Substitution and site-specific selection driving B cell affinity maturation is consistent across individuals

The antibody repertoire of each individual is continuously updated by the evolutionary process of B cell receptor mutation and selection. It has recently become possible to gain detailed information concerning this process through high-throughput sequencing. Here, we develop modern statistical molecular evolution methods for the analysis of B cell sequence data, and then apply them to a very deep short-read data set of B cell receptors. We find that the substitution process is conserved across individuals but varies significantly across gene segments. We investigate selection on B cell receptors using a novel method that side-steps the difficulties encountered by previous work in differentiating between selection and motif-driven mutation; this is done through stochastic mapping and empirical Bayes estimators that compare the evolution of in-frame and out-of-frame rearrangements. We use this new method to derive a per-residue map of selection, which we find is dominated by purifying selection, though not uniformly so. INTRODUCTION The spectrum of antibodies encoded by somatically rearranged human B cell receptor (BCR) genes can bind a vast array of pathogens, initiating an immune reponse or directly neutralizing their target. This diversity is made possible by the processes of VDJ recombination, in which combinatorial joining of V-, D-, and Jgenes generates a vastly broader collection of unique BCR sequences than could be directly encoded in the genome, and then further diversification and selection by affinity maturation. The affinity maturation process, in which antibodies increase binding affinity for their cognate antigens, is essential to mounting a precise humoral immune response. Affinity maturation proceeds via a nucleotide substitution process that combines Darwinian mutation and selection processes. Mutational diversity is generated by somatic hypermutation (SHM), in which a targeted molecular mechanism mutates the BCR sequence. This diversity is then passed through a selective sieve in which B cells that bind well to antigen are stimulated to reproduce, while those that do not bind well or bind to self are marked for destruction. The combination of VDJ recombination and affinity maturation enables B cells to respond to an almost limitless diversity of antigens. Understanding the substitution process and selective forces shaping the diversity of the memory B cell repertoire thus has implications for disease prophylaxis and treatment, including for the promise of rational vaccine design. It has recently become possible to gain detailed information about the B cell repertoire using high-throughput sequencing [1–5]. Recent reviews have highlighted the need for new computational tools that make use of BCR sequence data Date: March 13, 2014. 1 ar X iv :1 40 3. 30 66 v1 [ qbi o. PE ] 1 2 M ar 2 01 4 2 MCCOY, BEDFORD, MININ, ROBINS, AND MATSEN to bring new insight, including the need for reproducible computational pipelines [6–9]. Rigorous analysis of the B cell repertoire will require statistical analysis of how evolutionary processes define affinity maturation. Statistical nucleotide molecular evolution models are often described in terms of three interrelated processes: mutation, the process generating diversity, selection, the process determining survival, and substitution, the observed process of evolution that follows from the first two processes. Although researchers have made many observations concerning the affinity maturation process, this work has not yet been done using rigorous statistical criteria. One major vein of research has focused on how nucleotide mutation rates depend on the identity of surrounding nucleotides (reviewed in [10]; see also [11]), but little has been done concerning other aspects of the process, such as how the substitution process differs between gene segments. Along with mutation, selection due to competition for antigen binding forms the other key part of the affinity maturation process. Inference of selective pressures in this context is complicated by nucleotide context-dependent mutation, leading some authors to proclaim that such selection inference is not possible [12]. Indeed, if one does not correct for context-dependent mutation bias, interactions between those motifs and the genetic code can lead to false positive identification of selective pressure. Previous work has developed methodology to analyze selection on sequence tracts in this context (reviewed in Discussion), but no methods have yet achieved the goal of rigorous per-residue selection estimates. This has, however, been recently identified as an important goal [11]. Such per-residue estimates of selection would form a foundation for rational vaccine design by giving information on to what degree residues should be considered mutable versus being so essential to structure that they cannot be mutated. The ensemble of germline V, D, and J genes