CA2484625A1

CA2484625A1 - Methods for time-alignment of liquid chromatography-mass spectrometry data

Info

Publication number: CA2484625A1
Application number: CA002484625A
Authority: CA
Inventors: Scott M. Norton
Original assignee: Individual
Current assignee: Caprion Proteomics USA LLC
Priority date: 2002-05-09
Filing date: 2003-05-09
Publication date: 2003-11-20
Also published as: WO2003095978A3; US20040113062A1; US7628914B2; AU2003239409A8; US6989100B2; WO2003095978A2; US20060131222A1; AU2003239409A1

Abstract

A method for comparing mass spectrometer data comprising the steps of obtaining raw data (22), time aligning data set pairs (26), and comparing the resultant spectra (28).

Description

METHODS FOR TIME-ALIGNMENT OF LIQUID CI3ROMATOGRAPIISf-MASS
SPECTROMETRY DATA
FIELD OF THE INVENTION
[0003.] The present invention relates generally to analysis of data collected by analytical technques such as chromatography and spectrometry. More particularly, it relates to methods for time-aligning multi-dimensional chromatograms of different samples to enable automated comparison among sample data.
BACKGROUND OF THE INVENTION

[0002] The high sensitivity and resolution of liquid chromatography-mass spectrometry (LC-MS) male it an ideal tool for comprehensive analysis of cample~
biological samples. Comparing spectra obtained from samples canesponding to different patient cohorts (e.g., diseased versus non-diseased, or drug responders versus non-responders) or subjected to different stimuli (e.g., drag administration regimens) can yield valuable information about sample components correlated With particular conditions. Such components may serve as biological marl~ers that enable earlier and more precise diagnosis, patient stratifieati.on, or prediction of clixlrcal outcomes. They may also guide the discovery of suitable and novel drug targets. Because this approach extracts a large amount of information from a very small sample size, automated data collection and analysis methods are desirable.

[0003] LC-MS data are reported as intensity or abundance of ions of varying mass-to-charge ratio (mlz) at varying chromatographic retention times. A two-dimensional spectrum of LC-MS data from a single sample is shown in ~'IG. l, in which the darl~.ess of points corresponds to signal intensity. A horizontal slice of the spectrum yields a mass chromatogram, the abundance ofions in a particular m!z range as a function of retention time. A vertical slice is a mass spectnim, a plot of abundance of ions of varying m/z at a particular retention time interval. The tv~ro-dimensional data are acquired by performing a mass scan at regular intervals of retention time. Summing the mass spectntm at each retention time yields a total ion chromatogram (TIC}, the abundance of all ions as a function of retention time.
Local maxima in intensity (with respect to both retention time and m/z} are referred to as peals. W general, peaks may span several retention time scan intervals and m/z values.

[0004] One sig~iificant obstacle for automated analysis of LC-IVIS data is the nonlinear variability of chromatographic retention times, which can exceed the width of peaks along the retention time axis substantially. This variability arises from, for example, changes in column chemistry over time, instrument drift, interactions among sample components, protein modifications, and minor changes in mobile phase composition. While constant time offsets can be corrected for easily, nonlinear variations are mare problematic and significantly hamper the recognition of corresponding pealcs across sample spectra. This problem is illustrated by the chromatograms of FIB. 2, in which the dotted and solid curves represent total ion chromatograms of samples from two different patients. While it can be assumed that the dotted curve leas been time-shifted from the solid curve, it is cliff cult to predict from tl~e two curves to which of the two solid peaks the dotted peal corresponds.

[0005] Various methods have been provided in the art for addressing the problem of chromatographic retention time shifts, including correlation, curve fitting, and dynamic programming methods such as dynamic tine warping and correlation optimized warping. For example, a time warping algorithm is applied to gas chromatography/Fourier transform infrared (FT~IR}/mass spectrometry data from a gasoline sample in C.P. Wang and T.L. Isenhour, "Time-warping algorithm applied to chromatographic peals matching gas chromatography/Fourier transform infrared/mass spectrometry," flrral. CTzem. S9: 649-654, 1987. hi this method, a single FT-IR
interferogram is aligned with a TIC. While this method may be effective for simple samples, it may be inadequate for more complex samples such as biological fluids, which can contain thousands of different proteins and peptides, yielding thousands of potentially relevant anal, more importantly, densely spaced (in both m/z and retention time} peaks.

[0006] There is still a need, therefore, for a robust method for time-aligning chromatographic-mass spectrometric data.

BRIEF DESCRIPTION OF THE FIGURES
[000'l] FIG. 1 (prior art) shows a sample two-diznensianal liquid chrornatograplay-mass spectrometry {LC-MS) data set.
[0008] FIG. Z is a schematic diagram of portions of total ion chromatograms of t~va different samples, illustrating the difficulties in properly tune-aligning spectra.
[0009] FIG. 3 is a flow diagram of one embodiment of the present invention, a method fax comparing samples.
[0010] FIGS. 4A~4B illustrate aspects of a dynamic time warping {DTW) method according to one embodiment of the present invention.
[0011] FIG. 5 shows a grid of chxoznatagraphic time paints, used in DTW, ~cvith an optin~.al route through the grid indicated.
[0012] FIGS. 6A-6L illustrate two consfiraints on a DTW method according to one embodiment of the present invention.
[0013] FIGS. 7A-'7C illustrate aspects of a locally-weighted regression smoothing method according to one embodiment of the present invention.
[0014] FIGS. 8A-8E show corresponding peals of one reference and three test LC-MS data sets before and after tune-alignment by DTW.
[0015] FIG. 9 is a plot showing results of aligzunent of LC-MS data sets by robust LOESS and DTW.
DETAILED DESCRTPTION OF THE INVENTION
[0016] Various embodiments of the present invention provide methods far time-aligning tw o-dimensional chromatography-mass spectrometry data sets, such as liquid chromatography-mass spectrometry {LC-MS) data sets, also referred to as spectra.
These data sets can have nonlinear variations in retention time, so that corresponding peaks {i.e., peaks representing the same analyte) in different samples elute from the chromatographic column at different times. Additional embodiments provide methods for comparing samples and data sets, methods fox identifying biological markers {biorrzarkers), aligned spectra produced according to these methods, samples compared according to these zxzethods, biomarl~ers identified according to these methods, and methods for using the identified biomarl~ers far diagnostic and therapeutic applications.

