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13th Jan 2024: Normalisation based on Fv Fm

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Murray Cutforth edited this page Jan 13, 2024 · 1 revision

Motivation

We fundamentally need to be able to compare results between different plates for this experiment. However, we know that there will be differences between WTs on different plates due to environmental differences (temperature, agar, pressure, humidity, light, earthquakes etc.) and biological initial conditions (size of initial colony, state of initial colony). We want to be able to nullify the effect of these variables as much as possible, so that all the measured differences are just due to genetics.

I will show some results from a simple scale factor-based approach to normalise Fv/Fm and Y(II). I have not considered NPQ at this point. I have also reduced the subset of data I'm looking at to just the 20H ML and 20H HL light regimes, again for simplicity (although the light regime doesn't affect Fv/Fm of course).

Normalisation approach

It's pretty simple. I have data from 20 plates (10 plates x 2 light treatments). Each plate has either 3 or 384 WT wells on it. We compute Fv/Fm for each WT well, and then average these. Then we compute a "target" Fv/Fm as the average of these averages (in other words, weighting each plate equally). I then compute a scale factor for each plate such that the average WT Fv/FM equals the target value for each plate. If this isn't clear then the plots below should make it clearer.

Results

First, let's check the Fv/Fm for each plate, split between WT and mutant. I think these are ordered in time, so it's good that no obvious seasonal pattern is present.

fv_fm_avgs

If we assume I.I.D. data then the central limit theorem should apply to the sample means. If you squint a bit then this plot looks Gaussian: fv_fm_avgs_dist

The main point is that the differences are on the order of a few percent, so this normalisation scale factor will only slightly change the time series, which is probably good.

Next, we can look at all the Y(II) time series (with Fv/Fm prepended) after normalisation: all_y2_plots_overlaid

It's tricky to make much out with thousands of lines, so plotting the mean for each plate gives: all_y2_plots_means

The plate 99 ML WT average looks a bit anomalous.

To illustrate the effect of the normalisation, I zoomed in to the Fv/Fm for the un-normalised case: all_y2_plots_means_zoom_unnormalised

And then the normalised case: all_y2_plots_means_zoom

Other points about normalisation

  • Fv/Fm is a derived quantity from the underlying intensities: $F_v/F_m = \frac{F_m - F_0}{F_m}$. It would also be reasonable to compute a normalisation scale factor so that the average WT Fm is equal between plates. From the formula here, $\frac{\alpha F_m - \alpha F_0}{\alpha F_m} = \frac{F_m - F_0}{F_m}$, so scaling the raw intensities by a common scale factor $\alpha$ would have no effect on Fv/Fm. We could of course look at scaling different time points with different scale factors, but my feeling is that the data is too noisy for that.

  • We could consider the entire Y(II) and/or NPQ time series of the WTs, and normalise such that the entire time series line up as much as possible between plates. Again, this might be too aggressive.

  • We've only considered inter-plate normalisation here. There could also be intra-plate effects, i.e. systematic differences between different locations on a plate, caused by light or agar differences. These would be easiest to investigate using plate 99, which automatically controls for genetic variation.

  • Some time series analysis methods will be affected by normalisation, and some will not. For example, if we want to compare the similarity of a pair of time series using their mutual information or zero-normalised cross correlation, that would be invariant to linear transformations (shifts, scales) of the time series.

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