Reliability Measure of 2D-PAGE Spot Matching using Multiple Graphs

Transcription

1 Reliability Measure of 2D-PAGE Spot Matching using Multiple Graphs Dae-Seong Jeoune 1, Chan-Myeong Han 2, Yun-Kyoo Ryoo 3, Sung-Woo Han 4, Hwi-Won Kim 5, Wookhyun Kim 6, and Young-Woo Yoon 6 1 Department of Media Design, Daegu Future College, Kyungsan, Kyungbuk, Republic of Korea 2 M+VISION Co. Ltd., Daegu Metropolitan City, Republic of Korea 3 Department of Medical Computer Science, Daegu Health College, Daegu, Republic of Korea 4 Department of Computer Engineering, Daegu Science University, Daegu, Republic of Korea 5 Education Center for IT, Kyeongbuk College, Yeungju, Kyungbuk, Republic of Korea 6 Department of Computer Engineering, Yeungnam University, Kyungsan, Kyungbuk, Republic of Korea Abstract - This paper proposes the reliability measure scheme of 2D-PAGE spot matching based on the grassfire spot matching algorithm by introducing multiple graphs, whereas the previous research on spot matching took advantage of a single graph. Since the result of spot matching contains errors such as mismatching and false-positive matching, all of the matched spot pairs should be examined one by one to be confirmed. In the previous research on spot matching, either overall or randomly selected spot pairs from the spot matching result have to be inspected for final confirmation because it does not present data concerning matching reliability. In this paper, however, the matching reliability by accumulating individual matching result using multiple graphs is presented. As a consequence, the effort for verifying matching result in manual can be significantly reduced, and moreover which positively influences on the overall matching accuracy. Keywords: Matching Reliability, Spot Matching, 2D-PAGE, Grassfire Algorithm, k-nng, Multiple Graphs 1 Introduction In proteomics, the two-dimensional polyacrylamid gel electrophoresis(2d-page) is widely used to separate and indentify proteins. The principle of 2D-PAGE is to separate proteins in a sample on two dimensional gel plane by taking advantage of two distinct characterizing features such as isoelectric point and the mass of each protein. A resulting gel image after performing 2D-PAGE contains a number of spots representing separated proteins with different size, shape and location[1]. In the research of proteomics, it is very important to study the expression of individual protein in a specific tissue. Even in the experiement with samples of the same tissue, proteins are to be expressed differently according to environments. In order to trace this kind of different protein expressions, the reference gel of normal state is compared to the target gel of test sample. It is very hard or almost impossible to carry out this process in manual because hundreds or thousands of proteins are generally contained in a gel. Therefore, it is necessary to automate the analytical process of 2D-PAGE[2]. The experiment process of 2D-PAGE is straightforward, but involves experimental errors. The two experiments in the same laboratory even with the same sample, equipment and environment show considerable differences, especially in the displacement between the locations of the corresponding spots. This kind of low repeatability is main cause of making the automated analytical process of 2D-PAGE more difficult. So, many algorithms to resolve the problem and reflect the characteristics have been proposed. The automation process is commonly divided into two phases: spot detection and spot matching. The former is to separate for identifying spots from the background in a 2D-PAGE gel image, whereas the latter is to match the same or similar spot pairs in their locations between reference and target gels. In this paper, a novel method on how to measure the reliability of the spot matching results is proposed. The first step is the basic spot matching procedure that is repeated with the grassfire algorithm[3] using multiple k-nngs. And then, each result is accumulated to evaluate reliability of every matched spot pairs. With this scheme, researchers can verify their experiment results with reliability based on probabilistic way. At the same time, they can make decision on the range of spots that are manually verified. Therefore, the reduction of cost and time required for result verification in 2D-PAGE can be achieved. 2 Spot matching in 2D-PAGE 2.1 Definition Let the spot sets P and Q be reference and target gels, respectively. Every element of P and Q has its own twodimensional coordinate representing the central point of spot as p i =(x i, y i ) and q j =(x j, y j ). Here, the spot matching is to find out the set of matched spot pairs and simply defined as M

