Patent Publication Number: US-2007112534-A1

Title: Peak pattern calibration

Description:
BACKGROUND ART  
      The present invention relates to calibrating a sample peak pattern.  
     BRIEF DESCRIPTION OF RELATED DEVELOPMENTS  
      There exist a variety of different techniques for analyzing compounds of an unknown sample. In order to analyze the unknown sample, a sample peak pattern might be acquired, with the peaks representing compounds of the unknown sample. However, before the sample peak patterns can be used for further analysis, they have to be calibrated with regard to calibration samples comprising a set of known components. For example, in the field of DNA analysis or protein analysis, calibration samples comprising a set of well-known DNA fragments or proteins are employed. Before the calibration can be performed, the sample peak pattern has to be aligned relative to the one or more calibrations peak patterns. The accuracy of the calibration strongly depends on the accuracy of this alignment step.  
     SUMMARY OF THE INVENTION  
      It is an object of the invention to provide an improved calibration of a sample peak pattern with regard to at least one calibration peak pattern. The object is solved by the independent claim(s). Exemplary embodiments are shown by the dependent claim(s).  
      According to embodiments of the present invention, a method for calibrating a sample peak pattern with regard to a first and a second calibration peak pattern is provided. The respective peak patterns are acquired at different times. The calibration peak patterns each comprise a first reference peak and at least one second reference peak, and the sample peak pattern comprises a first reference peak, at least one of the second reference peaks, and any number of peaks of species of interest. The method comprises aligning at least one second reference peak of the first calibration peak pattern with at least one corresponding second reference peak of the second calibration peak pattern. The method further comprises performing an interpolation of the respective positions of the first reference peak in the first and the second calibration peak pattern, in order to derive a time dependence of the first reference peak&#39;s position. The method further comprises aligning the sample peak pattern relative to at least one of the calibration peak patterns in a way that 
          the sample peak pattern&#39;s first reference peak is aligned with an interpolated position of the first reference peak according to the time dependence determined precedingly, and that     at least one of the sample peak pattern&#39;s second reference peaks is aligned with at least one corresponding second reference peak of the calibration peak patterns.        

      The positions of peaks related to different compounds might be subjected to different types of time dependence. There might be a slight variation of the measuring conditions as a function of time. Because of the different chemical structure of the samples&#39; compounds, a small variation of the measuring conditions may affect the compounds in different ways. Accordingly, the peaks of the sample peak pattern and of the calibration peak patterns might be subjected to different types of time dependence. In particular, a relative time drift of one peak relative to other peaks might be observed.  
      The calibration peak patterns each comprise a first reference peak and one or more second reference peaks. In addition to peaks related to species of interest, the sample peak pattern also comprises the first reference peak and at least one of the second reference peaks. If there is a time drift of the first reference peak&#39;s position relative to the at least one second reference peak&#39;s position, this time drift can be derived from the two calibration peak patterns, which have been acquired at different times. One or more of the second reference peaks of the first calibration peak pattern are aligned with corresponding second reference peaks of the second calibration peak pattern. Then, the first reference peak&#39;s position is known at two different times, and a time dependence of the first reference peak&#39;s position can be derived there from. Now, the time dependence of the first reference peak&#39;s position is known.  
      Next, the sample peak pattern is aligned relative to at least one of the calibration peak patterns. The point in time when the sample peak pattern has been acquired is known. From the known time dependence of the first reference peak&#39;s position, it is possible to derive an interpolated position of the first reference peak that corresponds to the point in time when the sample peak pattern has been measured. Now, the measured position of the sample peak pattern&#39;s first reference peak can be aligned with this interpolated position derived from the first and the second calibration peak pattern. Additionally, at least one of the sample peak pattern&#39;s second reference peak is aligned with at least one corresponding second reference peak of one of the calibration peak patterns.  
      By considering the relative time drift between different reference peaks of the calibration peak pattern, it is possible to perform a high-precision alignment of the sample peak pattern&#39;s reference peaks relative to the calibration peak patterns&#39; reference peaks. The alignment is usually applied before a subsequent calibration. For this reason, the precision of a subsequent calibration is also improved.  
      According to a preferred embodiment, for determining the time dependence of the first reference peak&#39;s position, a linear interpolation between the first reference peak&#39;s position in the first and in the second calibration peak pattern is performed. In general, the first reference peak&#39;s time drift is substantially a linear time drift.  
