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BIOINFORMATICS
ORIGINAL PAPER
Vol. 26 no. 1 2010, pages 98–103
doi:10.1093/bioinformatics/btp610
Systems biology
Methods for combining peptide intensities to estimate relative
protein abundance
Brian Carrillo1 , Corey Yanofsky1 , Sylvie Laboissiere2 , Robert Nadon2,3
and Robert E. Kearney1,∗
of Biomedical Engineering, McGill University, 2 McGill University and Genome Quebec Innovation Centre
Proteomics Platform and 3 Department of Human Genetics, McGill University, Montreal, Canada
1 Department
Received on September 17, 2009; revised on October 15, 2009; accepted on October 19, 2009
Advance Access publication November 5, 2009
Associate Editor: Burkhard Rost
ABSTRACT
Motivation: Labeling techniques are being used increasingly to
estimate relative protein abundances in quantitative proteomic
studies. These techniques require the accurate measurement
of correspondingly labeled peptide peak intensities to produce
high-quality estimates of differential expression ratios. In mass
spectrometers with counting detectors, the measurement noise
varies with intensity and consequently accuracy increases with the
number of ions detected. Consequently, the relative variability of
peptide intensity measurements varies with intensity. This effect must
be accounted for when combining information from multiple peptides
to estimate relative protein abundance.
Results: We examined a variety of algorithms that estimate
protein differential expression ratios from multiple peptide intensity
measurements. Algorithms that account for the variation of
measurement error with intensity were found to provide the most
accurate estimates of differential abundance. A simple Sum-ofIntensities algorithm provided the best estimates of true protein ratios
of all algorithms tested.
Contact: [email protected]
Supplementary information: Supplementary data are available at
Bioinformatics online.
1
INTRODUCTION
Labeling techniques are an increasingly popular means to measure
relative protein abundances for studies that need to capture the
dynamics of cellular proteomes and/or to define differences between
the proteomes of biological samples. Current technologies generally
use a workflow in which:
(1) Particular amino acids (or classes of amino acids) of proteins
(ICAT/SILAC) or peptides (iTRAQ) are labeled to distinguish
the different samples in the resulting spectra.
(2) The labeled samples are mixed and the resulting peptides
identified in a bottom-up approach.
(3) Peak pairs corresponding to the different labeled versions of
the same peptides are located and their intensities measured.
∗ To
98
whom correspondence should be addressed.
(4) The relative intensities of the peak pairs are used to estimate
the relative abundances of the peptides (Gygi, et al., 1999;
Han et al., 2001; Ong et al., 2002; Ross et al., 2004; Schulze
and Mann, 2004; Stewart and Figeys, 2001).
Recent developments in labeling technology have improved the
ionization efficiencies of labeled peptides resulting in labels that
are purer and more similar chemically (Gygi et al., 1999; Hansen
et al., 2003; Kirkpatrick et al., 2005; Li et al., 2003). At the same
time, improvements in mass spectrometer technology have resulted
in: higher resolving powers, leading to better separation of labeled
peaks; faster collection cycles, leading to the fragmentation of
more peptides per unit time; and enhanced fragmentation, leading
to better mass spectra and/or more peptide identifications (Alan,
1998; Loboda, 2000; Syka et al., 2004). Algorithmic advances have
also improved the quality of protein quantification; however, as yet
there has been little consideration as to how to best combine the
information from different peptides to predict the protein abundance
(Anderle et al., 2004; Ishihama et al., 2005; Kyriacos, 2006).
Many current schemes, both open and closed source, estimate
relative protein abundance by averaging the label ratios of all
peptides belonging to a protein (Lin et al., 2006; Pedrioli, 2006;
Shadforth, 2005; Schulze and Mann, 2004). This approach has
one evident limitation; if the peptide intensities are noisy, the
estimated relative protein abundance will depend upon which labels
are selected as the numerator and denominator (See Supplementary
Material A). Clearly, analysis results should not depend on such
arbitrary decisions.
There have been attempts to use more sophisticated algorithms,
Andreev et al. presented an algorithm that incorporates peptide
intensity and quality of identification (Andreev et al., 2006)
and showed that removing peptides with low identification
scores or outlying ratios improved quantification but did not
demonstrate its effectiveness. Griffin et al. (2007) mention the
use of signal intensities to ‘weight’ iTRAQ reporter ratios, but
did not explain how it is used or document its effectiveness.
MacCoss et al. (2003) used linear-least squares to combine
information from multiple peptides but again did not demonstrate
its effectiveness.
