Mixture Models for Spherical Data with Applications to Protein Bioinformatics
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Mixture Models for Spherical Data with Applications to Protein Bioinformatics. / Mardia, Kanti V.; Barber, Stuart; Burdett, Philippa M.; Kent, John T.; Hamelryck, Thomas.
Directional Statistics for Innovative Applications: A Bicentennial Tribute to Florence Nightingale. Springer, 2022. p. 15-32 (Forum for Interdisciplinary Mathematics).Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
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TY - CHAP
T1 - Mixture Models for Spherical Data with Applications to Protein Bioinformatics
AU - Mardia, Kanti V.
AU - Barber, Stuart
AU - Burdett, Philippa M.
AU - Kent, John T.
AU - Hamelryck, Thomas
N1 - Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
PY - 2022
Y1 - 2022
N2 - Finite mixture models are fitted to spherical data. Kent distributions are used for the components of the mixture because they allow considerable flexibility. Previous work on such mixtures has used an approximate maximum likelihood estimator for the parameters of a single component. However, the approximation causes problems when using the EM algorithm to estimate the parameters in a mixture model. Hence, the exact maximum likelihood estimator is used here for the individual components. This paper is motivated by a challenging prize problem in structural bioinformatics of how proteins fold. It is known that hydrogen bonds play a key role in the folding of a protein. We explore this hydrogen bond geometry using a data set describing bonds between two amino acids in proteins. An appropriate coordinate system to represent the hydrogen bond geometry is proposed, with each bond represented as a point on a sphere. We fit mixtures of Kent distributions to different subsets of the hydrogen bond data to gain insight into how the secondary structure elements bond together, since the distribution of hydrogen bonds depends on which secondary structure elements are involved.
AB - Finite mixture models are fitted to spherical data. Kent distributions are used for the components of the mixture because they allow considerable flexibility. Previous work on such mixtures has used an approximate maximum likelihood estimator for the parameters of a single component. However, the approximation causes problems when using the EM algorithm to estimate the parameters in a mixture model. Hence, the exact maximum likelihood estimator is used here for the individual components. This paper is motivated by a challenging prize problem in structural bioinformatics of how proteins fold. It is known that hydrogen bonds play a key role in the folding of a protein. We explore this hydrogen bond geometry using a data set describing bonds between two amino acids in proteins. An appropriate coordinate system to represent the hydrogen bond geometry is proposed, with each bond represented as a point on a sphere. We fit mixtures of Kent distributions to different subsets of the hydrogen bond data to gain insight into how the secondary structure elements bond together, since the distribution of hydrogen bonds depends on which secondary structure elements are involved.
UR - http://www.scopus.com/inward/record.url?scp=85132883072&partnerID=8YFLogxK
U2 - 10.1007/978-981-19-1044-9_2
DO - 10.1007/978-981-19-1044-9_2
M3 - Book chapter
AN - SCOPUS:85132883072
SN - 978-981-19-1043-2
T3 - Forum for Interdisciplinary Mathematics
SP - 15
EP - 32
BT - Directional Statistics for Innovative Applications
PB - Springer
ER -
ID: 314302529