[001'7] The methods are effective at aligning two-dimensional data sets obtained from both simple and complex samples. Although complex and simple are relative terms and are xxot intended to Iimit the scope of the present invention in any way, complex samples typically have many more and more densely spaced spectral peals than do simple samples. For examples, complex samples such as biological saxuples may have upwards of hundreds or thousands of peals in sixty minutes of retention time, such that the total ion chromatogram (TIC) is too complex to alloy resolution of individual features. Rather than use composite one-dimensional data such as the TIC, tile methods in embodiments of the present invention use data from individual mass chromatograms, i.e., data representing abundances or intensities of ions in particular mlz ranges at particular retention times. The mlz range included within a single mass c2~roznatcagram xrzay reflect floe instrument precision or may be the result of preprocessing (e.g., binxxing) of the rave data, and is typically on the order of between about 0.1 axxd 1.0 atomic mass unit (amu). I.VIass scans typically occur at intezvals of between about one and about three seconds.
[0018 h1 some embodiments of the present invention, computations are referred to as being performed "in dependence on at least two mass chromatograms from each data set." This phrase is to be understood as referring to computations on individual data from a mass chromatogram, rather than to data summed over a number of chromatogr-axns.
[0~19~ While embodiments ofthe invention are described below vcrith reference to chrazxiatography and mass spectrometry, and particularly to liquid chromatography, it will be apparent to one of skill in the art how to apply the methods to any other hyphenated chroxuatographic technique. Fox example, the second dimension may be any type of electromagnetic spectroscopy such as microwave, fax infrared, infrared, Ramaxz ar resonance Raxxxan, visible, ultraviolet, far ultraviolet, vacwun ultraviolet, x-ray, or ultraviolet fluorescence or phosphorescence; any magnetic resonance spectroscopy, such as nuclear magnetic resonance {I~NIR) or electron paramagnetic resonance {EPR); and any type of mass spectrometry, including iozuzation methods such as electron impact, chemical, thermospray, electrospray, matrix assisted laser desorption, and inductively coupled plasma ioni2ation, and any detection methods, including sector, quadzupole, ion trap, time of flight, and Fourier transform detection.
~0020~, Time-alignmezlt methods are applied to data sets acquired by performing clzrornatographic and spectroznetrie or spectroscopic methods on chemical or biological samples. The samples can be in any homogeneous or heterogeneous form.
that is compatible with the chromatographic instnunent, for example, one or more of a gas, liquid, solid, gel, or liquid crystal. Biological samples that can be analyzed by embodiments of the present invention include, without limitation, whole organisms;
parts of organisms (e.g., tissue samples); tissue homogenates, extracts, infusions, suspensions, excretions, secretions, or emissions; administered and recovered material; and culture supernatants. Examples of biological fluids include, without limitation, whole blood, blood plasma, blood serum, urine, bile, cerebrospinal fluid, milk, saliva, mucus, sweat, gastric juice, pancreatic juice, seminal fluid, prostatic fluid, sputum, broncheoalveolar lavage, and synovial fluid, and any cell suspensions, extracts, or concentrates of these fluids. Non-biological samples include air, water, liquids from manufacturing wastes or processes, foods, and the like. Samples may be correlated with particular subjects, cohorts, conditions, time points, or any other suitable descriptor or category.
[fl(?21) FIG. 3 is a flaw diagram of a general method 20 accoxding to one embodin gent of the present invention. The method is typically implemented in soft'vare by a computer system in comn~uzaieation with an analytical instruzxzent such as a liquid chromatography-mass spectrometry (LC-MS} instrument. In a first step 22, raw data sets are obtained, e.g., fiom the instrument, from a different computer system, or from a data storage device. The data sets, which are also referred to as spectra or two-dimensional data sets or spectra, contain intensity values fox discrete values (or ranges of values} of chromatographic retez2tion time (or scan index) and mass-to-charge xatio (zxzlz}. At each scan time of the instrument, an entire mass spectrum is obtained, and the collection of mass spectra for the chromatographic z-an of that sample males up the data set. Typically, a collection of data sets is acquired from a large number (i.e., more than two} of samples before subsequent processing occurs.

