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Inferring time-derivatives, including cell growth rates, using Gaussian processes

Peter S. Swain, Keiran Stevenson, Allen Leary, Luis F. Montano-Gutierrez, Ivan B. N. Clark, Jackie Vogel, Teuta Pilizota
doi: https://doi.org/10.1101/055483
Peter S. Swain
*SynthSys - Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, U.K
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  • For correspondence: peter.swain@ed.ac.uk
Keiran Stevenson
*SynthSys - Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, U.K
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Allen Leary
‡Department of Biology, McGill University, Montreal, Quebec, Canada
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Luis F. Montano-Gutierrez
*SynthSys - Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, U.K
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Ivan B. N. Clark
*SynthSys - Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, U.K
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Jackie Vogel
‡Department of Biology, McGill University, Montreal, Quebec, Canada
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Teuta Pilizota
*SynthSys - Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, U.K
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Abstract

Often the time-derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we introduce a non-parametric method to infer first and second time-derivatives as a function of time from time-series data. Our approach is based on established properties of Gaussian processes and therefore applies to a wide range of data. In tests, the method is at least as accurate as others, but has several advantages: it estimates errors both in the inference and in any summary statistics, such as lag times, allows interpolation with the corresponding error estimation, and can be applied to any number of experimental replicates. As illustrations, we infer growth rate from measurements of the optical density of populations of microbial cells and estimate the rate of in vitro assembly of an amyloid fibril and both the speed and acceleration of two separating spindle pole bodies in a single yeast cell. Being accessible through both a GUI and from scripts, our algorithm should have broad application across the sciences.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-ND 4.0 International license.
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Posted May 25, 2016.
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Inferring time-derivatives, including cell growth rates, using Gaussian processes
Peter S. Swain, Keiran Stevenson, Allen Leary, Luis F. Montano-Gutierrez, Ivan B. N. Clark, Jackie Vogel, Teuta Pilizota
bioRxiv 055483; doi: https://doi.org/10.1101/055483
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Inferring time-derivatives, including cell growth rates, using Gaussian processes
Peter S. Swain, Keiran Stevenson, Allen Leary, Luis F. Montano-Gutierrez, Ivan B. N. Clark, Jackie Vogel, Teuta Pilizota
bioRxiv 055483; doi: https://doi.org/10.1101/055483

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