Package 'MBmca' reference manual

Title:	Nucleic Acid Melting Curve Analysis
Description:	Lightweight utilities for nucleic acid melting curve analysis are important in life sciences and diagnostics. This software can be used for the analysis and presentation of melting curve data from microbead-based assays (surface melting curve analysis) and reactions in solution (e.g., quantitative PCR (qPCR), real-time isothermal Amplification). Further information are described in detail in two publications in The R Journal [ <https://journal.r-project.org/archive/2013-2/roediger-bohm-schimke.pdf>; <https://journal.r-project.org/archive/2015-1/RJ-2015-1.pdf>].
Authors:	Stefan Roediger [cre, aut] , Michal Burdukiewicz [aut]
Maintainer:	Stefan Roediger <[email protected]>
License:	GPL (>= 2)
Version:	1.0.1
Built:	2024-10-12 05:56:14 UTC
Source:	https://github.com/pcruniversum/mbmca

Microbead Surface Nucleic Acid Melting Curve Analysis

Description

Nucleic acid Melting Curve Analysis is a powerful method to investigate the interaction of double stranded nucleic acids. The MBmca package provides data sets and lightweight utilities for nucleic acid melting curve analysis and presentation on microbead surfaces. However, the function of the package can also be used for the analysis of reactions in solution (e.g., qPCR). Methods include melting curve data preprocessing (smooth, normalize, rotate, background subtraction), data inspection (comparison of multiplex melting curves) with location parameters (mean, median), deviation parameters (standard of the melting peaks including the second derivative. The second derivative melting peaks is implemented as parameter to further characterize the melting behavior. Plot functions to illustrate data quality, smoothed curves and derivatives are available too.

Author(s)

Stefan Roediger <[email protected]>

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. 133:35–74, 2013. https://pubmed.ncbi.nlm.nih.gov/22437246/

Surface Melting Curve Analysis with R. S. Roediger, A. Boehm and I. Schimke. The R Journal. 5(2):37–52, 2013.

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

Calculation of the melting temperature (Tm) from the first derivative

Description

diffQ is used to calculate the melting temperature (Tm) but also for elementary graphical operations (e.g., show the Tm or the derivative). It does not require smoothed data for the MCA. The parameter rsm can be used to double the temperature resolution by calculation of the mean temperature and mean fluorescence. Note: mcaSmoother has the n parameter with a similar functionality. First the approximate Tm is determined as the min() and/or max() from the first derivative. The first numeric derivative (Forward Difference) is estimated from the values of the function values obtained during an experiment since the exact function of the melting curve is unknown. The method used in diffQ is suitable for independent variables that are equally and unequally spaced. Alternatives for the numerical differentiation include Backward Differences, Central Differences or Three-Point (Forward or Backward) Difference based on Lagrange Estimation (currently not implemented in diffQ). The approximate peak value is the starting-point for a function based calculation. The function takes a defined number n (maximum 8) of the left and the right neighbor values and fits a quadratic polynomial. The quadratic regression of the X (temperature) against the Y (fluorescence) range gives the coefficients. The optimal quadratic polynomial is chosen based on the highest adjusted R-squared value. diffQ returns an objects of the class list. To accessing components of lists is done as described elsewhere either by name or by number. diffQ has a simple plot function. However, for sophisticated analysis and plots its recommended to use diffQ as presented in the examples as part of algorithms.

Usage

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

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. 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., approximate derivative, ranges used for calculation, approximate Tm) of the calculation.
`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 swapping of the output.
`peak`	shows the peak in the plot (see examples).
`negderiv`	uses the positive first derivative instead of the negative.
`deriv`	shows the first derivative with the color assigned to `col` (see examples).
`derivlimits`	shows the neighbors (fws) used to calculate the Tm as points in the plot (see examples).
`derivlimitsline`	shows the neighbors (fws) 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 first derivatives using the five-point stencil. See `chipPCR` package for details.

Value

`diffQ()`	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 neighbors ("fws"), the adjusted R-squared ("adj.r.squared") and the normalized-root-mean-squared-error ("NRMSE") to fit. The quality of the calculated melting temperature ("Tm") can be checked with devsum which reports the relative deviation (in percent) between the approximate melting temperature and the calculated melting temperature, if NRMSE is less than 0.08 and the adjusted R-squared is less than 0.85. A relative deviation larger than 10 percent will result in a warning. Reducing fws might improve the result.
`Tm`	returns the calculated melting temperature ("Tm").
`fluoTm`	returns the calculated fluorescence at the calculated melting temperature.
`Tm.approx`	returns the approximate melting temperature.
`fluo.x`	returns the approximate fluorescence at the calculated melting temperature.
`xy`	returns the approximate derivative value used for the calculation of the melting peak.
`limits.xQ`	returns a data range of temperature values used to calculate the melting temperature.
`limits.diffQ`	returns a data range of fluorescence values used to calculate the melting temperature.
`adj.r.squared`	returns the adjusted R-squared from the quadratic model fitting function (see also `fit`).
`NRMSE`	returns the normalized root-mean-squared-error (NRMSE) from the quadratic model fitting function (see also `fit`).
`fws`	returns the number of points used for the calculation of the melting temperature.
`devsum`	returns measures to show the difference between the approximate and calculated melting temperature.
`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.
`fit`	returns the summary of the results of the quadratic model fitting function.

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. https://pubmed.ncbi.nlm.nih.gov/22437246/

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

Roediger S et al. R as an Environment for the Reproducible Analysis of DNA Amplification Experiments. The R Journal 2015;7:127–150.