j0i~22~ Zn an optional next step 24, the data sets are preprocessed using conventional algorithms. ~xaznples of preprocessing techniques applied include, without lizxzitation, baseline subtraction, smoothing, noise reduction, de-isatoping, nc~nnali~ation, and peak list creation. Additionally, the data can be bizmed into defned mlz intervals to create mass cl~roznatograms. Data are collected at discrete scan times, but zWz values in the mass spectra are typically of very high mass precision. lr~. order to create mass chromatograms, data falling Within a specified xnlz interval {e.g., d.5 emu) are combined into a composite value fox that intezval. Any suitable biz~nzrzg albarithm znay be employed; as is l~noutn in the art, tl~.e selection of a binning algorithm and its parameters znay leave implications far data smoothness, f delity, and quality.
(OQ23~ In step 26, a time-aligning algoritlun is applied to Qne oz more pair of data sets. One data set can be chosen {arbitrarily ox according to a criterions to serve as a reference spectz-~,tm and all other data sets tune-aligned to dais spectrum.
~'or example, assuming the samples are analyzed on the xnstz~.imezlt consecutively, the reference data set can correspond to the sample analyzed in the middle of the process.
Alternatively, a. feedback method can be implemented in ~vhzch tlae degree of time shift is measured for each data set, potentially with respect to one ox n~zore of the data sets chosen arbitrarily as a reference data set, and the one with a median time shift, according to some metric, selected as the reference data set. Data sets can also be evaluated by a perceived or actual quality znetrie to determine which to select as the reference data set.
(Q~i24~ After the data sets are aligned to a common retention time scale, the aligned data sets can be compared automatically in step 2$ to locate features that differentiate the spectra. For example, a pear that occurs in only certain.
spectra or at significantly different izztensity levels in different spectra may represent a biological marker or a component of a biological marker that is indicative of or diagnostic for a characteristic of the relevant samples {e.g., disease, response to therapy, patient group, disease progression). Zf desired, the identity of the ions responsible for the distinguishing features can be identified. Biological markers may also lee rxzore complex cozrzbinations of spectral features or sample con~ponezzts v~rith ar without other clinical or biological factors. Tdentifying spectral differences and biological d marl~ers is a inulti-step process and will not be described in detail herein.
For more information, see U.S. Patent Application No, 091994,576, "Methods for Efficiently Mining Broad Data Sets for Biological Maxlcexs," filed I l /?7/2~OI, which is incozporated herein by reference. In general, this step 28 is referred to as differential phenatyping, because differences among phenotypes, as represented by the comprehensive (rattier than selective) LC-MS spectrum of expressed proteins and small molecules, are detected.
[4025 Step 26, time-aligning pairs of spectra, can be implemented in many different ways. In one embodiment of the invention, spectra are aligned using a variation of a dyzlaznic time warping (DTW) rriethad. DTW is a dynamic programming techiuque that was developed in the field of speech recognition for time-aligning speech patterns and is described in H. Sakoe and S. Chiba, "Dynarrzic programming algorithm optimization for spol~en word recognition," .IEEE
T'~ans.
Acoust" ~'peecla, Sig-faal Pi°ocess. ASSP-26: ~3-49, 1978, which is incorporated herein by reference.
[0026 In embodiments of the present invention, DTW aligns two data sets by nonlinearly stretching and contracting ("warping") the time component of the data sets to synchronize spectral features and yield a minimum distance between the two spectra. In asymmetric DTW, a test data set is warped to align with a reference data set. Alternatively, in symmetric DTW, bath data sets are adjusted to fit a coinznon time index. The follo~,ving description is of asymrxzetric warping, but it will be apparent to one of ordinary shill in the art, upon reading this description, how to perform the analogous symmetric warping.
[OQ27] FIG. 4A is a plot of two chromato~'ams, labeled test and reference, whose time scales are nonlinearly related. That is, peaks representing identical analytes, referred to as corresponding peals (and the corresponding paints that male up these peaks), occur at different retention times, and there is no linear transformation of tune components that will map corresponding peals to the same retention times.
Although the data are shown as continzzaus curves, each data set consists of discrete values (an entire mass spect~zm) at a sequence of time indices; for clarity, only a single intensity value, rather than an entire mass spectzlun, is shown at each time point. Tzrz the figure, corresponding paints axe connected by dashed lines, which represent a mapping of time points in the reference data set to time points in the test data set.
This mapping is shown more explicitly in the table of FIG. 4B. The abject of a DTW algorithm is to identify this time point mapping, from which an aligned reference data set may be constructed. Note that DTW aligns the entire data set, and not dust peals of the data set, and that DTW yields a discxete time point mapping, rather than a function that transforms the original time points into aligned time paints. As a result, same paints (reference and test} do not get mapped, and unmapped points can be handled as described below.
(0028 Conceptually, the DTW method considers a set of possible time paint mappings and identifies the mapping that xnin~nizes an accumulated distance function between the reference and test data sets. Consider the grid in FIG. 5, in which rows correspond to r time indices i in the test data set and columns to Jtime indices j in the reference data set {I and .~ can be different). Each possible time point mapping can be represented as a route c{k) through this grid, where c(Ic) = [i(k), j(k)] and I <_k ~K.
Far example, if the test and reference data sets were perfectly aligned, the route would be a diagonal beginning in tile upper left cell and proceeding to the Iower right cell of the grid. The selected route represents the optimal time point mapping.
[0029] The set of possible routes is limited by three types of constraints:
endpoint constraints; a local continuity constraint, which defines Iacal features of the path; and a global constraint, wlxich defines the allowable search space for the path.
The endpoint constraint equates the first and last time paint in each data set. rn the grid, the upper left and lower right cells are fixed as the start and end of the path, respectively, i.e., c(1) _ [1, i] and c{l~ _ [I, J]. The local continuity constraint forces the path to be monatanic with a non-negative slaps, meaning that, for a path c(7~) _ [i(k), j{Iz)], i(k+1) >a(k) and j(k+1) >_j(k). This condition maintains the order of time points. An upper bound can also be placed an the slope to prevent excessive compression or expansion of time scales. The result of these conditions is that the path to an individual cell is limited to one of the three illustrated in FIG.
6A. Finally, the global constraint limits the path to a specified number of grid places from the diagonal, illustrated schematically in FTG. 6B. This latter constraints confines the solution to one that is physically realizable while also substantially limiting the computation time.
j003U] The optimal path through tile grid is one that minimizes the accumulated distaazce function between the test and reference data sets over the route.
Each cell [i, jj has an associated distance function between data sets at the particular z and,j time indices. The distance function can tale a variety of different fornzs. If only a single chron~.atogra~n {e.g., the TIC} were considered, the distance function di,~
between points t~'Ef and tlr~st would be:
~t.i -~~iE~'-~~est~~ {l) where ~'~~f is the jth intensity value of the reference spectrum and Izr~'t is the ifh intensity value of the test spectrum. In embodiments of the present invention, however, ,t~l mass chromatograms of each data set are considered in computing the distance function, where lYI ~, and so, in one embodiment, the distance fiuactian is:
~i>.i ~ ~~~kJf ~,r~est)" ' !z=~
where h~re~ is the j'j2 intensity value of the knt reference chromatogram and Ija'est is the itjj intensity value of the 7~jt test chromatogram. Both l~~' chromatograms are for a single m/z range. Each cell of the g~.-id in FIG. 5 is Palled with the appropriate value of the distance function, and a mute is chosen through the matrix that minin2izes the accumulated distance function obtained by summing the values in each cell traversed, subject to the above-described constraints. dote that the two terms distance and route are not related; the distance refers to a metric of the dissimilarity between data sets, while the route refers to a path tluough the grid and has no relevant distance.
(~03L] The route-finding problem can be addressed using a dynamic programming approach, in which the larger optimization problem is reduced to a series of focal problems. At each allowable cell in the grid (FIG. 6B), the optimal one of the three (FIG. 6A) single-step paths is identified. After all cells Izave been considered, a globally aptirnal route is reconstructed by stepping backwards through the grid from the last call. For more information on dynamic programming, see T.H.
Cormen et al., .Ittti°oductio~i to AZgor~ithhas (2"~ ed.}, Cambridge:
MIT Press {2001}, which is incorporated herein. by reference.

