Calculation of the melting temperatures (Tm, Tm1D2 and Tm2D2) from the first and the second derivative

Description

diffQ2() calls instances of diffQ() to calculate the Tm1D2 and Tm2D2. The options are similar to diffQ(). Both diffQ() and diffQ2() return objects of the class list. To accessing components of lists is done as described elsewhere either be name or by number. diffQ2 has no standalone plot function. For sophisticated analysis and plots its recommended to use diffQ2 as presented in the examples as part of algorithms.

Usage

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diffQ2(xy, fct = max, fws = 8, col = 2, plot = FALSE, verbose = FALSE,
  peak = FALSE, deriv = FALSE, negderiv = TRUE, derivlimits = FALSE,
  derivlimitsline = FALSE, vertiline = FALSE, rsm = FALSE,
  inder = FALSE, warn = TRUE)

Arguments

xy

is a data.frame containing in the first column the temperature and in the second column the fluorescence values. Preferably the output from mcaSmoother is used.

fct

accepts min or max as option and is used to define whether to find a local minimum (“negative peak”) or local maximum (“positive peak”).

fws

defines the number (n) of left and right neighbors to use for the calculation of the quadratic polynomial.

col

is a graphical parameter used to define the length of the line used in the plot.

plot

shows a plot of a single melting curve with (Tm) as vertical line and the second derivatives (Tm1D2 and Tm2D2). To draw multiple curves in a single plot set plot = FALSE and create and empty plot instead (see examples).

verbose

shows additional information (e.g., first and second approximate derivatives, ranges used for calculation, approximate Tm, Tm1D2, Tm2D2) of the calculation.

peak

shows the peak in the plot.

deriv

shows the first derivative with the color assigned to col (see examples).

negderiv

calculates the negative derivative (default). If FALSE the positive first negative is calculated.

derivlimits

shows the number (n) used to calculate the Tm as points in the plot (see examples).

derivlimitsline

shows the number (n) used to calculate the Tm as line in the plot (see examples).

vertiline

draws a vertical line at the Tms (see examples).

rsm

performs a doubling of the temperature resolution by calculation of the mean temperature and mean fluorescence between successive temperature steps. Note: mcaSmoother has the "n" parameter with a similar but advanced functionality.

inder

Interpolates derivatives using the five-point stencil. See chipPCR package for details.

warn

diffQ tries to keep the user as informed as possible about the quality of the analysis. However, in some scenarios are the warning and message about analysis not needed or disturbing. warn can be used to stop the flodding of the output.

Value

$TmD1

TmD1 returns a comprehensive list (if parameter verbose is TRUE) with results from the first derivative. The list includes a data.frame of the derivative ("xy"). The temperature range ("limits.xQ") and fluorescence range ("limits.diffQ") to calculate the peak value. "fluo.x" is the approximate fluorescence at the approximate melting temperature. The calculated melting temperature ("Tm") with the corresponding fluorescence intensity ("fluoTm"). The number of points ("fws") and the adjusted R-squared ("adj.r.squared") to fit.

$TmD1$Tm

returns the calculated melting temperature ("Tm") from the first derivative.

$TmD1$fluoTm

returns the calculated fluorescence at the calculated melting temperature ("Tm").

$TmD1$Tm.approx

returns the approximate melting temperature ("Tm") from the first derivative.

$TmD1$fluo.x

returns the approximate fluorescence at the calculated melting temperature ("Tm").

$TmD1$xy

is a data.frame containing in the first column the temperature and in the second column the fluorescence values. Preferably the output from mcaSmoother is used.

$TmD1$limits.xQ

returns a data range of temperature values used to calculate the melting temperature.

$TmD1$limits.diffQ

returns a data range of fluorescence values used to calculate the melting temperature.

$TmD1$adj.r.squared

returns the adjusted R-squared from the quadratic model fitting function (see also fit) of the first derivative.

$TmD1$NRMSE

returns the normalized root-mean-squared-error (NRMSE) from the quadratic model fitting function (see also fit) of the first derivative.

$TmD1$fws

returns the number of points used for the calculation of the melting temperature of the first derivative.

$TmD1$devsum

returns measures to show the difference between the approximate and calculated melting temperature of the first derivative.

