In rformassspectrometry/MetaboCoreUtils: Core Utils for Metabolomics Data

BiocStyle::markdown()

Package: r BiocStyle::Biocpkg("MetaboCoreUtils")
Authors: r packageDescription("MetaboCoreUtils")[["Author"]]
Last modified: r file.info("MetaboCoreUtils.Rmd")$mtime
Compiled: r date()

Introduction

The r Biocpkg("MetaboCoreUtils") package defines metabolomics-related core functionality provided as low-level functions to allow a data structure-independent usage across various R packages [@rainer_modular_2022]. This includes functions to calculate between ion (adduct) and compound mass-to-charge ratios and masses or functions to work with chemical formulas. The package provides also a set of adduct definitions and information on some commercially available internal standard mixes commonly used in MS experiments.

For a full list of function, see

library("MetaboCoreUtils")
ls(pos = "package:MetaboCoreUtils")

or the reference page on the package webpage.

Installation

The package can be installed with the BiocManager package. To install BiocManager use install.packages("BiocManager") and, after that, BiocManager::install("MetaboCoreUtils") to install this package.

Examples

The functions defined in this package utilise basic classes with the aim of being reused in packages that provide a more formal, high-level interface.

The examples below demonstrate the basic usage of the functions from the package.

library(MetaboCoreUtils)

Conversion between ion m/z and compound masses

The mass2mz() and mz2mass() functions allow to convert between compound masses and ion (adduct) mass-to-charge ratios (m/z). The MetaboCoreUtils package provides definitions of common ion adducts generated by electrospray ionization (ESI). These can be listed with the adductNames() function.

adductNames()

With that we can use the mass2mz() function to calculate the m/z for a set of compounds assuming the generation of certain ions. In the example below we define masses for some theoretical compounds and calculate their expected m/z assuming that ions "[M+H]+" and "[M+Na]+" are generated.

masses <- c(123, 842, 324)
mass2mz(masses, adduct = c("[M+H]+", "[M+Na]+"))

As a result we get a matrix with each row representing one compound and each column the m/z for one of the defined adducts. With the mz2mass() function we could perform the reverse calculation, i.e. from m/z to compound masses.

In addition, it is possible to calculate m/z values from chemical formulas with the formula2mz() function. Below we calculate the m/z values for [M+H]+ and [M+Na]+ adducts from the chemical formulas of glucose and caffeine.

formula2mz(c("C6H12O6", "C8H10N4O2"), adduct = c("[M+H]+", "[M+Na]+"))

Working with chemical formulas

The lack of consistency in the format in which chemical formulas are written poses a big problem comparing formulas coming from different resources. The MetaboCoreUtils package provides functions to standardize formulas as well as combine formulas or substract elements from formulas. Below we use an artificial example to show this functionality. First we standardize a chemical formula with the standardizeFormula() function.

frml <- "Na3C4"
frml <- standardizeFormula(frml)
frml

Next we add "H2O" to the formula using the addElements() function.

frml <- addElements(frml, "H2O")
frml

We can also substract elements with the subtractElements() function:

frml <- subtractElements(frml, "H")
frml

Chemical formulas could also be multiplied with a scalar using the multiplyElements() function. The counts for individual elements in a chemical formula can be calculated with the countElements() function.

countElements(frml)

The function adductFormula() allows in addition to create chemical formulas of specific adducts of compounds. Below we create chemical formulas for [M+H]+ and [M+Na]+ adducts for glucose and caffeine.

adductFormula(c("C6H12O6", "C8H10N4O2"), adduct = c("[M+H]+", "[M+Na]+"))

Finally, calculateMass() can be used to calculate the (exact) mass for a given chemical formula. This function supports also the definition of isotopes in the formula. As an example we calculate below the mass of two chemical formulas, one without isotopes and one with 3 of the carbon atoms replaced by the carbon 13 isotope.

calculateMass(c("C6H12O6", "[13C3]C3H12O6"))

Note that isotopes are supported for all elements (deuterium could for example be expressed as "[2H]").

