JP2007147459A - Information processing apparatus, program, and computer-readable recording medium - Google Patents

Abstract

To automatically and accurately associate mass spectra derived from the same compound between two-dimensional peak data obtained from a plurality of analytical experiments.
A spectrum analyzing apparatus compares a peak vector with a first peak vector creating unit that creates a peak vector as mass spectrum information from each two-dimensional peak data, and compares the peak vectors with each other. An internal standard identifying unit 22 for creating a set of standard peak vectors, a holding time correcting unit 23 for correcting the holding time in each two-dimensional peak data based on the holding time corresponding to the peak vector serving as the internal standard, The difference in holding time is within a predetermined range between the second mass spectrum extraction unit that creates a new peak vector from the two-dimensional peak information with the holding time corrected and the two-dimensional peak information with the holding time corrected. And a correspondence determination unit 26 for comparing new peak vectors.
[Selection] Figure 1

Description

  The present invention relates to an information processing apparatus for analyzing data obtained based on a combination of chromatography and mass spectrometry, a program for controlling the information processing apparatus, and a computer-readable recording medium on which the program is recorded. It is.

  Gas chromatography / mass spectrometry (GC / MS) and liquid chromatography / mass spectrometry (LC / MS) devices combine a large number of types of cells, tissues, or organs by combining chromatography and mass spectrometry. Biological components can be separated and identified. In these devices, first, biological components contained in a biological sample extracted from cells, tissues, or whole organs are separated into a single compound by gas chromatography (GC) or liquid chromatography (LC). Thereafter, the separated single compound is cleaved with an electron beam having a certain energy to obtain fragment ions. And the mass spectrum which shows the cleavage pattern of a certain compound can be obtained by detecting the ionic strength of a fragment ion for every mass ratio and charge ratio (m / z).

  Since the above apparatus performs these processes continuously, as shown in FIG. 2, the obtained data is an ion intensity spectrum with respect to retention time and m / z, that is, two-dimensional spectrum data. When this two-dimensional spectrum data is cut out in a cross section orthogonal to the retention time axis, information on the ion intensity along the m / z axis, that is, a mass spectrum can be obtained. On the other hand, when the two-dimensional spectrum data is cut out in a cross section orthogonal to the m / z axis, information on ion intensity along the retention time axis, that is, a mass chromatogram can be obtained.

  Here, when the resolution of the retention time is increased, in the mass chromatogram, as shown in FIG. 2, the ion intensity of a single fragment ion or quasi-molecular ion is in a state extending over a plurality of retention times. Therefore, as shown in FIG. 3, it is necessary to convert the two-dimensional spectrum data shown in FIG. 2 into the two-dimensional peak data shown in the upper part of FIG. 4 by combining the ion intensities over a plurality of holding times into one point. is there. A conventional method for converting two-dimensional spectrum data into two-dimensional peak data will be described as follows.

  In the conventional method, first, the mass chromatogram data shown in the upper part of FIG. 3 is extracted for a certain m / z from the two-dimensional spectrum data shown in FIG. Then, the retention time at which the ionic strength is maximized in the mass chromatogram is identified, and the identified retention time is recognized as the peak position of the spectrum.

  Subsequently, the sum of the ion intensities dispersed in the vicinity of the peak position is taken, and this sum is associated with the peak position. Thereby, the peak data shown in the lower part of FIG. 3 is obtained. By performing this process for all m / z, the two-dimensional peak data shown in the upper part of FIG. 4 is obtained.

  If a cross section perpendicular to the holding time axis is cut out from the two-dimensional peak data, the mass spectrum shown in the lower part of FIG. 4 can be obtained. Here, each mass spectrum includes a cleavage pattern of one compound. Therefore, the compound contained in the biological sample can be identified based on the cleavage pattern of the mass spectrum.

In recent years, exhaustive identification of various compounds contained in various biological samples has been performed using the above-described apparatus.
Mass spectrometry, “Identification method by spectrum of organic compounds-MS, IR, NMR, UV combined use-4th edition”, Silverstein RM, Bassler GC, by Morrill TC, Shu Araki, Yoichiro Masuko, Osamu Yamamoto, 2nd Chapter, Mass Spectrometry, pp. 3-40, Tokyo Chemical Doujin, Tokyo (1983) Yosuke Okura, Masaaki Kai, IV-5 Mass Spectrometry (Mass Spectrometry), “Analytical Chemistry II Rev. 4th Edition”, Yosuke Okura, Yoshimasa Tanaka, Masatoshi Yamaguchi, pp. 228-257, Nanedo, Tokyo (1997)

  However, a method for automatically associating mass spectra considered to be derived from the same compound between two-dimensional peak data obtained from different measurement experiments by an information processing device or the like has not yet been established.

  In general, when finding mass spectra derived from the same compound between two-dimensional peak data obtained from different biological samples, researchers use the intuition based on experience from the huge mass spectra included in the two-dimensional peak data. It is generally performed to select one spectrum at a time, compare each mass spectrum and subjectively determine whether or not they correspond. However, as described above, when comprehensively identifying various compounds contained in various biological samples, a conventional method in which researchers compare individual mass spectra with each other has a large amount of output at high throughput. It is difficult to deal with two-dimensional peak data. Therefore, there is a need for an information processing apparatus that can automatically associate mass spectra without depending on the intuition of a researcher.

  Here, when automating the association, the problem of retention time is the key. For example, when the same biological sample is analyzed multiple times under the same analysis conditions by GC / MS, LC / MS, etc., it is theoretically considered that the same compound is always included in the fraction having the same retention time. . However, in reality, it is impossible to completely maintain the same analysis conditions, and it is inevitable that the holding time will be different for each analysis experiment.

  This problem of deviation becomes even more pronounced when the analysis conditions change, such as differences in biological samples. Therefore, the mass spectrum cannot be accurately associated unless the holding time that is shifted for each experiment is corrected.

  Furthermore, as a problem before that, the conventional technique has a problem that the position of the peak may not be accurately identified.

  FIG. 5 is a diagram showing an example of ionic strength of different fragment ions derived from a single compound. The upper part of FIG. 5 is a mass chromatogram showing the ion intensity of a fragment ion with m / z being i, and the lower part of FIG. 5 is a mass chromatogram showing the ion intensity of a fragment ion with m / z being j. Gram. These two fragment ions are derived from the same compound, and each peak exists between retention times t + 2 and t + 3 as shown on the left side of FIG. And when the ion intensity of these fragment ions is sampled, it becomes as shown in the center of FIG.

  At this time, if the peak positions (retention times) of these two fragment ions are identified according to the conventional technique, the position where the sampled ion intensity is maximum is identified as the peak position in the conventional technique. As shown in FIG. 2, the peak position of one fragment ion is t + 3, and the peak position of the other fragment ion is t + 2. Thus, in the conventional method, two peaks that should be associated with the same retention time are associated with different retention times, and as a result, these fragment ions are treated as being derived from different compounds. It will be.

  Since researchers have to correct such problems sequentially based on experience-based intuition, it was difficult to quickly analyze a large amount of two-dimensional peak data.

  The present invention has been made in view of the above problems, and a first object thereof is to automatically and accurately mass spectra derived from the same compound between two-dimensional peak data obtained from a plurality of analytical experiments. An object is to realize an information processing apparatus that can be associated.

  A second object of the present invention is to realize an information processing apparatus capable of accurately identifying the position of each peak from sampled two-dimensional spectrum data.

  In order to solve the above problems, an information processing apparatus according to the present invention provides two-dimensional peak data that is information on retention time and peak ion intensity for each m / z obtained based on a combination of chromatography and mass spectrometry. 2 is a data processing apparatus for identifying a mass spectrum corresponding to two-dimensional peak data in a two-dimensional peak data set including a plurality of data, and first extracting mass spectrum data for each holding time from each two-dimensional peak data Internal standard mass spectrum data including mass spectrum data as internal standards extracted from each two-dimensional peak data by comparing mass spectrum data extracted from different two-dimensional peak data with the mass spectrum extraction unit Internal standard identification part to create a set and internal standard mass spectrum Based on the retention time corresponding to each mass spectrum data included in the data set, the retention time correction unit for correcting the retention time in each 2D peak data, and the retention time corrected 2D peak data Compare the new mass spectrum data within the predetermined range of the retention time difference between the second mass spectrum extraction unit that extracts new mass spectrum data every time and the two-dimensional peak data with the retention time corrected. And a correspondence determination unit that determines whether or not the new compared mass spectra correspond to each other.

  In the present specification, “two-dimensional peak data” is data obtained based on a combination of chromatography and mass spectrometry, and the ionic strength of each fragment ion or quasi-molecular ion is a single retention time. The data associated with. The ion intensity associated with the single retention time is referred to as “peak ion intensity”. Furthermore, in this specification, the “peak” refers to a point at which the ionic strength of the fragment ion or quasi-molecular ion is maximized. Further, in this specification, “mass spectrum data” is data indicating ion intensity information for each m / z. For example, from two-dimensional peak data, for each m / z for a certain holding time. It can be obtained by extracting ionic strength information.

  An information processing apparatus according to the present invention includes a two-dimensional peak data set including a plurality of two-dimensional peak data, which are information on retention time and peak ion intensity for each m / z obtained based on a combination of chromatography and mass spectrometry. In FIG. 2, the corresponding mass spectrum is identified between the two-dimensional peak data.

