PLATERO: A calibration protocol for plate reader green fluorescence measurements

Abstract

One of the most common sources of information in Synthetic Biology is the data coming from plate reader fluorescence measurements. These experiments provide a measure of the light emitted by a certain fluorescent molecule, such as the Green Fluorescent Protein (GFP). However, these measurements are generally expressed in arbitrary units and are affected by the measurement device gain. This limits the range of measurements in a single experiment and hampers the comparison of results among experiments. In this work, we describe PLATERO, a calibration protocol to express fluorescence measures in concentration units of a reference fluorophore. The protocol removes the gain effect of the measurement device on the acquired data. In addition, the fluorescence intensity values are transformed into units of concentration using a Fluorescein calibration model. Both steps are expressed in a single mathematical expression that returns normalized, gain-independent, and comparable data, even if the acquisition was done at different device gain levels. Most important, the PLATERO embeds a Linearity and Bias Analysis that provides an assessment of the uncertainty of the model estimations, and a Reproducibility and Repeatability analysis that evaluates the sources of variability originating from the measurements and the equipment. All the functions used to build the model, exploit it with new data, and perform the uncertainty and variability assessment are available in an open access repository.

Keywords: fluorescence measurements; measurement data standardization; measurement system analysis; plate reader; units conversion model.

FIGURE 1

(A) The PLATERO calibration model brings the experimental measurements into a common gain-independent domain using standard concentration MELF units. The calibration protocol embeds a Measurement System Analysis providing estimation for the uncertainty that can be expected on the predicted concentration value, and an assessment of the plate reader being used and the sources of uncertainty. (B) Diagram of the procedure to retrieve concentration values from observed fluorescence (F _observed ). The F _observed values are a function (f _G ) of the medium fluorescence (F _BLK ), the fluorescence of the reporter (F _reporter ), and the gain (G) at which fluorescence values are measured. Once the gain and background effects are removed, the F _reporter values are retrieved. The units conversion function (f _UC ) transforms these corrected fluorescence values into standard concentration units.

FIGURE 2

Schema representing the assessment on the proposed model done by a model building and a model validation step. Particularly, eleven out of the sixteen wells $(\approx 70\%)$ for each concentration level were randomly selected for the Model Building step, and the rest were used for the Model Validation.

FIGURE 3

Calibration data set before and after correction with Eq. 4. (A) Scatter plot of concentration vs. the raw original values (F _observed ). (B) Scatter plot of concentration vs. corrected fluorescence values (F _reporter ) using Eq. 4, assuming the exponential gain effect from Eq. 2, with a dashed line indicating the linear relationship described by the corrected values.

FIGURE 4

(A) Scatter plot of the scaled bias values, where black dots represent every scaled bias value and red squares are the mean scaled bias value for each concentration level. (B) Normal probability plot of the residuals quantifying the uncertainty using the scaling of the residuals (Eq. 12) by the concentration values. The red dashed line represents the ideal curve described by residuals perfectly following a normal distribution. Black crosses are the scaled residuals for every data point in the Model Building subset.

FIGURE 5

Analyses of the validation data set. (A) R&R analysis for the validation dataset. The total variability is decomposed into the Part–to–Part $({\sigma }_{\mathit{P2P}}^2)$ and the Measurement System contribution. In turn, the Measurement System contribution contains both Repeatability plus Reproducibility values. The Part-to-Part variability represents the differences between $\widehat{C}$ values for different wells with the same fluorescein concentration. The Reproducibility (Gain) variability $({\sigma }_{\mathit{Reprod}}^2)$ represents the differences between concentration values for the same measurement recorded at different gain levels. (B) L&B analysis for the validation data set, illustrating the scattering of the scaled bias values (black dots) for each Concentration⁻¹ level. The plot illustrates also if there is a tendency between average values of the scaled bias (red squares) and the Concentration⁻¹.

FIGURE 6

Confidence Intervals (95%) for the concentration values (shaded area) and reference concentration values (dashed line). Each row refers to one concentration level, the same ones as in the Model Building step, measured also at the same gains but from different wells. Each column corresponds to a different well and its location on the 96-well plate. For each well, we had a total of 32 (8 repetitions × 4 gains) predictions of $\widehat{C}$ .

FIGURE 7

Observed fluorescence values (F _observed ) for all wells of the validation data set containing the C _T = 0.039063 μM concentration level, measured at four different gain levels. The horizontal axes indicate the specific well yielding the F _observed measurements.

FIGURE 8

Results obtained with after using Calibration data set before and after correction with Eq. 27. (A) F _reporter values assuming a linear effect of the gain on the fluorescence measurements. Marker shapes and colors depend on the Gain level G used. (B) Normal probability plot of the scaled residuals after using the f _G expression from Eq. 27 to predict the concentration. R&R (C) and L&B (D) analyses of the validation data set after using the f _G correction from Eq. 27.

FIGURE 9

R&R (A) and L&B analysis (B) for a dataset with concentration values outside the calibration range used for the model building.

FIGURE 10

95% Confidence Intervals for the concentration values outside the model buildings’ concentration range (shaded area) and reference concentration values (dashed line). Each row refers to one concentration level. Each column corresponds to a well’s location on the 96-well plate.

FIGURE 11

Observed fluorescence values (F _observed ) for all wells in the 96-well plate with concentration values outside the calibration range used for the model building. Each row refers to one concentration level. Each plot contains the F _observed values recorded at a certain Gain level. The horizontal axes indicate the specific well identity (ID) yielding the F _observed measurements.

FIGURE 12

R&R analyses for the validation data sets measured with different plate readers and experimental procedures.