$TmD1$fit

returns the summary of the results of the quadratic model fitting function of the first derivative.

$Tm1D2

returns the "left" melting temperature ("Tm1D2 ") values from the second derivative.

$Tm1D2$Tm

returns the "left" calculated melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$fluoTm

returns the "left" calculated fluorescence at the calculated melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$Tm.approx

returns the "left" approximate melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$fluo.x

returns the "left" approximate fluorescence at the calculated melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$xy

is a data.frame containing in the first column the temperature and in the second column the fluorescence values of the "left" melting temperature ("Tm1D2") from the second derivative. Preferably the output from mcaSmoother is used.

$Tm1D2$limits.xQ

returns a data range of temperature values used to calculate the melting temperature of the "left" melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$limits.diffQ

returns a data range of fluorescence values used to calculate the melting temperature of the "left" melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$adj.r.squared

returns the adjusted R-squared from the quadratic model fitting function (see also fit) of the "left" melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$NRMSE

returns normalized root-mean-squared-error (NRMSE) from the quadratic model fitting function (see also fit) of the "left" melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$fws

returns the number of points used for the calculation of the melting temperature of the "left" melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$devsum

returns measures to show the difference between the approximate and alculated melting temperature of the "left" melting temperature ("Tm1D2") from the second derivative.

$Tm1D2$fit

returns the summary of the results of the quadratic model fitting function of the "left" melting temperature ("Tm1D2") from the second derivative.

$Tm2D2

returns the "right" melting temperature ("Tm2D2 ") values from the second derivative.

$Tm2D2$Tm

returns the "right" calculated melting temperature ("Tm2D2") from the second derivative.

$Tm2D2$fluoTm

returns the "right" calculated fluorescence at the calculated melting temperature ("Tm2D2") from the second derivative.

$Tm2D2$Tm.approx

returns the "right" approximate melting temperature ("Tm1D2") from the second derivative.

$Tm2D2$fluo.x

returns the "left" approximate fluorescence at the calculated melting temperature ("Tm2D2") from the second derivative.

$Tm2D2$xy

is a data.frame containing in the first column the temperature and in the second column the fluorescence values of the "right" melting temperature ("Tm2D2") from the second derivative. Preferably the output from mcaSmoother is used.

$Tm2D2$limits.xQ

returns a data range of temperature values used to calculate the melting temperature of the "right" melting temperature ("Tm2D2") from the second derivative.

$Tm2D2$limits.diffQ

returns a data range of fluorescence values used to calculate the melting temperature of the "right" melting temperature ("Tm"D2") from the second derivative.

$Tm2D2$adj.r.squared

returns the adjusted R-squared from the quadratic model fitting function (see also fit) of the "right" melting temperature ("Tm2D2") from the second derivative.

$Tm2D2$NRMSE

returns normalized root-mean-squared-error (NRMSE) from the quadratic model fitting function (see also fit) of the "right" melting temperature ("Tm2D2") from the second derivative.

$Tm2D2$fws

returns the number of points used for the calculation of the melting temperature of the "right" melting temperature ("Tm2D2") from the second derivative.

$Tm2D2$devsum

returns measures to show the difference between the approximate and calculated melting temperature of the "right" melting temperature ("Tm2D2") from the second derivative.

$Tm2D2$fit

returns the summary of the results of the quadratic model fitting function of the "right" melting temperature ("Tm2D2") from the second derivative.

$xTm1.2.D2

returns only the "left" and right calculated melting temperature ("Tm1D2, Tm2D2") from the second derivative.

$yTm1.2.D2

returns only the "left" and right calculated fluorescence ("Tm1D2, Tm2D2") from the second derivative.

$temperature

returns measures to investigate the temperature resolution of the melting curve. Raw fluorescence measurements at irregular temperature resolutions (intervals) can introduce artifacts and thus lead to wrong melting point estimations.

$temperature$T.delta

returns the difference between two successive temperature steps.

$temperature$mean.T.delta

returns the mean difference between two temperature steps.

$temperature$sd.T.delta

returns the standard deviation of the temperature.

$temperature$RSD.T.delta

returns the relative standard deviation (RSD) of the temperature in percent.