  According to the above configuration, mass spectrum data is extracted from each two-dimensional peak data for each holding time by the first mass spectrum extraction unit. This mass spectrum data is a clue for identifying a compound, and the same mass spectrum data can be obtained from the same compound. The internal standard identification unit compares the mass spectrum data extracted from the different two-dimensional peak data, and includes an internal standard mass spectrum data set including similar mass spectrum data extracted from each two-dimensional peak data. Is created. The mass spectrum data included in the internal standard mass spectrum data set is similar to each other, in other words, a mass spectrum commonly seen in each two-dimensional peak data.

  Since these mass spectrum data are similar to each other, it can be estimated that they were obtained from the same compound. According to the chromatographic principle, the same compound is contained in the fraction with the same retention time, so all the mass spectral data contained in the above set should correspond to the same retention time. Accordingly, it is possible to correct a shift in the holding time of each two-dimensional peak data using the mass spectrum data included in this set as an internal standard.

  In the information processing apparatus of the present invention, the holding time correction unit corrects the holding time in each two-dimensional peak information based on the holding time corresponding to each mass spectrum data included in the internal standard mass spectrum data set described above. Is done. Thereby, the shift | offset | difference of the holding time for each two-dimensional peak data is eliminated.

  Subsequently, new mass spectrum information is extracted for each holding time from each two-dimensional peak data with the holding time corrected by the second mass spectrum extraction unit. Then, the correspondence determination unit compares the new mass spectrum data in which the difference in the retention time is within a predetermined range between the two-dimensional peak data whose retention times have been corrected, and the newly compared mass spectra correspond to each other. It is determined whether it is what to do.

  That is, in the information processing apparatus according to the present invention, finally, only the mass spectrum data in which the difference in retention time is within a predetermined range is compared. Therefore, mass spectra having significantly different retention times are not associated with each other. As a result, mass spectra can be accurately associated. Furthermore, since the holding time used at this time is an accurate one in which the deviation for each experiment is corrected, the association can be performed more accurately.

  As described above, according to the information processing apparatus of the present invention, mass spectra derived from the same compound can be automatically and accurately associated with each other between two-dimensional peak data obtained from a plurality of analysis experiments.

  Moreover, it is preferable that the internal standard identification unit compares mass spectrum data having a retention time difference within a predetermined range between two-dimensional peak data.

  According to the above configuration, the mass spectrum data compared by the internal standard identification unit has a difference in retention time within a predetermined range. Therefore, it is possible to prevent unintentional use of a set of mass spectrum data having similar peak patterns but significantly different retention times as an internal standard.

  Moreover, it is preferable that the said 1st mass spectrum extraction part extracts each mass spectrum data as a vector which makes ion intensity for every m / z an element.

  According to the above configuration, the similarity between the mass spectrum data is determined based on the comparison between the vectors. There are various known methods for determining the similarity of vectors, and the similarity between mass spectrum data can be objectively determined by calculating the similarity.

  Further, the second mass spectrum extraction unit extracts each new mass spectrum data as a new vector having an ion intensity for each m / z as an element, and the correspondence determination unit is configured to perform different corrected two-dimensional data. It is preferable to determine whether or not the mass spectrum data corresponds to each other by calculating the similarity between new vectors extracted from the peak data and comparing the calculated similarity with a threshold value.

  According to the above configuration, the correspondence determination unit calculates the similarity between vectors corresponding to each mass spectrum data, and further, the mass spectrum data corresponds based on the comparison result between the calculated similarity and the threshold value. It is determined whether it is what to do. As described above, in the information processing apparatus according to the present invention, it is possible to associate mass spectrum data based on an objective index called vector similarity.

  Further, the information processing apparatus creates a correspondence table in which identification information of each new mass spectrum is arranged in the same row or column for new mass spectra determined to correspond by the correspondence determination unit. It is preferable to further include a portion.

  According to the above configuration, it is possible to know which mass spectrum corresponds to which mass spectrum between different two-dimensional peak data by referring to the created correspondence table.

  In order to solve the above problems, another information processing apparatus according to the present invention is information on retention time and ion intensity for each m / z obtained based on a combination of chromatography and mass spectrometry 2. A two-dimensional peak data creation unit for creating two-dimensional peak data, which is information on the retention time and peak ion intensity for each m / z, from the two-dimensional spectrum data; A total peak generator that calculates total sum as total peak intensity and generates total peak data that is information of total peak intensity for each holding time, and a section where the total peak intensity is always greater than or equal to the threshold in the total peak data, or always threshold And the total peak intensity is maximized in that section. That the retention time, characterized in that it comprises a first peak position identifying unit for identifying as a true retention time corresponding to the peaks included in the section of the two-dimensional peak data.

  In this specification, “two-dimensional spectral data” is data obtained based on a combination of chromatography and mass spectrometry, and the ionic strength of each fragment ion or pseudo-molecular ion extends over a plurality of retention times. It means the data.

According to the above configuration, first, the two-dimensional peak data is created from the two-dimensional spectrum data by the two-dimensional peak data creation unit. Here, as an example, in the created two-dimensional peak data, peaks that should be associated with the same retention time, such as the peak 101 and the peak 102 in FIG. Assume that these are associated with t ₁ and t ₂ ). According to the above configuration, the total peak intensity is calculated for each holding time by the total peak creating unit. As a result, the total peak intensity at the holding times t ₁ and t ₂ becomes larger than the threshold (or becomes greater than or equal to the threshold). Therefore, the section from the retention time t ₁ to t ₂ is identified by the first peak identification unit as a section where the total peak intensity is always greater than or equal to the threshold (or a section where the total peak intensity is always greater than the threshold). Then, the holding time t _{1 at} which the total peak intensity is maximized in the section is identified as the true holding time of the peak 101 and the peak 102 by the first peak identifying unit. Thus, the peak 101 and peak 102 is located in the same retention time t _1, it can be treated as the peak derived from a single compound.

  As described above, according to the information processing apparatus of the present invention, the position of each peak can be accurately identified from the sampled two-dimensional spectrum data.

  Moreover, it is preferable that the first peak position identifying unit further associates the peak ion intensity included in the section of the two-dimensional peak data with the identified true retention time.

  According to the above configuration, two-dimensional peak data in which peak ion intensity is associated with an accurate holding time can be obtained.

  In addition, the two-dimensional peak data creation unit performs mass chromatography for each m / z from two-dimensional spectrum data, which is information on retention time and ion intensity for each m / z obtained based on a combination of chromatography and mass spectrometry. In addition to extracting gram data, each mass chromatogram data includes a second peak position identifying unit that identifies a tentative peak retention time based on a retention time at which the ionic strength becomes maximum, and each mass chromatogram data By calculating the peak ion intensity by adding the ion intensity at the holding time adjacent to the peak holding time to the ion intensity at the temporary peak holding time and associating the calculated peak ion intensity with the temporary peak holding time. , Spectral intensity to create the above two-dimensional peak data Preferably contains a body portion.

  According to the above configuration, first, the mass chromatogram data is extracted for each m / z from the two-dimensional spectrum data by the second peak position identification unit. Then, a temporary peak retention time is identified based on the retention time at which the ionic strength is maximized in each mass chromatogram data. Subsequently, in each mass chromatogram data, the ion intensity at the holding time adjacent to the temporary peak holding time is added to the ion intensity at the temporary peak holding time by the spectrum intensity merging unit. This added ion intensity becomes the peak ion intensity. This peak ionic strength is associated with a temporary peak retention time. As a result, the ion intensity over a plurality of holding times is collected into a temporary peak holding time. In this way, two-dimensional peak data can be created from the two-dimensional spectrum data.

  In addition, the information processing apparatus obtains mass chromatogram data for each m / z from two-dimensional spectrum data that is information on retention time and ion intensity for each m / z obtained based on a combination of chromatography and mass spectrometry. It is preferable to further include a smoothing unit that creates two-dimensional spectrum data to be input to the two-dimensional peak data creation unit by extracting and smoothing the ion intensity in each mass chromatogram data.

  Usually, when sampling ion intensity, it is inevitable that random noise is mixed. Here, according to the above configuration, since the ion intensity in the two-dimensional spectrum data is smoothed along the holding time axis by the smoothing unit, the influence of random noise can be suppressed.

  By the way, the information processing apparatus may be realized by hardware or may be realized by causing a computer to execute a program. Specifically, a program according to the present invention is a program that causes a computer to operate as each of the above-described units, and the program is recorded on a recording medium according to the present invention.

  When these programs are executed by a computer, the computer operates as the information processing apparatus. Therefore, the same effects as those of the information processing apparatus are achieved.

  As described above, the information processing apparatus according to the present invention includes a first mass spectrum extraction unit that extracts mass spectrum data from each two-dimensional peak data for each holding time, and a mass spectrum extracted from different two-dimensional peak data. Included in the internal standard mass spectrum data set and an internal standard mass spectrum data set that creates internal standard mass spectrum data sets that contain similar mass spectrum data extracted from each two-dimensional peak data by comparing the data A holding time correction unit for correcting the holding time in each two-dimensional peak data based on the holding time corresponding to each mass spectrum data, and a new one for each holding time from the two-dimensional peak data in which the holding time is corrected. Second mass spectrum to extract mass spectrum data New mass spectra that correspond to each other by comparing the new mass spectrum data in which the difference in retention time is within a predetermined range between the output portion and the two-dimensional peak data with the retention time corrected. It is the structure provided with the corresponding | compatible determination part which determines whether it is. Therefore, as described above, there is an effect that mass spectra derived from the same compound can be automatically and accurately associated between two-dimensional peak data obtained from a plurality of analysis experiments.