Kendrick mass defect calculation

Lipids and other homologous series based on fatty acyls can be found in data by using Kendrick mass defects (KMD) or referenced kendrick mass defects (RKMD). The MetaboCoreUtils package provides functions to calculate everything around Kendrick mass defects. The following example calculates the KMD and RKMD for three lipids (PC(16:0/18:1(9Z)), PC(16:0/18:0), PS(16:0/18:1(9Z))) and checks, if they fit the RKMD of PCs detected as [M+H]+ adducts.

lipid_masses <- c(760.5851, 762.6007, 762.5280)
calculateKmd(lipid_masses)

Next the RKMD is calculated and checked if it fits to a specific range. RKMDs are either 0 or negative integers according to the number of double bonds in the lipids, e.g. -2 if two double bonds are present in the lipids.

lipid_rkmd <- calculateRkmd(lipid_masses)
isRkmd(lipid_rkmd)

Retention time indexing

Retention times are often not directly comparable between two LC-MS systems, even if nominally the same separation method is used. Conversion of retention times to retetion indices can overcome this issue. The MetaboCoreUtils package provides a function to perform this conversion. Below we use an example based on indexing with a homologoues series af N-Alkyl-pyridinium sulfonates (NAPS).

rti <- read.table(system.file("retentionIndex",
                              "rti.txt",
                              package = "MetaboCoreUtils"),
                  header = TRUE,
                  sep = "\t")

rtime <- read.table(system.file("retentionIndex",
                                "metabolites.txt",
                                package = "MetaboCoreUtils"),
                    header = TRUE,
                    sep = "\t")

A data.frame with the retetion times of the NAPS and their respective index value is required.

head(rti)

The indexing is peformed using the function indexRtime().

rtime$rindex_r <- indexRtime(rtime$rtime, rti)

For comparison the manual calculated retention indices are included.

head(rtime)

Conditions that shall be compared by the retention index might not perfectly match. In case the deviation is linear a simple two-point correction can be applied to the data. This is performed by the function correctRindex(). The correction requires two reference standards and their measured RIs and reference RIs.

ref <- data.frame(rindex = c(1709.8765, 553.7975),
                  refindex = c(1700, 550))

rtime$rindex_cor <- correctRindex(rtime$rindex_r, ref)

Linear model-based adjustment of LC-MS feature abundances

Feature abundances from untargeted LC-MS-based metabolomics experiments can be affected by technical noise or signal drifts. In particular, some of these technical variances can be specific for individual metabolites, requiring hence a per-feature adjustment of the abundances. One example of such noise is an injection order dependent signal drift that can sometimes be observed in untargeted metabolomics data from LC-MS experiments. The fit_lm() function can be used to model such drifts in the observed data of each single feature, for example with a model of the form y ~ injection_index that models the relationship between the measured abundances of a metabolite y on the index in which the respective sample was injected (injection_index). Subsequently, the data can be adjusted for the modeled drift with the adjust_lm() function. This approach is similar to the one described by [@wehrens_improved_2016].

Below we perform such an injection order dependent signal adjustment on a small test data set representing abundances of LC-MS features from an untargeted metabolomics experiment. All samples were measured within the same measurement run and QC samples were measured repeatedly after 8 study samples.

vals <- read.table(system.file("txt", "feature_values.txt",
                               package = "MetaboCoreUtils"), sep = "\t")
vals <- as.matrix(vals)
head(vals)

The samples are provided in the columns of the matrix vals, in the order in which they were measured. We next define a data.frame with the injection index of the individual samples and identify the columns containing the QC samples.

#' Define a data frame with the injection index
sdata <- data.frame(injection_index = seq_len(ncol(vals)))

#' Identify columns representing QC samples
qc_index <- grep("^POOL", colnames(vals))

length(qc_index)

We can next model an injection order dependent signal drift for each feature (row) in the data. To ensure independence of the fitted regression models on any experimental covariate we estimate the drift on values observed for QC samples (which represent repeated injections of the same sample pool and hence any differences observed in these are supposed to be of only technical nature). Also, we fit the model on log2 transformed abundances assuming hence a log linear relationship between abundances and injection index. By setting minVals = 9 we require at least 9 non-missing values in QC samples (n = 11) of each row for the model to be fitted - for fewer values, model fitting is skipped and an NA is returned for the particular feature (row). The default for the minVals parameter is to fit models only for features with at least 75% of non-missing values. For lower values of minVals model fitting can become unstable and users should thus evaluate (and visually inspect) the estimated signal drifts.

