  The human immune system depends on a highly diverse collection of
antibody-making B cells. B cell receptor sequence diversity is generated by a
random recombination process called "rearrangement" forming progenitor B cells,
then a Darwinian process of lineage diversification and selection called
"affinity maturation." The resulting receptors can be sequenced in high
throughput for research and diagnostics. Such a collection of sequences
contains a mixture of various lineages, each of which may be quite numerous, or
may consist of only a single member. As a step to understanding the process and
result of this diversification, one may wish to reconstruct lineage membership,
i.e. to cluster sampled sequences according to which came from the same
rearrangement events. We call this clustering problem "clonal family
inference." In this paper we describe and validate a likelihood-based framework
for clonal family inference based on a multi-hidden Markov Model (multi-HMM)
framework for B cell receptor sequences. We describe an agglomerative algorithm
to find a maximum likelihood clustering, two approximate algorithms with
various trade-offs of speed versus accuracy, and a third, fast algorithm for
finding specific lineages. We show that under simulation these algorithms
greatly improve upon existing clonal family inference methods, and that they
also give significantly different clusters than previous methods when applied
to two real data sets.