  In addition, another information processing apparatus according to the present invention provides a retention time and m from two-dimensional spectrum data which is information on retention time and ion intensity for each m / z obtained based on a combination of chromatography and mass spectrometry. For the two-dimensional peak data creating unit that creates two-dimensional peak data that is information of peak ion intensity for each / z, and for the two-dimensional peak data, the sum of peak ion intensities for each holding time is calculated as the total peak intensity, A total peak creation unit that creates total peak data that is information on the total peak intensity for each holding time, and a section in which the total peak intensity is always greater than or equal to the threshold in the total peak data or a section that is always greater than the threshold, The retention time at which the total peak intensity becomes maximum in that section is the two-dimensional peak. It has a configuration that includes a first peak position identifying unit for identifying as a true retention time corresponding to the peaks included in the section of the chromatography data. Therefore, as described above, there is an effect that the position of each peak can be accurately identified from the sampled two-dimensional spectrum data.

Embodiment 1
An embodiment of an information processing apparatus according to the present invention will be described below with reference to FIGS.

  The spectrum analysis apparatus (information processing apparatus) of the present embodiment is an apparatus that analyzes data sampled by a measurement apparatus that combines chromatography and mass spectrometry, such as GC / MS and LC / MS. It can be said that the data of the ionic strength information obtained by the above measuring device is two-dimensional spectral data on the ratio of mass number to electric charge by ionization (hereinafter referred to as “m / z”) and retention time. The spectrum analysis apparatus of this embodiment is used to accurately identify the position of a peak (that is, m / z and retention time corresponding to the peak) included in the two-dimensional spectrum data.

First, a description method of data obtained by the measuring apparatus is defined. As described above, the ion intensity information (hereinafter referred to as “spectral intensity”) obtained by the measuring apparatus varies for each m / z and holding time. Here, in the obtained spectrum data, the m / z number is 1, 2,..., M in order from the smallest value, and the retention time number is 1, 2,. Let x _{k, m} denote the spectral intensity of the sample point with the retention time kth and m / z mth.

  FIG. 6 is a functional block diagram showing the main configuration of the spectrum analyzing apparatus according to the present embodiment. As shown in FIG. 6, the spectrum analysis apparatus 1 according to the present embodiment is a microcomputer mainly including a peak data creation unit 10 and a peak association unit 20 as functional blocks.

  The peak data creation unit 10 identifies the peak retention time and ion intensity in the two-dimensional spectral data obtained from the LC / MS 100 (or GC / MS), and the ion intensity of each fragment ion and / or quasi-molecular ion is simple. This is for creating two-dimensional peak data associated with one holding time and m / z. The peak association unit 20 compares two-dimensional peak data related to a plurality of experiments obtained by the peak data creation unit 10 and associates peaks derived from the same compound among the plurality of experiments. It is.

(1. Peak data creation unit / peak data creation process)
FIG. 7 is a block diagram showing a detailed functional configuration of the peak data creation unit 10. As shown in FIG. 7, the peak data creation unit 10 in this embodiment includes a smoothing unit 11, a peak time identification unit (second peak position identification unit) 12, a spectral intensity coalescence unit 13, a total peak creation unit 14, and a total A peak merging portion (first peak position identifying portion) 15 and a peak merging portion (first peak position identifying portion) 16 are included.

  The smoothing unit 11 extracts the mass chromatogram data for each m / z from the two-dimensional spectrum data, and smoothes the ion intensity in each mass chromatogram. The smoothed two-dimensional spectrum data is input to the peak time identification unit 12.

  The peak time identification unit 12 extracts mass chromatogram data for each m / z from the two-dimensional spectrum data input from the smoothing unit 11, and based on the retention time at which the ion intensity is maximized in each mass chromatogram. The temporary peak retention time (retention time corresponding to the peak) is identified. This temporary peak position information is input to the spectral intensity combining unit 13 together with the extracted mass chromatogram data.

  In each mass chromatogram data input from the peak time identifying unit 12, the spectrum intensity combining unit 13 adds the ion intensity at the holding time adjacent to the temporary peak holding time to the ion intensity at the temporary peak holding time. Thus, the peak ion intensity is calculated, and the calculated peak ion intensity is associated with the temporary peak retention time. By this process, the ionic strength of fragment ions or quasi-molecular ions over a plurality of holding times becomes a single holding time and a peak ion strength associated with m / z, and as a result, two-dimensional peak data is created. The The created two-dimensional peak data is input to the total peak creation unit 14.

  The total peak creating unit 14 calculates the sum of peak ion intensities for each holding time for the two-dimensional peak data input from the spectral intensity combining unit 13. The total sum of the calculated peak ion intensities is referred to as total peak intensity and serves as an index indicating the relative amount of the compound contained in each retention time fraction. Since this total peak intensity is calculated for each holding time, total peak data indicating the relationship between the holding time and the total peak intensity is created. The total peak data is input to the total peak combining unit 15.

  The total peak merging unit 15 obtains a section in which the total peak intensity is always greater than or equal to the threshold in the total peak data or a section in which the total peak intensity is always greater than the threshold, and identifies a holding time in which the total peak intensity is maximum in that section. The retention time identified here is a true retention time corresponding to all the peaks included in the same section of the two-dimensional peak data. The section and true retention time information obtained here are input to the peak merger 16 together with the two-dimensional peak data. Further, the total peak merging unit 15 calculates the sum of the total peak intensities included in the section obtained here, and associates the calculated sum with the true holding time. Thereby, updated total peak data is created. The updated total peak data is input to the first peak vector creation unit 21 of the peak association unit 20.

  In the two-dimensional peak data input from the total peak merging unit 15, the peak merging unit 16 associates all peak positions included in the section with the true retention time. Specifically, the sum of peak intensities of peaks included in the section is calculated for each m / z, and the calculated sum is associated with the true retention time. Thereby, updated two-dimensional peak data is created. The updated two-dimensional peak is input to the first peak vector creation unit 21 of the association unit 20.

  Next, the operation of the peak data creation unit 10 will be described. The processing steps (peak analysis method) of the peak data creation unit 10 include a smoothing step, a peak time identification step, a spectrum intensity coalescence step, a total peak creation step, a total peak coalescence step, and a peak coalescence step. These steps will be described in order as follows.

(1-1. Smoothing part / smoothing step)
First, the two-dimensional spectrum data obtained from the measuring device is smoothed along the holding time axis. The detailed procedure for smoothing is as follows.

In a mass chromatogram obtained by cutting out a two-dimensional spectrum on a plane orthogonal to the m / z axis, let x _{k be} the spectral intensity at the k-th sample point with a retention time. Smoothing is performed by calculating an average value of the spectrum intensity for a total of N sample points centered on the kth sample point and assigning the calculated average value to the spectrum intensity of the kth sample point. Thereby, the ion intensity x ′ _k after the smoothing of the k-th sample point is expressed by the following equation (1).

(However, N ′ = (N−1) / 2)
Represented by

This process is performed for all planes orthogonal to each m / z. Accordingly, the smoothed spectral intensity x ′ _{k, m} of the sample point with the retention time kth and m / z _mth is expressed by the following equation (2).

Represented by By this processing, the two-dimensional spectrum data is smoothed along the holding time axis. This smoothing step is performed by the smoothing unit 11.

  The effects of the smoothing process are as follows. Usually, in data obtained by GC / MS, LC / MS, or the like, the measured ion intensity includes a random error. Therefore, if the peak retention time is identified using the measured ion intensity information as it is, the peak retention time may deviate from the original due to a random error. However, if the above smoothing step is performed, the influence of random errors can be suppressed and the peak position can be accurately detected.

(1-2. Peak time identification unit / peak time identification step)
Next, the peak position (retention time corresponding to the peak) in the mass chromatogram obtained by cutting the smoothed two-dimensional spectrum along a plane orthogonal to the m / z axis is identified. When identifying the position of the peak, an operation for examining whether or not a sample point at a certain holding time is a peak is sequentially performed along the holding time axis. The test method is as follows.

  The determination as to whether or not the k-th sample point at the holding time is a peak is made based on the slope of the curve at the (k−1) -th sample point and the slope of the curve at the (k + 1) -th sample point. Specifically, when the slope at the (k−1) th sample point is larger than 0 and the slope at the (k + 1) th sample point is smaller than 0, it is determined that the kth sample point is a peak.

The slope of the curve at each sample point can be easily obtained using a linear regression equation based on the spectral intensities of a total of N sample points with the sample point as the center. Specifically, when the slope of the curve at the k-th sample point and b _k, b _k, the following equation (3)

Represented by

This process is performed for all mass chromatograms orthogonal to each m / z. Therefore, the inclination of _{b k} of the curve m / z retention time at k-th in the m-th sample _point, when _{m, b k, m,} the following formula (4)

Represented by This peak time identification step is performed by the peak time identification unit 12.

(1-3. Spectral intensity coalescence part / spectral intensity coalescence process)
Subsequently, the smoothed two-dimensional spectrum is cut out in a cross section orthogonal to the m / z axis. In the obtained mass chromatogram, if a section consisting of a minimum value, a maximum value, and a minimum value is defined as one “mountain”, the spectral intensities of all sample points included in this mountain are calculated from the peak positions of the peaks. It is considered to be derived.

  Therefore, a process for collecting the spectral intensities of all the sample points included in each mountain at the peak position is performed. This processing is performed by adding the spectral intensity of the sample points around the peak to the spectral intensity of the peak sample points, and setting the spectral intensity of the sample points around the peak to zero.

