filterMsLevel: Filter and subset Spectra objects

In rformassspectrometry/Spectra: Spectra Infrastructure for Mass Spectrometry Data

Filter and subset Spectra objects

Description

A variety of functions to filter or subset Spectra objects are available. These can be generally separated into two main classes: I) classical subset operations that immediately reduce the number of spectra in the object and II) filters that reduce the content of the object without changing its length (i.e. the number of spectra). The latter can be further subdivided into functions that affect the content of the spectraData (i.e. the general spectrum metadata) and those that reduce the content of the object's peaksData (i.e. the m/z and intensity values of a spectrum's mass peaks).

A description of functions from these 3 different categories are given below in sections Subset Spectra, Filter content of spectraData() and Filter content of peaksData(), respectively.

Usage

deisotopeSpectra(
  x,
  substDefinition = isotopicSubstitutionMatrix("HMDB_NEUTRAL"),
  tolerance = 0,
  ppm = 20,
  charge = 1
)

reduceSpectra(x, tolerance = 0, ppm = 20)

filterPrecursorMaxIntensity(x, tolerance = 0, ppm = 20)

filterPrecursorIsotopes(
  x,
  tolerance = 0,
  ppm = 20,
  substDefinition = isotopicSubstitutionMatrix("HMDB_NEUTRAL")
)

filterPrecursorPeaks(
  object,
  tolerance = 0,
  ppm = 20,
  mz = c("==", ">="),
  msLevel. = uniqueMsLevels(object)
)

## S4 method for signature 'Spectra'
dropNaSpectraVariables(object)

## S4 method for signature 'Spectra'
selectSpectraVariables(
  object,
  spectraVariables = union(spectraVariables(object), peaksVariables(object))
)

## S4 method for signature 'Spectra'
x[i, j, ..., drop = FALSE]

## S4 method for signature 'Spectra'
filterAcquisitionNum(
  object,
  n = integer(),
  dataStorage = character(),
  dataOrigin = character()
)

## S4 method for signature 'Spectra'
filterEmptySpectra(object)

## S4 method for signature 'Spectra'
filterDataOrigin(object, dataOrigin = character())

## S4 method for signature 'Spectra'
filterDataStorage(object, dataStorage = character())

## S4 method for signature 'Spectra'
filterFourierTransformArtefacts(
  object,
  halfWindowSize = 0.05,
  threshold = 0.2,
  keepIsotopes = TRUE,
  maxCharge = 5,
  isotopeTolerance = 0.005
)

## S4 method for signature 'Spectra'
filterIntensity(
  object,
  intensity = c(0, Inf),
  msLevel. = uniqueMsLevels(object),
  ...
)

## S4 method for signature 'Spectra'
filterIsolationWindow(object, mz = numeric())

## S4 method for signature 'Spectra'
filterMsLevel(object, msLevel. = integer())

## S4 method for signature 'Spectra'
filterMzRange(
  object,
  mz = numeric(),
  msLevel. = uniqueMsLevels(object),
  keep = TRUE
)

## S4 method for signature 'Spectra'
filterMzValues(
  object,
  mz = numeric(),
  tolerance = 0,
  ppm = 20,
  msLevel. = uniqueMsLevels(object),
  keep = TRUE
)

## S4 method for signature 'Spectra'
filterPolarity(object, polarity = integer())

## S4 method for signature 'Spectra'
filterPrecursorMz(object, mz = numeric())

## S4 method for signature 'Spectra'
filterPrecursorMzRange(object, mz = numeric())

## S4 method for signature 'Spectra'
filterPrecursorMzValues(object, mz = numeric(), ppm = 20, tolerance = 0)

## S4 method for signature 'Spectra'
filterPrecursorCharge(object, z = integer())

## S4 method for signature 'Spectra'
filterPrecursorScan(object, acquisitionNum = integer(), f = dataOrigin(object))

## S4 method for signature 'Spectra'
filterRt(object, rt = numeric(), msLevel. = uniqueMsLevels(object))

## S4 method for signature 'Spectra'
filterRanges(
  object,
  spectraVariables = character(),
  ranges = numeric(),
  match = c("all", "any")
)

## S4 method for signature 'Spectra'
filterValues(
  object,
  spectraVariables = character(),
  values = numeric(),
  ppm = 0,
  tolerance = 0,
  match = c("all", "any")
)