j0032] Locally optimal paths are selected by mizumizing the accumulated distance from the initial cell to the current cell. For the three potential single-step paths to the cell [i, j~, the accutrzulated distances are:
cu __ Di,J Dr_2,f-i ~' ~C~=_l,.l + dx,J
D=,~{23 ~ D=-i,i-i + 2dt,J ~ (~) ~~,1 ~3) ~ Dt_h %-2 + ~~x.l'-1 -~- ~~,J
where Dj~;~~~ repxesents tl~e accumulated distance from [l, l~ to [i, j~ when path p is traversed, dl~; is con~.puted from equation (2), and D,_~~_z, D,_2~_z, and Dl_l~_2 are evaluated in previous steps. The coefficient 2 is a weighting factor that inclines the path to follow the diagonal. It may tale on other values as desired. The minimized accumulated distance fox the cell (i, j] is given by:
( ~P)), G~, p~.~ ~ min Dt,3 ( ) P
This value is stored in an accumulated distance matrix for use in subsequent calculations, and the selected value ofp is stored in an izadex matrix.
[0033 The dynamic progran~nning algorithm proceeds by stepping through each cell and fixzding and storing the minimum. accumulated distances and optimal indices.
Typically the process begins at the top left cell of the grid and moves down through all allowed cells before moving to the next column, with the allowable cells in each column defined by the global search space. After the fzrzal cell has been computed, the optimal route is found by traversing the grid bacl~uards to the starting cell [l, 1~
based on optimal paths stored in the index matrix. Note that the route cannot be constructed in the forurard direction, because .it is not l~nown until subsequent calculations whethex the cuz~rent cell will lie on the optimal route. t)nce the optimal route has been determined, an aligned test data set can be constructed.
[0034 Unless the test and reference data sets are perfectly aligned, there are paints in both sets that do not get mapped. When the test time scale is compressed, some intermediate test points do not get mapped. These points are discarded.
When the test time scale is expanded, there are reference time points for which no corresponding test point exists. Values of the points can be estimated, e.g., by linearly interpolating between intensity values of surrounding points that have been napped to reference points.
~Oa3S] The above-described methads and steps can be varied in many ways without departing from the scope of the inventiola. For example, alternative constraints can be applied to the route (e.g., different allowable local slopes, end points not fixed but rather constrained to allowable xegions, different global search space), and alternative dista~ace functions can be employed. The weighting factors for local paths can be varied from the value 2 used in equations (3).
Additionally, a normalization factor can be included in the distance function. The distance function above is based on intensity, but, depending on how the data set is represented, can be based on any other coefficient of features of the data set. For example, the function can be computed from coefficients of wavelets, peaks, or derivatives by which the data set is represented. In this case, the distance is a measure of the degree of alignment of these features.
j0036~ In the equations above, the distance function is computed based on data from ltd individual mass chromatograms. Any value of M is within the scope of the present invention, as are any selection criteria by which chromatograms are selected for inclusion. Reducing the number of chromatograms fiom the total number in the data set (e.g., 2000) to O.~ can decrease the computation time substantially.
Additionally, excluding noisy chromatograms or those without peaks can improve the alignment accuracy. There is generally an optimal range of M that balances alignment accuracy and computation time, and it is beneficial to choose a value of M in the lower end of the range, i.e., a value that minimizes computation time without sacrificing substantially the accuracy of time~alignment. It is also beneficial to include chromatograms containing peals throughout the range of retention time;
this is particularly important near the beginning and end of the chromatographic run, when there are fewer peaks. In one embodiment, between about 200 and about 400 chromatograms are used. Alternatively, between about 2(30 and about 300 chromatograms are used. hz aa2other embodiment, M is about 200.
[003'7] A variety of selection criteria can be applied individually or jointly to select the chromatograms with which the distance function is computed. The selection criteria or their parameters (e.g., intensity thresholds) can be predetermined, computed at run time, or selected by a user. NI can be a selected value (manually or automatically) ar the result of applying the ci~terion ar criteria (i.e., tt1 chromatograms happen to fit the criteria).
[003$j One selection criterion is that a mass chroznatagram have peaks in both the reference and test data sets, as determined by a manual ox automated peals selection algorithm. Peak selection algorithms typically apply an intensity threshold and identify local maxima exceeding the threshold as peals. The peaks may or may not be required to be corresponding (in m/z and retention time) for the ck~ramatogram to meet the criterion. If coz~esponding peals are required, a relatively large window in retention time is applied to account for floe to-be~carrected retention time shifts.
[0039) Another selection criterion is that maximum, median., ar average intensity values in a mass chron satogram exceed a specified intensity threshold, or that a single peal intensity or maximum, median, or average peak intensity values in the chromatogram exceed an intensity threshold. Alternatively, at least one individual peak intensity or the maximlun, median, ar average peak intensity can be required to fall between upper and lo-cver intensity level thresholds. Another selection criterion is that the number of peaks in a mass chroxnatagram exceed a threshold value.
These criteria are typically applicable to bath the reference and test mass chromatograms.
[0040j When the selection criterion involves an intensity threshold, the threshold can be constant ox vary with retention time to accommodate variations in mean ar median signal intensity throiighout~a chromatographic run. Often, the beginning and end of the run yields fewer and lower intensity peals than accw- in the middle of the run, and lower thresholds may be suitable for these regions.
[0041j According to an alternative selection criterion, a set of the most orthogonal chromatograms is selected, i.e., the set that provides the most information.
When an analyte is present in chromatograms of adjacent n~/z values, these chromatograms may be redundant, providing na mare information than is provided by a single chromatogram. Standard correlation methods can be applied to select orthogonal chromatograms. The orthogonal chromatograms are selected to span the elution time range, so that just enough information is provided to align the data sets accurately throughout the entire r ange. Zn this case, the selection criterion contains an orthogonality metric and a retention time range.
[0042 Individual selection criteria nay be combined in many different ways.
Fox example, in one coxnposite selection criterion, peaks are first selected in the reference and test data sets using any suitable manual ar autam.atic pear selection method.
Next, a filter is applied separately to the two data sets to yield two subsets of peaks.
This f lter cax2 be a single threshold or two (upper and lower) thresholds. A
lower threshold ensures that peaks are above the noise level, while an upper threshold excludes falsely elevated ~Talues reflecting a saturated instrument detector.
Conespanding peaks are then selected that appear in bath the test and reference peak subsets, Cluamatograms corresponding to these peaks are included in computing the distance function. Alternatively, from the list of corresponding peals, M
chromatograms are chosen randomly. For example, if ~ corresponding peals are found, the chromatograms corresponding to every NIMt~' mlz value are selected.
Alternatively, the M chromatograms can be selected from flee corresponding peaks based an an intensity threshold or some other criterion.
[0043] When more than one test data set is aligned to the reference data set, each pairwise alignment can be computed based on a different set of independently_ selected chramatograzns.
[0044) In one embodiment of the invention, a weighting factor ~~ is included in the distance function, causing different chromatograms to contribute unequally. As a result, certain chromatograms tend to dominate the sum and dictate the alignment.
The weighted distance function is:
j ~ ref ~ lest ~ (71 ~t,i ~x ~~ Ikr ' l>
x=~
where IrY~,: is the chromatogram-dependent -weighting factor. The functional farm or value of the weighting factor can be determined a p~~iori based on user Knowledge of the mast relevant mass ranges. Alternatively, the weighting factor can be computed based an characteristics a~ the data. For example, the weighting factor can be a function of one or more of the following variables: the number of peaks per chromatogram (pear number), selected by any manual or automatic method; the signal-to-noise ratio in a chromatogram; and peal threshold ox intensities.
Chromatograms having more peals, higher signal-to-noise ratio, ar higher peals intensities are typically weiglxted more than other claromatograxns. Axzy additional variables can be included in the weiglxting factox. The factor can also depend on a combination of user lmowledge axed data values.
j004S~ In an alternative embodiment of the invention, the time-aligning step employs locally-weighted regression smoothing. Ratlxer than. act on the raw (or preprocessed) data, this method time-aligns selected peals in test and reference data sets. Peals, defined by mlz and retention time values, are first selected from each data set by manual or automatic means. Potentially corresponding peals are identified from the lists as peaks that fall within a specified range of xn/z and retention time values. FIG. 7A shows an excerpt of a reference peals list and test peak list with potentially corresponding peaks shaded. These peaks are plotted in FIG. 7B, which shows the ~cvindow surrounding the reference peal that defines a region of potentially corresponding test peaks. Because the nonlinear time variations have not yet been corrected, the window has a relatively large retention time range, accounting for the maximum retention time variation throxzglzout the chromatographic run (e.g., five minutes).
j0046] For every pair of reference pear and potentially corresponding test peal, the data are transformed from (tref taESZ) to (~avg~ ~~)r Where ~~v~ =
(t~.pf';' ttest)~~ and ~1~
tY~~ -- t~e~~. The resulting plot, for exemplary data sets, is shown in FIG.
7C. It is apparent from FIG. 7C that the points tend to cluster around a curve that represents the nonlinear time variation between reference and test data sets. Knowing this curve would enable correction of the time ~rariation and alignrzaent of the data sets. To do so, a smoothing algorithm is applied to the transformed variables to yield a set of discrete values (ta"~, dt}, which can be transformed back to (t,.~f, tt~.r).
Because the smoothing is applied to data points representing peaks, and because the result is a discrete mapping of points rather than a fixnction, adjusted time values of data points between the peals are then computed, e.g., by interpolation. After all points have been mapped, aligned data sets can be constxzzcted. Typically, tune points of the reference data set are fixed and the test data set modified. This process can be repeated to align all data sets to the reference data set.
[0047] One suitable smoothing algorithm is a LOESS algorithm locally weighted scatterplot smooth), originally proposed in W.S, Cleveland, "Robust locally weighted regression and smoothing scattexplots," J. Am. Stat. ~ssoc. 74: $29-$36, 1979, and further de~creloped in W.S. Cleveland and S.J. Devlin, "Locally weighted regression:
an approach to regression analysis by local fitting," J Vim. Stat. Assoc. $3:
596-610, 1988, both of which are incorporated herein by reference. A LOESS function (sometimes called LOWESS) is available in many commercial ~~.athematxcs and statistics software packages such as S-PLUS~, SAS, Mathenaatica, and MATLAB~'.
[0048] The LOESS method, described in more detail below, fits a polynorrzial locally to paints in a window centered on a given point to be smoothed. Both the window size ("span") and polynomial degree must be selected. The span is typically specified as a percentage of the total number of points. In standard LOESS, a polynomial is ~t to the span by weighting points in tl~e window based on their distance from the point to be smoothed. After fitting the polynomial, the srnoathed point is replaced by the computed point, and the method proceeds to the next point, recalculating weights and fitting a new polynomial. Each time, even though the entire span is fit by the polynomial, only the center point is adjusted. Because the method operates locally, it is quite effective at representing the fine nonlinear variations an chromatographic retention tune.
[0049] A robust version of LOESS, wlxich is more resistant to outliers, computes the smoothed points in an iterative fashion by contitluing to modify the weighfs until convergence (or based on a selected number of iterations). The iterative corrections axe based on the residuals between the polynomial fit and the raw data paints.
After the paints ara fit using initial weights, subsequent weights are computed as the products of the initial weights and the new weights. Upon convergence, the span is moved by one point and the entire process repeated. In this manner, the polynomial regression weights are based on both the distance from the point to be smoothed (distance in abscissa value) and the distance between the point and the curve fit (distance in ordinal value), yielding a very robust fit.
IS