FIG. 8 is a flowchart for explaining this processing procedure in detail. Assume that the kth sample point is determined to be a peak. Here, if the k-th holding time is t _k and the variable indicating the peak intensity at the holding time t _k is P (t _k ), first, the spectrum intensity x _k of the k-th sample point is set to P (t _k ). Substitute (S31). Next, the following processing is performed in order to sequentially add the spectral intensity of the sample points existing on the left side of the peak to the peak.

First, in order to set the sample point to be processed on the left side of the peak, k−1 is assigned to the variable s indicating the sample number to be processed (S32). Subsequently, the slope b _s of the curve at the sample point to be processed is compared with 0 (S33). If the slope b _s is larger than 0, it is determined that the sample point to be processed is a sample point that should be included in the current peak, and the process proceeds to the next step S34.

In step S34, the spectrum intensity x _s of the sample point to be processed is added to P (t _k ). Then, in order to shift the sample point to be processed by one to the left, the value of the variable s is decreased by one (S35). Then, the process returns to step S33.

On the other hand, if the slope b _s is 0 or less in step S33, it is determined that the sample point to be processed should not be included in the current peak, and the process proceeds to step S36. Then, this time, the following processing is performed in order to sequentially add the spectral intensity of the sample points existing on the right side of the peak to the peak.

First, in order to set the sample point to be processed to the right of the peak, k + 1 is substituted for the variable s (S36). Subsequently, the slope b _s of the curve at the sample point to be processed is compared with 0 (S37). If the slope b _s is smaller than 0, it is determined that the sample point to be processed is a sample point that should be included in the current peak, and the process proceeds to the next step S38.

In step S38, the spectral intensity x _s of the sample point to be processed is added to P (t _k ). Then, in order to shift the sample point to be processed by one to the right, the value of the variable s is increased by one (S35). Then, the process returns to step S37.

On the other hand, if the slope b _s is greater than or equal to 0 in step S37, it is determined that the sample point to be processed should not be included in the current peak, and the process ends. As described above, the spectrum intensities of the sample points that should belong to one peak are all collected at the peak position. As a result, the peak intensities are summarized in t th retention time t _k can be obtained as P (t _k). Note that P (t _k ) at positions other than the peak is 0.

This processing is performed for all peaks included in all cross sections orthogonal to each m / z. Hereinafter, the peak intensity at the holding time t _k and m / z is m-th is expressed as P (t _k ) _m . Data having retention time, m / z, and peak intensity as elements are referred to as two-dimensional peak data. The upper part of FIG. 9 is a visualization of this two-dimensional peak data. The spectral intensity combining step is performed by the spectral intensity combining unit 13.

  According to the first peak time identifying step and the spectral intensity merging step, even when ion intensity information obtained from the same fragment ion spans a plurality of holding times, the respective ion intensity information is summarized, It can be calculated as one peak intensity information corresponding to a single holding time. That is, the intensity of the peak derived from each fragment ion and the retention time corresponding to the peak can be obtained.

(1-4. Total peak creation part / Total peak creation process)
Next, the total peak intensity is calculated by cutting out the two-dimensional peak data after the spectral intensity merging step in a cross section orthogonal to the retention time axis and summing the peak intensities of all the peaks included in the obtained mass spectrum. . This process is performed for all mass spectra orthogonal to each holding time. In other words, the operation of combining all the peaks corresponding to a certain holding time into one is performed for all the holding times.

Therefore, when the total peak intensity at the holding time t _k is TI (t _k ), TI (t _k ) is expressed by the following equation (5).

Represented by

This total peak creation step is performed by the total peak creation unit 14. Hereinafter, the data of the total peak intensity TI (t _k ) for each holding time is referred to as total peak data. The middle part of FIG. 9 is a visualization of the total peak data. In addition, a peak group that is combined into one total peak when creating the total peak data is referred to as a total peak group. The total peak group corresponds to a mass spectrum obtained from a single compound.

(1-5. Total peak coalescence part / total peak coalescence process)
In the total peak data shown in the middle part of FIG. 9, the total peak intensities at the retention times t ₁ and t ₂ are considered to be derived from the same compound. Therefore, in the total peak merging step, a process of combining the total peaks considered to be derived from these same compounds into one is performed according to the following procedure.

First, an interval in which the total peak intensity is always greater than 0 in continuous holding times t _{i to} t _{i + n} (where n is a natural number) is identified. In this section, the holding time t _{u at} which the total peak intensity becomes maximum (maximum) and the holding times t _su and t _eu at both ends (minimum points) of the peaks are identified. Note that, for example, when there are only two total peak intensities included in one peak, t _u may be equal to t _su or t _eu . The retention time t _u obtained here becomes the true retention time of all peaks included in the interval t _{su to} t _eu of the two-dimensional peak data later.

Then, the total peak intensity from t _su except holding time t _u to t _eu, adds to the total peak intensities in the retention time t _u, the total peak intensity other than the retention time t _u is zero. This process is performed for all mountains in all sections.

  As described above, a plurality of total peak intensities derived from one compound are collected at one position representing the retention time of the compound (the retention time at which the total peak intensity is maximized).

As an example, in the total peak data in the middle stage of FIG. 9, the total peak intensity is greater than 0 in the continuous holding times t ₁ and t ₂ . In this case, t _u = t ₁ , t _su = t ₁ , and t _eu = t ₂ . Then, by adding the total peak intensities in the retention time t ₂ to the total peak intensities in the retention time t _1, the total peak intensities in the retention time t ₂ to 0. As a result, the total peak data is as shown in the lower part of FIG.

  As another example, in FIG. 10 (1), two continuous total peaks are combined into one peak, and in (2), there is a retention time of 0 between the two total peaks. Thus, the two peaks remain, and in the case of (3), the four total peaks are combined into two peaks.

  In this embodiment, a section in which the total peak intensity is always greater than 0 is identified. However, when noise or the like is included in the total peak intensity, a predetermined threshold is set, and a section in which the total peak intensity is always greater than the threshold is set. A section that is always greater than or equal to the threshold may be identified.

  This total peak merging step is performed by the total peak merging unit 15.

(1-6. Peak coalescence part / peak coalescence process)
Next, for the two-dimensional peak data in the upper part of FIG. 4, a process for collecting the peak intensities included in the section obtained in the total peak coalescing process is performed. In other words, taking the sum of the peak intensities of the peaks included in the retention time _t su _{~t eu} for each m / z, associated to hold the total time _{t u.}

Explaining with the above-described example, the peak intensity P (t ₁ ) _M and P (t ₂ ) _M are added to the peak of m / z of M in the two-dimensional peak data in the upper part of FIG. Is associated with the holding time t ₁ . Here, since P (t ₂ ) _M = 0, there is no change in the position and intensity of the peak before and after the processing.

Similarly, for the peak with m / z of m, the peak intensities P (t ₁ ) _m and P (t ₂ ) _m are added, and the added peak intensity is associated with the holding time t ₁ . In this case, since P (t ₁ ) _m = 0, the peak intensity does not change before and after the processing, but the peak position changes to t ₁ . The result of the above processing is as shown in FIG.

  This process is performed for every m / z for all sections obtained in the total peak merging step. The peak merging step is performed by the peak merging unit 16.

  The effects of the total peak merging step and the peak merging step are as follows. In the peak data for each m / z shown in the upper part of FIG. 9, the peak 101 and the peak 102 are considered to be due to fragment ions or pseudo-molecular ions dissociated from the same compound. However, since the measurement data includes random errors, even if the peaks are fragment ions dissociated from the same compound, such as the peak 101 and the peak 102 in the upper part of FIG. It may be associated with different holding times. As a result, the two peaks 101 and 102 that should be treated as peaks related to the same compound are handled as peaks related to different compounds.

  However, according to the total peak merging step and the peak merging step described above, as shown in FIG. 11, the peak 101 and the peak 102 are associated with the same holding time. As a result, the peak 101 and the peak 102 can be handled as peaks related to the same compound.

(2. Peak association unit / peak data association step)
The peak association unit 20 associates total peak groups (mass spectra) derived from the same compound between a plurality of two-dimensional peak data when a set of two-dimensional peak data is obtained from a plurality of experiments. Is. Note that the two-dimensional peak data input to the peak association unit 20 does not necessarily have to be created by the above-described peak data creation unit 10, and may be created by a known method as long as it is similar data.

  The outline of the peak data association process by the peak data association unit 20 will be described as follows. In separation methods such as gas chromatography and liquid chromatography, since the retention time includes an error for each experiment, in order to associate the total peak groups between the two-dimensional peak data obtained from each experiment, Correction is required. For this purpose, the peak data association unit 20 detects a total peak group that exists in common in all of the two-dimensional peak data to be compared as an internal standard peak group, and the two-dimensional peak based on the retention time of the internal standard peak group. Correct the retention time in the data. Further, the peak data association unit 20 associates the total peak groups between experiments within an allowable range designated by the user based on the corrected holding time, and represents the result as a correspondence table.

  In the following, the two-dimensional peak data obtained by the peak data creation unit 10 from the experiment s (s = 1, 2,..., S) is expressed as shown in Table 1 below.

However, P ^(s) (t _{k (s)} ) _m is the two-dimensional peak data obtained from the experiment s, and the peak intensity at the m-th sample point with the retention time t _{k (s)} and m / z. Show.

  The total peak data obtained by the peak data creation unit 10 from the experiment s (s = 1, 2,..., S) is as shown in Table 2 below.