Arguments

x	Spectra object.
substDefinition	For deisotopeSpectra() and filterPrecursorIsotopes(): matrix or data.frame with definitions of isotopic substitutions. Uses by default isotopic substitutions defined from all compounds in the Human Metabolome Database (HMDB). See isotopologues() or isotopicSubstitutionMatrix() in the MetaboCoreUtils for details.
tolerance	For filterMzValues() and reduceSpectra(): numeric(1) allowing to define a constant maximal accepted difference between m/z values for peaks to be matched (or grouped). For containsMz() it can also be of length equal mz to specify a different tolerance for each m/z value. For filterPrecursorMaxIntensity(): numeric(1) defining the (constant) maximal accepted difference of precursor m/z values of spectra for grouping them into precursor groups. For filterPrecursorIsotopes(): passed directly to the isotopologues() function. For filterValues(): numeric of any length allowing to define a maximal accepted difference between user input values and the spectraVariables values. If it is not equal to the length of the value provided with parameter spectraVariables, tolerance[1] will be recycled. Default is tolerance = 0.
ppm	For filterMzValues() and reduceSpectra(): numeric(1) defining a relative, m/z-dependent, maximal accepted difference between m/z values for peaks to be matched (or grouped). For filterPrecursorMaxIntensity(): numeric(1) defining the relative maximal accepted difference of precursor m/z values of spectra for grouping them into precursor groups. For filterPrecursorIsotopes(): passed directly to the isotopologues() function. For filterValues(): numeric of any length allowing to define a maximal accepted difference between user input values and the spectraVariables values. If it is not equal to the length of the value provided with parameter spectraVariables, ppm[1] will be recycled.
charge	For deisotopeSpectra(): expected charge of the ionized compounds. See isotopologues() for details.
object	Spectra object.
mz	For filterIsolationWindow(): numeric(1) with the m/z value to filter the object. For filterPrecursorMz() and filterMzRange(): numeric(2) defining the lower and upper m/z boundary. For filterMzValues() and filterPrecursorMzValues(): numeric with the m/z values to match peaks or precursor m/z against. For filterPrecursorPeaks(): character(1) defining whether mass peaks with an m/z matching the spectrum's precursor m/z (mz = "==", the default) or mass peaks with a m/z that is equal or larger (mz = ">=") should be removed.
msLevel.	integer defining the MS level(s) of the spectra to which the function should be applied (defaults to all MS levels of object. For filterMsLevel(): the MS level to which object should be subsetted.
spectraVariables	For selectSpectraVariables(): character with the names of the spectra variables to which the backend should be subsetted. For filterRanges() and filterValues(): character vector specifying the column(s) from spectraData(object) on which to filter the data and that correspond to the the names of the spectra variables that should be used for the filtering.
i	For [: integer, logical or character to subset the object.
j	For [: not supported.
...	Additional arguments.
drop	For [: not considered.
n	for filterAcquisitionNum(): integer with the acquisition numbers to filter for.
dataStorage	For filterDataStorage(): character to define which spectra to keep. For filterAcquisitionNum(): optionally specify if filtering should occur only for spectra of selected dataStorage.
dataOrigin	For filterDataOrigin(): character to define which spectra to keep. For filterAcquisitionNum(): optionally specify if filtering should occurr only for spectra of selected dataOrigin.
halfWindowSize	For filterFourierTransformArtefacts(): numeric(1) defining the m/z window left and right of a peak where to remove fourier transform artefacts.
threshold	For filterFourierTransformArtefacts(): the relative intensity (to a peak) below which peaks are considered fourier artefacts. Defaults to threshold = 0.2 hence removing peaks that have an intensity below 0.2 times the intensity of the tested peak (within the selected halfWindowSize).
keepIsotopes	For filterFourierTransformArtefacts(): whether isotope peaks should not be removed as fourier artefacts.
maxCharge	For filterFourierTransformArtefacts(): the maximum charge to be considered for isotopes.
isotopeTolerance	For filterFourierTransformArtefacts(): the m/z tolerance to be used to define whether peaks might be isotopes of the current tested peak.
intensity	For filterIntensity(): numeric of length 1 or 2 defining either the lower or the lower and upper intensity limit for the filtering, or a function that takes the intensities as input and returns a logical (same length then peaks in the spectrum) whether the peak should be retained or not. Defaults to intensity = c(0, Inf) thus only peaks with NA intensity are removed.
keep	For filterMzValues() and filterMzRange(): logical(1) whether the matching peaks should be retained (keep = TRUE, the default) or dropped (keep = FALSE).
polarity	for filterPolarity(): integer specifying the polarity to to subset object.
z	For filterPrecursorCharge(): integer() with the precursor charges to be used as filter.
acquisitionNum	for filterPrecursorScan(): integer with the acquisition number of the spectra to which the object should be subsetted.
f	For filterPrecursorScan(): defining which spectra belong to the same original data file (sample): Defaults to f = dataOrigin(x).
rt	for filterRt(): numeric(2) defining the retention time range to be used to subset/filter object.
ranges	for filterRanges(): A numeric vector of paired values (upper and lower boundary) that define the ranges to filter the object. These paired values need to be in the same order as the spectraVariables parameter (see below).
match	For filterRanges() and filterValues(): character(1) defining whether the condition has to match for all provided ranges/values (match = "all"; the default), or for any of them (match = "any") for spectra to be retained.
values	for filterValues(): A numeric vector that define the values to filter the Spectra data. These values need to be in the same order as the spectraVariables parameter.