One must remember that intensity measurements from mass
spectrometers with counting detectors will display random errors
due to counting statistics. Thus, their intensity values can be
© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
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Methods for combining peptide intensities to estimate relative protein abundance
expected to follow a Poisson distribution
f (n ) =
λn e−λ
n!
to indicate the intensity of the j-th peptide of the i-th protein with label k.
We generated a data set simulating a labeling experiment as follows:
(1)
where f (n) is the probability of detecting n ions in an interval
and λ is the average number of ions (i.e. the noise-free intensity
value) for the interval. (See Supplementary Material B for full
derivation). The variance of the Poisson distribution is equal
to its mean λ, consequently data with Poisson statistics violate
the constant variance assumption of least-squares regression.
Moreover, most peptide to protein algorithms use only relative
intensity information and do not make explicit use of the
absolute peak intensity, the key indicator of the reliability of
the ratio estimate. We believe that these intensity dependent
effects must be accounted for explicitly when combining multiple
measurements.
This article addresses the question of how to best account
for Poisson statistics when using data from multiple peptides to
estimate relative abundance of proteins. The article is developed
in three parts. Part I demonstrates that peptide intensities observed
in a Q-TOF instrument do indeed follow a Poisson distribution.
Part II presents a simulation study that examines different ways
of combining peptide information and evaluates the accuracy of
the resulting protein abundance estimates. Our results show that
methods that combine absolute peptide intensities prior to estimating
relative abundances are most accurate. Part III concludes the article
by presenting experimental results that confirm the findings of the
simulation study.
(1) The peptide intensities measured from a protein with label 1 were
simulated by sampling seven values from Poisson distributions with a
randomly selected mean intensities (λi ), less than some predetermined
maximum (λmax )
p1i,1..7 = λi,1..7
(3)
(2) The peptide intensities measured from the protein with label 2 were
simulated by sampling a corresponding set of values from Poisson
distributions having mean values a multiple (α = fold-change) larger
than the first set. To give:
p2i,1..7 = α×λi,1..7
(3) In some cases, where noted, an additional outlier peptide was
generated having a random intensity and fold change (β), to simulate
a misidentified peptide.
p1i,8 = λi,8 ;
2.1
(5)
(5) Steps 1 through 5 were repeated for different predetermined maximum
intensities (step 1).
The fold change for each simulated protein pair was estimated using six
peptide-to-protein algorithms:
(1) Average of the ratios: The intensity ratios for all peptides belonging
to the same protein, including possible outliers, were computed and
their arithmetic mean used to estimate protein abundance.
1 pi,j
n
p2i,j
n
1
(6)
j=1
METHODS
Part I
It is difficult to estimate the statistical distributions of peptide intensity in
most LC/MS experiments because the peptide intensity changes continuously
with the gradient. Consequently, we ran a separate experiment in which
a solution containing the peptide fibrinogen was injected directly into
a Q-TOF mass spectrometer. The direct injection bypassed the usual
rise and fall of peptide concentration in a typical LC/MS experiment.
This allowed us to acquire 1000 fragmentation spectra sequentially under
stationary conditions. We analyzed these using in-house algorithms to
extract the intensity and area of 12 prominent b and y ions in each
of the 1000 runs. Peak intensities of a single scan on our instruments
ranged from 0 to 1000 counts while peak areas were ∼10 times
the peak height; the sum of several Poisson distributions is also a
Poisson distribution so the area of a peak should exhibit the same
behaviour as the intensity. Consequently, we used area as well as peak
intensity measures to increase the dynamic range for this part of the
analysis.
We also conducted a statistical simulation of the results expected from
an experiment in which the same peptide is present in two samples with
an abundance ratio of three. A first set of intensities were generated from a
Poisson random number generator with a range of mean intensities covering
the operating range of the mass spectrometer. A second set of intensities
was then generated from a Poisson distribution with mean values three times
those of the first set. The simulation was repeated 500 times to estimate the
statistical behavior.
(2) Libra ratio: An outlier rejection scheme was applied to the average
of the ratios algorithm. Ratios that were greater than two standard
deviations from the mean were discarded and a new average of the
ratios computed (Pedrioli, 2006).
(3) Linear regression: Standard linear regression was used to fit a line
through the peak intensities, and the slope of the line (β) was used as
the estimate of relative abundance.