However, TI ^(s) (t _{k (s)} ) represents the total peak intensity with a retention time t _{k (s)} in the total peak data obtained from the experiment s.

  FIG. 1 is a block diagram illustrating a detailed functional configuration of the peak association unit 20. As shown in FIG. 1, the peak association unit 20 in the present embodiment includes a first peak vector creation unit (first mass spectrum extraction unit) 21, an internal standard identification unit 22, an internal standard confirmation unit 23, and a retention time correction unit. 24, a second peak vector creation unit (second mass spectrum extraction unit) 25, a correspondence determination unit 26, and a table creation unit 27.

  The first peak vector creation unit 21 extracts mass spectrum data for each holding time from each two-dimensional peak data, and creates a peak vector whose peak intensity is included in each mass spectrum data. In the present embodiment, the first peak vector creation unit 21 creates this peak vector for all two-dimensional peak data. The created peak vector is input to the internal standard identification unit 22.

  The internal standard identification unit 22 compares a peak vector created from certain two-dimensional peak data with a peak vector created from other two-dimensional peak data, and identifies similar peak vectors between different two-dimensional peak data To do. A peak vector similar between the different two-dimensional peak data is referred to as an internal standard peak vector. The internal standard identification unit 22 creates a set of internal standard peak vectors commonly found in all two-dimensional peak data. The subsequent holding time correction unit 24 corrects the holding time of each two-dimensional peak data based on the holding time of each internal standard vector included in this set. Note that only one set of internal standard peak vectors may be created, or a plurality of sets may be created. This set of internal standard peak vectors is input to the internal standard confirmation unit 23.

  The internal standard confirmation unit 23 is for confirming whether or not the internal standard peak vector identified by the internal standard identification unit 22 is appropriate. Specifically, it has a function of visually displaying the internal standard peak vector to the user and excluding inappropriate internal standard peak vectors according to the user's instructions. Moreover, the internal standard confirmation part 23 can also change an internal standard peak vector into another peak vector according to a user's instruction | indication. The set of internal standard peak vectors changed in this way is input to the holding time correction unit 24.

  The holding time correction unit 24 corrects the holding time of two-dimensional peak data obtained from different experiments based on the holding time corresponding to each internal standard peak vector included in the set of internal standard peak vectors. Specifically, the retention times of the respective two-dimensional peak data are corrected so that the internal standard peak vectors obtained from different two-dimensional peak data have the same retention time. The two-dimensional peak data with the holding time corrected is input to the second peak vector creation unit 25.

  The second peak vector creation unit 25 extracts one-dimensional peak data (mass spectrum data) for each retention time from the two-dimensional peak data with the retention time corrected, and uses the peak intensity included in each mass spectrum data as an element. Create a new peak vector. The second peak vector creating unit 25 creates this peak vector for all two-dimensional peak data. The newly created peak vector is input to the correspondence determination unit 26.

  The correspondence determination unit 26 compares the peak vectors in which the difference in retention time is within a predetermined range between the two-dimensional peak information with the retention times corrected, so that the compared peak vectors correspond to each other. Determine whether or not.

  The table creation unit 27 is for creating a table showing the correspondence relationship between the total peak groups. In this embodiment, the table creation unit 27 creates a correspondence table in which the identification information of the corresponding total peak group is described in the same column. . The table creation unit 27 may create a correspondence table in which the identification information of the corresponding total peak group is described in the same row.

  Next, the operation of the peak association unit 20 will be described. The peak association process by the peak association unit 20 includes a first peak vector creation process, an internal standard identification process, an internal standard confirmation process, a holding time correction process, a second peak vector creation process, a correspondence determination process, and a table creation process. Is included. These steps will be described in order as follows.

(2-1. First Peak Vector Creation Unit / First Peak Vector Creation Step)
First, from the two-dimensional peak data shown in Table 1 above, a peak vector having the peak intensity of each peak included in the total peak group as an element is created for each holding time. This peak vector is created for all experiments.

Assuming that the peak vector of the holding time t _{k (s)} in the s-th experiment is f ^(s) (t _{k (s)} ), f ^(s) (t _{k (s)} ) is expressed by the following equation (6).
f ^(s) (t _{k (s)} ) = (P ^(s) (t _{k (s)} ) ₁ , P ^(s) (t _{k (s)} ) ₂ ,..., P ^(s) (t _{k (s )} ) _m , ...
…, P ^(s) (t _{k (s)} ) _M ) (6)
Can be represented by

  In other words, it can be said that this step is a step of extracting one-dimensional peak data (mass spectrum data) from the two-dimensional peak data for each holding time for each experiment. This first peak vector creation step is performed by the first peak vector creation unit 21.

(2-2. Internal Standard Identification Unit / Internal Standard Identification Step)
Next, a set of peak vectors that are similar between different experiments are identified. Since the peak vector is one-dimensional peak data cut out for each holding time, that is, mass spectrum data, the peak vector is a vector depending on the compound included in the fraction of the holding time. Therefore, if the same compound is contained in a mixture obtained from different experiments, it is considered that a similar peak vector can be obtained. Therefore, this similar peak vector is identified as the internal standard peak vector, and the deviation of the holding time for each experiment is corrected based on the holding time corresponding to the internal standard peak vector.

In this embodiment, three threshold values TIP, NTP, and _Tint are introduced when comparing peak vectors. These thresholds can be set by the user.

TIP and NTP are used to test whether a peak vector is suitable as a candidate for an internal standard peak vector. TIP indicates the peak intensity threshold, while NTP indicates the peak number threshold. T _int is a threshold value for defining an allowable range of retention time when comparing peak vectors.

  FIG. 12 is a flowchart showing a process of searching for an internal standard peak vector from peak vectors.

First, one experiment is arbitrarily selected from S experiments. Here, for simplification of explanation, the first experiment is selected. Then, the first peak vector f ⁽¹⁾ (t _{1 (1)} ) of the first experiment is selected (S801).

Next, whether or not this peak vector f ⁽¹⁾ (t _{1 (1)} ) is suitable as a candidate for the internal standard peak vector is tested using the above TIP and NTP (S802). Specifically, among the elements P ⁽¹⁾ (t _{1 (1)} ) _m (m = 1, 2,..., M) included in the peak vector f ⁽¹⁾ (t _{1 (1)} ), than TIP. If there are more than NTP elements having a large value, it is determined that the peak vector can be a candidate for the internal standard peak vector, and the process proceeds to step S803. On the other hand, if the above condition is not satisfied, it is determined that the peak vector cannot be a candidate for the internal standard vector, and the process proceeds to steps S810, S811, and S802 in order, and the next peak vector of Experiment 1 is verified.

  In step S803, an experiment to be compared with the first experiment is selected. Here, the selection is made in order from Experiment 2.

Then, the peak vector most similar to f ⁽¹⁾ (t _{1 (1)} ) among the peak vectors f ⁽²⁾ (t _{k (2)} ) (k = 1, 2,..., K) of Experiment 2 Is identified as f ⁽²⁾ _max (S804). Here, among the peak vectors f ⁽²⁾ (t _{k (2)} ) (k = 1, 2,..., K) of Experiment 2, the search target is set for f ⁽¹⁾ (t _{1 (1)} ). The following formula (7)
t _{1 (1)} −T _int <t _{k (2)} <t _{1 (1)} + T _int (7)
F ⁽²⁾ (t _{k (2)} ) that satisfies That is, the peak vector most similar to the peak vector f ⁽¹⁾ (t _{1 (1)} ) of Experiment 1 among the peak vectors f ⁽²⁾ (t _{k (2)} ) of Experiment 2 that satisfy Equation (7). _Is identified as f ⁽²⁾ _max .

Here, for example, it is assumed that f ⁽²⁾ (t _{2 (2)} ) is obtained as the peak vector f ⁽²⁾ _max . Then, the peak vector f ⁽¹⁾ _max of Experiment 1 that is most similar to the peak vector f ⁽²⁾ (t _{2 (2)} ) of Experiment ₂ is searched for (S805). In this case as well, the peak vector of Experiment 1 to be searched is limited to that within the allowable range defined by T _int as described above. Specifically, the following equation (8)
_{t 2 (2) -T int <} t k (1) <t 2 (2) + T int ... (8)
A peak vector most similar to f ⁽²⁾ (t _{2 (2)} ) is searched from f ⁽¹⁾ (t _{k (1)} ) satisfying the above.

Next, it is determined whether or not the obtained peak vector f ⁽¹⁾ _max matches the original peak vector f ⁽¹⁾ (t _{1 (1)} ) (S806). That is, when f ⁽¹⁾ (t _{1 (1)} ) is obtained as the peak vector f ⁽¹⁾ _max , the peak vectors f ⁽¹⁾ (t _{1 (1)} ) and f ⁽²⁾ (t _{2 ( 2)} ) are determined to be truly similar, and these peak vectors are associated as candidates for the internal standard peak vector, and the process proceeds to step S807. On the other hand, when f ⁽¹⁾ (t _{1 (1)} ) is not obtained as the peak vector f ⁽¹⁾ _max , the peak vector f ⁽¹⁾ (t _{1 (1)} ) is changed to the internal standard peak vector. It is determined that it is not possible to proceed, and the process proceeds to steps S810, S811, and S802, and the next peak vector of Experiment 1 is tested.

  FIG. 13A and FIG. 13B are generalized views of this. As described above, in the internal standard identification process of the present embodiment, the similarity between the peak vectors is examined bi-directionally between the two experiments, and when the two peak vectors are most similar to each other, the internal standard peak vector is determined. These two peak vectors are associated with each other as candidates.