Subset Spectra

These functions affect the number of spectra in a Spectra object creating a subset of the original object without affecting its content.

• [: subsets the spectra keeping only selected elements (i). The method always returns a Spectra object.

• filterAcquisitionNum(): filters the object keeping only spectra matching the provided acquisition numbers (argument n). If dataOrigin or dataStorage is also provided, object is subsetted to the spectra with an acquisition number equal to n in spectra with matching dataOrigin or dataStorage values retaining all other spectra. Returns the filtered Spectra.

• filterDataOrigin(): filters the object retaining spectra matching the provided dataOrigin. Parameter dataOrigin has to be of type character and needs to match exactly the data origin value of the spectra to subset. Returns the filtered Spectra object (with spectra ordered according to the provided dataOrigin parameter).

• filterDataStorage(): filters the object retaining spectra stored in the specified dataStorage. Parameter dataStorage has to be of type character and needs to match exactly the data storage value of the spectra to subset. Returns the filtered Spectra object (with spectra ordered according to the provided dataStorage parameter).

• filterEmptySpectra(): removes empty spectra (i.e. spectra without peaks). Returns the filtered Spectra object (with spectra in their original order).

• filterIsolationWindow(): retains spectra that contain mz in their isolation window m/z range (i.e. with an isolationWindowLowerMz <= mz and isolationWindowUpperMz >= mz. Returns the filtered Spectra object (with spectra in their original order).

• filterMsLevel(): filters object by MS level keeping only spectra matching the MS level specified with argument msLevel. Returns the filtered Spectra (with spectra in their original order).

• filterPolarity(): filters the object keeping only spectra matching the provided polarity. Returns the filtered Spectra (with spectra in their original order).

• filterPrecursorCharge(): retains spectra with the defined precursor charge(s).

• filterPrecursorIsotopes(): groups MS2 spectra based on their precursor m/z and precursor intensity into predicted isotope groups and keep for each only the spectrum representing the monoisotopic precursor. MS1 spectra are returned as is. See documentation for deisotopeSpectra() below for details on isotope prediction and parameter description.

• filterPrecursorMaxIntensity(): filters the Spectra keeping for groups of (MS2) spectra with similar precursor m/z values (given parameters ppm and tolerance) the one with the highest precursor intensity. The function filters only MS2 spectra and returns all MS1 spectra. If precursor intensities are NA for all spectra within a spectra group, the first spectrum of that groups is returned. Note: some manufacturers don't provide precursor intensities. These can however also be estimated with estimatePrecursorIntensity().

• filterPrecursorMzRange() (previously filterPrecursorMz() which is now deprecated): retains spectra with a precursor m/z within the provided m/z range. See examples for details on selecting spectra with a precursor m/z for a target m/z accepting a small difference in ppm.

• filterPrecursorMzValues(): retains spectra with precursor m/z matching any of the provided m/z values (given ppm and tolerance). Spectra with missing precursor m/z value (e.g. MS1 spectra) are dropped.