      According to a preferred embodiment, the sample peak pattern is acquired by analyzing a sample of interest. In addition to various species of interest, the sample of interest comprises a marker and at least one labelled fragment, whereby the sample peak pattern&#39;s first reference peak corresponds to the marker, and whereby the one or more second reference peaks of the sample peak pattern correspond to the one or more labelled fragments. It is common practice to add a marker and at least one labelled fragment to a sample of interest, in order to be able to perform a calibration of the obtained sample peak pattern. For example, a rather small molecule might be used as a marker molecule, whereas the labelled fragments are molecules of considerable size. Therefore, the migration behaviour of the marker might differ significantly from the labelled fragments&#39; migration behaviour, and a time drift between the first reference peak and the at least one second reference peaks might be observed.  
      According to a preferred embodiment, the first and the second calibration peak pattern are acquired by analyzing compounds of a calibration sample, with the calibration sample comprising the marker and a set of labelled fragments. Further preferably, the calibration peak patterns&#39; first reference peak corresponds to the marker, whereas the one or more second reference peaks of the calibration peak patterns relate to the set of labelled fragments.  
      In a preferred embodiment, a so-called ladder is used as a calibration sample. A ladder is a calibration sample comprising a plurality of well-known components, whereby the name “ladder” is due to the fact that the calibration peak pattern looks like a “ladder” of peaks related to the various components. For example, in the field of DNA analysis and protein analysis, many manufacturer offer ladders for calibration purposes.  
      In a preferred embodiment, the compounds of the calibration sample and of the sample of interest are separated in a separation flow path. For example, the respective samples may be provided to an input of the separation flow path, and at the separation flow path&#39;s outlet, separated compounds of the sample may be obtained as a function of time. The separation flow path might e.g. be implemented as a separation column filled with some kind of packing material. Preferably, one of the following separation techniques is used: electrophoresis, chromatography, electrochromatography.  
      According to a preferred embodiment, the sample peak pattern and the calibration peak patterns are obtained by detecting fluorescence intensity of compounds that have been separated in a preceding separation flow path. In this embodiment, the marker is a fluorescence marker, and the fragments of the calibration sample are labelled with fluorescence tags. Also the compounds of the sample of interest are labelled with fluorescence tags. Accordingly, the respective peak patterns are acquired by detecting fluorescence intensity as a function of time.  
      According to another preferred embodiment, the marker emits fluorescence light of a first wavelength, whereas the labelled fragments emit fluorescence light of a second wavelength, which is different from the first wavelength. Some of the available ladders comprise two or more different fluorescence dyes adapted for emitting fluorescence light of two or more different wavelengths. Correspondingly, there exist fluorescence detection units adapted for simultaneously tracking fluorescence intensity at two or more different wavelengths.  
      According to another preferred embodiment, the sample peak pattern is measured between the first and the second calibration peak pattern. Thus, the interpolation of the first reference peak&#39;s position becomes more accurate.  
      Embodiments of the present invention further relate to a method for determining a set of linear transformations from a calibration peak pattern, wherein the calibration peak pattern comprises n reference peaks. The set of linear transformations is set up with regard to a reference data set comprising data about reference position of the n reference peaks of the calibration peak pattern. Firstly, the time axis of the calibration peak pattern is split up into a series of n−1 adjacent subintervals, with an i th  subinterval ranging from reference peak i to reference peak i+1 of the calibration peak pattern, and with i being a natural number, 1≦i≦n. Next, for each of the n−1 subintervals, a corresponding linear transformation is set up, with the i th  linear transformation being adapted for mapping the i th  subinterval into a corresponding i th  target interval, said i th  target interval ranging from the reference position of reference peak i to the reference position of reference peak i+1 of the reference data set.  
      According to this embodiment of the invention, the time scale is divided into subintervals, and for each of the subintervals, the original time scale is converted into a transformed time scale. Thus, it can be accomplished that each of the measured reference peaks is shifted to a corresponding reference position of said reference peak. This is accomplished by defining, for each subinterval delimited by two adjacent reference peaks, a linear transformation, whereby the linear transformation is set up in a way that both the left reference peak and the right reference peak are shifted to their corresponding reference positions, respectively. Thus, a piecewise transformation of the original time scale is defined.  
      In general, reference positions of the calibration peak pattern&#39;s reference peaks are well-known. For example, these reference positions might be provided by a manufacturer of calibration samples. Alternatively, these reference positions may be determined by performing a large number of reference measurements, and by averaging the measured positions of the reference peaks.  
