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 and Teuta Pilizota
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Peter S. Swain: SynthSys—Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh
Keiran Stevenson: SynthSys—Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh
Allen Leary: McGill University
Luis F. Montano-Gutierrez: SynthSys—Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh
Ivan B.N. Clark: SynthSys—Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh
Jackie Vogel: McGill University
Teuta Pilizota: SynthSys—Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh

Nature Communications, 2016, vol. 7, issue 1, 1-8

Abstract: 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 Gaussian processes and 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, and allows interpolation with the corresponding error estimation. As illustrations, we infer growth rates of microbial cells, the rate of assembly of an amyloid fibril and both the speed and acceleration of two separating spindle pole bodies. Our algorithm should thus be broadly applicable.

Date: 2016
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DOI: 10.1038/ncomms13766

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