⎡
p1i,1
⎤
⎡
Part II
We will use the notation:
pki,j
(2)
p2i,1
⎤
⎡
ε1
⎤
⎢ ⎥
⎢ 1 ⎥ ⎢ 2 ⎥
⎢ ε2 ⎥
⎢ pi,2 ⎥ ⎢ pi,2 ⎥
⎥ ⎢
⎥
⎢ ⎥
⎢
⎢ . ⎥ = ⎢ . ⎥ βi + ⎢ . ⎥
⎢ . ⎥
⎢ . ⎥ ⎢ . ⎥
⎢ . ⎥
⎢ . ⎥ ⎢ . ⎥
⎦ ⎣
⎦
⎣ ⎦
⎣
εn
p1i,n
p2i,n
(7)
(4) Principle component analysis: The set of direction axes for which
the greatest variance of the data was projected onto the principal
axes was determined. This may be thought of as treating the data as a
multivariate normal data set and estimating the axes of the underlying
ellipsoid (Duda et al., 2001). The slope of the principal axis was used
as the estimate of relative abundance.
(5) Sum of intensities: The intensities of all peaks for the same label and
protein were summed. The ratio of the sums was the estimate of the
relative abundance.
n
n
Si =
p1i,j
p2i,j
(8)
j=1
2.2
p2i,8 = β ×λi,8
(4) Steps 1 through 4 were repeated 1000 times to gather statistical
information.
Ai =
2
(4)
j=1
(6) Total least squares: A straight line was fit between the peak values
for the two labels. However, unlike linear regression, the method
recognizes that there are errors in both variables and so it minimizes
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B.Carrillo et al.
the orthogonal distance between the points and the best fit line (Huffel
and Vandewalle, 1991).
In addition, the last four algorithms were applied in conjunction with an
outlier rejection scheme. This scheme weighted the data using a ‘Fair’
weighting scheme where intensity values were divided by their distance to
the current ‘best’ fit line (Coleman et al., 1980). The process was repeated
until the change in the slope of the “best fit” line was less than a set
threshold (10−6 ).
The estimates from the six algorithms were compared with the known
fold change to determine estimation errors.
2.3
Part III
To validate the results of the simulations, the six algorithms were tested using
data from a standard set of eight proteins, prepared as follows. Eight proteins
were mixed together using half of a double Latin square design (as depicted
in Table 1), creating 16 different mixes. Each mix was recreated four more
times to give five identical sets of 16 mixes. Each set was analyzed by Mass
Spectrometry sequentially with the order of analysis of the mixes randomized
within each set. Each sample was analyzed twice, once by MS/MS and once
by MS.
Sample preparation (other than noted above), liquid chromatography,
mass spectrometry and preliminary data processing (Mascot and in house
algorithms) are described in detail by Bell et al. (2009).
Search results from all MS/MS runs were pooled and used to compile
a list of identified peptides that originated from the eight proteins of
interest. The retention time and m/z ratios of these peptides were then
used by in-house algorithms to extract peak intensity information from
the MS runs. The data extracted included the intensity of the first three
isotopes of each peptide peak as well as the intensity of the signal in
a neighbourhood (±0.07Th and ±15s) around each peak. This yielded
three matrices (15×31) of intensity data that were matched in acquisition
time ensuring that major sources of variability (errors caused by retention
time differences, sample handling errors, etc.) were equal. The second
and third matrices were shifted in the m/z axis by an amount determined
by the peptide charge (1/2Th for a doubly charged peptide, 1/3Th for a
triply charged peptide, etc.). The intensity of the three matrices should
therefore differ only by their isotopic ratios and measurement errors.
Note that because of the different mixes and repeated runs, any one peptide
was present in the data set as many as 80 times with a wide range of
intensities.
The data were analyzed as follows:
(1) A data point (p11 ) was selected randomly from the matrix of the base
isotope [M], of a peptide from a MS run (solid yellow arrow on the
left in Fig. 1). Using the position (row, column) in the matrix of p1 ,
a second data point (p21 ) was selected from the matrix of the second
isotope [M+1] (dashed yellow arrow); this matching of data points
ensures that the retention times are identical and that both points arise
from the same relative position in the peak shape. A second set of
two points (p12 and p22 ) were selected from the same peptide matrices
(purple arrows in Fig. 1) in a similar manner. The second set shares
the same underlying ratio, but at a different intensity. The two sets
are thus considered
p21..2 = α×p11..2
(9)
where the fold-change, α, was determined by the isotopic ratio of
the particular peptide. The ‘true’ fold-change (α) was computed by
isotopic elemental composition (Palmblad, 1999) using the peptide
sequences identified by Mascot with <5% chance of being a random
match (Mascot Scores > ID).
