino acid models are reflective of conservation at the protein level due to functional constraints, with most frequent amino acids exchanges taking place between residues with the same or similar physicochemical properties. In contrast, within the variable part of antibody sequences we observed an elevated frequency of exchanges between amino acids with distinct physicochemical properties. This is indicative of a sui generis mutational mechanism, specific to antibody somatic hypermutation. We illustrate this property of antibody sequences by a comparative analysis of the network modularity implied by the AB model and general amino acid substitution models. We recommend using the new model for computational studies of antibody sequence maturation, including inference of alignments and phylogenetic trees describing antibody somatic hypermutation in large NGS data sets. The AB model is implemented in the open-source software CodonPhyML (http://sourceforge.net/projects/codonphyml) and can be downloaded and supplied by the user to ProGraphMSA (http://sourceforge.net/projects/prographmsa) or other alignment and phylogeny reconstruction programs that allow for user-defined substitution models.

Quantitative social science. A network framework of cultural history.

The emergent processes driving cultural history are a product of complex interactions among large numbers of individuals, determined by difficult-to-quantify historical conditions. To characterize these processes, we have reconstructed aggregate intellectual mobility over two millennia through the birth and death locations of more than 150,000 notable individuals. The tools of network and complexity theory were then used to identify characteristic statistical patterns and determine the cultural and historical relevance of deviations. The resulting network of locations provides a macroscopic perspective of cultural history, which helps us to retrace cultural narratives of Europe and North America using large-scale visualization and quantitative dynamical tools and to derive historical trends of cultural centers beyond the scope of specific events or narrow time intervals.