2 between a reference gel P and a target gel Q that satisfy the given conditions[4], as shown in the equation (1). P={p 1, p 2,, p n }, where p i =(x i, y i ), 1 i n Q={q 1, q 2,, q m }, where q j =(x j, y j ), 1 j m M = {(p i1, q j1 ), (p i2, q j2 ),, (p il, q jl )}, (1) where p il P, q jl Q and l min(m, n) 2.2 Spot matching algorithm As the 2D-PAGE gel images have characteristics of not only showing low repeatability of experiment process but also both including global and local distortions, various spot matching methods have been proposed. One of them is known as image matching approach that has been proposed in order to resolve spot matching problems using reference and target gels involving nonlinear distortions[5-6]. And another is point pattern matching that utilizes geometric property of a graph transformed with respect to central positions of spots from gel image. So far, the spot matching algorithm using the geometric property can be classified into several categories. There include spot matching methods using the landmark spots, graph theory, iterative closest point, similarity the neighboring spots, etc. 2.3 Grassfire algorithm In this paper, the grassfire algorithm[3] that is based on the topological pattern of neighboring spots in a graph is adopted to perform basic spot matching with 2D-PAGE images. The grassfire algorithm is characterized by three important factors: selection of graph type, determining the initial point called the seed spot, and the direction of spot matching. The algorithm shows different result according to the type of a graph. Among the commonly used graphs in spot matching such as the Delaunay triangulation graph, the Gabriel graph, the relative neighbor graph and the k-nng (nearest neighbor graph), the last one is used in the grassfire algorithm. Spot matching in the grassfire algorithm starts at a single matched spot pair that is confirmed, which is called the seed spot pair. It should be clearly determined as a positive matching spot pair, otherwise unreliable matching result can be produced due to false candidates. In general, the seed spot pair is determined in manual or by an algorithm using the landmark spots. As a next step, a single spot pair with most similarly matched is selected among the neighboring spots of the seed spot to perform spot matching. The grassfire spot matching scheme shows good performance in accuracy and speed because it takes advantage of matching information of the previous matching stage at the next stage. And spot matching between spot pairs is spread toward the direction of showing higher matching accuracy because the next matching candidate is determined as a spot pair of the highest topological similarity among neighboring spots. Also, the position of seed spot that is closely related to the direction influences on matching order because matching starts at that point. Nevertheless, the grassfire algorithm shows the same matching result regardless of its position because a spot pair with best matching score among neighboring spots in the previous stage is selected as the next matching candidate. 3 Reliability measure 3.1 Verification of spot matching result In spot matching algorithm, accuracy is the most important. Therefoe, it is necessary to verify spot matching result by the automated method because the accuracy of 100% is not guaranteed. The only way for verification is absolutely processed by human in manual, but how to verify the spot matching result is not a trivial thing. When verifying spot matching result at random, there is possibility not to involve the false- matched spot pairs in the verification candidates. In case overall matched spot pairs are examined, it requires so much time and cost. If the matching reliability for each matched spot pair after spot matching can be presented, one can easily determine the range of spot pairs that should be verified from the overall matched spot pairs. And then, all the spot pairs within a certain range are verified for confirmation accurately. Let us, i.e., suppose that all the spot pairs whose reliability is less than or equal to 30% is verified in manual. When every spot pair is to be correct, each of the remaining spot pairs with reliability of higher than 30% is likely to be confirmed and regarded as correct matching pairs. To the contrary, when there exits spot pair(s) that turns out to be incorrect, the reliability for verification should be raised, for instance, up to 50%. In this manner, manual verification can be done with minimum cost with no verification for the overall spot pairs in the spot matching result by algorithm. 3.2 Reliability measure using multiple graphs Once the grassfire algorithm is executed, then a set of matched spot pairs is obtained as a spot matching result. The matched spot pair is a tuple that consists of number of the spot in the reference and the target gels, forming (p i, q j ). The performance of the grassfire spot matching algorithm is influenced only by the set of spots in reference and target gels and the type of graph. So, the result of the grassfire scheme can be expressed as grassfire(p, Q, G). In this paper, multiple k-nngs are applied in turn to the same sets of the reference gel P and the target gel Q for each iteration of the grassfire spot matching algorithm. The result for each k-nng is produced and accumulated in the accumulated frequency matrix(afm). The AFM is twodimensional array and its X- and Y-axes consist of spot number in the reference and target gels, respectively. When the spot pair (p i, q j ) is included in the result, then the array AFM(p i, q j ) is increased by 1.