Examples


# First Example
# Plot the first derivative of different samples for single melting curve
# data. Note that the argument "plot" is TRUE.

default.par <- par(no.readonly = TRUE)

data(MultiMelt)
par(mfrow = c(1,2))
sapply(2L:14, function(i) {
        tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, i])
        diffQ(tmp, plot = TRUE)
  }
)
par(mfrow = c(1,1))
# Second example
# Plot the first derivative of different samples from MultiMelt
# in a single plot.
data(MultiMelt)

# First create an empty plot
plot(NA, NA, xlab = "Temperature", ylab ="-d(refMFI)/d(T)",
        main = "Multiple melting peaks in a single plot", xlim = c(65,85),
        ylim = c(-0.4,0.01), pch = 19, cex = 1.8)
# Prepossess the selected melting curve data (2,6,12) with mcaSmoother 
# and apply them to diffQ. Note that the argument "plot" is FALSE
# while other arguments like derivlimitsline or peak are TRUE. 
sapply(c(2,6,12), function(i) {
	tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, i], 
			    bg = c(41,61), bgadj = TRUE)
	diffQ(tmp, plot = FALSE, derivlimitsline = TRUE, deriv = TRUE, 
	      peak = TRUE, derivlimits = TRUE, col = i, vertiline = TRUE)
  }
)
legend(65, -0.1, colnames(MultiMelt[, c(2,6,12)]), pch = c(15,15,15), 
	col = c(2,6,12))

# Third example
# First create an empty plot
plot(NA, NA, xlim = c(50,85), ylim = c(-0.4,2.5), 
     xlab = "Temperature", 
     ylab ="-refMFI(T) | refMFI'(T) | refMFI''(T)",
     main = "1st and 2nd Derivatives", 
     pch = 19, cex = 1.8)

# Prepossess the selected melting curve data with mcaSmoother 
# and apply them to diffQ and diffQ2. Note that 
# the argument "plot" is FALSE while other 
# arguments like derivlimitsline or peak are TRUE.

tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 2], 
		    bg = c(41,61), bgadj = TRUE)
lines(tmp, col= 1, lwd = 2)

# Note the different use of the argument derivlimits in diffQ and diffQ2
diffQ(tmp, fct = min, derivlimitsline = TRUE, deriv = TRUE, 
	    peak = TRUE, derivlimits = FALSE, col = 2, vertiline = TRUE)
diffQ2(tmp, fct = min, derivlimitsline = TRUE, deriv = TRUE, 
	    peak = TRUE, derivlimits = TRUE, col = 3, vertiline = TRUE)

# Add a legend to the plot
legend(65, 1.5, c("Melting curve",
		  "1st Derivative", 
		  "2nd Derivative"), 
		  pch = c(19,19,19), col = c(1,2,3))

# Fourth example
# Different curves may potentially have different quality in practice. 
# For example, using data from MultiMelt should return a 
# valid result and plot.
data(MultiMelt)

diffQ(cbind(MultiMelt[, 1], MultiMelt[, 2]), plot = TRUE)$Tm
# limits_xQ
#  77.88139

# Imagine an experiment that went terribly wrong. You would 
# still get an estimate for the Tm. The output from diffQ, 
# with an error attached, lets the user know that this Tm 
# is potentially meaningless. diffQ() will give several 
# warning messages.

set.seed(1)
y = rnorm(55,1.5,.8)
diffQ(cbind(MultiMelt[, 1],y), plot = TRUE)$Tm

# The distribution of the curve data indicates noise.
# The data should be visually inspected with a plot 
# (see examples of diffQ). The Tm calculation (fit, 
# adj. R squared ~ 0.157, NRMSE ~ 0.279) is not optimal 
# presumably due to noisy data. Check raw melting 
# curve (see examples of diffQ).
# Calculated Tm 
#      56.16755


# Sixth example
# Curves may potentially have a low temperature resolution. The rsm 
# parameter can be used to double the temperature resolution.
# Use data from MultiMelt column 15 (MLC2v2).
data(MultiMelt)
tmp <- cbind(MultiMelt[, 1], MultiMelt[, 15])

# Use diffQ without and with the rsm parameter and plot
# the results in a single row
par(mfrow = c(1,2))

diffQ(tmp, plot = TRUE)$Tm
  text(60, -0.15, "without rsm parameter")

diffQ(tmp, plot = TRUE, rsm = TRUE)$Tm
  text(60, -0.15, "with rsm parameter")
par(default.par)

# First Example
# Plot the first derivative of different samples for single melting curve
# data. Note that the argument "plot" is TRUE.

default.par <- par(no.readonly = TRUE)

data(MultiMelt)
par(mfrow = c(1,2))
sapply(2L:14, function(i) {
        tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, i])
        diffQ(tmp, plot = TRUE)
  }
)
par(mfrow = c(1,1))
# Second example
# Plot the first derivative of different samples from MultiMelt
# in a single plot.
data(MultiMelt)

# First create an empty plot
plot(NA, NA, xlab = "Temperature", ylab ="-d(refMFI)/d(T)",
        main = "Multiple melting peaks in a single plot", xlim = c(65,85),
        ylim = c(-0.4,0.01), pch = 19, cex = 1.8)
# Prepossess the selected melting curve data (2,6,12) with mcaSmoother 
# and apply them to diffQ. Note that the argument "plot" is FALSE
# while other arguments like derivlimitsline or peak are TRUE. 
sapply(c(2,6,12), function(i) {
	tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, i], 
			    bg = c(41,61), bgadj = TRUE)
	diffQ(tmp, plot = FALSE, derivlimitsline = TRUE, deriv = TRUE, 
	      peak = TRUE, derivlimits = TRUE, col = i, vertiline = TRUE)
  }
)
legend(65, -0.1, colnames(MultiMelt[, c(2,6,12)]), pch = c(15,15,15), 
	col = c(2,6,12))

# Third example
# First create an empty plot
plot(NA, NA, xlim = c(50,85), ylim = c(-0.4,2.5), 
     xlab = "Temperature", 
     ylab ="-refMFI(T) | refMFI'(T) | refMFI''(T)",
     main = "1st and 2nd Derivatives", 
     pch = 19, cex = 1.8)

# Prepossess the selected melting curve data with mcaSmoother 
# and apply them to diffQ and diffQ2. Note that 
# the argument "plot" is FALSE while other 
# arguments like derivlimitsline or peak are TRUE.

tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 2], 
		    bg = c(41,61), bgadj = TRUE)
lines(tmp, col= 1, lwd = 2)

# Note the different use of the argument derivlimits in diffQ and diffQ2
diffQ(tmp, fct = min, derivlimitsline = TRUE, deriv = TRUE, 
	    peak = TRUE, derivlimits = FALSE, col = 2, vertiline = TRUE)
diffQ2(tmp, fct = min, derivlimitsline = TRUE, deriv = TRUE, 
	    peak = TRUE, derivlimits = TRUE, col = 3, vertiline = TRUE)

# Add a legend to the plot
legend(65, 1.5, c("Melting curve",
		  "1st Derivative", 
		  "2nd Derivative"), 
		  pch = c(19,19,19), col = c(1,2,3))

# Fourth example
# Different curves may potentially have different quality in practice. 
# For example, using data from MultiMelt should return a 
# valid result and plot.
data(MultiMelt)

diffQ(cbind(MultiMelt[, 1], MultiMelt[, 2]), plot = TRUE)$Tm
# limits_xQ
#  77.88139

# Imagine an experiment that went terribly wrong. You would 
# still get an estimate for the Tm. The output from diffQ, 
# with an error attached, lets the user know that this Tm 
# is potentially meaningless. diffQ() will give several 
# warning messages.

set.seed(1)
y = rnorm(55,1.5,.8)
diffQ(cbind(MultiMelt[, 1],y), plot = TRUE)$Tm

# The distribution of the curve data indicates noise.
# The data should be visually inspected with a plot 
# (see examples of diffQ). The Tm calculation (fit, 
# adj. R squared ~ 0.157, NRMSE ~ 0.279) is not optimal 
# presumably due to noisy data. Check raw melting 
# curve (see examples of diffQ).
# Calculated Tm 
#      56.16755


# Sixth example
# Curves may potentially have a low temperature resolution. The rsm 
# parameter can be used to double the temperature resolution.
# Use data from MultiMelt column 15 (MLC2v2).
data(MultiMelt)
tmp <- cbind(MultiMelt[, 1], MultiMelt[, 15])

# Use diffQ without and with the rsm parameter and plot
# the results in a single row
par(mfrow = c(1,2))

diffQ(tmp, plot = TRUE)$Tm
  text(60, -0.15, "without rsm parameter")

diffQ(tmp, plot = TRUE, rsm = TRUE)$Tm
  text(60, -0.15, "with rsm parameter")
par(default.par)

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 it is recommended to use diffQ2 as presented in the examples as part of algorithms.

Usage

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
)
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 swapping 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 calculated 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. https://pubmed.ncbi.nlm.nih.gov/22437246/

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

Roediger S et al. R as an Environment for the Reproducible Analysis of DNA Amplification Experiments. The R Journal 2015;7:127–150.

Examples


default.par <- par(no.readonly = TRUE)
# 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(default.par)

default.par <- par(no.readonly = TRUE)
# 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(default.par)

Bimodal melting curve experiment on the surface of microbeads.

Description

A melting curve experiment with six microbead populations and short oligonucleotide probes (direct hybridization). Detection probes for human VIM (vimentin), MLC-2v (myosin regulatory light chain 2, ventricular/cardiac muscle isoform), SERCA2 (Atp2a2 - ATPase, Calcium-transporting ATPase sarcoplasmic reticulum type, slow twitch skeletal muscle isoform), HRPT1 (hyperparathyroidism 1) and the artificial sequences Poly(dA)20 (20 nt of dA) and aCS (artificial Control Sequence).

Format

A data frame with the melting curves of six different capture and detection probe pairs on six microbeads populations for VIM, MLC-2v, SERCA2, Poly(dA)20, aCS and HPRT1. First column contains the temperature (in degree Celsius, 1 degree Celsius per step) followed by melting curves of VIM, MLC-2v, SERCA2, Poly(dA)20, aCS and HPRT1 with bimodal melting pattern. The dyes and quencher used were Atto 647N and BHQ2.

T: a numeric vector, Temperature in degree Celsius.
VIM.no.Q: a numeric vector, VIM without quencher and without Poly(dT)20 region.
MLC2v.w.Q.w.dT20: a numeric vector, MLC-2v with quencher-labeled detection probe and fluorescent Poly(dA)20 detection probe.
SERCA2.no.Q.w.dT20: a numeric vector, SERCA2 without quencher-labeled detection probe and Poly(dA)20 detection probe.
PolydA20.w.Q: a numeric vector, Poly(dT)20 with fluorescent Poly(dA)20 detection probe (quencher labeled).
aCS.w.Q.w.dT20: a numeric vector, artificial Control Sequence without quencher-labeled detection probe and fluorescent Poly(dA)20 detection probe.
HPRT1.no.Q.w.dT20: a numeric vector, HPRT1 without quencher-labeled detection probe and fluorescent Poly(dA)20 detection probe.

Source

Data were measured with the VideoScan platform:

Surface Melting Curve Analysis with R. S. Roediger, A. Boehm and I. Schimke. The R Journal. 5(2):37–52, 2013.

Examples


data(DMP)

data(DMP)

Surface melting curve data from direct hybridization experiment of short oligonucleotide probes with bimodal melting curve pattern.

Description

A melting curve experiment with four microbead populations and short oligonucleotide probes (direct hybridization) and longer probes (dual-hybridization probes) capture probe. Detection probes for human VIM (vimentin), MLC-2v (myosin regulatory light chain 2, ventricular/cardiac muscle isoform) and SERCA2 (Atp2a2 - ATPase, Calcium-transporting ATPase sarcoplasmic reticulum type, slow twitch skeletal muscle isoform). One sequence of VIM contained a mutation at position 41.

Format

A data frame with the melting curves of three different capture and detection probe pairs for HRPT1 and MLC-2v. First column contains the temperature (in degree Celsius, 0.5 degree Celsius per step) followed by melting curves of HRPT1 on 12 microbead populations and melting curves of MLC-2v on 12 microbead populations.

