TY - JOUR

T1 - Robust k-mer frequency estimation using gapped k-mers

AU - Ghandi, Mahmoud

AU - Mohammad-Noori, Morteza

AU - Beer, Michael A.

N1 - Funding Information:
We thank the reviewers for their comments and suggestions which significantly improved the manuscript. We also thank users of math.stackexchange.com online community, specifically users Joriki and Siva for their useful comments which helped us in the development of the proof. Dongwon Lee graciously provided the processed CTCF sequence data. The research of M.M. was in part supported by a grant from IPM (No. CS1390-4-07), and M.B. was supported by the Searle Scholars Program and in part by NIH grant NS062972.

PY - 2014/7

Y1 - 2014/7

N2 - Oligomers of fixed length, k, commonly known as k-mers, are often used as fundamental elements in the description of DNA sequence features of diverse biological function, or as intermediate elements in the constuction of more complex descriptors of sequence features such as position weight matrices. k-mers are very useful as general sequence features because they constitute a complete and unbiased feature set, and do not require parameterization based on incomplete knowledge of biological mechanisms. However, a fundamental limitation in the use of k-mers as sequence features is that as k is increased, larger spatial correlations in DNA sequence elements can be described, but the frequency of observing any specific k-mer becomes very small, and rapidly approaches a sparse matrix of binary counts. Thus any statistical learning approach using k-mers will be susceptible to noisy estimation of k-mer frequencies once k becomes large. Because all molecular DNA interactions have limited spatial extent, gapped k-mers often carry the relevant biological signal. Here we use gapped k-mer counts to more robustly estimate the ungapped k-mer frequencies, by deriving an equation for the minimum norm estimate of k-mer frequencies given an observed set of gapped k-mer frequencies. We demonstrate that this approach provides a more accurate estimate of the k-mer frequencies in real biological sequences using a sample of CTCF binding sites in the human genome.

AB - Oligomers of fixed length, k, commonly known as k-mers, are often used as fundamental elements in the description of DNA sequence features of diverse biological function, or as intermediate elements in the constuction of more complex descriptors of sequence features such as position weight matrices. k-mers are very useful as general sequence features because they constitute a complete and unbiased feature set, and do not require parameterization based on incomplete knowledge of biological mechanisms. However, a fundamental limitation in the use of k-mers as sequence features is that as k is increased, larger spatial correlations in DNA sequence elements can be described, but the frequency of observing any specific k-mer becomes very small, and rapidly approaches a sparse matrix of binary counts. Thus any statistical learning approach using k-mers will be susceptible to noisy estimation of k-mer frequencies once k becomes large. Because all molecular DNA interactions have limited spatial extent, gapped k-mers often carry the relevant biological signal. Here we use gapped k-mer counts to more robustly estimate the ungapped k-mer frequencies, by deriving an equation for the minimum norm estimate of k-mer frequencies given an observed set of gapped k-mer frequencies. We demonstrate that this approach provides a more accurate estimate of the k-mer frequencies in real biological sequences using a sample of CTCF binding sites in the human genome.

KW - DNA sequence

KW - Frequency estimation

KW - Oligomer

KW - Statistical learning

KW - k-mer

UR - http://www.scopus.com/inward/record.url?scp=84904385033&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904385033&partnerID=8YFLogxK

U2 - 10.1007/s00285-013-0705-3

DO - 10.1007/s00285-013-0705-3

M3 - Article

C2 - 23861010

AN - SCOPUS:84904385033

VL - 69

SP - 469

EP - 500

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 2

ER -