• filterPrecursorScan(): retains parent (e.g. MS1) and children scans (e.g. MS2) of acquisition number acquisitionNum. Returns the filtered Spectra (with spectra in their original order). Parameter f allows to define which spectra belong to the same sample or original data file ( defaults to f = dataOrigin(object)).

• filterRanges(): allows filtering of the Spectra object based on user defined numeric ranges (parameter ranges) for one or more available spectra variables in object (spectra variable names can be specified with parameter spectraVariables). Spectra for which the value of a spectra variable is within it's defined range are retained. If multiple ranges/spectra variables are defined, the match parameter can be used to specify whether all conditions (match = "all"; the default) or if any of the conditions must match (match = "any"; all spectra for which values are within any of the provided ranges are retained).

• filterRt(): retains spectra of MS level msLevel with retention times (in seconds) within (>=) rt[1] and (<=) rt[2]. Returns the filtered Spectra (with spectra in their original order).

• filterValues(): allows filtering of the Spectra object based on similarities of numeric values of one or more spectraVariables(object) (parameter spectraVariables) to provided values (parameter values) given acceptable differences (parameters tolerance and ppm). If multiple values/spectra variables are defined, the match parameter can be used to specify whether all conditions (match = "all"; the default) or if any of the conditions must match (match = "any"; all spectra for which values are within any of the provided ranges are retained).

Filter content of spectraData()

The functions described in this section filter the content from a Spectra's spectra data, i.e. affect values of, or complete, spectra variables. None of these functions reduces the object's number of spectra.

• dropNaSpectraVariables(): removes spectra variables (i.e. columns in the object's spectraData that contain only missing values (NA). Note that while columns with only NAs are removed, a spectraData() call after dropNaSpectraVariables() might still show columns containing NA values for core spectra variables. The total number of spectra is not changed by this function.

• selectSpectraVariables(): reduces the information within the object to the selected spectra variables: all data for variables not specified will be dropped. For mandatory columns (i.e., those listed by coreSpectraVariables(), such as msLevel, rtime ...) only the values will be dropped but not the variable itself. Additional (or user defined) spectra variables will be completely removed. Returns the filtered Spectra.

Filter content of peaksData()

The functions described in this section filter the content of the Spectra's peaks data, i.e. either the number or the values (m/z or intensity values) of the mass peaks. Also, the actual operation is only executed once peaks data is accessed (through peaksData(), mz() or intensity()) or applyProcessing() is called. These operations don't affect the number of spectra in the Spectra object.

• deisotopeSpectra(): deisotopes each spectrum keeping only the monoisotopic peak for groups of isotopologues. Isotopologues are estimated using the isotopologues() function from the MetaboCoreUtils package. Note that the default parameters for isotope prediction/detection have been determined using data from the Human Metabolome Database (HMDB) and isotopes for elements other than CHNOPS might not be detected. See parameter substDefinition in the documentation of isotopologues() for more information. The approach and code to define the parameters for isotope prediction is described here.

• filterFourierTransformArtefacts(): removes (Orbitrap) fast fourier artefact peaks from spectra (see examples below). The function iterates through all intensity ordered peaks in a spectrum and removes all peaks with an m/z within +/- halfWindowSize of the current peak if their intensity is lower than threshold times the current peak's intensity. Additional parameters keepIsotopes, maxCharge and isotopeTolerance allow to avoid removing of potential ⁠[13]C⁠ isotope peaks (maxCharge being the maximum charge that should be considered and isotopeTolerance the absolute acceptable tolerance for matching their m/z). See filterFourierTransformArtefacts() for details and background and deisitopeSpectra() for an alternative.

• filterIntensity(): filters mass peaks in each spectrum keeping only those with intensities that are within the provided range or match the criteria of the provided function. For the former, parameter intensity has to be a numeric defining the intensity range, for the latter a function that takes the intensity values of the spectrum and returns a logical whether the peak should be retained or not (see examples below for details) - additional parameters to the function can be passed with .... To remove only peaks with intensities below a certain threshold, say 100, use intensity = c(100, Inf). Note: also a single value can be passed with the intensity parameter in which case an upper limit of Inf is used. Note that this function removes also peaks with missing intensities (i.e. an intensity of NA). Parameter msLevel. allows to restrict the filtering to spectra of the specified MS level(s).