T: a numeric vector, Temperature in degree Celsius.
MLC2v: a numeric vector, MLC-2v with quencher-labeled detection probe
SERCA2: a numeric vector, SERCA2 without quencher-labeled detection probe
VIM.w.Mutation: a numeric vector, mutated VIM with quencher-labeled detection probe
VIM.wo.Mutation: a numeric vector, native VIM with quencher-labeled detection probe

Details

The melting curve was conducted with short oligonucleotide probes (direct hybridization) and longer probes (dual-hybridization probes) on the surface of microbeads (sequences and materials according to Roediger et al. (2012)) using the VideoScan platform by Roediger et al. (2012). The dyes and quencher used were Atto 647N and BHQ2.

Source

Data were measured with the VideoScan platform:

Surface Melting Curve Analysis with R. S. Roediger, A. Boehm and I. Schimke. The R Journal. 5(2):37–52, 2013.

Examples


data(DualHyb)

data(DualHyb)

Function to estimate the approximate local minima and maxima of melting curve data.

Description

The mcaPeaks() is used to estimate the approximate local minima and maxima of melting curve data. This can be useful to define a temperature range for melting curve analysis, quality control of the melting curve or to define a threshold of peak heights. Melting curves may consist of multiple significant and insignificant melting peaks. mcaPeaks() uses estimated the temperatures and fluorescence values of the local minima and maxima. The original data remain unchanged and only the approximate local minima and maxima are returned. mcaPeaks() takes modified code proposed earlier by Brian Ripley (https://stat.ethz.ch/pipermail/r-help/2002-May/021934.html).

Usage

mcaPeaks(x, y, span = 3)
mcaPeaks(x, y, span = 3)

Arguments

`x`	`x` is the column of a data frame for the temperature.
`y`	`y` is the column of a data frame for the fluorescence values.
`span`	`span` is used to adjust the window span.

Value

`p.min`	returns a `data.frame` with the temperatures ("T (minima)") and the fluorescence ("F (minima)") for the local minima of the processed data.
`p.max`	returns a `data.frame` with the temperatures ("T (minima)") and the fluorescence ("F (minima)") for the local maxima of the processed data.

Author(s)

Stefan Roediger

Examples


# First Example
data(DMP)
# Smooth and Min-Max normalize melting curve data with mcaSmoother()
tmp <- mcaSmoother(DMP[, 1], DMP[,6], minmax = TRUE, n = 2)

# Extract the first derivative melting curve data
tmp.d <- diffQ(tmp, verbose = TRUE)$xy

# Determine the approximate local minima and maxima of a curve
peak.val <-mcaPeaks(tmp.d[, 1], tmp.d[, 2])
peak.val

# Plot the first derivative melting curve
# Add a horizontal line and points for the approximate local minima 
# and maxima to the plot
plot(tmp.d, type = "l", 
     main = "Show the approximate local minima and maxima of a curve")
  abline(h = 0)
  points(peak.val$p.min, col = 1, pch = 19)
  points(peak.val$p.max, col = 2, pch = 19)
  legend(25, 0.08, c("Minima", "Maxima"), col = c(1,2), pch = c(19,19))

# Second example
# Signifcant peaks can be distinguished by peak hight
plot(tmp.d, type = "l", 
      main = "Show the approximate local minima and maxima of a curve")
  abline(h = 0)
  points(peak.val$p.min, col = 1, pch = 19)
  points(peak.val$p.max, col = 2, pch = 19)
  legend(25, 0.08, c("Minima", "Maxima"), col = c(1,2), pch = c(19,19))

# Test which local maxima peak is above the median + 3 * Median Absolute 
# Add a threshold (th) line to the plot
th.max <- median(peak.val$p.max[, 2]) + 3 * mad(peak.val$p.max[, 2])
abline(h = th.max, col = 3)

# add the approximate temperatures of the local minima and 
# maxima to the plot
T.val <- c(peak.val$p.min[, 1], peak.val$p.max[, 1])
text(T.val, rep(-0.05, length(T.val)), round(T.val,0))

# Use a temperature range from the plot to calculate the Tm of 
# the maximum Trange is used between 37 and 74 degree Celsius

tmp <- mcaSmoother(DMP[, 1], DMP[, 6], minmax = TRUE, Trange = c(37,74), 
		    n = 2)
# Tm 48.23, fluoTm 0.137
diffQ(tmp, fct = max, plot = TRUE)


# First Example
data(DMP)
# Smooth and Min-Max normalize melting curve data with mcaSmoother()
tmp <- mcaSmoother(DMP[, 1], DMP[,6], minmax = TRUE, n = 2)

# Extract the first derivative melting curve data
tmp.d <- diffQ(tmp, verbose = TRUE)$xy

# Determine the approximate local minima and maxima of a curve
peak.val <-mcaPeaks(tmp.d[, 1], tmp.d[, 2])
peak.val

# Plot the first derivative melting curve
# Add a horizontal line and points for the approximate local minima 
# and maxima to the plot
plot(tmp.d, type = "l", 
     main = "Show the approximate local minima and maxima of a curve")
  abline(h = 0)
  points(peak.val$p.min, col = 1, pch = 19)
  points(peak.val$p.max, col = 2, pch = 19)
  legend(25, 0.08, c("Minima", "Maxima"), col = c(1,2), pch = c(19,19))

# Second example
# Signifcant peaks can be distinguished by peak hight
plot(tmp.d, type = "l", 
      main = "Show the approximate local minima and maxima of a curve")
  abline(h = 0)
  points(peak.val$p.min, col = 1, pch = 19)
  points(peak.val$p.max, col = 2, pch = 19)
  legend(25, 0.08, c("Minima", "Maxima"), col = c(1,2), pch = c(19,19))

# Test which local maxima peak is above the median + 3 * Median Absolute 
# Add a threshold (th) line to the plot
th.max <- median(peak.val$p.max[, 2]) + 3 * mad(peak.val$p.max[, 2])
abline(h = th.max, col = 3)

# add the approximate temperatures of the local minima and 
# maxima to the plot
T.val <- c(peak.val$p.min[, 1], peak.val$p.max[, 1])
text(T.val, rep(-0.05, length(T.val)), round(T.val,0))

# Use a temperature range from the plot to calculate the Tm of 
# the maximum Trange is used between 37 and 74 degree Celsius

tmp <- mcaSmoother(DMP[, 1], DMP[, 6], minmax = TRUE, Trange = c(37,74), 
		    n = 2)
# Tm 48.23, fluoTm 0.137
diffQ(tmp, fct = max, plot = TRUE)

Function to pre-process melting curve data.