(2) Step 1 was repeated using different combinations of isotope sets in
step 1 ([M] versus [M+2], and [M+1] versus [M+2]) to vary the range
of ratios and intensities (ratios range from 1 : 1 to 8 : 1 with ∼90%
between 1 : 1 and 3 : 1).
(3) Steps 1 and 2 were repeated for the 228 other peptides identified and
across all 80 experiments to provide a range of ratios and intensities.
(4) Each analysis was repeated 500 times to gather data for statistical
analysis.
The analysis was repeated with the number of matched pairs varied from 2
through 12, to evaluate the effects of using different numbers of peptides per
protein.
The fold-change (α) for each set was estimated using the algorithms from
Part 2. All custom algorithms were written in the MATLAB programming
environment and will be made available upon request.
Table 1. Half a ‘double Latin square’ showing the amount (in nanograms)
of each protein in each of the 16 mixes
MIX
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Protein
P1
P2
P3
P4
P5
P6
P7
P8
10
10
640
640
160
160
40
40
960
960
320
320
80
80
20
20
20
960
960
320
320
80
80
20
10
640
640
160
160
40
40
10
40
40
10
10
640
640
160
160
320
320
80
80
20
20
960
960
80
20
20
960
960
320
320
80
40
10
10
640
640
160
160
40
160
160
40
40
10
10
640
640
80
80
20
20
960
960
320
320
320
80
80
20
20
960
960
320
160
40
40
10
10
640
640
160
640
640
160
160
40
40
10
10
20
20
960
960
320
320
80
80
960
320
320
80
80
20
20
960
640
160
160
40
40
10
10
640
Fig. 1. The three matrices of the first three isotopes of a peptide. The solid
arrows show two data points selected randomly from the monoisotopic
matrix; the dashed arrows indicate the ‘matched’ data points selection
selected from the [M+1] matrix.
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Methods for combining peptide intensities to estimate relative protein abundance
Fig. 3. Mean value bracketed by ±1 SD of the ratio of two simulated Poisson
variables whose mean values differ by a factor of three as a function of
intensity.
Fig. 2. Ion intensity data from the fragmentation of the Fibrinogen peptide
(EGVNDNEEGFFSAR) injected directly into a q-TOF mass spectrometer.
(A) Mean and variance of peaks co-vary linearly as expected for a Poisson
distribution. (B) Coefficient of variation varies inversely as the square-root
of the mean intensity.
3
3.1
RESULTS
Part I
Figure 2 shows the results derived from the analysis of the first
experiment. Figure 2A shows that the mean and variance of
intensity and area co-vary; the superimposed linear fit demonstrates
that the relation is close to linear, as expected for a Poisson
distribution. Because of this linear increase in variance, the standard
deviation will increase more slowly than the mean and consequently,
the relative noise will decrease as the mean increases. This is
demonstrated in Figure 2B that shows the coefficient of variation
(σ/µ) of the peak intensity as a function of the mean. As expected,
it follows an inverse square-root relation.
Thus, low intensity (low count) peaks will be relatively more noisy
than high intensity peaks. Consequently, the accuracy of any peptide
ratio will depend upon the absolute intensity of the two peaks under
consideration. Figure 3 shows the results of the simulation study that
examined how the mean and standard deviation of the abundance
ratio estimates vary as a function of intensity. At low intensities, the
mean value differs from the true value and the standard deviation
is large. The mean of the estimate converges to the true value
as the intensity increases while the standard deviation decreases.
This demonstrates, clearly, that the accuracy with which a peptide
abundance ratio can be estimated depends strongly on the absolute
intensities.
Fig. 4. Error versus intensity for six peptide-to-protein algorithms as a
function of intensity. The sum of intensities and total least squares algorithms
provide the most accurate estimates. Data were generated from 1000
simulated experiments in which seven peptides were observed from proteins
with an true fold change of 2.
3.2
Part II
Figure 4 shows the mean fold-change errors as a function of
maximum intensity for simulations with no outliers and a true foldchange of two. All algorithms behaved similarly; the error decreased
as the intensity increased. However, the sum of intensities and the
total least squares methods consistently performed best, giving a fold
change error that was ∼10% lower than that of the other methods.
In practice, it is quite likely that quantitative data will have
outliers. For example, if a protein is identified using nine peptides,
each with 95% confidence of identification, there will be a 37%
chance that there will be at least one outlier. Figure 5 summarizes
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Fig. 5. Error versus intensity for six algorithms with one outlier. Data were
generated from 1000 simulated experiments in which seven peptides were
observed from proteins with an true fold change of 2 with one outlier peptide
with random intensity and fold change.