Author(s)

Stefan Roediger

References

A Highly Versatile Microscope Imaging Technology Platform for the Multiplex Real-Time Detection of Biomolecules and Autoimmune Antibodies. S. Roediger, P. Schierack, A. Boehm, J. Nitschke, I. Berger, U. Froemmel, C. Schmidt, M. Ruhland, I. Schimke, D. Roggenbuck, W. Lehmann and C. Schroeder. Advances in Biochemical Bioengineering/Biotechnology. 133:33–74, 2013. http://www.ncbi.nlm.nih.gov/pubmed/22437246

Nucleic acid detection based on the use of microbeads: a review. S. Roediger, C. Liebsch, C. Schmidt, W. Lehmann, U. Resch-Genger, U. Schedler, P. Schierack. Microchim Acta 2014:1–18. DOI: 10.1007/s00604-014-1243-4

Roediger S, Boehm A, Schimke I. Surface Melting Curve Analysis with R. The R Journal 2013;5:37–53.

See Also

diffQ, mcaSmoother

Examples

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# First Example
# Plot the first and the second derivative melting curves of MLC-2v
# for a single melting curve. Should give a warning message but the graph
# will show you that the calculation is ok
data(MultiMelt)
tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14])
diffQ2(tmp, fct = min, verbose = FALSE, plot = TRUE)

# Second Example
# Calculate the maximum fluorescence of a melting curve, Tm,
# Tm1D2 and Tm2D2 of HPRT1 for 12 microbead populations and assign the
# values to the matrix HPRT1
data(MultiMelt)
HPRT1 <- matrix(NA,12,4,
	dimnames = list(colnames(MultiMelt[, 2L:13]),
	    c("Fluo", "Tm", "Tm1D2", "Tm2D2")))
for (i in 2L:13) {
       tmp <- mcaSmoother(MultiMelt[, 1],
                     MultiMelt[, i])
       tmpTM <- diffQ2(tmp, fct = min, verbose = TRUE)
       HPRT1[i-1, 1] <- max(tmp$y)
       HPRT1[i-1, 2] <- tmpTM$TmD1$Tm
       HPRT1[i-1, 3] <- tmpTM$Tm1D2$Tm
       HPRT1[i-1, 4] <- tmpTM$Tm2D2$Tm
}
HPRT1

# Third Example
# Use diffQ2 to determine the second derivative.

data(MultiMelt)
HPRT1 <- matrix(NA,12,4,
	dimnames = list(colnames(MultiMelt[, 2L:13]),
	    c("Fluo", "Tm", "Tm1D2", "Tm2D2")))
for (i in 2L:13) {
       tmp <- mcaSmoother(MultiMelt[, 1],
                     MultiMelt[, i])
       tmpTM <- diffQ2(tmp, fct = min, verbose = TRUE)
       HPRT1[i-1, 1] <- max(tmp[["y.sp"]])
       HPRT1[i-1, 2] <- tmpTM[["TmD1"]][["Tm"]]
       HPRT1[i-1, 3] <- tmpTM[["Tm1D2"]][["Tm"]]
       HPRT1[i-1, 4] <- tmpTM[["Tm2D2"]][["Tm"]]
}
plot(HPRT1[, 1], HPRT1[, 2],
       xlab = "refMFI", ylab = "Temperature",
       main = "HPRT1", xlim = c(2.1,2.55),
       ylim = c(72,82), pch = 19,
       col = 1:12, cex = 1.8)
points(HPRT1[, 1], HPRT1[, 3], pch = 15)
points(HPRT1[, 1], HPRT1[, 4], pch = 15)
abline(lm(HPRT1[, 2] ~ HPRT1[, 1]))
abline(lm(HPRT1[, 3] ~ HPRT1[, 1]))
abline(lm(HPRT1[, 4] ~ HPRT1[, 1]))

# Fourth Example
# Use diffQ2 with inder parameter to determine the second derivative.
data(MultiMelt)

tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14])
diffQ2(tmp, fct = min, verbose = FALSE, plot = TRUE, inder = FALSE)
diffQ2(tmp, fct = min, verbose = FALSE, plot = TRUE, inder = TRUE)
par(mfrow = c(1,1))