#' Fit linear models explaining observed abundances by injection index.
#' Linear models are fitted row-wise to data of QC samples.
qc_lm <- fit_lm(y ~ injection_index,
                data = sdata[qc_index, , drop = FALSE],
                y = log2(vals[, qc_index]),
                minVals = 9)

The function returned a list of linear models. Each model describing the observed relationship between feature abundances and injection index of the samples. Below we extract the first of these models.

qc_lm[[1]]

The coefficient for the injection index represents the dependency of the measured abundances (in QC samples) for that feature on the index in which the samples were injected, with positive coefficients indicating increasing abundances with injection index and negative coefficients decreasing intensities. The magnitude of the value represents the strength of this association.

For some features no model was fitted, because too few non-missing data points were available (parameter minVals above).

sum(is.na(qc_lm))

We can also plot the data and indicate the fitted model.

plot(x = sdata$injection_index, y = log2(vals[1, ]),
     xlab = "injection_index", ylab = expression(log[2]~abundance))
#' Indicate QC samples
points(x = sdata$injection_index[qc_index],
       y = log2(vals[1, qc_index]), pch = 16, col = "#00000080")
grid()
abline(qc_lm[[1]])

For that feature a very slight increase of abundances over the measurement run was estimated. In contrast, for the second feature a stronger, but decreasing, signal drift was estimated on the QC samples (see below). Also the study samples seem to follow this drift.

plot(x = sdata$injection_index, y = log2(vals[2, ]),
     xlab = "injection_index", ylab = expression(log[2]~abundance))
#' Indicate QC samples
points(x = sdata$injection_index[qc_index],
       y = log2(vals[2, qc_index]), pch = 16, col = "#00000080")
grid()
abline(qc_lm[[2]])

Thus, generally, for LC-MS data, not all features need be affected by the same injection order-dependent signal drift. We next extract the coefficient (or slope, representing the magnitude of the association with the injection order), its p-value (providing the significance from the hypothesis test that the coefficient is different from 0) and the (adjusted) R squared (variance explained by the fitted model) for each feature.

#' Extract slope, F-statistic and R squared from each model, skipping
#' features for which no model was fitted.
qc_lm_summary <- lapply(qc_lm, function(z) {
    if (length(z) > 1) {
        s <- summary(z)
        c(slope = coefficients(s)[2, "Estimate"],
          p.value = coefficients(s)[2, 4],
          adj.r.squared = s$adj.r.squared)
    } else c(slope = NA_real_, F = NA_real_,
             adj.r.squared = NA_real_) # returning NA for skipped models
}) |> do.call(what = rbind)

head(qc_lm_summary)

We below plot the slope (x-axis) against its p-value for the fitted models. For the p-values we plot the negative logarithm so that larger values represent smaller p-values.

plot(qc_lm_summary[, "slope"], -log10(qc_lm_summary[, "p.value"]),
     xlab = "injection order dependency", ylab = expression(-log[10](p~value)),
     pch = 21, col = "#00000080", bg = "#00000040")
grid()
abline(h = -log10(0.05))

The p-value represents the significance of the slope being different from 0. Large slopes with poor p-values indicate that the measured values (in QC samples) don't fit the model well.

We next select the feature with the largest slope (i.e., strongest estimated dependency on the injection index) and plot its data.

idx <- which.max(qc_lm_summary[, "slope"])
plot(x = sdata$injection_index, y = log2(vals[idx, ]),
     xlab = "injection_index", ylab = expression(log[2]~abundance))
#' Indicate QC samples
points(x = sdata$injection_index[qc_index],
       y = log2(vals[idx, qc_index]), pch = 16, col = "#00000080")
grid()
abline(qc_lm[[idx]])

Also for this feature, the study samples show a similar trend (along injection index) than the QC samples. The p-value and R squared for this feature are:

qc_lm_summary[idx, ]

As an additional example we plot the data for a model with a large slope, but a high p-value.