Fig. 6. Effects of an outlier rejection on the sum of intensities and total least
squares algorithms. Outlier rejection decreases the errors particularly at high
mean intensities.
the results of simulations with one outlier. As expected, the error
in all algorithms increased; nevertheless, the sum of intensities and
the total least squares methods still gave the best results with errors
∼10% lower than the other methods.
Adding the outlier rejection scheme significantly improved both
the sum of intensities and the total least squares algorithms. Figure 6
shows that the error for both algorithms was reduced by ∼20% by
the addition of outlier rejection when one outlier was present.
3.3
Part III
Figure 7 shows the average fold-change error as a function of the
number of peptides used to estimate the fold-change. The trend
Fig. 7. Validation experiment results showing average error versus number
of peptides for five peptide-to-protein algorithms. Total least squares and
sum-of-intensities perform best irrespective of the number of peptides used.
Fig. 8. Experimental cumulative distributions of ratio errors showing larger
populations with less error for the sum of intensities and total least squares
algorithms. The dashed lines highlight the 10% error mark; 50% of the Linear
Regression estimates and 63% of the sum-of-intensities estimates show errors
<10%.
was the same for all methods; the error decreased as the number
of peptides increased. However, as with simulations, the sum of
intensities and total least squares algorithms performed best. Note
that these averages incorporate results from a range of intensities and
fold changes and so provide only a rough metric of performance.
To provide a better understanding of error behavior, Figure 8
shows the cumulative probability of the number of data sets as a
function of error for the different methods. This figure shows that
linear regression estimated the abundances with an error of <10% for
50% of the data sets. In contrast, the sum of intensities and total least
squares performed substantially better giving estimates with <10%
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Methods for combining peptide intensities to estimate relative protein abundance
error for 63% of the data sets. Moreover, for 90% of the peptides
examined, the sum of intensities and total least squares algorithms
estimated the abundance ratios most accurately (their curves are the
farthest left in Fig. 8).
4
DISCUSSION
This article examines how to combine abundance information from
multiple peptides to predict protein abundance most accurately.
Our results demonstrate that the sum of intensities and total
least squares algorithms provided the most accurate estimates of
protein abundance for a wide range of simulated and experimental
conditions. The commonly used average of ratios algorithm
consistently provided estimates with the highest errors. The linear
regression algorithm performed poorly consistently; this is likely
because the algorithm did not account for errors on both axes.
Principal component analysis performed midrange to all the
algorithms, with or without the presence of outliers.
A novel feature of the analysis presented here is that it does
not rely on an exact knowledge of the relative abundances of the
proteins in the different mixtures. These were varied experimentally
by carefully combining different amounts of pure proteins manually
and will inevitably lead to some (unknown) error in the relative
abundance. Rather, we opted to use the relative intensity of the
different isotopic peaks for the same peptide as a means of evaluating
accuracy. By selecting peptides of different mass we were able to
investigate a range of abundance ratios while data from the different
mixtures resulted in a wide range of intensities.
The sum of intensities and total least squares both performed well
with the performance of the sum of intensities being marginally
better. The sum of intensities has the added advantage of being
computationally simple; it required 1/16 of the time needed by
the total least squares method. The sum of intensities algorithm is
a simple, computationally efficient algorithm that (i) incorporates
intensity, or data quality into the estimates of fold change; (ii) does
not fail when only few peptides are identified (no singularities);
and (iii) consistently provides the best estimates of protein
quantification. We therefore believe that the sum of intensities
algorithm is optimal amongst the algorithms tested. The results
presented should be generally applicable to all mass spectrometers
using counting detectors including all time-of-flight and most ion
trap mass spectrometers.
ACKNOWLEDGMENTS
The authors are indebted to John Bergeron for securing funding
(GQ/GC, CFI, VRQ). We would like to acknowledge the McGill
University and Genome Quebec Innovation Centre Proteomics
Platform, and in particular Pascal Pleynet, Daniel Boismenu, Line
Roy and Nathalie Hamel for technical support and Benoit Houle for
securing GC/GQ-funding.
Funding: Genome Quebec; Genome Canada; Natural Sciences and
Engineering Research Council of Canada; Canadian Institutes of
Health Research (to R.K.); McGill Majors fellowship (to B.C.).
Conflict of Interest: none declared.
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