In step S807, it is determined whether or not the next experiment to be compared with experiment 1 remains. If the next experiment remains, the next experiment is selected (S808). In the above example, Experiment 3 is selected. In Experiment 3 as well, a peak vector most similar to f ⁽¹⁾ (t _{1 (1)} ) is searched for in the same procedure as above (S804 to S806). This will be repeated until the S-th ^{experiment, f} (1) _{when (t 1 (1))} and the most similar to the peak vector each other are obtained for all _{^{experiments, f (1) (t 1}} (1) ) Is an internal standard peak vector (S809), and f ⁽¹⁾ (t _{1 (1)} ) and similar f ^(s) _max (s = 2, 3,..., S) Map as a set of standard peak vectors. In step S810, a further set of internal standard peak vectors is searched.

On the other ^{hand, if _{f (1) (t 1 (}} 1)) and the most similar to the peak vector each other was not obtained for all ^{experiments, _{f (1) (t 1 (}} 1)) The internal standard peak vector It is determined that this is not possible (S810 to S811), and the same processing is performed for the next peak vector f ⁽¹⁾ (t2 ₍₁₎ ) of Experiment 1 (S804 to S809).

  Note that the similarity between peak vectors can be determined according to a known method. Specifically, for example, determination can be made based on the number of peaks having the same m / z, a cosine coefficient, a Spearman correlation coefficient, and the like.

By performing this process for all the peak vectors of Experiment 1, a set of one or more internal standard peak vectors can be obtained. Here, _assuming that N sets of internal standard peak vectors are obtained, the set of the obtained internal standard peak vectors Rf ^(s) (T _{n (s)} ) (n = 1, 2,..., N) is It can be expressed as in Table 3.

However, T _{n (s)} indicates the retention time of the peak vector recognized as the n-th internal standard peak vector in the experiment s, and T _{1 (s)} <T _{2 (s)} <. <T _{n (s)} <... <T _{N (s)} .

  This internal standard identification step is performed by the internal standard identification unit 22.

(2-3. Internal standard confirmation part / Internal standard confirmation process)
Subsequently, in the internal standard confirmation step, the internal standard confirmation unit 23 visually presents the correspondence relationship between the internal standard peak vectors obtained in the internal standard identification step to the user. Specifically, each of the internal standard peak vectors obtained from each experiment is displayed as a mass spectrum. The user compares the displayed mass spectra between experiments, and determines whether the obtained internal standard peak is appropriate.

  If it is determined that the obtained internal standard peak is inappropriate, the user can delete the internal standard peak or change the internal standard peak vector for a certain experiment to another peak vector. An instruction is given to the internal standard confirmation unit 23 of the analysis apparatus 1 by a keyboard or mouse operation.

  In response to this, the internal standard confirmation unit 23 changes the obtained set of internal standard peak vectors in accordance with a user instruction. Specifically, when the deletion of the internal standard peak vector is instructed, the corresponding internal standard peak vector is deleted from the table shown in Table 3 above. On the other hand, when it is instructed to change the internal standard peak vector to another peak vector, the holding time of the corresponding internal standard peak vector in the above table is rewritten.

(2-4. Holding Time Correction Unit / Holding Time Correction Step)
Next, in the holding time correction step, the holding time that does not match between experiments is corrected based on the holding time associated with the obtained internal standard peak vector. Specifically, any one experiment is selected as the reference experiment, and the holding time corresponding to the internal standard peak vector of the reference experiment is matched with the holding time corresponding to the internal standard peak vector of the other experiment. The retention time of other experiments is corrected by linear interpolation.

Here, the c-th experiment is selected as the reference experiment. When the corrected holding time obtained by correcting the holding time t _{k (s)} of the experiment s is tc _{k (s)} , tc _{k (s)} can be calculated by the following linear interpolation.

First, in the case of t _{k (s)} <T _{1 (c)} , tc _{k (s)} is expressed by the following equation (9)

Can be calculated. On the other hand, when T _{i (c)} <t _{k (s)} <T _{i + 1 (c)} (i = 1, 2,..., N−1), tc _{k (s)} is expressed by the following equation (10).

Can be calculated. When t _{k (s)} > T _{N (c)} , tc _{k (s)} is expressed by the following equation (11).

Can be calculated.

  With the above calculation, the holding time in the experiment other than the reference experiment c is corrected so as to follow the holding time of the reference experiment c. That is, the retention time of the two-dimensional peak data of each experiment is interpolated to the scale of the retention time of the two-dimensional peak data of the reference experiment c. This holding time correction step is performed by the holding time correction unit 24.

  In the above description, the holding time is corrected by linear interpolation. However, the present invention is not limited to this, and the holding time may be corrected by nonlinear interpolation.

  The two-dimensional peak data with the holding time corrected can be expressed as shown in Table 4 below.

  The total peak data is as shown in Table 5 below.

(2-5. Second peak vector creation unit / second peak vector creation step)
In this step, the same processing as in the first peak vector creation step is performed on the two-dimensional peak data with the holding time corrected. That is, a peak vector having the peak intensity of each peak included in the total peak group as an element is created for each holding time from the two-dimensional peak data shown in Table 4 above. This peak vector is created for all experiments.

Assuming that the peak vector of the holding time tc _{k (s)} in the s-th experiment is F ^(s) (tc _{k (s)} ), F ^(s) (tc _{k (s)} ) is expressed by the following equation (12):
F ^(s) (tck _(s) ) = (P ^(s) (tck _(s) ) ₁ , P ^(s) (tkk _(s) ) ₂ , ...
..., P ^(s) (tck _(s) ) _m , ..., P ^(s) (tkk _(s) ) _M ) (12)
Can be represented by

  In other words, it can be said that this step is a step of extracting mass spectrum data for each holding time from the two-dimensional peak data with the holding time corrected for each experiment. The second peak vector creation step is performed by the second peak vector creation unit 25.

(2-6. Correspondence determination unit / correspondence determination step, table creation unit / table creation step)
Next, a threshold value C used when a user or the like determines the similarity between peak vectors extracted from different two-dimensional peak data is set. Similarly, the user sets a threshold T for defining an allowable range of holding time when comparing peak vectors.

Then, the table creation unit 27 substitutes the identification information of each total peak group (mass spectrum) of Experiment 1 into the first row of the table. At this time, the identification information stored in each cell of the table is expressed as TI (tc _{1i (1)} ) ⁽¹⁾ (i = 1, 2,..., N ₁ ). N ₁ represents the total number of total peak groups included in the two-dimensional peak data of Experiment 1. In addition, let TI (tc _{ki (s)} ) ^(s) be the element assigned to the table for the first time in the k-th column. As a result, the table is as shown in Table 6 below.

Next, the correspondence determination unit 26 compares each peak vector of Experiment 2 with the peak vector of Experiment 1. First, the correspondence determination unit 26 selects F ⁽²⁾ (tc _{1 (2)} ) from the peak vectors in Experiment 2. Of the peak vectors F ⁽¹⁾ (tk _{k (1)} ) (k = 1, 2,..., K) of Experiment 1, the following equation (13)
tc _{1 (2)} -T <tc _{k (1)} <tc _{1 (2)} + T (13)
The similarity between all of F ⁽¹⁾ (tc _{k (1)} ) satisfying and selected F ⁽²⁾ (tc _{1 (2)} ) is evaluated.

For example, the number of peaks having the same m / z, a cosine coefficient, a Spearman correlation coefficient, and the like can be used for evaluating the similarity. The correspondence determination unit 26 quantifies the similarity between the two peak vectors using these, and compares this similarity with the threshold value C. Here, if there is no peak vector of Experiment 1 to be compared that has a similarity exceeding the threshold value C, the correspondence determination unit 26 determines that F ⁽²⁾ (tc _{1 (2)} ) It is determined that none of the peak vectors correspond.

In this case, the table creation unit 27 stores the identification information of the total peak group corresponding to F ⁽²⁾ (tc _{1 (2)} ) in the N ₁ +1 column of the second row. The stored identification information is TI (tc _{21 (2)} ) ⁽²⁾ .

On the other hand, in the case where the peak vector of Experiment 1 to be compared has a similarity that exceeds the threshold C, the correspondence determination unit 26 has the highest similarity with F ⁽²⁾ (tc _{1 (2)} ). It is determined that the peak vector F ⁽¹⁾ (tc _{i (1)} ) in Experiment 1 is a vector corresponding to F ⁽²⁾ (tc _{1 (2)} ).

In this case, the table creating unit 27 displays the identification information of the total peak group corresponding to F ⁽²⁾ (tc _{1 (2)} ) on the second line, the total peak group TI (tc _{1i (1) of} Experiment _1). ) Store in the same column as ⁽¹⁾ . The stored identification information is TI (tc _{11 (2)} ) ⁽²⁾ .

Similarly, for the other peak vectors F ⁽²⁾ (t c _{h (2)} ) (h = 2, 3,..., N ₂ ) in Experiment 2, the correspondence determination unit 26 uses the following equation (14).
tc _{h (2)} −T <tc _{k (1)} <t _{h h (2)} + T (14)
If there is nothing exceeding the threshold C compared with the peak vector F ⁽¹⁾ (t _{k k (1)} ) of Experiment 1 that satisfies the conditions, the table creation unit 27 identifies the new column on the right side of the second row of the table When information is stored and there is an item that exceeds the threshold C, the table creation unit 27 identifies the second row in the same column as the identification information of the total peak group corresponding to the peak vector of the most similar experiment 1 Store information.

