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Nat Commun. 2016 Dec 12;7:13766. doi: 10.1038/ncomms13766.

Inferring time derivatives including cell growth rates using Gaussian processes.

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SynthSys-Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3BF, UK.
Department of Biology, McGill University, Montreal, Quebec, Canada H3G 0B1.
Integrated Quantitative Biology Initiative, McGill University, Montreal, Quebec, Canada H3G 0B1.


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.

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