This makes mapping from k-mer locations to the corresponding sequences more efficient.
We used a simple approach to select sig-mers from all sig-mers found by the previous step: for every transcript, sig-mers are evenly chosen based on the sig-mer locations such that any two sig-mers are at least 50 base pair away from each other in the given transcript.
The program was run genome wide on each species, and each 6-mer exhibiting location-specific overrepresentation at a P value under P < 1 × 10−15 was considered for subsequent analyses.
k-mer homoplasy may incorrectly inflate the proportion of shared k-mers because (i) multiple copies of the same k-mer at different locations in species A must all experience mutations before this k-mer is no longer shared with species B, and (ii) a k-mer that does undergo a mutation may turn into a k-mer that already exists elsewhere in the genomes of species A or B (see Methods: k-mer homoplasy).
They considered the effects of all possible 4,096 6-mers at five locations in two model exons.
In no instance was there a shortening of survival time following administration of MER at a location away from the tumour implant.
Comparing sequence evolution simulated from random and real ancestral sequences, k must be larger to reduce k-mer homoplasy with the real ancestral sequence (Fig. 2c); this is because the lower complexity in the real ancestral sequence increases the probability that a k-mer appears at multiple locations in the genome by chance.
We scanned for patterns of evolutionary modifications within the comprehensive list of predicted 6-mer motifs exhibiting location-specific overrepresentation.
For both human and mouse, we determined a set of 6-mer motifs exhibiting location-specific overrepresentation using the Functional Region Evaluation Engine (FREE) (Yokoyama et al. 2009).
YAHA uses a hash table index to locate the set of locations (seeds) where each k-mer in the query sequence appears as a subsequence of the reference.
Let Q k denote the random variable for the number of copies of a k-mer in a genome above 1; thus, if q k (i) denotes the probability distribution of Q k, q k (0) is the probability that a k-mer is unique, q k (1) is the probability that a k-mer occurs at two different locations in the genome, etc.
