  B cells develop high affinity receptors during the course of affinity
maturation, a cyclic process of mutation and selection. At the end of affinity
maturation, a number of cells sharing the same ancestor (i.e. in the same
"clonal family") are released from the germinal center, their amino acid
frequency profile reflects the allowed and disallowed substitutions at each
position. These clonal-family-specific frequency profiles, called "substitution
profiles", are useful for studying the course of affinity maturation as well as
for antibody engineering purposes. However, most often only a single sequence
is recovered from each clonal family in a sequencing experiment, making it
impossible to construct a clonal-family-specific substitution profile. Given
the public release of many high-quality large B cell receptor datasets, one may
ask whether it is possible to use such data in a prediction model for
clonal-family-specific substitution profiles. In this paper, we present the
method "Substitution Profiles Using Related Families" (SPURF), a penalized
tensor regression framework that integrates information from a rich assemblage
of datasets to predict the clonal-family-specific substitution profile for any
single input sequence. Using this framework, we show that substitution profiles
from similar clonal families can be leveraged together with simulated
substitution profiles and germline gene sequence information to improve
prediction. We fit this model on a large public dataset and validate the
robustness of our approach on an external dataset. Furthermore, we provide a
command-line tool in an open-source software package
(https://github.com/krdav/SPURF) implementing these ideas and providing easy
prediction using our pre-fit models.
