DESDE SU REACTIVACIÓN EN
REGISTRO AFM LB
5.3. CALIBRACIÓN DE LOS INSTRUMENTOS
5.3.1. ESTACIÓN JUI-
*PhD Scholar, Department of Statistics, Manipal University, Manipal, India E-mail: [email protected]
**Associate Professor, Department of Statistics, Manipal University, Manipal, India E-mail: [email protected]
ABSTRACT :
In cDNA microarray experiments, the measurement of interest is signal intensity ratio of spots. Each spot have four types of pixel intensities namely red foreground, green foreground, red background and green background. The uncertainty associated with the signal intensity ratio depends on the correlation between pixel intensities of spots. It is important to estimate these correlations of pixel intensities of spots to propagate the uncertainty associated with the intensity ratio as well as to address the systematic errors arise from the chip artifacts. The present study is a review to identify various methods to estimate the correlation of various pixel intensities of microarray spots. Articles published from 1994 to 2015 are searched in various databases like PubMed, Scopus, Web of Science, and Google Scholar. Six articles are selected for the review based on selection criteria. We observed that there is very little literature available which deals with the impotence of the correlation between various pixel intensities of microarray spots.
Keywords: cDNA microarray, Pixel intensities, Intensity ratio, Correlation, Pixel correlations
I INTRODUCTION
In cDNA microarray experiments, the measurement of interest is average of red to green pixel intensity ratio at each spot that gives the expression level of a particular gene in a diseased sample compared to normal. The cDNA microarray image files have thousands of spots and each spot is differentiated into foreground area and background area [1]. Each pixel of these areas has both red and green pixel intensity measurements (Fig: 1). For a spot, let Rf,
b
R ,
G
f andG
b denote the average foreground red pixel intensity, average background red pixel intensity, averageforeground green pixel intensity and average background green pixel intensity respectively. The background corrected intensity ratio for a spot is given by
b f b f G G R R y − −
= [2,3]. Due to the presence of chip artefacts, there will be correlation between various pixel intensities [2] (i.e. between red foreground (Rf) and red background (Rb) ; between green foreground (Gf) and green background (Gb) ;between red foreground (Rf) and green background (Gb) ;between green foreground (Gf) and red background (Rb) ; between red foreground (Rf) and green foreground (Gf);between red background (Rb) and green background (Gf) within a spot.
Figure 1: Image of a single spot from a cDNA microarray image file
The estimated value of any measurement may deviate from the true value and this deviation is called error or uncertainty associated with that estimate. Binu et.al (2012) demonstrated that the uncertainty in the estimate of intensity ratio depends on the correlation between various pixel intensities [4]. The correlation between intensities of green and red foreground pixels in a spot can be calculated using Pearson correlation coefficient, because we have paired values of intensities for red and green foreground pixels. Similarly, we can estimate the correlation between intensities of red and green background pixels using Pearson correlation coefficient. However, it is not straight forward to estimate the remaining four correlations (between red foreground and red background; between green foreground and green background; between red foreground and green background; between green foreground and red background) by means of Pearson’s correlation coefficient because the number of pixels in the foreground and in the background differs and the position also differs. Hence this review is trying to identify the methodology to estimate the above mentioned four correlations of pixel intensities of microarray spots.
II METHODOLOGY
Articles published from 1st January 1994 to 1st June 2015 are searched in various databases Pubmed, Scopus, Web of Science and Google Scholar. The key words used for the review includes, “correlation of pixels and microarray”, "relationship between pixels and microarray”. Each keyword is entered in the above databases and articles are selected based on the following criteria.
First the titles of the articles published since 1994 were scrutinized. The titles which are found to be relevant for the study were selected and abstract of these articles are studied. Full text of those abstracts which appeared to be relevant for the review was obtained. Finally the full articles which found to be relevant for the current study were selected.
III RESULTS AND DISCUSSION
The results of initial screening and number of articles selected for the study are given in the table 1.
We selected six articles in this review, after eliminating the duplicated files obtained from various databases. More information about the selected articles are given below.
In 2001, Carl et al., in the article entitled “Image metrics in the statistical analysis of DNA microarray data” used pixel-by-pixel analysis of individual spots to estimate the sources of error and establish the precision and accuracy with which gene expression ratios are determined. According to the authors the average correlation coefficient r is a good indicator of overall scan quality, and the authors estimated the correlation by pairing the red and green intensities of the pixels of the spots. The authors observed that high correlation between red and green channels appears to arise from an intrinsic granularity generated during array fabrication and hybridization. In some spots however, red and green signals fluctuate independently of each other causing the apparent gene expression ratio to vary from one place in the spot to the next [5].
In 2003, Qian et al., estimated the correlation between pixel intensities of spots in microarray chip by means of Pearson product moment correlation coefficient. According to the authors the average correlation coefficient should be independent of the chip distance if there are no chip artifacts. They observed that the closer two genes are on the chip, the higher their average correlation coefficient is, which is an indication for chip artifacts [6]. In 2005, Claus et al., compared five spatial correlation structures like exponential, Gaussian, linear, rational quadratic and spherical for selected genes that accommodate errors by allowing the spatial correlation among pixels in the microarray slide. In this study the authors considered only the immediate neighboring pixels in the spatial correlation models and not mentioned the method to estimate the correlations of various pixel intensities of a spot [7].