idx2 <- which(qc_lm_summary[, "slope"] > 0.01 &
              qc_lm_summary[, "p.value"] > 0.05)
plot(x = sdata$injection_index, y = log2(vals[idx2, ]),
     xlab = "injection_index", ylab = expression(log[2]~abundance))
points(x = sdata$injection_index[qc_index],
       y = log2(vals[idx2, qc_index]), pch = 16, col = "#00000080")
grid()
abline(qc_lm[[idx2]])

For that particular feature no (or only a very low) injection order dependency of abundances can be observed in study samples while a rather strong signal drift was estimated on the QC samples. This strong dependency was driven mostly by 3 QC samples with low intensities at the beginning of the measurement run, that might however represent outlier signals. The p-value, slope and R squared values for this features are:

qc_lm_summary[idx2, ]

The p-value is much larger for this feature and the R squared lower compared to the first feature, which suggests that the fitted model, although the coefficient (slope) is different from one, does not describe the data well.

It is thus suggested to not blindly apply these feature-wise adjustments but to evaluate the estimated signal drifts (ideally for border cases) to determine whether they fit the data or to define strategies to identify cases for which the estimated signal drift should be discarded.

As an example, we might want to remove linear model fits with a p-value larger 0.05. While this cut-off is arbitrary, it will avoid adjusting the data in cases for which there is no injection dependent signal drift (i.e. when the slope/coefficient is close to 0) or for which the fitted model does not well explain the measured abundances (as in our example above).

qc_lm[qc_lm_summary[, "p.value"] > 0.05] <- NA

We can next adjust the data for the estimated signal drifts using the adjust_lm() function. We will thus adjust abundances in all samples (including the study samples) using the linear models estimated on the QC samples. For features for which no linear model is provided (i.e., with an NA in the list of linear models) the original abundances will be returned as is. With parameter data we need to provide a data.frame with all required covariates for the fitted models (i.e., defined by the formula passed to the fit_lm() call). Also, since we fitted the models to the data in log2 scale, we need also to provide log2 transformed values to the adjust_lm() function.

#' Adjust the data for the estimated signal drift
vals_adj <- adjust_lm(log2(vals), data = sdata, lm = qc_lm)

#' Transform data again into natural scale
vals_adj <- 2^vals_adj

Finally, we can (and should) evaluate the impact of the adjustment by plotting the raw and adjusted values into the same plot. Below we plot these values (raw values as open circles, adjusted values as filled circles) for the 2nd feature.

plot(x = sdata$injection_index, y = log2(vals[2, ]),
     xlab = "injection_index", ylab = expression(log[2]~abundance),
     col = "#00000080")
points(x = sdata$injection_index, y = log2(vals_adj[2, ]),
       pch = 16, col = "#00000080")
grid()
abline(qc_lm[[2]], col = "grey", lty = 2)

#' fit a model to the QC samples of the adjusted data
l <- lm(log2(vals_adj[2, qc_index]) ~ sdata$injection_index[qc_index])
abline(l, col = "grey")

As expected, the signal drift was removed by the adjustment.

We can also evaluate the performance of the whole adjustment by comparing the correlation of abundances with injection index before and after adjustment. Below we calculate the correlation between abundances in QC samples and the respective injection index of these samples using the non-parametric Spearman method.

We restrict the calculation to features that were also adjusted using the signal dependent

#' Identify features for which the adjustment was performed
fts_adj <- which(!is.na(qc_lm))

#' Define a function to calculate the correlation
cor_fun <- function(i, y) {
    values <- y[i, qc_index]
    if (sum(!is.na(values)) >= 9)
        cor(values, sdata$injection_index[qc_index],
            method = "spearman", use = "pairwise.complete.obs")
    else NA_real_
}

#' Calculate correlations for raw data, skipping features
#' with less than 9 non-missing values
cor_raw <- vapply(seq_along(qc_lm), cor_fun, numeric(1), y = vals)

We repeat the same for the values after adjustment.

#' Calculate correlations for adjusted data
cor_adj <- vapply(seq_along(qc_lm), cor_fun, numeric(1), y = vals_adj)

We next plot the (ordered) correlation coefficients before and after adjustment to globally evaluate the impact of the correction.

plot(sort(cor_raw), col = "#00000080", main = "QC samples", ylab = "rho",
     xlab = "rank")
idx <- order(cor_adj)
bg <- rep(NA, length(cor_adj))
bg[fts_adj] <- "#ff000040"
points(cor_adj[idx], pch = 21, col = "#ff000080", bg = bg[idx])

Adjustment, while not completely removing it for all features, globally reduced the dependency of abundances on the injection index.