[OQ50] Specific details of the robust LOESS fit are described below. Tt is to be understood that any variations in parameters, Weighting factors, and polynomial degree are within the scope of the present inventioz~z. Each discrete (ta,;gz, ~tt) point is represez~.ted in the formulae below as {xi, yi). The approxizrzated valve of yz computed from the polynomial ht is represented as yi.
[0051 First, a window size is chosen and centered on the point to be sxrzoothed, x.
Suitable window sizes are between about 10% and about 50% (e.g., about 30%) of the total span of xt values. The results may be sensitive to the span, and the optimal span depends on a number of factors, including the threshold by which peals are selected.
For example, if the peals selection threshold is low, yielding a large number of densely located points, the optin zal span size may be larger than if the peal selection threshold were to yield fewer, less dense points. The span can also be selected by performing the smoothing using a few different spans and selecting the one that yields the best alignrrzent according to a fit metric, a measure of how well tlxe smoothed values ht the apparent alignment function or of how much the ~t ~cTalue varies locally or globally across the retention time range. The smoothing can also be evaluated based on l~nowledge of the expected result. The !'~ points within the chosen span are ht to a weighted polynomial of degree L (typically, L = 2) by minimizing the regression merit function, ,~:
N L
r~ ' ~ Wi ~~i ~ ~kxi ~ , i=1 k=a where a~~ are the polynomial coefficients to be salved for and iwi are the regression weights for each point x~ in the span. Izutially, the weights w; are given by a tricubic function:
~ tnitiat 1 ~ x -" xi ~ ) i x --- x~,aX
where x is the point being smoothed, xz are the individual points within the span, and x",~x is the point farthest from. x. The weights vary smoothly from 0, for the point farthest froze the smoothed point to 1, for the smoothed point. All weights are zero for points outside the span. The regression merit function in equation (5) is minimized to determine th.e polynon~a.al coefficients c~k. For standard LOESS, the smoothed value y is computed from the polyjlomial, and the span is moved one point to the right to smooth the next point.
[111152] For robust LOESS, these results are used t0 compute the robust weights based on the residual ~l between the raw data value yl and polynolx~ial Vahle yz far each point in the span:
~'t = Y; - Yt~ (~) and on the median absolute deviation MAD:
MAD -- median (~f°t(). ($) From these, the robust ~~~eights awr'~~6"st are computed:
z ,~.rabust ~ 1 6 MAD ~~ ~ < 6 .tl~lA.D . 8 r () 0 ~~~>6M~D
The regression is performed again for the span (from equation (S)) using newly computed WelflltS YVz = ~.irltnitial ~ ~lnohust t~ obtain a new curve flt, a new set OfpOIntS~}~p, and new residuals ri. This procedure (computing robust weights and fitting the polynomial) is repeated until the curve f t converges to a desired precision or for a predetermined number of iterations, e.g., about 5. Upon convergence, the y value of the paint being smoothed, x, is replaced with the curve fit value. Only that point is replaced-all other points in the span remain the same. The span is then shifted one point to the right and the entire procedure repeated to smooth the point in the canter of the span. Each time tl~e curve fit is performed, the yt values used are the raw data values, not the smoothed ones. End points are treated as is commonly done in smoothing.
[0053) After all yt values are obtained, a mapping from t,.ef to nest is determined, and values for intermediate points are computed by interpolation. The retention time values of mapped test poznts are then adjusted to align the complete data sets. The process is repeated for all test data sets. Note that if the goal of the method is to align corresponding peaks only, it is not necessary to find aligned time point values far the intermediate points.

