Pre-processing time-series for ARCOS

Source: vignettes/ARCOS-binTimeseries.Rmd

Intro

Using ARCOS to detect collective activation events in biological systems requires identification of active objects, i.e., objects that will be passed to the clustering algorithm. In practice the single-cell activity obtained from image segmentation needs to be thresholded and binarised. ARCOS offers several approaches to perform such approaches that will be covered below.

The pipeline

Load time-series data

Time-series data obtained, for example, from image segmentation should be in long format. Here we use a sample dataset of single-cell ERK activity from MCF10A WT epithelial cells. See the associated publication on bioRxiv for more details about biological problems that can be analysed with ARCOS.

# define column names
lCols = list()
lCols$frame = 'frame'
lCols$trackid = 'trackid'
lCols$posx = 'x'
lCols$posy = 'y'
lCols$meas = 'meas'

# Load from file
dts = fread(system.file('testdata/sampleTS.csv.gz',
                        package = 'ARCOS'))

# create an ARCOS ts object
ARCOS::arcosTS(dts, 
               colPos = c(lCols$posx, lCols$posy), 
               colMeas = lCols$meas,
               colFrame = lCols$frame, 
               colIDobj = lCols$trackid)

knitr::kable(head(dts, 4), digits = 2)
frame trackid x y meas
0 16 682.21 148.14 0.49
1 16 679.79 149.04 0.48
2 16 678.68 149.87 0.48
3 16 680.24 148.45 0.48

Measurement interpolation

The measurement may contain missing values or NAs, which can be interpolated using the ARCOS::interpolMeas function.

# interpolate
dts = ARCOS::interpolMeas(dts)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo

Measurement distribution

Point outliers in the measurement can be clipped using the ARCOS::clipMeas function.

ARCOS::histMeas(dts, 
                clip = c(0.001, 0.999),
                quant = TRUE) + 
  ggthemes::theme_clean()

ARCOS::clipMeas(dts, 
                clip = c(0.001, 0.999),
                quant = TRUE)

Track lengths

De-trending is based on a running median, therefore, it requires time series that are approximately at least 4 times longer than the length of the de-trending median filter.

ARCOS::histTrackLen(dts, binwidth = 10)

Length of time series in frames. Frames acquired every 1 minute.

dts = ARCOS::selTrackLen(dts, lenmin = 660)

knitr::kable(
  dts[, 
      .N, 
      by = trackid])
trackid N
16 661
20 661
22 661
74 661
107 661
108 661
118 661
131 661
230 661

Identify activity

Regions of measurement activity identified with several methods available in the ARCOS::binMeas function.

runmed

This approach uses a short-term smoothing filter to remove noise from time series and a long-term filter to remove trends.

  1. Short-term smoothing to filter noise (median filter with \(k = 5\) frames).
  2. Long-term smoothing to de-trend (median filter with \(k = 201\) frames).
  3. Rescale if the difference between min and max is greater than \(peakThr = 0.05\).
  4. Binarise the final signal with \(binThr = 0.1\).
# binarise the measurement
ARCOS::binMeas(dts,
               biasMet = "runmed", 
               smoothK = 5L,
               biasK = 501L,
               peakThr = 0.05,
               binThr = 0.1)

The ARCOS::binMeas function adds meas.resc and meas.bin columns to the original dataset. Below is the plot of original time series compared to de-trended/rescaled and binarised output. The meas.bin column should be used to filter the rows such that only active cells are used to detect collective events, i.e., ARCOS::trackColl(dts[meas.bin > 0]).

knitr::kable(head(dts), digits = 2)
frame trackid x y meas meas.resc meas.bin
0 16 682.21 148.14 0.49 0 0
1 16 679.79 149.04 0.48 0 0
2 16 678.68 149.87 0.48 0 0
3 16 680.24 148.45 0.48 0 0
4 16 679.30 149.14 0.47 0 0
5 16 678.61 148.03 0.47 0 0 
p1 = ARCOS::plotBinMeas(dts, 
                        ntraj = 0L, 
                        xfac = 1 / 60.,
                        plotResc = TRUE,
                        inSeed = 3L) +
  geom_hline(yintercept = 0.1, 
             color = "#F28E2B", 
             linetype = "dashed") +
  ggthemes::theme_few() +
  xlab("Time [h]") +
  ylab("C/N ERK-KTR")

p1
#> Warning: Removed 304 rows containing missing values (`geom_path()`).

lm

In this approach, a fit to a linear function is used to de-trend the time series.

  1. Short-term smoothing to filter noise (median filter with \(k = 5\)).
  2. De-trend by fitting a 5th order polynomial (median filter with \(polyDeg = 5\)).
  3. Rescale if the difference between min and max is greater than \(peakThr = 0.2\).
  4. Binarise the final signal with \(binThr = 0.2\).
# binarise the measurement
ARCOS::binMeas(dts,
               biasMet = "lm", 
               smoothK = 5L,
               peakThr = 0.05,
               polyDeg = 5L,
               binThr = 0.2)

ARCOS::plotBinMeas(dts, 
                   ntraj = 0L, 
                   xfac = 1 / 60.,
                   plotResc = TRUE,
                   inSeed = 3L) +
  geom_hline(yintercept = 0.2, 
             color = "#F28E2B", 
             linetype = "dashed") +
  ggthemes::theme_few() +
  xlab("Time [h]") +
  ylab("C/(C+N) ERK-KTR")
#> Warning: Removed 131 rows containing missing values (`geom_path()`).

none

In this approach a fixed threshold is applied to rescaled time series.

  1. Rescale all time series between global min and max.
  2. Short-term smoothing to filter noise (median filter with \(k = 5\)).
  3. Binarise the final signal with \(binThr = 0.3\).
# binarise the measurement
ARCOS::binMeas(dts,
               biasMet = "none", 
               smoothK = 5L,
               binThr = 0.3)

ARCOS::plotBinMeas(dts, 
                   ntraj = 0L, 
                   xfac = 1 / 60.,
                   plotResc = TRUE,
                   inSeed = 3L) +
  geom_hline(yintercept = 0.3, 
             color = "#F28E2B", 
             linetype = "dashed") +
  ggthemes::theme_few() +
  xlab("Time [h]") +
  ylab("C/(C+N) ERK-KTR")
#> Warning: Removed 57 rows containing missing values (`geom_path()`).