are divided into nested sets. They can be first identified by their segment, which is whether they are a V, D, or J gene. Each set of genes for a given segment is divided into subgroups which share at least 75% nucleotide identity. Genes also have polymorphisms that are grouped into alleles, which are variants of the gene between individuals. In this paper, we develop modern statistical molecular evolution methods for the analysis of high-throughput B cell sequence data, and then apply them to a very deep short-read data set of B cell receptors. Specifically, first we apply model selection criteria to find patterns in the affinity maturation single-nucleotide substitution process and find that it is similar across individuals but varies significantly across gene segments. Second, we develop the first statistical methodology for comprehensive per-residue selection estimates for B cell receptors. We avoid difficulties encountered by previous work in differentiating between selection and motif-driven mutation by developing statistical means to compare in-frame and out-of-frame rearrangements. A key part of our method is an empirical Bayes regularization process for selection inference, which we develop for non-constant sequencing coverage and adapt to the case of a fixed ancestral sequence. Using this new method, we are able to derive a per-residue map of selection, which we find is dominated by purifying selection with patterns that are consistent among individuals in our study. RESULTS Substitution model inference and testing. SUBSTITUTION AND SITE-SPECIFIC SELECTION IN B CELL AFFINITY MATURATION 3 name branch length GTR transition matrix across-site rate variation (discrete Gamma) total parameters ti Qi Γi One branch length per segment per sequence (n× 3) One matrix per segment (8 × 3) One distribution per segment (3) 3n + 27 tr Qi Γi One branch length per sequence (n) + relative rate between segments (2) One matrix per segment (8 × 3) One distribution per segment (3) n + 29 tr Qi Γs One branch length per sequence (n) + relative rate between segments (2) One matrix per segment (8 × 3) One shared distribution (1) n + 27 tr Qs Γs One branch length per sequence (n) + relative rate between segments (2) One shared matrix (8) One shared distribution (1) n + 11 TABLE 1. The models of molecular evolution evaluated, including the number of free parameters introduced in parentheses. The setting of B cell affinity maturation is substantially different than that typically encountered in molecular evolution studies, and hence there are some differences between our model fitting procedure compared to common practice. For B cell receptors outside of nontemplated insertions, the root state is the V, D, and J genes encoded in the germline from which a sequenced BCR derives. Thus, we analyze changes that have occurred in going from germline sequences to observed BCR reads, ignoring sites comprising nontemplated insertions. We apply our methods to a data set of memory B cell populations isolated from three healthy volunteers, referred throughout the manuscript as individuals A, B and C. Deep sequencing these B cell populations resulted in 15,023,951 unique 130bp reads spanning the heavy chain CDR3 region. Although there are certainly some clones in our data set that derive from a single rearrangement event but differ due to somatic hypermutation, the probability that a given pair of sequences derives from a single common ancestor is small: targeted searches for clonally related antibodies during infection have identified them at 0.003% to 0.5% [13]. The classical situation for molecular evolution, on the other hand, assumes all sequences in a data set have common ancestry. Additionally, we encountered significant computational barriers analyzing the the volume of sequences available, and in fact we believe the 15 million unique sequences used in this study to be the largest number analyzed in a molecular evolution study from a single data set to date. For these reasons, we performed model fitting on a set of two-taxon trees, each connecting an observed read to its best scoring germline sequence according to Smith-Waterman alignment. This best scoring sequence was taken to be its ancestor. We then calculated model likelihood as the product of likelihoods over these two taxon trees. We evaluated the fit of models with varying complexity, ranging from a simple model with shared branch lengths and rates for the three independent segments of the BCR to a complex model with independent branch lengths for each segment (Tab. 1). For the underlying nucleotide substitution model, we fit a general time-reversible (GTR) nucleotide model [14] to subsets of the data, using 20,000 unique sequences from each individual. The choice of a reversible model, rather than a more general model, was based on the similarity of base frequencies between the germline sequences and observed reads (Tab. S1). 4 MCCOY, BEDFORD, MININ, ROBINS, AND MATSEN model log likelihood df AIC ∆AIC A tr Qi Γi -650,916 20,029