Phillips NE et al. (2017), Identifying stochastic oscillations in single-c...

XB-ART-56276

PLoS Comput Biol 2017 May 11;135:e1005479. doi: 10.1371/journal.pcbi.1005479.

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Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes.

Phillips NE , Manning C , Papalopulu N , Rattray M .

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Multiple biological processes are driven by oscillatory gene expression at different time scales. Pulsatile dynamics are thought to be widespread, and single-cell live imaging of gene expression has lead to a surge of dynamic, possibly oscillatory, data for different gene networks. However, the regulation of gene expression at the level of an individual cell involves reactions between finite numbers of molecules, and this can result in inherent randomness in expression dynamics, which blurs the boundaries between aperiodic fluctuations and noisy oscillators. This underlies a new challenge to the experimentalist because neither intuition nor pre-existing methods work well for identifying oscillatory activity in noisy biological time series. Thus, there is an acute need for an objective statistical method for classifying whether an experimentally derived noisy time series is periodic. Here, we present a new data analysis method that combines mechanistic stochastic modelling with the powerful methods of non-parametric regression with Gaussian processes. Our method can distinguish oscillatory gene expression from random fluctuations of non-oscillatory expression in single-cell time series, despite peak-to-peak variability in period and amplitude of single-cell oscillations. We show that our method outperforms the Lomb-Scargle periodogram in successfully classifying cells as oscillatory or non-oscillatory in data simulated from a simple genetic oscillator model and in experimental data. Analysis of bioluminescent live-cell imaging shows a significantly greater number of oscillatory cells when luciferase is driven by a Hes1 promoter (10/19), which has previously been reported to oscillate, than the constitutive MoMuLV 5' LTR (MMLV) promoter (0/25). The method can be applied to data from any gene network to both quantify the proportion of oscillating cells within a population and to measure the period and quality of oscillations. It is publicly available as a MATLAB package.

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Species referenced: Xenopus
Genes referenced: hes1

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	Fig 1. Simulated time series examples from the OU and OUosc covariance functions in one dimension.(A) Simulation of OU covariance function with α = 0.5, σ = 1. (B) Simulation of OU covariance function with α = 0.01, σ = 1. (C) Simulation of OUosc covariance function with α = 0.04, β = 0.5, and σ = 1. (D) Simulation of OUosc covariance function with α = 0.2, β = 0.5, and σ = 1. Dotted lines in (C) and (D) are sinusoids with frequency β = 0.5, where the first peak is fitted to the first peak of the data.
	Fig 2. An illustrative example of the detrending pipeline.(A) Simulation sample from OUosc covariance function with α = 0.2, β = 0.5, and σ = 1. (B) Simulation of 3 different samples of SE covariance function with αSE = 0.01 and σSE = 1. Solid black example is used then added to signal (C) Superposition of original signal (A) with long term trend ((B), shown as dotted black line). Dotted green line represents trend fitted from data. (D) Detrended final signal used for analysis, found by subtracting the fitted trend from (C).
	Fig 3. The network topology of the Hes1 transcription factor.
	Fig 4. Time series examples from the stochastic Hes1 model.(A), (B) Power spectra of protein concentrations calculated from 1000 independent Gillespie simulations. Measurements start at t = 5000 mins in order to allow for equilibration. Model parameters for (A) are P0 = 300, h = 1, τ = 0, αm = αp = 1, μm = μp = 0.07 and Ω = 20. Model parameters for (B) are P0 = 100, h = 3, τ = 18, αm = αp = 1, μm = μp = 0.03 and Ω = 20. (C), (D) Time series examples and associated LLR scores from (A) and (B), respectively. (E), (F) LSP of time series (C) and (D), respectively.
	Fig 5. Comparing the LSP and Gaussian process method using ROC curves from synthetic data.(A, D and G) Representative time series of non-oscillatory gene expression at different noise levels and time lengths. (B, E and H) Representative time series of oscillatory gene expression at different noise levels and time lengths. (C, F and I) ROC curves: the true positive against false positive rate at different noise levels and time lengths. Red, LLR Gaussian process method; blue, LSP.
	Fig 6. The detrending length scale affects the classification of cells and the estimated period.(A) Representative time series of oscillatory gene expression with trend added. Green, raw expression; red, added trend; blue, the sum of the two signals. (B, D and F) The fitted trend line using upper bound of αSE = exp(−6), exp(−4) and exp(−2), respectively. Blue, signal; red, fitted trend. (C, E and G) The estimated period of the detrended time series.
	Fig 7. Bioluminescence imaging of C17 neural progenitor cells with luciferase expression driven by the oscillatory Hes1 or constitutive MMLV promoter.(A) Bioluminescence images of an individual cell with luciferase driven by Hes1 promoter. (B) Raw time series of bioluminescence quantification from A. (C) Detrended bioluminescence time series. (D) Bioluminescence images of an individual cell with luciferase driven by MMLV promoter. (E) Raw time series of bioluminescence quantification from D. (F) Detrended bioluminescence time series. Both reporters show dynamic expression.
	Fig 8. The LLR between OU and OUosc model fits to the single-cell experimental data and synthetic non-oscillatory data.(A) The LLR distribution of 19 cells with the Hes1 promoter. (B) The LLR distribution of 25 cells with the MMLV promoter. (C) The LLR distribution of 2000 synthetic cells generated from the OU model using parameters fitted to A and B.

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