Description

The function mcaSmoother() is used for data preprocessing. Measurements from experimental systems may occasionally include missing values (NA). mcaSmoother() uses approx() to fill up NAs under the assumption that all measurements were equidistant. The original data remain unchanged and only the NAs are substituted. Following it calls smooth.spline() to smooth the curve. Different strengths can be set using the option df.fact (f default~0.95). Internally it takes the degree of freedom value from the spline and multiplies it with a factor between 0.6 and 1.1. Values lower than 1 result in stronger smoothed curves. The outcome of the differentiation depends on the temperature resolution of the melting curve. It is recommended to use a temperature resolution of at least 0.5 degree Celsius. Besides, for the temperature steps equal distances 60 degree Celsius) rather than unequal distances (e.g., 50 -> 50.4 -> 60.1 (e.g., 50 -> 50.5 -> degree Celsius) are recommended. The parameter n can be used to increase the temperature resolution of the melting curve data. mcaSmoother uses the spline function for this purpose. A temperature range for a simple linear background correction. The linear trend is estimated by a robust linear regression using lmrob(). In case criteria for a robust linear regression are violated lm() is automatically used. The parameter n can be combined with the parameter Trange to make transform all melting curves of question to have the #same range and similar resolution. Optionally a Min-Max normalization between 0 and 1 can be used by setting the option minmax to TRUE. This is useful in many situations. For example, if the fluorescence values between samples vary considerably (e.g., due to high background, different reporter dyes, ...), particularly in solution or for better comparison of results.

Usage

mcaSmoother(
  x,
  y,
  bgadj = FALSE,
  bg = NULL,
  Trange = NULL,
  minmax = FALSE,
  df.fact = 0.95,
  n = NULL
)
mcaSmoother(
  x,
  y,
  bgadj = FALSE,
  bg = NULL,
  Trange = NULL,
  minmax = FALSE,
  df.fact = 0.95,
  n = NULL
)

Arguments

`x`	is the column of a data frame for the temperature.
`y`	is the column of a data frame for the fluorescence values.
`bgadj`	is used to adjust the background signal. This causes `mcaSmoother` to use the data subset defined by `bg` for the linear regression and background correction.
`bg`	is used to define the range for the background reduction (e.g., `bg = c(50,55)`, between 50 and 55 degree Celsius)).
`Trange`	is used to define the temperature range (e.g., `Trange = c(50,95)`, between 50 and 95 degree Celsius) for melting curve analysis.
`minmax`	is used to scale the fluorescence a Min-Max normalization between 0 and 1 can be used by setting the option `minmax` to `TRUE`.
`df.fact`	is a factor to smooth the curve. Different strengths can be set using the option `df.fact` (f default ~ 0.95). Internally it takes the degree of freedom value from the spline and multiplies it with a factor between 0.6 and 1.1. Values lower than 1 result in stronger smoothed curves.
`n`	is number of interpolations to take place. This parameter uses the spline function and increases the temperature resolution of the melting curve data.

Value

`xy`	returns a `data.frame` with the temperature ("x") in the first and the preprocessed fluorescence values ("y.sp") in the second column.

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. https://pubmed.ncbi.nlm.nih.gov/22437246/

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

Examples


default.par <- par(no.readonly = TRUE)
# First Example
# Use mcaSmoother with different n to increase the temperature 
# resolution of the melting curve artificially. Compare the 
# influence of the n on the Tm and fluoTm values
data(MultiMelt)

Tm	<- vector()
fluo	<- vector()
for (i in seq(1,3.5,0.5)) {
  res.smooth <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14], n = i)
  res <- diffQ(res.smooth)
  Tm <- c(Tm, res$Tm)
  fluo <- c(fluo, res$fluoTm)
}
plot(fluo, Tm, ylim = c(76,76.2))
abline(h = mean(Tm))
text(fluo, seq(76.1,76.05,-0.02), 
      paste("n:", seq(3.5,1,-0.5), sep = " "), col = 2)
abline(h = c(mean(Tm) + sd(Tm), mean(Tm) - sd(Tm)), col = 2)

legend(-0.22, 76.2, c("mean Tm", "mean Tm +/- SD Tm"), 
	col = c(1,2), lwd = 2)

# Second Example
# Use mcaSmoother with different strengths of smoothing 
# (f, 0.6 = strongest, 1 = weakest). 
data(DMP)
plot(DMP[, 1], DMP[,6], 
      xlim = c(20,95), xlab = "Temperature",
      ylab = "refMFI", pch = 19, col = 8)
f <- c(0.6, 0.8, 1.0)
for (i in c(1:3)) { 
 	lines(mcaSmoother(DMP[, 1],
         DMP[,6], df.fact = f[i]),
         col = i, lwd = 2)
}
legend(20, 1.5, paste("f", f, sep = ": "),
      cex = 1.2, col =  1:3, bty = "n",
      lty = 1, lwd = 4)

# Third Example
# Plot the smoothed and trimmed melting curve
data(MultiMelt)
tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14])
tmp.trimmed <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14], 
			    Trange = c(49,85))
plot(tmp, pch = 19, xlab = "Temperature", ylab = "refMFI", 
	  main = "MLC-2v, mcaSmoother using Trange")
  points(tmp.trimmed, col = 2, type = "b", pch = 19)
  legend(50, 1, c("smoothed values",
		  "trimmed smoothed values"), 
		   pch = c(19,19), col = c(1,2))

