## Model description

VDJsolver was developed using Yabasic (www.yabasic.de).
The program uses the maximum likelihood
method to obtain the best fit to the following model:

VH-P_{H}-N1-P_{Ddown}-D-P_{Dup}-N2-P_{J}-JH,

where Nx designates N and P palindromic nucleotides upstream or downstream of
the D gene as indicated. Any segment may be omitted except VH and JH.
VH was compared with the IGHV3-23*01 germline gene (GenBank accession
number M99660) while JH was compared with the germline JH gene with the
highest identity score from codon 114 through the splice site among all
JH-genes in the IMGT database. The D segments were compared with any
germline D segment available in the IMGT database.
P segments were defined as 2-8 nucleotide long
extensions from the VH, Dx or JH genes reverse complementary to the
corresponding germline sequence. Maximum likelihood was determined by
running through all possible combinations of segments for a given
rearrangement and finding the combination maximizing the likelihood
score. The score was defined as the product of estimated probabilities
for any event deviating from the germline sequences in question.
Probabilities for transitions and transversions in VH, Dx and JH
segments were calculated from the number of substitutions found in the
VH region from codon 1 through 100 (assuming a 5/4 ratio of transitions
to transversions). For un-mutated sequences, the estimated Taq error
rate was used. A given N nucleotide was attributed a probability equal
to its frequency in all N segments (determined by iteration of the
model on all sequences). To reduce stochastic assignment of D segments,
D segments shorter than 4 nucleotides were not accepted and D segments
with more mutations than the 95 percentile of that expected by the
assumed mutation rate and length of the D segment (Poisson
distribution) were not accepted either. A dynamic probability for
including a D segment was introduced, dependent on the length of the
joint region (codons 101 through the downstream splice site) and the
mutation rate of the VH region. The parameters were fine tuned to find
a D gene in 5% of the sequences from a set of artificial
rearrangements made by a random permutation of the bases between the VH
and JH segments of real rearrangements. D segments were generally at
least eight nucleotides long.