Summarizing, feature-wise biases in LC-MS data can be estimated, and adjusted for using the fit_lm() and adjust_lm() functions. Ideally, such biases should be estimated on (repeatedly measured) QC samples, with the QC samples being representative of the study samples (e.g. a pool of all study samples). In addition, due to the generally relatively low number of available data points, the estimation of the signal drift can be unreliable and it is thus strongly suggested to evaluate or visually inspect some of them to derive strategies identifying and handling problematic cases and skip adjustment for them. In addition or as an alternative, problematic cases could also manually identified and flagged or removed.

Generally, injecting study samples in random order can reduce (or even avoid) influence of any related technical bias in the downstream analysis and is highly suggested to improve and assure data quality.

Basic quality assessment and pre-filtering of metabolomics data

When dealing with metabolomics results, it is often necessary to filter features based on certain criteria. These criteria are typically derived from statistical formulas applied to full rows of data, where each row represents a feature. In this tutorial, we'll explore a set of functions designed designed to calculate basic quality assessment metrics on which metabolomics data can subsequently be filtered.

First, to get more information on the available function you can check the documentation

?quality_assessment

We will use a matrix representing metabolomics measurements from different samples. Let's start by introducing the data:

# Define sample data for metabolomics analysis
set.seed(123)
metabolomics_data <- matrix(rnorm(100), nrow = 10)
colnames(metabolomics_data) <- paste0("Sample", 1:10)
rownames(metabolomics_data) <- paste0("Feature", 1:10)

We will begin by calculating the coefficient of variation (CV) for each feature. This measure helps assess the relative variability of each metabolite across different samples.

# Calculate and display the coefficient of variation
cv_result <- rowRsd(metabolomics_data)
print(cv_result)

Next, we will compute the D-ratio [@broadhurst_guidelines_2018], a measure of dispersion, by comparing the standard deviation of QC samples to that of biological test samples.

# Generate QC samples
qc_samples <- matrix(rnorm(40), nrow = 10)
colnames(qc_samples) <- paste0("QC", 1:4)

# Calculate D-ratio and display the result
dratio_result <- rowDratio(metabolomics_data, qc_samples)
print(dratio_result)

Now, let's analyze the percentage of missing values for each metabolite. This information is crucial for quality control and data preprocessing.

# Introduce missing values in the data
metabolomics_data[sample(1:100, 10)] <- NA

# Calculate and display the percentage of missing values
missing_result <- rowPercentMissing(metabolomics_data)
print(missing_result)

Finally, we will identify features where the mean of test samples is lower than twice the mean of blank samples. This can be indicative of significant contamination in the solvent of the samples.

# Generate blank samples
blank_samples <- matrix(rnorm(30), nrow = 10)
colnames(blank_samples) <- paste0("Blank", 1:3)

# Detect rows where mean(test) > 2 * mean(blank)
blank_detection_result <- rowBlank(metabolomics_data, blank_samples)
print(blank_detection_result)

All of these computations can then be used to easily filter our data and remove the features that do not fit our quality criteria. Below we remove all features that have a D-ratio and coefficeint of variation < 0.8 with no missing values and is not flagged to be a possible solvent contaminant.

# Set filtering thresholds
cv_threshold <- 8
dratio_threshold <- 0.8

# Apply filters
filtered_data <- metabolomics_data[
  cv_result <= cv_threshold &
  dratio_result <= dratio_threshold &
  missing_result <= 10 &
  !blank_detection_result, , drop = FALSE]

# Display the filtered data
print(filtered_data)

Contributions

If you would like to contribute any low-level functionality, please open a GitHub issue to discuss it. Please note that any contributions should follow the style guide and will require an appropriate unit test.

If you wish to reuse any functions in this package, please just go ahead. If you would like any advice or seek help, please either open a GitHub issue.

Session information {-}

sessionInfo()

References

rformassspectrometry/MetaboCoreUtils documentation built on April 15, 2024, 10:27 p.m.