3 When executing the grassfire algorithm, the k-nng is used by varying the degree k=5 to 8 with step size as 1 in turn because the number of neighboring spots in the same kind of graph is sequentially increased, which holds the similar property between graphs and, at the same time, the difference between them. The similarity helps the algorithm to determine the distinct matched spot pair by allowing higher frequency. And the difference contributes accurate matching rate enhancement for the uncertain spot pair with no topology conservation by allowing attempt to matching with several different spots. When four kinds of graphs are used in the spot matching and the frequency stored in the AFM for a specific spot pairs is four, the reliability for that matched spot pair becomes 100%. In other words, it means that the spot pair is positively matched because the matching for it is included in the results of every spot matching using four different graphs. 4 Experiment and result 4.1 Data set for experiment A pair of reference and target gels whose matching result is already known is needed to test and verify the proposed reliability measure scheme. However, it is very time-/costconsuming process to prepare samples after confirming every matching spot pairs in manual because hundreds or thousands of spots are contained in a single gel. Therefore, a pair of gels is generated using simulation method for convenience in this paper. First of all, 25 spots in a gel with the size of pixels are randomly generated and it is regarded as a reference gel. In random process of spot generation, the minimum distance between spots should be limited lest they should be overlapped or placed too close. After the spots of a reference gel are generated, they are transformed to produce spots for a corresponding target gel. This paper uses random number of the normal distribution to produce the target gel from the reference gel. The displacements for every spots in the reference gel is calculated using the normal distribution to the X- and Y-axis, respectively. And then, they are added to the coordinates of the corresponding spots in the reference gel, resulting in the target gel. Here, it is assumed to have no outlier spots for simplification. As a next step, the same number is assigned to the matched spots in the reference and the target gels. It provides easy way to identify the matched spot pairs of the matching result by spot matching algorithm whether each pair belongs to false-positive or true-positive with pre-assigned spot numbers. The Figure 1 shows an example of the generated gel data for experiment to verify the proposed scheme. 4.2 Experiment and result For brevity and clarity of experiment, a pair of gels with 25 spots is used in the experiment, even though hundreds or thousands of spots exists in a gel in real. The procedure of experment is straightforward. First, Spot matching using the grassfire algorithm using a single graph of k-nng from k=5 to 8 is performed one by one. And then, the matching result using the grassfire algorithm with each graph is accumulated in the AFM, as described in the previous chapter. The spot matching performance for each graph is summarized in the Table 1. In the table, the spot detection rate is ratio of the number of the matched spots over that of overall spots in a gel. And, the accuracy is ratio of the number of the true-positive matched spot pairs over that of overall matched spot pairs. After all, it is shown that the false-positive spot pairs are included in the matching results for the k-nngs with degree k=5, k=6, and k=7. As the next step, the reliability measure is performed using the spot matching results with multiple graphs. When the result using the grassfire algorithm with 5-NNG is produced, the value of 1 is stored to the corresponding positon in the AFM for every matched spot pairs. In turn, the same procedure is performed except that the graph is changed to 6- NNG, 7-NNG, and 8-NNG in turn, and the array of the AFM (a) Reference gel (b) Target gel (c) Overlapped image Figure 1. The generated gel image data for experiment (image size of pixels, 25spots, and the minimum distance of 10 pixels)

