In ec363/fpcountr: Fluorescent Protein Calibration For Plate Readers

knitr::opts_chunk$set(eval = FALSE)
knitr::opts_chunk$set(echo = TRUE)

Path length determination is a key step in working out protein concentrations from absorbance data with process_absorbance_spectrum().

As absorbance depends on the path length, and microplate readers necessitate that absorbance readings are carried out from bottom to top, the path length of the sample is not fixed as it is in a cuvette or Nanodrop. Instead, it depends on a number of other factors, such as the volume used, the composition of the buffer, and the temperature.

Consider this code from the 'Getting Started' vignette: the path length correction method pl_method, along with three helper parameters (buffer_used, concentration_used and temperature_used) need to be specified for path length estimation.

# Process spectra
processed_data_spectrum <- process_absorbance_spectrum(

  # basics
  spectrum_csv = "data/example_absorbance_parsed.csv",
  subset_rows = TRUE, rows_to_keep = c("A","B"), columns_to_keep = c(1:12),
  xrange = c(250,1000),

  # path length calcs
  pl_method = "calc_blanks",
  buffer_used = "TBS", concentration_used = 0.005, temperature_used = 30,

  # saving
  outfolder = "fp_quantification"
)

Estimating Path Length

There are 2 methods for estimating path length in fpcountr. The first relies on measurements within the absorbance data, and the second relies on the sample's volume.

(1) Estimating Path Length Using Infrared Wavelengths (K-Factors)

The path length of a sample in a well may be estimated from its absorbance readings in the infrared range, and the k-factor of the same buffer at the same temperature.

The k-factor of an aqueous buffer is the observed difference between its absorbance at 975 nm and its absorbance at 900 nm.

The path length of a sample may be estimated by taking the ratio of the measured k-factor in the sample vs the known k-factor of the same buffer at 1cm path length. Therefore, in order to calculate path lengths, we need:

known k-factor of the same buffer at 1cm path length: a reference dataset on k-factors of a range of buffers
measured k-factor in the sample: data on sample absorbance at 900-975nm, information about the identity of the buffer used, its concentration, and the temperature of the assay

Reference k-factors dataset

fpcountr uses reference datasets from Thermo Fisher.

The first is a dataset of k-factors of a range of buffers:

data_to_display <- fpcountr::kfactors_buffers_data
data_to_display |>
  gt::gt() |>
  # TABLE HEADER
  # header style
  gt::tab_style(
    locations = gt::cells_column_labels(),
    style = list(
      gt::cell_text(size = "small"),
      gt::cell_text(weight = "bold")
    )
  ) |>
  # TABLE BODY
  # font smaller
  gt::tab_style(
    locations = gt::cells_body(
      columns = tidyselect::everything()
    ),
    style = list(
      gt::cell_text(size = "small")
    )
  )

Notice that not all buffers are represented and we need to pick the closest match. For our calibrations, we used a buffer consisting of 5 mM Tris and 15 mM NaCl, so we chose buffer_used = "TBS" and concentration_used = 0.005 (M).

The second lists how the k-factor changes with temperature:

data_to_display <- fpcountr::kfactors_temperature_data
data_to_display |>
  gt::gt() |>
  # TABLE HEADER
  # header style
  gt::tab_style(
    locations = gt::cells_column_labels(),
    style = list(
      gt::cell_text(size = "small"),
      gt::cell_text(weight = "bold")
    )
  ) |>
  # TABLE BODY
  # font smaller
  gt::tab_style(
    locations = gt::cells_body(
      columns = tidyselect::everything()
    ),
    style = list(
      gt::cell_text(size = "small")
    )
  )

Run the view_kfactors() function (as is) to get these datasets printed in the console. Use them to help decide what to add for buffer_used and what units to use for concentration_used.

# message("\nThe k-factor of water (A975-A900 at 1cm) at ~25oC is 0.172.")
# message("Increasing the temperature has a small effect: 30oC = 3% increase to 0.176.")
# message("The volume of water is minimally effected by temperature, so path lengths calculated at 25oC should apply to other temperatures.")
# 
# message("\nMost aqueous buffers with low salt will be ~ 0.170 and can therefore be approximated to the k-factor of pure water.")
# message("eg.")
# message("153mM (0.9%) NaCl = 0.168, TE = 0.169, 50mM TBS = 0.166")
# message("1M Tris-HCl = 0.157, 2M H2SO4 = 0.154")
# 
# message("\nOther solvents, like DMSO, EtOH and MeOH have a bigger effect.")
# message("eg.")
# message("10% DMSO = 0.148")
# message("20% EtOH = 0.092, 20% MeOH = 0.100")
# message("100% EtOH and MeOH have negative k-factors, and k-factors with these solvents are no longer reliable methods for calculating path lengths.")

When to use `"calc_each"` vs `"calc_blanks"`

To request path length calculation via this method you have two options:

Use pl_method = "calc_each" to estimate pathlength of each well individually.
Use pl_method = "calc_blanks" to estimate pathlength of all wells from an average of the blank wells. This is usually recommended.

(2) Estimating Path Length Using Sample Volume

To request path length estimation via the volume, use pl_method = "volume".

The volume method calculates path length using a reference experiment in which a microplate was filled with specified volumes of water (50-300 ul), and the path lengths of each were measured and fitted to a linear model.

df <- fpcountr::pathlength_water_data

df <- df |>
  dplyr::group_by(volume) |>
  dplyr::mutate(mean = mean(pathlength, na.rm = TRUE)) |>
  dplyr::mutate(sd = sd(pathlength, na.rm = TRUE) )

model <- stats::lm(mean ~ volume, data = df)

data_to_display <- df
ggplot2::ggplot(data_to_display) +
  ggplot2::geom_point(ggplot2::aes(x = volume, y = pathlength, colour = expt)) +
  # ggplot2::geom_errorbar(ggplot2::aes(x = volume, ymin = mean-sd, ymax = mean+sd, colour = expt)) +
  ggplot2::geom_line(ggplot2::aes(x = .data$volume,
                                  y = stats::predict(model, df))) +
  ggplot2::scale_x_continuous("volume (ul)", limits=c(0,NA)) +
  ggplot2::scale_y_continuous("pathlength (cm)", limits=c(0,NA)) +
  ggplot2::scale_colour_manual(values = c("black", "black", "black")) +
  ggplot2::theme_bw() +
  ggplot2::theme(
    aspect.ratio = 1,
    panel.grid = ggplot2::element_blank(),
    legend.position = "none"
  )