• filterMzRange(): filters mass peaks in the object keeping or removing those in each spectrum that are within the provided m/z range. Whether peaks are retained or removed can be configured with parameter keep (default keep = TRUE).

• filterMzValues(): filters mass peaks in the object keeping all peaks in each spectrum that match the provided m/z value(s) (for keep = TRUE, the default) or removing all of them (for keep = FALSE). The m/z matching considers also the absolute tolerance and m/z-relative ppm values. tolerance and ppm have to be of length 1.

• filterPeaksRanges(): filters mass peaks of a Spectra object using any set of range-based filters on numeric spectra or peaks variables. See filterPeaksRanges() for more information.

• filterPrecursorPeaks(): removes peaks from each spectrum in object with an m/z equal or larger than the m/z of the precursor, depending on the value of parameter mz: for ⁠mz = ==" (the default) peaks with matching m/z (considering an absolute and relative acceptable difference depending on ⁠toleranceandppm⁠, respectively) are removed. For ⁠mz = ">="⁠all peaks with an m/z larger or equal to the precursor m/z (minus⁠tolerance⁠and the⁠ppm⁠of the precursor m/z) are removed. Parameter⁠msLevel.⁠allows to restrict the filter to certain MS levels (by default the filter is applied to all MS levels). Note that no peaks are removed if the precursor m/z is⁠NA' (e.g. typically for MS1 spectra).

• reduceSpectra(): keeps for groups of peaks with similar m/z values in (given ppm and tolerance) in each spectrum only the mass peak with the highest intensity removing all other peaks hence reducing each spectrum to the highest intensity peaks per peak group. Peak groups are defined using the group() function from the MsCoreUtils package. See also the combinePeaks() function for an alternative function to combine peaks within each spectrum.

Author(s)

Sebastian Gibb, Johannes Rainer, Laurent Gatto, Philippine Louail, Nir Shahaf

See Also

• combineSpectra() for functions to combine or aggregate Spectra.

• combinePeaks() for functions to combine or aggregate a Spectra's peaksData()

Examples

## Load a `Spectra` object with LC-MS/MS data.
fl <- system.file("TripleTOF-SWATH", "PestMix1_DDA.mzML",
    package = "msdata")
sps_dda <- Spectra(fl)
sps_dda


##  --------  SUBSET SPECTRA  --------

## Subset to the first 3 spectra
tmp <- sps_dda[1:3]
tmp
length(tmp)

## Subset to all MS2 spectra; this could be done with [, or, more
## efficiently, with the `filterMsLevel` function:
sps_dda[msLevel(sps_dda) == 2L]
filterMsLevel(sps_dda, 2L)

## Filter the object keeping only MS2 spectra with an precursor m/z value
## between a specified range:
filterPrecursorMzRange(sps_dda, c(80, 90))

## Filter the object to MS2 spectra with an precursor m/z matching a
## pre-defined value (given ppm and tolerance)
filterPrecursorMzValues(sps_dda, 85, ppm = 5, tolerance = 0.1)

## The `filterRanges()` function allows to filter a `Spectra` based on
## numerical ranges of any of its (numerical) spectra variables.
## First, determine the variable(s) on which to base the filtering:
sv <- c("rtime", "precursorMz", "peaksCount")
## Note that ANY variables can be chosen here, and as many as wanted.

## Define the ranges (pairs of values with lower and upper boundary) to be
## used for the individual spectra variables. The first two values will be
## used for the first spectra variable (e.g., `"rtime"` here), the next two
## for the second (e.g. `"precursorMz"` here) and so on:
ranges <- c(30, 350, 200, 500, 350, 600)

## Input the parameters within the filterRanges function:
filt_spectra <- filterRanges(sps_dda, spectraVariables = sv,
                ranges = ranges)
filt_spectra

## `filterRanges()` can also be used to filter a `Spectra` object with
## multiple ranges for the same `spectraVariable` (e.g, here `"rtime"`)
sv <- c("rtime", "rtime")
ranges <- c(30, 100, 200, 300)
filt_spectra <- filterRanges(sps_dda, spectraVariables = sv,
                ranges = ranges, match = "any")
filt_spectra

## While `filterRanges()` filtered on numeric ranges, `filterValues()`
## allows to filter an object matching spectra variable values to user
## provided values (allowing to configure allowed differences using the
## `ppm` and `tolerance` parameters).
## First determine the variable(s) on which to base the filtering:
sv <- c("rtime", "precursorMz")
## Note that ANY variables can be chosen here, and as many as wanted.