# Fourth Example
# Use mcaSmoother with different n to increase the temperature 
# resolution of the melting curve. Caution, this operation may 
# affect your data negatively if the resolution is set to high. 
# Higher resolutions will just give the impression of better 
# data quality. res.st uses the default resolution (no 
# alteration)
# res.high uses the double resolution.
data(MultiMelt)
res.st <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14])
res.high <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14], n = 2)

par(fig = c(0,1,0.5,1))
plot(res.st, xlab = "Temperature", ylab = "F", 
	main = "Effect of n parameter on the temperature 
	resolution")
points(res.high, col = 2, pch = 2)
  legend(50, 1, c(paste("default resolution.", nrow(res.st), 
		  "Temperature steps", sep = " "), 
		  paste("double resolution.", nrow(res.high),
		  "Temperature steps", sep = " ")), 
		  pch = c(1,2), col = c(1,2))
par(fig = c(0,0.5,0,0.5), new  =  TRUE)
diffQ(res.st, plot = TRUE)
  text(65, 0.025, paste("default resolution.", nrow(res.st), 
			"Temperature steps", sep = " "))
par(fig = c(0.5,1,0,0.5), new = TRUE)
diffQ(res.high, plot = TRUE)
  text(65, 0.025, paste("double resolution.", nrow(res.high), 
			"Temperature steps", sep = " "))

# Fifth example
# Different experiments may have different temperature 
# resolutions and temperature ranges. The example uses a 
# simulated melting curve with a temperature resolution of 
# 0.5 and 1 degree Celsius and a temperature range of 
# 35 to 95 degree Celsius.
#
# Coefficients of a 3 parameter sigmoid model.  Note: 
# The off-set, temperature range and temperature resolution 
# differ between both simulations. However, the melting 
# temperatures should be very 
# similar finally.
b <- -0.5; e <- 77

# Simulate first melting curve with a temperature 
# between 35 - 95 degree Celsius and 1 degree Celsius 
# per step temperature resolution.

t1 <- seq(35, 95, 1)
f1 <- 0.3 + 4 / (1 + exp(b * (t1 - e)))

# Simulate second melting curve with a temperature 
# between 41.5 - 92.1 degree Celsius and 0.5 degree Celsius 
# per step temperature resolution.
t2 <- seq(41.5, 92.1, 0.5)
f2 <- 0.2 + 2 / (1 + exp(b * (t2 - e)))

# Plot both simulated melting curves
plot(t1, f1, pch = 15, ylab = "MFI", 
     main = "Simulated Melting Curves", 
     xlab = "Temperature", col = 1)
points(t2, f2, pch = 19, col = 2)
legend(50, 1, 
       c("35 - 95 degree Celsius, 1 degree Celsius per step", 
       "41.5 - 92.1 degree Celsius, 0.5 degree Celsius per step", 
       sep = " "), pch = c(15,19), col = c(1,2))

# Use mcaSmoother with n = 2 to increase the temperature 
# resolution of the first simulated melting curve. The minmax 
# parameter is used to make the peak heights compareable. The 
# temperature range was limited between 45 to 90 degree Celsius for 
# both simulations

t1f1 <- mcaSmoother(t1, f1, Trange= c(45, 90), minmax = TRUE, n = 2)
t2f2 <- mcaSmoother(t2, f2, Trange= c(45, 90), minmax = TRUE, n = 1)

# Perform a MCA on both altered simulations. As expected, the melting
# temperature are almost identical.
par(mfrow = c(2,1))
# Tm 77.00263, fluoTm -0.1245848
diffQ(t1f1, plot = TRUE)
text(60, -0.08, 
     "Raw data: 35 - 95 degree Celsius,\n 1 degree Celsius per step")

# Tm 77.00069, fluoTm -0.1245394
diffQ(t2f2, plot = TRUE)
text(60, -0.08, "Raw data: 41.5 - 92.1 degree Celsius,
      \n 0.5 degree Celsius per step")
par(default.par)

default.par <- par(no.readonly = TRUE)
# First Example
# Use mcaSmoother with different n to increase the temperature 
# resolution of the melting curve artificially. Compare the 
# influence of the n on the Tm and fluoTm values
data(MultiMelt)

Tm	<- vector()
fluo	<- vector()
for (i in seq(1,3.5,0.5)) {
  res.smooth <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14], n = i)
  res <- diffQ(res.smooth)
  Tm <- c(Tm, res$Tm)
  fluo <- c(fluo, res$fluoTm)
}
plot(fluo, Tm, ylim = c(76,76.2))
abline(h = mean(Tm))
text(fluo, seq(76.1,76.05,-0.02), 
      paste("n:", seq(3.5,1,-0.5), sep = " "), col = 2)
abline(h = c(mean(Tm) + sd(Tm), mean(Tm) - sd(Tm)), col = 2)

legend(-0.22, 76.2, c("mean Tm", "mean Tm +/- SD Tm"), 
	col = c(1,2), lwd = 2)

# Second Example
# Use mcaSmoother with different strengths of smoothing 
# (f, 0.6 = strongest, 1 = weakest). 
data(DMP)
plot(DMP[, 1], DMP[,6], 
      xlim = c(20,95), xlab = "Temperature",
      ylab = "refMFI", pch = 19, col = 8)
f <- c(0.6, 0.8, 1.0)
for (i in c(1:3)) { 
 	lines(mcaSmoother(DMP[, 1],
         DMP[,6], df.fact = f[i]),
         col = i, lwd = 2)
}
legend(20, 1.5, paste("f", f, sep = ": "),
      cex = 1.2, col =  1:3, bty = "n",
      lty = 1, lwd = 4)

# Third Example
# Plot the smoothed and trimmed melting curve
data(MultiMelt)
tmp <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14])
tmp.trimmed <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14], 
			    Trange = c(49,85))
plot(tmp, pch = 19, xlab = "Temperature", ylab = "refMFI", 
	  main = "MLC-2v, mcaSmoother using Trange")
  points(tmp.trimmed, col = 2, type = "b", pch = 19)
  legend(50, 1, c("smoothed values",
		  "trimmed smoothed values"), 
		   pch = c(19,19), col = c(1,2))