(0054] Although not limited to any particular hardware configuration, the present invention is typically implemented in software by a system containing a computer that obtains data sets from an analytical instrument ~e.g., LC-MS instnuznen t) or other source. The LC-MS instrument includes a Iiduid clzrozn.atagraphy instrtunent corrected to a mass spectrometer by an interface. The computer implementing the invention typically contains a processor, memory, data storage medium, display, and input device (e.g., lceyboaxd and mouse). Methods of the invention are executed by the processor under the direction of computer program code stared in the computer.
Using techniques well l~nown in the computer ants, such code is tangibly embodied within a computex program storage device accessible by the processor, e.g., within system memory or on a computer-readable storage medizun such as a hard disk or Cl3-ROM. The methods may be implemented by any means lcrzawn in the art. For example, any number of computer progranuning languages, such as JavaTM, C++, or Perl, may be used. Furthermore, various pxogramzning approaches such as procedural or object oriented may be employed. It is to be understood that the steps described above are highly simplified versions of the actual processing performed by the computer, and that methods containing additional steps or rearranger~c~.ent of the steps described are within the scope of the present invention.
E~MPLES
(0055] The following examples are provided solely to illustrate various embodiments of the present invention and are not intended to limit the scope of the invention to the disclosed details.
EXAMPLE 2: Fears aligned by dynamic time warping [0056] Pooled human serum from blood banl~ samples eras ultrafiltered through a 10-l~Da membrane, and the resulting high-molecular weight fraction was reduced with dithiotlueitol (PTT) and carboxymethylated with iodoacetic acidlNaC~I~ before being digested with trypsin. Digested samples were analyzed on a binary HP 1100 series I-~'LC coupled directly to a Micromass (Manchester, UK) LCTT~ eleetrospray 1On12at10i1 (EST) time-of flight {TOF') mass spectrometer equipped with a micraspray source. PicoFritT~'~ fused-silica capillary columns ~S ~zn BioBasic Cl&, '75 ~.m x 10 crn, _New C7bjective, Waburn, MA) were run at a flow xate of 300 nLlmin after flour splitting. An on-line trapping ea~-tridge {Peptide CapTrap, Micluom Bioresaurces, Auburn, CA} allowed fast loading unto the capillary column. Injection volume was 20 1CL. Gradient elution was achieved using 100% solvent A
{0.1°l° formic acid in water) to 40°I° solvent B (0.1% formic acid i~1 acetanitriie}
over 100 min.
[OOS7] Data sets were aligned by dynamic time warping {DTW} implemented in MATLAB° (The MathW'orlcs, Cambridge, MA} with custom code.
(0058] FTGS. 8A-8B show a small region of data sets camesponding to four different samples, before and after alignment of the bottom three data sets (test) to the top (reference) data set using DTW. Corresponding peaks are indicated. In all cases, the aligned peaks are much closer (in retention time) to the reference peals than they were before alignment.
EXAMPLE 2: Data sets aligned by dynamic time warping and LOESS
[0059] Pooled human serum from bland ba~2t~ samples was ultrafiltered through a 10-l~Da nmmbrane, and the resulting hzgh-molecular weight fraction was reduced with dithiothreitol (DTT) and carboxymethylated with iodaacetic acid/NaOH before being digested with trypsin. Digested samples were analyzed on a binary HP 1100 series HPLC coupled directly to a ThermoFinnigan (San dose, CA) LCQ DECAT~
electrospray ionization (ESI) ion-trap mass spectrometex using automatic gain control.
PicoFritTM fused-silica capillary calun~r~s (5 ~m F3iaBasic C18, ?5 ~.m x 10 cm, New Objective, Waburn, MA.) were rtu~ at a flaw rate of 30Q nLhrzin after flow splitting.
An an-line trapping cartridge (Peptide CapTrap, Michrom Bioresources, Aubuna, CA) allowed fast loading onto the capillary Column. Injection volume was 20 p.L.
Gradient elution was aehi.eved using 100% solvent A (0.1 % formic acid in water) to 40°I° solvent B (0. I % formic acid in acetanitrile) ovex 100 xnin.
[0060] Spectra were aligned using bath dynamic time warping (DTW) and robust LOESS. Algorithms were implemented in MATLAB° (The lVIathWorl~s, Cambridge, MA}. Robust LOESS smoothing was performed using a prepackaged routine in the MATLAB° Curve Fitting Toolbo;~. DTW was implemented v~rith custom MATLAB°
code following the algorithms described above.