      By applying the set of n−1 linear transformations, the original time scale is converted into a transformed time scale such that all the reference peaks are shifted to their reference positions. Thus, any non-linear distortions and artifacts introduced by the measurement set-up can be compensated. By applying the set of linear transformations, comparability of calibration peak patterns acquired at different times with different measuring systems can be ensured. Furthermore, the set of n−1 linear transformation s might as well be applied to sample peak patterns. Thus, sample peak patterns and calibration peak patterns acquired at different times with different measurement set-ups become comparable.  
      According to a preferred embodiment, the n reference peaks of the calibration peak pattern correspond to n labelled fragments contained in a calibration sample.  
      In yet another preferred embodiment, the i th  linear transformation is defined as t′ i =scale i ·t i +bias i , with t i  denoting an original time, with t′ i  denoting a transformed time, with scale i  denoting a scaling factor, and with bias i  denoting an offset. The i th  linear transformation is applied to the i th  subinterval. The parameters scale i  and bias i  can be chosen such that the respective positions of the i th  reference peak and the i+1 th  reference peak are shifted to their corresponding reference positions, respectively.  
      According to another preferred embodiment, a first calibration peak pattern is acquired before a sample peak pattern is acquired, and a second calibration peak pattern is acquired after a sample peak pattern is acquired. Then, a first set of linear transformations is determined from the first calibration peak pattern, and a second set of linear transformations is determined from the second calibration peak pattern. From the first and the second set of linear transformations, an interpolated set of n−1 linear transformations is derived, which is applied to the corresponding n−1 subintervals of the sample peak pattern. Preferably, the interpolation is performed according to the respective measuring times of the first calibration peak pattern, the sample peak pattern and the second calibration peak pattern.  
      In yet another preferred embodiment, the method further comprises applying the n−1 linear transformations to the corresponding n−1 subintervals of at least one of the calibration peak pattern and a sample peak pattern of a sample of interest.  
      By applying the n−1 linear transformations to a calibration peak pattern or a sample peak pattern, the transformed peak patterns can be related to one common time scale. Thus, calibration peak patterns and sample peak patterns acquired at different times with different measurements set-ups become comparable. Furthermore, it is possible to assign a common size axis both to calibration peak patterns and sample peak patterns, whereby the common size axis might indicate the compounds&#39; respective sizes in terms of base pairs.  
      According to a preferred embodiment, the method further comprises re-sampling the sampled data values of at least one of the calibration peak pattern and the sample peak pattern in a way that an equidistant spacing between adjacent sampled data values is accomplished. Thus, further processing of the adjusted calibration peak pattern is simplified.  
      Embodiments can be partly or entirely embodied or supported by one or more suitable software programs, which can be stored on or otherwise provided by any kind of data carrier, and which might be executed in or by any suitable data processing unit.  
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
      Other objects and many of the attendant advantages of embodiments of the present invention will be readily appreciated and become better understood by reference to the following more detailed description of preferred embodiments in connection with the accompanied drawing(s). Features that are substantially or functionally equal or similar will be referred to with the same reference sign(s).  
       FIG. 1  shows a measurement set-up;  
       FIG. 2  depicts two fluorescence intensity signals related to a calibration sample;  
       FIG. 3  shows two fluorescence intensity signals related to a sample of interest;  
       FIG. 4A  shows measured peaks in dependence on an absolute time scale;  
       FIG. 4B  shows an alignment of peak patterns according to the prior art;  
       FIG. 4C  shows an alignment of peak patterns according to embodiments of the present invention;  
       FIG. 5  illustrates a relative time drift of the lower marker peak LM relative to the ladder peaks;  
       FIGS. 6A, 6B , and  6 C show the effects of global alignment and piecewise alignment; and  
       FIG. 7  depicts how a piecewise alignment is performed. 
    
    
       FIG. 1  shows a measurement set-up for separating and analyzing a fluid sample comprising a plurality of different sample compounds. Each of the sample&#39;s compounds is characterized by an individual migration time required for traveling through a separation flow path  1 . The separation flow path  1  might e.g. be an electrophoresis flow path, a chromatography flow path, or an electrochromatography flow path. At the outlet of the separation flow path  1 , a detection cell is located. The detection cell might e.g. be implemented as an fluorescence detection cell  2  comprising a light source  3  and a fluorescence detection unit  4 . The fluorescence detection cell  2  is adapted for detecting sample bands of fluorescence labelled species as a function of time.  