# Fourth Example
# Use mcaSmoother with different n to increase the temperature 
# resolution of the melting curve. Caution, this operation may 
# affect your data negatively if the resolution is set to high. 
# Higher resolutions will just give the impression of better 
# data quality. res.st uses the default resolution (no 
# alteration)
# res.high uses the double resolution.
data(MultiMelt)
res.st <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14])
res.high <- mcaSmoother(MultiMelt[, 1], MultiMelt[, 14], n = 2)

par(fig = c(0,1,0.5,1))
plot(res.st, xlab = "Temperature", ylab = "F", 
	main = "Effect of n parameter on the temperature 
	resolution")
points(res.high, col = 2, pch = 2)
  legend(50, 1, c(paste("default resolution.", nrow(res.st), 
		  "Temperature steps", sep = " "), 
		  paste("double resolution.", nrow(res.high),
		  "Temperature steps", sep = " ")), 
		  pch = c(1,2), col = c(1,2))
par(fig = c(0,0.5,0,0.5), new  =  TRUE)
diffQ(res.st, plot = TRUE)
  text(65, 0.025, paste("default resolution.", nrow(res.st), 
			"Temperature steps", sep = " "))
par(fig = c(0.5,1,0,0.5), new = TRUE)
diffQ(res.high, plot = TRUE)
  text(65, 0.025, paste("double resolution.", nrow(res.high), 
			"Temperature steps", sep = " "))

# Fifth example
# Different experiments may have different temperature 
# resolutions and temperature ranges. The example uses a 
# simulated melting curve with a temperature resolution of 
# 0.5 and 1 degree Celsius and a temperature range of 
# 35 to 95 degree Celsius.
#
# Coefficients of a 3 parameter sigmoid model.  Note: 
# The off-set, temperature range and temperature resolution 
# differ between both simulations. However, the melting 
# temperatures should be very 
# similar finally.
b <- -0.5; e <- 77

# Simulate first melting curve with a temperature 
# between 35 - 95 degree Celsius and 1 degree Celsius 
# per step temperature resolution.

t1 <- seq(35, 95, 1)
f1 <- 0.3 + 4 / (1 + exp(b * (t1 - e)))

# Simulate second melting curve with a temperature 
# between 41.5 - 92.1 degree Celsius and 0.5 degree Celsius 
# per step temperature resolution.
t2 <- seq(41.5, 92.1, 0.5)
f2 <- 0.2 + 2 / (1 + exp(b * (t2 - e)))

# Plot both simulated melting curves
plot(t1, f1, pch = 15, ylab = "MFI", 
     main = "Simulated Melting Curves", 
     xlab = "Temperature", col = 1)
points(t2, f2, pch = 19, col = 2)
legend(50, 1, 
       c("35 - 95 degree Celsius, 1 degree Celsius per step", 
       "41.5 - 92.1 degree Celsius, 0.5 degree Celsius per step", 
       sep = " "), pch = c(15,19), col = c(1,2))

# Use mcaSmoother with n = 2 to increase the temperature 
# resolution of the first simulated melting curve. The minmax 
# parameter is used to make the peak heights compareable. The 
# temperature range was limited between 45 to 90 degree Celsius for 
# both simulations

t1f1 <- mcaSmoother(t1, f1, Trange= c(45, 90), minmax = TRUE, n = 2)
t2f2 <- mcaSmoother(t2, f2, Trange= c(45, 90), minmax = TRUE, n = 1)

# Perform a MCA on both altered simulations. As expected, the melting
# temperature are almost identical.
par(mfrow = c(2,1))
# Tm 77.00263, fluoTm -0.1245848
diffQ(t1f1, plot = TRUE)
text(60, -0.08, 
     "Raw data: 35 - 95 degree Celsius,\n 1 degree Celsius per step")

# Tm 77.00069, fluoTm -0.1245394
diffQ(t2f2, plot = TRUE)
text(60, -0.08, "Raw data: 41.5 - 92.1 degree Celsius,
      \n 0.5 degree Celsius per step")
par(default.par)

Multiple comparison of the temperature dependent variance of the refMFI

Description

MFIerror is used for a fast multiple comparison of the temperature dependent variance of the refMFI. MFIerror returns an object of the class data.frame with columns “Temperature”, “Location” (Mean, Median), “Deviation” (Standard Deviation, Median Absolute Deviation) and “Coefficient of Variation”.

Usage

MFIerror(
  x,
  y,
  CV = FALSE,
  RSD = FALSE,
  rob = FALSE,
  errplot = TRUE,
  type = "p",
  pch = 19,
  length = 0.05,
  col = "black"
)
MFIerror(
  x,
  y,
  CV = FALSE,
  RSD = FALSE,
  rob = FALSE,
  errplot = TRUE,
  type = "p",
  pch = 19,
  length = 0.05,
  col = "black"
)

Arguments

`x`	is the column of a data frame for the temperature.
`y`	are multiple columns of fluorescence values from a `data.frame` (e.g., [, c(1:n)]).
`CV`	If `CV` is true the coefficient of variation (RSD, CV) is plotted. If set to FLASE the deviation as Standard Deviation or Median Absolute Deviation is plotted.
`RSD`	Setting the option `RSD = TRUE` shows the relative standard deviation (RSD) in percent.
`rob`	Using the option `rob` as TRUE the median and the median absolute deviation (MAD) is plotted instead of the mean and standard deviation.
`errplot`	sets `MFIerror()` to plot the results (default). In the default setting (`CV = FALSE`) the mean with the standard deviations is plotted.
`type`	is a graphical parameter setting the plot use lines, points or both (see `plot`).
`pch`	is a graphical parameter used to define the symbol used in the plot.
`length`	`length` is a graphical parameter used to define the length of the error bar used in the plot.
`col`	`col` is a graphical parameter used to define the color of the error bar used in the plot.

