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Branch-recombinant Gaussian processes for analysis of perturbations in biological time series

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Penfold, Christopher A., Sybirna, Anastasiya, Reid, John E., Huang, Yun, Wernisch, Lorenz, Ghahramani, Zoubin, Grant, Murray R. and Surani, M. Azim (2018) Branch-recombinant Gaussian processes for analysis of perturbations in biological time series. Bioinformatics, 34 (17). i1005-i1013. doi:10.1093/bioinformatics/bty603

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Official URL: http://dx.doi.org/10.1093/bioinformatics/bty603

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Abstract

Motivation
A common class of behaviour encountered in the biological sciences involves branching and recombination. During branching, a statistical process bifurcates resulting in two or more potentially correlated processes that may undergo further branching; the contrary is true during recombination, where two or more statistical processes converge. A key objective is to identify the time of this bifurcation (branch or recombination time) from time series measurements, e.g. by comparing a control time series with perturbed time series. Gaussian processes (GPs) represent an ideal framework for such analysis, allowing for nonlinear regression that includes a rigorous treatment of uncertainty. Currently, however, GP models only exist for two-branch systems. Here, we highlight how arbitrarily complex branching processes can be built using the correct composition of covariance functions within a GP framework, thus outlining a general framework for the treatment of branching and recombination in the form of branch-recombinant Gaussian processes (B-RGPs).

Results
We first benchmark the performance of B-RGPs compared to a variety of existing regression approaches, and demonstrate robustness to model misspecification. B-RGPs are then used to investigate the branching patterns of Arabidopsis thaliana gene expression following inoculation with the hemibotrophic bacteria, Pseudomonas syringae DC3000, and a disarmed mutant strain, hrpA. By grouping genes according to the number of branches, we could naturally separate out genes involved in basal immune response from those subverted by the virulent strain, and show enrichment for targets of pathogen protein effectors. Finally, we identify two early branching genes WRKY11 and WRKY17, and show that genes that branched at similar times to WRKY11/17 were enriched for W-box binding motifs, and overrepresented for genes differentially expressed in WRKY11/17 knockouts, suggesting that branch time could be used for identifying direct and indirect binding targets of key transcription factors.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QH Natural history > QH301 Biology
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Branching processes, Gaussian processes, Time-series analysis, Perturbation (Mathematics), Bifurcation theory
Journal or Publication Title: Bioinformatics
Publisher: Oxford University Press
ISSN: 1367-4803
Official Date: 1 September 2018
Dates:
DateEvent
1 September 2018Published
8 September 2018Available
UNSPECIFIEDAccepted
Volume: 34
Number: 17
Page Range: i1005-i1013
DOI: 10.1093/bioinformatics/bty603
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
083089/Z/07/ZWellcome Trusthttp://dx.doi.org/10.13039/100010269
PhD scholarshipWellcome Trusthttp://dx.doi.org/10.13039/100010269
Cambridge International Trust scholarshipCambridge Overseas Trusthttp://dx.doi.org/10.13039/501100003341
BB/L014130/1[BBSRC] Biotechnology and Biological Sciences Research Councilhttp://dx.doi.org/10.13039/501100000268
UNSPECIFIEDHuman Frontier Science Programhttp://dx.doi.org/10.13039/501100000854
Senior Investigator AwardWellcome Trusthttp://dx.doi.org/10.13039/100010269
MC_U105260799[MRC] Medical Research Councilhttp://dx.doi.org/10.13039/501100000265
UNSPECIFIEDJames Baird Fund, University of Cambridgehttp://dx.doi.org/10.13039/501100003987
BB/F005903/1[BBSRC] Biotechnology and Biological Sciences Research Councilhttp://dx.doi.org/10.13039/501100000268
BB/P002560/1[BBSRC] Biotechnology and Biological Sciences Research Councilhttp://dx.doi.org/10.13039/501100000268
UNSPECIFIEDAlan Turing Institutehttp://dx.doi.org/10.13039/100012338
UNSPECIFIEDGooglehttp://dx.doi.org/10.13039/100006785
UNSPECIFIEDMicrosoft Researchhttp://dx.doi.org/10.13039/100006112
EP/N014162/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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