## Define the values that will be used to filter the spectra based on their
## similarities to their respective `spectraVariables`.
## The first values in the parameters values, tolerance and ppm will be
## used for the first spectra variable (e.g. `"rtime"` here), the next for
## the second (e.g. `"precursorMz"` here) and so on:
values <- c(350, 80)
tolerance <- c(100, 0.1)
ppm <- c(0, 50)

## Input the parameters within the `filterValues()` function:
filt_spectra <- filterValues(sps_dda, spectraVariables = sv,
                values = values, tolerance = tolerance, ppm = ppm)
filt_spectra


##  --------  FILTER SPECTRA DATA  --------

## Remove spectra variables without content (i.e. with only missing values)
sps_noNA <- dropNaSpectraVariables(sps_dda)

## This reduced the size of the object slightly
print(object.size(sps_dda), unit = "MB")
print(object.size(sps_noNA), unit = "MB")

## With the `selectSpectraVariables()` function it is in addition possible
## to subset the data of a `Spectra` to the selected columns/variables,
## keeping only their data:
tmp <- selectSpectraVariables(sps_dda, c("msLevel", "mz", "intensity",
    "scanIndex"))
print(object.size(tmp), units = "MB")

## Except the selected variables, all data is now removed. Accessing
## core spectra variables still works, but returns only NA
rtime(tmp) |> head()


##  --------  FILTER PEAKS DATA  --------

## `filterMzValues()` filters the mass peaks data of a `Spectra` retaining
## only those mass peaks with an m/z value matching the provided value(s).
sps_sub <- filterMzValues(sps_dda, mz = c(103, 104), tolerance = 0.3)

## The filtered `Spectra` has the same length
length(sps_dda)
length(sps_sub)

## But the number of mass peaks changed
lengths(sps_dda) |> head()
lengths(sps_sub) |> head()

## This function can also be used to remove specific peaks from a spectrum
## by setting `keep = FALSE`.
sps_sub <- filterMzValues(sps_dda, mz = c(103, 104),
    tolerance = 0.3, keep = FALSE)
lengths(sps_sub) |> head()

## With the `filterMzRange()` function it is possible to keep (or remove)
## mass peaks with m/z values within a specified numeric range.
sps_sub <- filterMzRange(sps_dda, mz = c(100, 150))
lengths(sps_sub) |> head()

## See also the `filterPeaksRanges()` function for a more flexible framework
## to filter mass peaks


## Removing fourier transform artefacts seen in Orbitra data.

## Loading an Orbitrap spectrum with artefacts.
data(fft_spectrum)
plotSpectra(fft_spectrum, xlim = c(264.5, 265.5))
plotSpectra(fft_spectrum, xlim = c(264.5, 265.5), ylim = c(0, 5e6))

fft_spectrum <- filterFourierTransformArtefacts(fft_spectrum)
fft_spectrum
plotSpectra(fft_spectrum, xlim = c(264.5, 265.5), ylim = c(0, 5e6))

## Using a few examples peaks in your data you can optimize the parameters
fft_spectrum_filtered <- filterFourierTransformArtefacts(fft_spectrum,
                                               halfWindowSize = 0.2,
                                               threshold = 0.005,
                                               keepIsotopes = TRUE,
                                               maxCharge = 5,
                                               isotopeTolerance = 0.005
                                               )

fft_spectrum_filtered
length(mz(fft_spectrum_filtered)[[1]])
plotSpectra(fft_spectrum_filtered, xlim = c(264.5, 265.5), ylim = c(0, 5e6))


## *Reducing* a `Spectra` keeping for groups of mass peaks (characterized
## by similarity of their m/z values) only one representative peak. This
## function helps cleaning fragment spectra.
## Filter the data set to MS2 spectra
ms2 <- filterMsLevel(sps_dda, 2L)

## For groups of fragment peaks with a difference in m/z < 0.1, keep only
## the largest one.
ms2_red <- reduceSpectra(ms2, ppm = 0, tolerance = 0.1)
lengths(ms2) |> tail()
lengths(ms2_red) |> tail()

rformassspectrometry/Spectra documentation built on Sept. 27, 2024, 5:43 a.m.