Value

res

returns a data.frame containing the "Temperature", "Location" (mean, median), "Deviation" (standard deviation, median absolute deviation), "Coefficient of Variance" (CV, RSD) sequential in the columns.

Author(s)

Stefan Roediger

Examples


# First Example
# Temperature dependent variance of the refMFI using standard measures 
# (Mean, Standard Deviation (SD)).
# Use Standard Deviation (SD) in the plot

data(MultiMelt)
MFIerror(MultiMelt[, 1], MultiMelt[, c(2L:13)])

# Second Example
# Temperature dependent relative variance of the refMFI using robust 
# measures (Median, Median Absolute Deviation (MAD)). The parameter 
# errplot is set to FALSE in order to prevent the plot of the 
# coefficient of variation versus the temperature.

MFIerror(MultiMelt[, 1], MultiMelt[, c(2L:13)], errplot = FALSE, 
	  RSD = TRUE, rob = TRUE)

# Third Example
# Temperature dependent relative variance of the refMFI using 
# robust measures (Median, Median Absolute Deviation (MAD)).
MFIerror(MultiMelt[, 1], MultiMelt[, c(2L:13)], RSD = TRUE, 
  rob = TRUE)

# First Example
# Temperature dependent variance of the refMFI using standard measures 
# (Mean, Standard Deviation (SD)).
# Use Standard Deviation (SD) in the plot

data(MultiMelt)
MFIerror(MultiMelt[, 1], MultiMelt[, c(2L:13)])

# Second Example
# Temperature dependent relative variance of the refMFI using robust 
# measures (Median, Median Absolute Deviation (MAD)). The parameter 
# errplot is set to FALSE in order to prevent the plot of the 
# coefficient of variation versus the temperature.

MFIerror(MultiMelt[, 1], MultiMelt[, c(2L:13)], errplot = FALSE, 
	  RSD = TRUE, rob = TRUE)

# Third Example
# Temperature dependent relative variance of the refMFI using 
# robust measures (Median, Median Absolute Deviation (MAD)).
MFIerror(MultiMelt[, 1], MultiMelt[, c(2L:13)], RSD = TRUE, 
  rob = TRUE)

Surface melting curve data from direct hybridization experiment of short oligonucleotides.

Description

A melting curve experiment with twelve microbead populations and the short oligonucleotide capture probe and detection probe for human HRPT1 (hyperparathyroidism 1) and MLC-2v (myosin regulatory light chain 2, ventricular/cardiac muscle isoform).

Format

A data frame with the melting curves of two different capture and detection probe pairs for HRPT1 and MLC-2v. First column contains the temperature (in degree Celsius, 1 degree Celsius per step) followed by melting curves of HRPT1 on twelve microbead populations and melting curves of MLC-2v on twelve microbead populations.

T: a numeric vector for the temperature in degree Celsius
HPRT1.1: a numeric vector, as HPRT1.1 of detection/capture probe HPRT1/HPRT1-cap on microbead population 1
HPRT1.2: a numeric vector, as HPRT1.2 on microbead population 2
HPRT1.3: a numeric vector, as HPRT1.3 on microbead population 3
HPRT1.4: a numeric vector, as HPRT1.4 on microbead population 4
HPRT1.5: a numeric vector, as HPRT1.5 on microbead population 5
HPRT1.6: a numeric vector, as HPRT1.6 on microbead population 6
HPRT1.7: a numeric vector, as HPRT1.7 on microbead population 7
HPRT1.8: a numeric vector, as HPRT1.8 on microbead population 8
HPRT1.9: a numeric vector, as HPRT1.9 on microbead population 9
HPRT1.10: a numeric vector, as HPRT1.10 on microbead population 10
HPRT1.11: a numeric vector, as HPRT1.11 on microbead population 11
HPRT1.12: a numeric vector, as HPRT1.12 on microbead population 12
MLC2v1: a numeric vector, as MLC2v1 of detection/capture probe MLC-2v/MLC-2v-cap on microbead population 1
MLC2v2: a numeric vector, as MLC2v2 on microbead population 2
MLC2v3: a numeric vector, as MLC2v3 on microbead population 3
MLC2v4: a numeric vector, as MLC2v4 on microbead population 4
MLC2v5: a numeric vector, as MLC2v5 on microbead population 5
MLC2v6: a numeric vector, as MLC2v6 on microbead population 6
MLC2v7: a numeric vector, as MLC2v7 on microbead population 7
MLC2v8: a numeric vector, as MLC2v8 on microbead population 8
MLC2v9: a numeric vector, as MLC2v9 on microbead population 9
MLC2v10: a numeric vector, as MLC2v10 on microbead population 10
MLC2v11: a numeric vector, as MLC2v11 on microbead population 11
MLC2v12: a numeric vector, as MLC2v12 on microbead population 12

Details

The melting curve was conducted with short oligonucleotide probes on the surface of microbeads using the VideoScan platform according to Roediger et al. (2012). The dyes and quencher used were Atto 647N and BHQ2.

Source

Data were measured with the VideoScan platform:

Surface Melting Curve Analysis with R. S. Roediger, A. Boehm and I. Schimke. The R Journal. 5(2):37–52, 2013, 2013.

Examples


data(MultiMelt)

data(MultiMelt)

Package 'MBmca'

Help Index

Microbead Surface Nucleic Acid Melting Curve Analysis

Description

Author(s)

References

Calculation of the melting temperature (Tm) from the first derivative

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

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

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Bimodal melting curve experiment on the surface of microbeads.

Description

Format

Source

See Also

Examples

Surface melting curve data from direct hybridization experiment of short oligonucleotide probes with bimodal melting curve pattern.

Description

Format

Details

Source

See Also

Examples

Function to estimate the approximate local minima and maxima of melting curve data.

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Function to pre-process melting curve data.

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Multiple comparison of the temperature dependent variance of the refMFI

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Surface melting curve data from direct hybridization experiment of short oligonucleotides.

Description

Format

Details

Source

See Also

Examples