[006I] ~'I~, 9 is a plat of transformed data set variables 0t vs. tn"~ shaving alignment by robust LC.~ESS and DTW. Inverted triangles represent potentially corresponding automatically-selected peaks, filled circles are paints smoothed by robust LOESS, and the thin solid line is the data set corrected by DTW . The DTW
points are much more densely spaced, because they are taken from the entire data set, rather than selected peaks only. In this example, both robust LOESS and DTW
accurately tracl~ tlxe time shift, with LOESS following the Local variations more closely.
[0062a It should be noted that the foregoing description is only illustrative of the invention. Various alternatives and modifzGations can be devised by those spilled in the arfi without departing from the invention. Accordingly, the present invention is intended to embrace all such alternatives, modifications and variances which fall wvithin the scope of the disclosed invention,

Claims

What is claimed is:

1. A computer-implemented method for time-aligning at least two chromatography-mass spectrometry data sets, each comprising a plurality of mass chromatograms, said method comprising:
a) computing a distance function between said data sets in dependence on at least two mass chromatograms from each data set; and b) aligning said data sets by minimizing said distance function to obtain aligned data sets.

2. The method of claim 1, wherein one of said data sets is a reference data set and one of said data sets is a test data set, and wherein said test data set is aligned to said reference data set.

3. The method of claim 1, wherein said data sets are liquid chromatography-mass spectrometry data sets.

4. The method of claim 1, wherein said distance function is computed in dependence on between about 200 and about 400 mass chromatograms from each data set.

5. The method of claim 1, further comprising selecting said at least two mass chromatograms according to a selection criterion.