  As a result, the table is as shown in Table 7 below.

Similarly, for the experiment s, the correspondence determination unit 26 converts the peak vector F ^(s) (tc _{j (s)} ) to the peak vector F ^(r) (b) of the experiment r (r = 1, 2,..., S−1). tc _{m (r)} ) (where tc _{j (s)} −T <tc _{m (r)} <tc _{j (s)} + T). If there is no similarity exceeding the threshold value C, the table creation unit 27 identifies the total peak group identification information corresponding to F ^(s) (tc _{j (s)} ) in the new column z of the s-th row. TI (tc _{zj (s)} ) ^(s) is stored.

On the other hand, if the similarity exceeds the threshold C, the correspondence determination unit 26 identifies the most similar peak vector F ^(r) (tcn _(r) ), and the table creation unit 27 performs the s-th row The identification information is stored in the same column as the total peak group corresponding to the peak vector F ^(r) (tcn _(r) ).

  By repeating the above processing until Experiment S, the table becomes as shown in Table 8 below. It is assumed that 0 is stored for a cell having no corresponding total peak group.

  In the table obtained as described above, the identification information of the total peak group (mass spectrum) obtained from the same experiment is arranged in the same row, and the identification information of the corresponding total peak group (mass spectrum) is displayed. They will be arranged in the same column. From this table, it is shown that the total peak groups (mass spectra) arranged in the same column are derived from the same compound.

  Then, with respect to the cells in which values other than 0 are stored, the average value of the retention times corresponding to the stored total peak group is obtained for each column, and the average value is set as the representative retention time of the column.

  Through the above steps, a total peak group (mass spectrum) that can be regarded as originating from the same compound can be detected and expressed in a matrix (Table 8). The compound of the total peak group can be identified based on the commonality between the peak vector corresponding to each total peak group and the peak vector of the purification slip or the commercially available mass library. At this time, by defining a representative peak vector for the peak vectors of the total peak group arranged in the same column and grouped, the substance search efficiency can be increased.

Hereinafter, a process of creating a table will be described using a simple example. As an example, assume that three corrected two-dimensional peak data are obtained from three experiments. It is assumed that three mass spectra are obtained from each two-dimensional peak data. Here, the peak vectors of Experiment 1 are F ⁽¹⁾ (tc _{1 (1)} ), F ⁽¹⁾ (tc _{2 (1)} ), F ⁽¹⁾ (tc _{3 (1)} ), and Experiment 2 The peak vectors of F ⁽²⁾ (tc _{1 (2)} ), F ⁽²⁾ (tc _{2 (2)} ), F ⁽²⁾ (tc _{3 (2)} ), and the peak vector of Experiment 3 is F ⁽³⁾ (tc _{1 (3)} ), F ⁽³⁾ (tc _{2 (3)} ), F ⁽³⁾ (tc _{3 (3)} ).

Also, the difference in retention time between tc _{1 (1)} , tc _{1 (2)} and tc _{1 (2)} is within the threshold T, and similarly, tc _{2 (1)} , tc _{2 (2)} and tc _{2 (} The difference in holding time from ₂₎ is also within the threshold T, and the difference in holding time between tc _{3 (1)} , tc _{3 (2),} and tc _{3 (2)} is also within the threshold T.

The similarity between F ⁽¹⁾ (tc _{2 (1)} ) and F ⁽²⁾ (tc _{2 (2)} ) is greater than the threshold C, and F ⁽¹⁾ (tc _{2 (1)} ) and F ^{( 3)} The similarity with (tc _{2 (3)} ) is also larger than the threshold value C. And other peak vectors do not show similarity.

  At this time, the table creation unit 27 first stores the identification information of each mass spectrum of Experiment 1 in each cell in the first row of the table. Here, it is assumed that peak vector identification information is stored as mass spectrum identification information. As a result, the following Table 9 is obtained.

Subsequently, the correspondence determination unit 26 compares the peak vector F ⁽²⁾ (tc _{1 (2)} ) of Experiment 2 with the peak vector F ⁽¹⁾ (tc _{1 (1)} ) of Experiment 1. Here, since the similarity is equal to or less than the threshold value C, it is determined that these peak vectors do not correspond to each other. As a result, the peak vector F ⁽²⁾ (tc _{1 (2)} ) is stored in the second row and the fourth column.

Next, the correspondence determination unit 26 compares the peak vector F ⁽²⁾ (tc _{2 (2)} ) of Experiment 2 with the peak vector F ⁽¹⁾ (tc _{2 (1)} ) of Experiment 1. Here, since the similarity is greater than the threshold C and the similarity is the highest, it is determined that these peak vectors correspond to each other. As a result, the peak vector F ⁽²⁾ (tc _{2 (2)} ) is stored in the second row and second column.

Subsequently, the correspondence determination unit 26 compares the peak vector F ⁽²⁾ (tc _{3 (2)} ) of Experiment 2 with the peak vector F ⁽¹⁾ (tc _{3 (1)} ) of Experiment 1. Here, since the similarity is equal to or less than the threshold value C, it is determined that these peak vectors do not correspond to each other. As a result, the peak vector F ⁽²⁾ (tc _{3 (2)} ) is stored in the second row and the fifth column.

Similarly for Experiment 3, the peak vector F ⁽³⁾ (tc _{1 (3)} ) is in the third row and the sixth column, and the peak vector F ⁽³⁾ (tc _{2 (3)} ) is in the third row and the second column. The eye and peak vector F ⁽³⁾ (tc _{3 (3)} ) are respectively stored in the third row and the seventh column.

  As a result, the table is as shown in Table 10 below.

In this table, the mass spectrum of retention time tc _{2 (1)} of Experiment 1, the mass spectrum of retention time tc _{2 (2)} of Experiment 2, and the mass spectrum of retention time tc _{2 (3)} of Experiment 3 are It is expressed that they are derived from the same compound. And each peak contained in these mass spectra will correspond between mass spectra.

The representative retention time of the mass spectrum in the second column is given by the following equation (15)
{Tc _{2 (1)} + tc _{2 (2)} + tc _{2 (3)} } / 3 (15)
Sought by.

(3. Other)
Finally, each block of the spectrum analyzer 1, particularly the smoothing unit 11, the peak time identification unit 12, the spectral intensity coalescence unit 13, the total peak creation unit 14, the total peak coalescence unit 15, the peak coalescence unit 16, and the first peak vector The creation unit 21, the internal standard identification unit 22, the internal standard confirmation unit 23, the retention time correction unit 24, the second peak vector creation unit 25, the correspondence determination unit 26, and the table creation unit 27 may be configured by hardware logic. Alternatively, it may be realized by software using a CPU as follows.

  That is, the spectrum analyzer 1 includes a CPU (central processing unit) that executes instructions of a control program that realizes each function, a ROM (read only memory) that stores the program, and a RAM (random access memory) that expands the program. And a storage device (recording medium) such as a memory for storing the program and various data. An object of the present invention is to provide a recording medium in which a program code (execution format program, intermediate code program, source program) of a control program of the spectrum analyzer 1 which is software for realizing the above-described functions is recorded so as to be readable by a computer. This can also be achieved by supplying the spectrum analysis apparatus 1 and reading and executing the program code recorded on the recording medium by the computer (or CPU or MPU).

  Examples of the recording medium include a tape system such as a magnetic tape and a cassette tape, a magnetic disk such as a floppy (registered trademark) disk / hard disk, and an optical disk such as a CD-ROM / MO / MD / DVD / CD-R. Card system such as IC card, IC card (including memory card) / optical card, or semiconductor memory system such as mask ROM / EPROM / EEPROM / flash ROM.

  Moreover, the spectrum analyzer 1 may be configured to be connectable to a communication network, and the program code may be supplied via the communication network. The communication network is not particularly limited. For example, the Internet, intranet, extranet, LAN, ISDN, VAN, CATV communication network, virtual private network, telephone line network, mobile communication network, satellite communication. A net or the like is available. Also, the transmission medium constituting the communication network is not particularly limited. For example, even in the case of wired such as IEEE 1394, USB, power line carrier, cable TV line, telephone line, ADSL line, etc., infrared rays such as IrDA and remote control, Bluetooth ( (Registered trademark), 802.11 wireless, HDR, mobile phone network, satellite line, terrestrial digital network, and the like can also be used. The present invention can also be realized in the form of a computer data signal embedded in a carrier wave in which the program code is embodied by electronic transmission.

  The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope shown in the claims, and embodiments obtained by appropriately combining technical means disclosed in different embodiments. Is also included in the technical scope of the present invention.

  It is verified that the spectrum analysis apparatus according to the above-described embodiment is useful. In this example, the retention times in the GC / MS time-series measurement were performed on the drug-treated Arabidopsis cultured cells T87.

  In order to analyze changes in metabolites in response to drug A in Arabidopsis thaliana, GC / MS analysis of Arabidopsis cultured cell strain T87 treated with drug A was performed. Drug A (dissolved in DMSO) is added to the cultured cells of Arabidopsis thaliana on the 10th day after subculture in a fresh liquid medium, and added immediately (0 minutes), 5 minutes, and 30 minutes after addition. And after 1, 2, 4, 6, 8, 10, 12, 16, 20, 24, 36, 48, 96 hours. The collected cells were washed with distilled water, dehydrated by suction, and stored at −80 ° C. In addition, the same amount of DMSO was added instead of the drug A, and the cells collected after the same time as above were used as a control. A biological component was extracted from 100 mg of cells by a liquid layer-liquid layer partition method using methanol, water, and chloroform, and a water-soluble fraction was derivatized with methoxyamine and MSTFA, and then Pegasus III (GC-) of LECO was used. Analysis was performed by TOF-MS). Data acquisition by TOF-MS was performed at 20 times / second for 22 minutes for m / z from 82 to 500. The analysis data was output as a CSV file holding the signal intensity for each m / z, and as a result, a CSV file of about 147 MB for one sample could be obtained. This CSV file was analyzed by the spectrum analyzer of the embodiment described above. FIG. 14 shows a menu screen of the spectrum analyzer.