In 2006, R Nagarajan et al., used correlation statistics for segmentation of spots in microarray. In this article the authors used Pearson’s correlation coefficient to find the correlation between red and green pixels of the spot. Also, they used correlation statistics like Pearson’s correlation and Spearman rank correlation to segment pixels belonging to the foreground and background by statistically comparing only the adjacent rows and columns of pixels in the spot. The performance of correlation-based segmentation is compared to clustering-based (PAM, k- means) and seeded region growing techniques (SPOT). It is shown that correlation-based segmentation is useful in flagging poorly hybridized spots, thus minimizing false-positives. In this article the authors are not provided any method to estimate the correlation between foreground and background pixels of the same spot instead they provided a segmentation method which is based on the correlation between pixels of the adjacent rows or columns of the pixels in the spot grid [8].
In 2010, Bergmann et al., proposed two quantities as measure of spot quality which uses the spatial correlation between intensities of pixels in a spot. The spatial structure assumes that correlation decays with increasing distance. Newton-Raphson algorithm is used to calculate the optimal estimate for correlation between pixels. The main limitations of proposed methods are the assumption of multivariate normal distribution of intensities of pixels in the spot which may not be always true and considered only correlation between neighboring pixels [9].
Binu et al., identified the role of correlation between pixel intensities within a spot in cDNA microarray chip on uncertainty estimation. The authors demonstrated the importance of correlation between the intensities of pixels while estimating the uncertainty associated with each spot. They observed that as correlation between pixels in the spot increases the uncertainty associated with the intensity ratio decreases. However in that study the author’s assumed equal correlation between the various types of pixel intensities of spot which is not true [2,4].
The estimate of correlations will help us to propagate the error associated with the functions of genes which can be incorporated in statistical analysis like cluster analysis, multivariate analysis of gene expression data. It also provides information about the presence of chip artifacts. Hence it is recommended to consider correlation between intensities of various types of pixels between the spots. But all the reviewed articles are describing the importance of the correlation but none of them explained how to estimate the correlation between pixels from foreground and background area of the spots.
IV Conclusion
In cdna microarray image the pixel intensities of the spots are correlated because of various chip artefacts. it is important to estimate these correlations of pixel intensities of spots to propagate the uncertainty associated with the intensity ratio as well as to address the systematic errors arise from the chip artifacts. the current review tried to identify the methodologies used to estimate these correlations between various types of pixel intensities of the spots of microarray image file and we identified that,
• There are very few studies that explain the importance of correlation between various pixel intensities of spots in microarray experiments.
• None of the studies explored the method to estimate the correlation between pixels from foreground and background area of the microarray spots.
References
1. Yang, Y. H., Buckley, M. J., & Speed, T. P, 2001, Analysis of cDNA microarray images. Briefings in bioinformatics, 2(4), 341-349.
2. Binu, V. S., Nair, N. S., Manjunatha, P. K., & Kalesh, M. K, 2015, Impact of pixel intensity correlations on statistical inferences of expression levels in cDNA microarray experiments. International Journal of Bioinformatics Research and Applications, 11(3), 257-267.
3. Causton, H.C., Quackenbush, J. and Brazma, A, (2003). Microarray Gene Expression Data Analysis: A Beginner’s Guide, Blackwell Publishing, Malden, MA.
4. Binu, V. S., Prasad K, M., & Kalesh, K. M, 2012, Estimation of Uncertainty Associated with Intensity Ratio in CDNA Microarray Experiments. Research & Reviews: Journal of Statistics, 1(2), 24-33.
5. Brown, C. S., Goodwin, P. C., & Sorger, P. K, 2001, Image metrics in the statistical analysis of DNA microarray data. Proceedings of the National Academy of Sciences, 98(16), 8944-8949.
6. Qian, J., Kluger, Y., Yu, H., & Gerstein, M, 2003, Identification and correction of spurious spatial correlations in microarray data. Biotechniques, 35(1), 42-49.
7. Ekstrøm, C. T., Bak, S., & Rudemo, M, 2005, Pixel-level signal modelling with spatial correlation for two- colour microarrays. Statistical applications in genetics and molecular biology, 4(1).
8. Nagarajan, R., & Upreti, M, 2006, Correlation statistics for cDNA microarray image analysis. IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB), 3(3), 232-238.
9. Bergemann, T. L., & Zhao, L. P, 2010, Signal quality measurements for cDNA microarray data. IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB), 7(2), 299-308.
Aryabhatta Journal of Mathematics & Informatics Vol. 7, No. 2, July-Dec., 2015 ISSN (Print) : 0975-7139
Scientific Journal Impact Factor SJIF (2014) : 4.1 ISSN (Online) : 2394-9309