6. The method of claim 1, wherein said distance function is computed in dependence on a chromatogram-dependent weighting factor.

7. The method of claim 6, wherein said chromatogram-dependent weighting factor is a function of at least one of a pear number, an intensity threshold, and a signal-to-noise ratio.

8. A plurality of chromatography-mass spectrometry data sets aligned according to the method of claim 1.

9. A program storage device accessible by a processor, tangibly embodying a program of instructions executable by said processor to perform method steps for a method for time-aligning chromatography-mass spectrometry data sets, each comprising a plurality of mass chromatograms, said method steps comprising:
a) computing a distance function between said data sets in dependence on at least two mass chromatograms from each data set; and b) aligning said data sets by minimizing said distance function to obtain aligned data sets.

10. A method for comparing at least two samples, comprising:
a) performing chromatography-mass spectrometry on each sample to obtain at least two data sets, each comprising a plurality of mass chromatograms;
b) computing a distance function between two selected data sets in dependence on at least two mass chromatograms from each selected data set;
c) aligning said selected data sets by minimizing said distance function to obtain aligned selected data sets; and d) comparing said aligned selected data sets.

11. The method of claim 10, wherein one of said selected data sets is a reference data set and another of said selected data sets is a test data set, and wherein said test data set is aligned to said reference data set.

12. The method of claim I0, wherein said chromatography-mass spectrometry is liquid chromatography-mass spectrometry.

13. The method of claim 10, further comprising aligning two additional data sets, wherein at least one of said additional data sets differs from said selected data sets.

14. The method of claim 10, further comprising selecting said at least two mass chromatograms according to a selection criterion.

15. The method of claim 14, wherein said selection criterion is a user-provided selection criterion.

16. The method of claim 14, wherein said selection criterion comprises an intensity threshold.

17. The method of claim 14, wherein said selection criterion comprises a number of chromatograms.

18. The method of claim 14, wherein said selection criterion comprises an orthogonality metric.

19. The method of claim 14, wherein said selection criterion comprises a retention time range.

20. The method of claim 10, wherein said distance function is computed in dependence on between about 200 and about 400 mass chromatograms.

21. The method of claim 10, wherein said distance function is computed in dependence on between about 200 and about 300 mass chromatograms.

22. The method of claim 10, wherein said distance function is computed in dependence on about 200 mass chromatograms.

23. The method of claim 10, wherein said distance function is computed in dependence on a weighting factor.

24. The method of claim 23, wherein said weighting factor is a chromatogram-dependent weighting factor.

25. The method of claim 24, wherein said chromatogram-dependent weighting factor is a function of at least one of a peals number, an intensity threshold, and a signal-to-noise ratio.

26. The method of claim 10, further comprising identifying features that differentiate said aligned selected data sets.

27. A plurality of samples compared according to the method of claim 10.

28. A method for identifying a biomarker differentiating two cohorts, comprising:
a) comparing at least two samples according to the method of claim 10, at least one each of said samples representing a different one of said two cohorts; and b) identifying a biomarker in dependence on said comparison.

29. A biomarker identified by the method of claim 28.

30. A diagnostic method comprising detecting a biomarker identified by the method of claim 28.

31. A computer-implemented method for time-aligning at least two two-dimensional chromatography-mass spectrometry data sets, comprising:
a) selecting peaks in said data sets;
b) identifying potentially corresponding peaks from said selected peaks; and c) performing a locally-weighted regression smoothing on said potentially corresponding peaks to obtain aligned data sets.

32. The method of claim 31, wherein one of said data sets is a reference data set and one of said data sets is a test data set, and wherein said test data set is aligned to said reference data set.

33. The method of claim 31, wherein said data sets are liquid chromatography-mass spectrometry data sets.

34. The method of claim 31, wherein said locally-weighted regression smoothing is a robust locally-weighted regression smoothing.

35. The method of claim 34, wherein said robust locally-weighted regression smoothing comprises robust LOESS.

36. The method of claim 31, wherein said peaks are selected automatically.

37. The method of claim 31, wherein said locally-weighted regression smoothing is performed in dependence on a span.

38. A plurality of chromatography-mass spectrometry data sets aligned according to the method of claim 31.

39. A program storage device accessible by a processor, tangibly embodying a program of instructions executable by said processor to perform method steps for a method for time-aligning two-dimensional chromatography-mass spectrometry data sets, said method steps comprising:
a) selecting peaks in said data sets;
b) identifying potentially corresponding peaks from said selected peaks; and c) performing a locally-weighted regression smoothing on said potentially corresponding peaks to obtain aligned data sets.

40. A method for comparing at least two samples, comprising:
a) performing chromatography-mass spectrometry on each sample to obtain at least two two-dimensional data sets;
b) selecting peaks in two selected data sets;
c) identifying potentially corresponding peaks from said selected peaks;
d) performing a locally-weighted regression smoothing on said potentially corresponding peaks to obtain aligned selected data sets; and e) comparing said aligned selected data sets.

41. The method of claim 4fl, wherein one of said selected data sets is a reference data set and another of said selected data sets is a test data set, and wherein said test data set is aligned to said reference data set.

42. The method of claim 40, wherein said chromatography-mass spectrometry is liquid chromatography-mass spectrometry.

43. The method of claim 40, further comprising aligning two additional data sets, wherein at least one of said additional data sets differs from said selected data sets.

44. The method of claim 40, further comprising identifying features that differentiate said aligned selected data sets.

45. A plurality of samples compared according to the method of claim 40.

46. A method for identifying a biomarker differentiating two cohorts, comprising:
a) comparing at least two samples according to the method of claim 40, at least one each of said samples representing a different one of said two cohorts; and b) identifying a biomarker in dependence on said comparison.

47. A biomarker identified by the method of claim 40.