4 is accumulated by increasing 1 for the every matched spot pairs. Finally, the matching reliability is calculated for every matched spot pair using the information in the AFM. The result of the reliability measure using multiple graphs is shown in the Table 2. If the matched spot pairs whose matching reliability is higher than 50% are determined to be matched, both the spot matching detection rate and the accuracy become 100%. The matched spot pairs (24-6), (4-11), (12-23) and (23-12) are false-positive matching spot pairs resulted from the grassfire spot matching algorithm using 5- NNG, 6-NNG and/or 7-NNG. In the proposed multiple graph method, the inaccurate matched spot pairs can be excluded by calculating matching reliability for all the matched spot pairs. Actually, the spot pairs matched by chance in a certain repetition of the grassfire algorithm shown in the shaded rows of the Table 2 show very low reliability compared to the others. Measures Table 1. Grassfire spot matching result using multiple k-nngs Matched spot pairs k=5 k=6 k=7 k=8 Detection rate(%) Matching accuracy(%) Note : The value k denotes the degree of k-nng in each repetition using the grassfire spot matching algorithm. Spot pairs (i, j) Table 2. Reliability measure for the matched spot pairs using multiple k-nngs Matched spot pairs k=5 k=6 k=7 k=8 Cumulative matching frequency Matching reliability (%) (1-1) (2-2) (3-3) (4-4) (5-5) (6-6) (11-11) (12-12) (23-23) (24-24) (25-25) (24-6) (4-11) (12-23) (23-12) Note : A spot pair (i, j) denotes epresents a matched spot pairs with a spot number in the reference gel i and that of in the target gel j.

5 5 Concluding remarks In the field of proteomics, the spot matching algorithm has been devised to automate one or more 2D-PAGE phases, which reduces not only time and cost but also endeavor of researchers. However, every spot matching result from the automated method should be examined manually one by one with large amount of time and cost because it contains errors such as false-positively matched spot pair(s). For this reason, the reliability measure using multiple graphs has proposed in this paper. The proposed scheme can provide a method of reliability measure for each of the matched pair using the grassfire spot matching algorithm with multiple graphs. And then, the experiment is performed to verify the effectiveness using the generated 2D-PAGE data images with 25 spots in a pixels. From the experiment result, it has shown that enhancement of spot matching detection rate can be achieved by examining every reliability of the whole matched pairs to determine the appropriate threshold on reliability. And, it helps to minimize the time and cost of manual verification process that should be done in the automated process. Moreover, it is far more cost-effective when many of reference gels are to be compared with a single target gel. The contribution of this study can give new opportunity to use spot matching algorithm more in practical use because it helps to increase manual verification efficiency with the minimum cost. The further research includes the automatic determination of reliability threshold by analyzing the frequency distribution histogram of matching reliability. Biomedical Engineering: Applications, Basis and Communications, Vol. 18, No. 4, pp , August [6] G. Shi, T. Jiang, W. Zhu, B. Liu and H. Kao, "Alignment of Two-Dimensional Electrophoresis Gels", Biochemical and Biophysical Research Communications, Vol. 357, pp , References [1] P. H. O Farrel, "High Resolution Two-Dimensional Electrophoresis of Proteins", Journal of Biological Chemistry, Vol. 250, No. 10, pp , May [2] T. Srinark and C. Kambhamettu, "An Image Analysis Suite for Spot Detection and Spot Matching in Two- Dimensional Electrophoresis Gels", Electrophoresis, Vol. 29, pp , [3] Yun-Kyoo Ryoo, Chan-Myeong Han, Ja-Hyo Ku, Dae- Seong Jeoune, and Young-Woo Yoon, "Grassfire Spot Matching Algorithm in 2-DE", International Journal of Bio- Science and Bio-Technology, Vol. 5, No. 4, pp , [4] Chan-Myeong Han, Dae-Seong Jeoune, Hwi-Won Kim, and Young-Woo Yoon, "A Spot Matching Algorithm using the Topology of Neighbor Spots in 2D-PAGE Images", International Journal of Software Engineering and Its Applications, Vol. 7, No. 5, pp , [5] Jiann-Der Lee and Wei-Chun Chen, "A Novel Scheme for Registration of Two Dimensional Gel Electrophoresis Images",