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
      Before a sample comprising a plurality of unknown species can be analyzed, the measurement set-up shown in  FIG. 1  has to be calibrated. For this purpose, there exist a large variety of different calibration samples comprising a set of well-known compounds of different size. These compounds can be separated and analyzed by a measurement set-up as shown in  FIG. 1 , whereby a characteristic calibration peak pattern is obtained. For each compound of the calibration sample, the calibration peak pattern comprises a respective calibration peak. Because the set of calibration peaks look like a ladder, calibration samples are often referred to as “ladders”. A lot of manufacturers produce calibration samples or “ladders” for electrophoresis systems, chromatography systems or electrochromatography systems. In the field of DNA analysis, ladders comprising a set of different DNA fragments are used, whereas in the field of protein analysis, calibration samples comprising a set of different proteins are used.  
      In case fluorescence detection is used for detecting different species, ladders comprising fragments labelled with fluorescence tags are employed. When the species of the calibration sample are stimulated with incident light, the tags attached to the species emit fluorescence light. There also exist calibration samples or “ladders” comprising a marker that fluoresces at a first wavelength, and a set of labelled fragments that emit fluorescent light at a second wavelength.  
       FIG. 2  shows two different fluorescence intensity signals  5 ,  6  as a function of time. The two fluorescence intensity signals  5 ,  6  have been acquired by detecting fluorescence intensity at two different wavelengths. The signals of  FIG. 2  relate to a calibration sample comprising a marker and a set of labelled fragments. The marker is a small dye molecule adapted for emitting red fluorescence light. In general, the labelled fragments are larger in size than the marker. They are labelled with fluorescence tags adapted for emitting green fluorescence light. In addition to the fluorescence intensity signals  5 ,  6 , a time axis  7  is shown. First, the small marker molecules appear at the separation column&#39;s outlet, and accordingly, a lower marker peak LM appears in the fluorescence intensity signal  5  related to red fluorescence light. Next, the labelled fragments arrive at the detection cell, whereby small, light fragments migrate through the separation column more quickly than large, heavy fragments. Hence, the fluorescence intensity signal  6  related to green fluorescence light comprises a set of ladder peaks LP 1 , LP 2 , LP 3 , . . . LPn, with ladder peak LP 1  corresponding to the smallest labelled fragment, and with LPn corresponding to the largest labelled fragment.  
      After the fluorescence peak pattern of the calibration sample has been acquired, a sample of interest is analyzed. In order to allow for an alignment with the calibration peak pattern, a certain concentration of the marker and a certain concentration of the largest labelled ladder fragment is added to the sample of interest. Then, the compounds of the sample of interest are separated, and the sample bands obtained at the separation column&#39;s outlet are analyzed.  
       FIG. 3  shows two fluorescence intensity signals  8 ,  9  obtained by analysing the sample of interest. The fluorescence intensity signal  8  relates to red fluorescence light, whereas the fluorescence intensity signal  9  relates to green fluorescence light. Furthermore, a time axis  10  is shown. First, the marker appears at the column&#39;s outlet, and a corresponding lower marker peak LM shows up in the fluorescence intensity signal  8 . Next, sample bands related to compounds of the sample of interest arrive at the fluorescence detection cell. The sample compounds have been labelled with a fluorescence tag adapted for emitting green fluorescence light. Accordingly, the fluorescence intensity signal  9  comprises peaks  11  that correspond to these sample compounds. At last, the largest labelled fragment appears at the detection cell, and accordingly, the fluorescence intensity signal  9  comprises a ladder peak LPn.  
       FIG. 4A  shows a sequence of measurements comprising both calibration measurements and sample measurements. First, a calibration sample or ladder L 1  is analyzed, then, sample peak patterns of samples S 1  to S 4  are acquired, and at last, a calibration peak pattern of a ladder L 2  is measured. Below the measurements, a time axis  12  indicates an absolute time scale that has been used for recording the peak patterns. For each of the two calibration sample measurements L 1  and L 2 , the respective positions of the lower marker peak LM, of the first labelled fragment&#39;s peak LP 1 , and of the last labelled fragment&#39;s peak LPn are indicated. For each of the sample measurements S 1  to S 4 , the position of the lower marker peak LM and the position of the last labelled fragment&#39;s peak LPn are indicated.  