  First, chromatogram information for each m / z was converted into information corresponding to retention time and peak area (peak intensity). As a result, the file could be converted into a file having an average file size of about 2.5 MB. Next, the retention time in the column used in this analysis was converted into a retention index based on standard fatty acid groups having different side chain lengths so that the samples could be compared with each other. The peak intensity was corrected so that the peak intensity of ribitol was 100, based on ribitol added to the extracted sample as an internal standard at the time of analysis. Using the corrected data, detection of an endogenous internal standard for correction between retention time index samples (peak drift correction) was performed. As a result, 36 peaks could be detected as endogenous internal standard candidates in 3 replicate experiments (96 analyzes in total) at 16 sampling times of the drug A-treated sample and the control sample. Evaluation was performed to confirm that the detected endogenous internal standard showed the same fragmentation pattern between samples and was the same substance. In this analysis, nine compound peaks containing ribitol were selected as internal standards used for linear correction of retention time (FIGS. 15 (a) and 15 (b)). Using the output file (average of about 270 kB), the compound peaks were matched between samples. The result of visualizing the result of matching is shown in FIG. In FIG. 16, in the upper table, each row indicates the average retention time index, each column indicates a sample, and the magnitude of the peak intensity is indicated by red shading. In the table, 48 samples on the right side show time-series changes of T87 cultured cells treated with drug A, and 48 samples on the left side show changes in untreated control. A compound in which the difference in the accumulation of the compound was recognized between the treated cell and the control cell was detected. By comparing the fragmentation pattern of the detected peak with the fragmentation pattern (and retention time) of known substances, the peak for some compounds such as myo-inositol, gamma-aminobutyrate, D-malate, ethanolamine, sucrose, etc. Could be identified.

  According to the present invention, it is possible to accurately identify the position of a peak indicating the characteristics of a compound from data obtained based on a combination of chromatography and mass spectrometry. Moreover, according to the present invention, in a set of two-dimensional peak data obtained from a plurality of experiments based on a combination of chromatography and mass spectrometry, mass spectra derived from the same compound can be associated between experiments. . Therefore, the present invention can be used for an analysis apparatus that analyzes data obtained by GC / MS or LC / MS.

1, showing an embodiment of the present invention, is a block diagram illustrating a detailed functional configuration of a peak association unit of a spectrum analyzer. FIG. It is the figure which visualized the two-dimensional spectrum data obtained by GC / MS or LC / MS. It is a figure which shows the prior art and shows the conversion method from mass chromatogram data to peak data. It is a figure which shows the method of extracting a mass spectrum from two-dimensional peak data. It is a figure which shows the prior art and shows the process of converting from mass chromatogram data to peak data. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 illustrates an embodiment of the present invention and is a block diagram illustrating a main configuration of a spectrum analysis apparatus. 1, showing an embodiment of the present invention, is a block diagram illustrating a detailed functional configuration of a peak data creation unit of a spectrum analyzer. FIG. It is a figure which shows one Embodiment of this invention and shows the process process by a spectrum intensity | strength uniting part. FIG. 5 is a diagram illustrating an embodiment of the present invention, and is a diagram illustrating data conversion by a total peak creation step and a total peak merge step. FIG. 5 is a diagram illustrating an embodiment of the present invention and illustrating data conversion by a total peak coalescing process. FIG. 5 is a diagram illustrating one-dimensional embodiment of the present invention and showing two-dimensional spectrum data after a peak coalescence step. It is a figure which shows one Embodiment of this invention and shows the process process by an internal standard identification part. FIG. 2 shows an embodiment of the present invention, and (a) and (b) are diagrams showing a method for comparing peak vectors in an internal standard identification step. It is a figure which shows one Example of this invention and shows the menu screen of a spectrum analyzer. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows an embodiment of the present invention, (a) is a diagram showing an example of evaluating an intrinsic internal standard peak identified by an internal standard identification unit, and (b) is selected as a candidate for an intrinsic internal standard. It is a figure which shows the example of the fragment pattern in each sample of the obtained compound peak, The mass fragment pattern of 8 samples was shown about the peak selected in the table | surface of (a). It is a figure which shows one Example of this invention and shows the correspondence of the mass spectrum between samples.

Explanation of symbols

1 Spectrum analyzer (information processing equipment)
11 Smoothing unit 12 Peak time identification unit (two-dimensional peak data creation unit, second peak position identification unit)
13 Spectral intensity coalescence part (two-dimensional peak data creation part)
14 Total peak creation part 15 Total peak uniting part (1st peak position identification part)
16 Peak coalescence part (first peak position identification part)
21 1st peak vector preparation part (1st mass spectrum extraction part)
22 internal standard identification unit 24 retention time correction unit 25 second peak vector creation unit (second mass spectrum extraction unit)
26 Correspondence determination unit 27 Table creation unit

Claims (11)

Corresponding between two-dimensional peak data in a two-dimensional peak data set that includes multiple two-dimensional peak data, which is information on retention time and peak ion intensity for each m / z obtained based on the combination of chromatography and mass spectrometry An information processing apparatus for identifying a mass spectrum to be performed,
A first mass spectrum extraction unit for extracting mass spectrum data from each two-dimensional peak data for each holding time;
Internal standard identification that creates an internal standard mass spectral data set that includes similar mass spectral data extracted from each two-dimensional peak data by comparing mass spectral data extracted from different two-dimensional peak data And
Based on the retention time corresponding to each mass spectrum data included in the internal standard mass spectrum data set, a retention time correction unit that corrects the retention time in each two-dimensional peak data;
A second mass spectrum extraction unit for extracting new mass spectrum data for each holding time from the two-dimensional peak data with the holding time corrected;
Whether or not the new mass spectra compared with each other correspond to each other by comparing the new mass spectrum data in which the difference in the retention time is within a predetermined range between the two-dimensional peak data whose retention times are corrected. An information processing apparatus comprising: a correspondence determination unit that determines whether or not.   The information processing apparatus according to claim 1, wherein the internal standard identification unit compares mass spectrum data having a retention time difference within a predetermined range between two-dimensional peak data.   The information processing apparatus according to claim 1 or 2, wherein the first mass spectrum extraction unit extracts each mass spectrum data as a vector having an ion intensity for each m / z as an element. The second mass spectrum extraction unit extracts each new mass spectrum data as a new vector having an ion intensity for each m / z as an element,
The correspondence determination unit calculates the similarity between new vectors extracted from different corrected two-dimensional peak data, and compares the calculated similarity with a threshold value, so that mass spectrum data correspond to each other. The information processing apparatus according to claim 1, wherein it is determined whether or not.   A table creation unit for creating a correspondence table in which identification information of each new mass spectrum is arranged in the same row or column for new mass spectra determined to correspond by the correspondence determination unit. The information processing apparatus according to any one of claims 1 to 4, wherein the information processing apparatus is characterized in that: Two-dimensional information about retention time and peak ion intensity for each m / z from two-dimensional spectrum data, which is information about retention time and ion intensity for each m / z, based on a combination of chromatography and mass spectrometry A two-dimensional peak data creation unit for creating peak data;
For the two-dimensional peak data, a total peak creation unit that calculates the sum of peak ion intensities for each holding time as total peak intensity and creates total peak data that is information on the total peak intensity for each holding time;
In the total peak data, a section in which the total peak intensity is always greater than or equal to the threshold is identified, and a retention time in which the total peak intensity is maximized in the section is included in the section of the two-dimensional peak data. An information processing apparatus comprising: a first peak position identifying unit that identifies a true retention time corresponding to a peak to be detected.   The information processing apparatus according to claim 6, wherein the first peak position identifying unit further associates the peak ion intensity included in the section of the two-dimensional peak data with the identified true retention time. The two-dimensional peak data creation unit is
Mass chromatogram data is extracted for each m / z from the two-dimensional spectrum data, which is information on the retention time and ion intensity for each m / z, obtained based on the combination of chromatography and mass spectrometry. A second peak position identifying unit for identifying a temporary peak retention time based on a retention time at which the ionic strength is maximized in the gram data;
In each mass chromatogram data, the peak ion intensity is calculated by adding the ion intensity at the holding time adjacent to the temporary peak holding time to the ion intensity at the temporary peak holding time, and the calculated peak ion intensity is The information processing apparatus according to claim 6, further comprising a spectrum intensity merging unit that creates the two-dimensional peak data by associating with a provisional peak retention time.   Mass chromatogram data is extracted for each m / z from the two-dimensional spectrum data, which is information on the retention time and ion intensity for each m / z, obtained based on the combination of chromatography and mass spectrometry. The smoothing part which produces the two-dimensional spectrum data input into the said two-dimensional peak data creation part by smoothing the ion intensity in Gram data is further provided. The information processing apparatus according to item 1.   A program for operating the information processing apparatus according to any one of claims 1 to 9, wherein the program causes a computer to function as each unit.   A computer-readable recording medium on which the program according to claim 10 is recorded.