      The time axis  12  indicates an absolute time scale that has been used for recording the peak patterns. From  FIG. 4A , it can be seen that the absolute time positions of corresponding peaks vary considerably. Furthermore, also the time intervals between the lower marker peak LM and the last labelled fragment&#39;s peak LPn vary to some extent. This variation indicates a compression or an expansion of the absolute time scale, which might e.g. be caused by fluctuations of the solvent composition, by chemical modifications of the column&#39;s packing material, or by any other changes of the measuring environment.  
      For these reasons, in order to achieve comparability between the peak patterns, it can be necessary to convert the absolute time scale into a relative time scale and to align the peaks of the sample peak pattern relative to the peaks of the calibration peak patterns.  
      According to a solution of the prior art, which is depicted in  FIG. 4B , a first fixed time value  13  is assigned to the lower marker peaks LM of the calibration measurements L 1  and L 2  and to the lower marker peaks LM of the sample measurements S 1  to S 4 . Furthermore, a second fixed time value  14  is assigned to the respective peaks LPn of the measurements L 1 , L 2 , S 1  to S 4 . As a consequence, the positions of the respective lower marker peaks LM are aligned, and the positions of the respective ladder peaks LPn are aligned.  
      By assigning fixed time values to the peaks LM and LPn of each peak pattern, respectively, a relative time scale is set up for each of the peak patterns L 1 , S 1  to S 4 , L 2 . Now, the peaks&#39; absolute time values, which are depicted in  FIG. 4A , can be converted into corresponding relative time values of this relative time scale.  
      However, the prior art solution shown in  FIG. 4B  has some shortcomings. When converting the absolute time position of peak LP 1  of calibration measurement L 1  into a corresponding relative time value, a relative time value  15  of peak LP 1  is determined. When converting the absolute time value of peak LP 1  of calibration measurement L 2  into a corresponding relative time value, a relative time value  16  of peak LP 1  is obtained. Obviously, the relative time value  16  of peak LP 1  derived from calibration measurement L 2  does not match with the relative time value  15  obtained from calibration measurement L 1 . This means that the ratio  
         (       Δ   ⁢           ⁢     T   LM     LP   ⁢           ⁢   1           Δ   ⁢           ⁢     T     LP   ⁢           ⁢   1     LPn         )       L   ⁢           ⁢   1         
 
 derived from calibration measurement L 1  differs from the ratio  
         (       Δ   ⁢           ⁢     T   LM     LP   ⁢           ⁢   1           Δ   ⁢           ⁢     T     LP   ⁢           ⁢   1     LPn         )       L   ⁢           ⁢   2         
 
 derived from L 2 :  
           (       Δ   ⁢           ⁢     T   LM     LP   ⁢           ⁢   1           Δ   ⁢           ⁢     T     LP   ⁢           ⁢   1     LPn         )       L   ⁢           ⁢   1       ≠       (       Δ   ⁢           ⁢     T   LM     LP   ⁢           ⁢   1           Δ   ⁢           ⁢     T     LP   ⁢           ⁢   1     LPn         )       L   ⁢           ⁢   2           
 
      with ΔT LM   LP1  denoting the time interval between LM and LP 1  according to the absolute time scale of  FIG. 4A , and with ΔT LP1   LPn  denoting the time interval between LP 1  and LPn according to the absolute time scale of  FIG. 4A .  
      This effect is due to a relative time drift between the position of the lower marker peak LM and the positions of the labelled fragments&#39; peaks LP 1  to LPn. The fragments are labelled with a fluorescence tag, whereas the marker is a free dye that is not bound to any fragment. When passing through the separation column, the migration behaviour of the free dye differs considerably from the migration behaviour of the labelled fragments.  
       FIG. 5  illustrates the relative time drift of the lower marker peak&#39;s position relative to the peak positions of the other ladder peaks.  FIG. 5  shows a set of different calibration peak patterns that have been recorded at different points in time. First, the calibration measurement L 1  is performed, then, four sample measurements S 1  to S 4  are acquired, followed by another calibration measurement L 2 . After the calibration measurement L 2  has been carried out, another set of four sample measurements S 5  to S 8  is performed, followed by a third calibration measurement L 3 . This sequence of calibration measurements is continued, whereby further calibration measurements L 4 , L 5  are performed. The first diagram  17  of  FIG. 5  relates to the calibration measurement L 1 . The first fluorescence intensity signal  18  comprises a lower marker peak LM, whereas the second fluorescence intensity signal  19  comprises four ladder peaks LP 1 , LP 2 , LP 3 , LP 4 . The following diagrams  20  to  23  relate to the calibration measurements L 2  to L 5 , respectively. It can be seen that the respective positions of the ladder peaks LP 1  to LP 4  remain unchanged, whereas there is a time drift of the lower marker peak LM relative to the ladder peaks LP 1  to LP 4 . Relative to the position  24  of ladder peak LP 1 , the respective positions  25   a  to  25   e  of the lower marker peak LM are continuously moving as a function of time.  
      The relative time drift between the peak positions of the marker on the one hand and the labelled fragments on the other hand has to be taken into account when aligning the peak patterns shown in  FIG. 4A . According to embodiments of the present invention, it is proposed to perform the alignment in a way shown in  FIG. 4C . Firstly, the first ladder peak LP 1  and the last ladder peak LPn of calibration measurement L 1  are aligned with the ladder peaks LP 1  and LPn of calibration sample L 2 . This can e.g. be done by assigning a first fixed time value  26  to ladder peak LP 1  of calibration measurement L 1  and to ladder peak LP 1  of calibration measurement L 2 , and by assigning a second fixed time value  27  to ladder peak LPn of calibration measurement L 1  and to ladder peak LPn of calibration measurement L 2 . As a result of this assignment, peak LP 1  of L 1  is aligned with peak LP 1  of L 2 , and furthermore, peak LPn of L 1  is aligned with peak LPn of L 2 .  
      By assigning a first fixed time value to LP 1  and a second fixed time value to LPn, both for calibration measurement L 1  and for calibration measurement L 2 , a relative time scale is established. Hence, both for L 1  and L 2 , the absolute time scale, which has been used for measuring the peak patterns, is transformed to a relative time scale.  
      Using the relative time scale of L 1 , the absolute time value  28  of the lower marker peak LM shown in  FIG. 4A  can be converted into a corresponding relative time value  29 . Accordingly, the absolute time value  30  of the lower marker peak LM shown in  FIG. 4A  can be converted into a corresponding relative time value  31 .  
      In general, the relative time value  29  differs from the relative time value  31 . However, from these two values, a time drift of the lower marker&#39;s peak position relative to the ladder peaks can be derived, preferably by performing a linear interpolation. In  FIG. 4C , the linear time drift of the lower marker peak LM is indicated as a straight line  32 . Instead of a linear interpolation, a more complex type of interpolation can be used for modeling the lower marker peak&#39;s time drift.  
      As soon as the time dependence of the lower marker&#39;s peak position is known, it is possible to determine interpolated relative time values  33 ,  34 ,  35 ,  36  indicating the lower marker&#39;s peak position at the respective points in time when the sample measurements S 1  to S 4  have been performed.  
      Now, for each of the sample measurements S 1  to S 4 , the absolute time scale shown in  FIG. 4A  is transformed into a relative time scale in a way that the position of the lower marker peak LM is aligned with a respective one of the interpolated relative time values  33  to  36 , and that the position of the ladder peak LPn is aligned with the second fixed time value  27 . For each of the sample measurements S 1 , S 2 , S 3 , S 4 , a relative time scale is established by assigning a respective one of the relative time values  33  to  36  to the lower marker peak LM, and by assigning the second fixed time value  27  to the ladder peak LPn. Thus, the absolute time values are converted into corresponding relative time values, whereby the lower marker peak&#39;s time drift is taken into account.  
      In  FIG. 6A , measured time values of the ladder peaks LP 1  to LPn are shown before an alignment is performed. The time axis  37  indicates an absolute time scale that has been used when acquiring the data. The data shown in  FIG. 6A  relates to 12 different calibration measurements L 1  to L 12 .  
       FIG. 6B  shows the same data after an alignment according to  FIG. 4C  has been performed. On the left side, a time axis  38  indicating a relative time scale is shown, with the relative time scale being determined in accordance with  FIG. 4C . For each of the  12  calibration measurements L 1  to L 12 , the respective peak positions of the ladder peaks LP 1  to LPn are indicated. From  FIG. 6B , it can be seen that both the first ladder peaks LP 1  and the last ladder peaks LPn are perfectly aligned, whereas the peak positions of the other ladder peaks LP 2  to LP(n−1) may still vary. However, this variation is much smaller in scale than the marker&#39;s drift that has been described above. Furthermore, this variation is not related to the different chemical structures of the marker and the labelled fragments, but is rather due to other types of fluctuations of the measuring set-up.  
      Therefore, in addition to the global alignment shown in  FIG. 4C , which is performed firstly, a subsequent piecewise alignment is carried out.  
       FIG. 7  shows how to perform a piecewise alignment of a calibration peak pattern. The piecewise alignment is performed with regard to a set of reference time values of the ladder peaks LP 1  to LPn. For each ladder peak LP 1 , a reference time value T′ i  indicating the ladder peak&#39;s reference position is provided, whereby the set of reference time values T′ i , 1≦i≦n is specified on a relative time scale. The set of reference time values might e.g. be obtained from a manufacturer of a calibration sample. Alternatively, the reference positions of the ladder peaks might be determined by performing a large number of reference measurements of a calibration sample, and by determining average values of the calibration peaks&#39; relative time values.  
      In the upper part of  FIG. 7 , a relative time scale  39  is shown, whereby the ladder peaks LP 1 , LP 2 , . . . LPn are those obtained after a global alignment according to  FIG. 4C  has been performed. First, a set of time intervals [T i ; T i+1 ] is defined, with T i  denoting the relative time value of ladder peak LPi, and with T i+1  denoting the relative time value of ladder peak LP(i+1). For each of the intervals extending from LPi to LP(i+1), a separate linear transformation is defined in a way that the interval [T i , T i+1 ] is mapped to a corresponding target interval [T′ i , T′ i+1 ] of a reference time scale  40 . T′ i  denotes the reference time value of ladder peak LPi, and T′ i+1  denotes the reference time value of ladder peak LP(i+1). Thus, a set of (n−1) linear transformations is obtained.  
      Each of the (n−1) linear transformations might e.g. be defined as: 
 
t′ i =scale i ·t i +bias i ,
 
      with scale i  denoting a scaling factor, bias i  denoting an offset, t i ∈[T i ,T +1 ] denoting a relative time value according to the relative time scale  39 , and with t i ∈[T′ i ,T′ i+1 ] denoting a corresponding relative time value of the reference time scale  40 . Each of the (n−1) linear transformations is applied to a corresponding subinterval [T i , T i+1 ], 1≦i≦n−1 of the relative time scale  39 . By subjecting the calibration peak pattern to this set of piecewise transformations, each ladder peak LPi is mapped to its reference time value T′ 1 .  
      When the calibration measurement or the sample measurement are performed, sample values are recorded at a constant rate. Therefore, the spacing between neighboring sample values is constant. However, after the time intervals have been mapped to their corresponding target time intervals, the distances between neighboring sample values are either stretched ( 41 ) or compressed ( 42 ). Therefore next, a re-sampling  43  of the sample values is performed. As a result, a re-sampled reference time scale  44  is obtained.  
      The set of linear transformations derived from the calibration peak pattern can be applied to subsequent sample measurements. A first possibility is to apply the set of transformations as derived from a calibration measurement L 1  to the subsequent sample measurements S 1  to S 4 . Another possibility is to consider both the calibration measurement L 1  that is performed before the sample measurements S 1  to S 4  are carried out and the calibration measurement L 2  performed after the sample measurement S 1  to S 4  have been carried out. From L 1 , a first set of linear transformations is derived, and from L 2 , a second set of linear transformations is derived. For correcting any one of the sample measurements S 1  to S 4 , e.g. S 2 , an interpolated set of (n−1) linear transformations is derived from the first and the second set of linear transformations.  
      In  FIG. 6C , the calibration peak patterns L 1  to L 12  are shown after a piecewise alignment according to  FIG. 7  has been performed. It can be seen that an alignment of all the ladder peaks LP 1 , LP 2 , . . . LPn has been accomplished.  
      By converting both calibration measurements and sample measurements to a reference time scale, it is possible to assign a common time axis both to the ladder peak patterns and the sample peak patterns. Thus, comparability between different calibration measurements and sample measurements is promoted. Furthermore, instead of a time axis indicating relative time values, both the calibrations peak patterns and the sample peak patterns may be calibrated in terms of base pairs. In particular, a size axis  45  indicating the number of corresponding base pairs may be employed. The processed signals may then be used for further analysis, such as .g. profiling.