{"id":81,"date":"2018-10-03T22:01:11","date_gmt":"2018-10-04T05:01:11","guid":{"rendered":"http:\/\/blogs.reed.edu\/bytes-of-the-apple\/?p=81"},"modified":"2018-10-03T22:01:11","modified_gmt":"2018-10-04T05:01:11","slug":"manders-coefficient","status":"publish","type":"post","link":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/2018\/10\/03\/manders-coefficient\/","title":{"rendered":"Mander&#8217;s Coefficient"},"content":{"rendered":"<p><span style=\"font-weight: 400\">One aspect of my thesis is exploring co-localization of Split Discs with other proteins in <\/span><i><span style=\"font-weight: 400\">drosophila <\/span><\/i><span style=\"font-weight: 400\">cells. In order to do this, not only does wet lab work need to be accomplished, but mathematical analysis (in this case using Mander\u2019s coefficient). <\/span><\/p>\n<p><span style=\"font-weight: 400\">Fluorescence microscopy does not have the ability to see whether or not two molecules are directly interacting. However, by looking to see if they co-localize in the cell, it can be determined whether they interact with the same complexes in the cell. The limit for fluorescence microscopy is the resolution of the images produced. Because of this, small numbers of puncta are not sufficient for determining whether or not the experimental molecules are actually co-localized. Multiple puncta from different regions within the cell must be used in analysis so the data is not limited to overlapping puncta which are a result of organelles that are close in proximity to one another. <\/span><\/p>\n<p><span style=\"font-weight: 400\">In order to quantitatively determine the correlation of co-localization in the cell, mathematical analysis of the data is employed. For my thesis, I am employing Mander\u2019s Overlap Coefficient (MOC) for this analysis because it does not require distinguishing fluorescence as being the result of a fluorescent protein or background noise. MOC is able to do this because it only compares the co-occurrence of fluorescence among pixels. MOC = \u2211<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">(R<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">\u00d7G<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">) \/ \u221a(\u2211<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">R<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">\u00d7\u2211<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">G<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">) where R<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> and G<\/span><span style=\"font-weight: 400\">i <\/span><span style=\"font-weight: 400\">are the average level of grey from the red and green fluorescence respectively<\/span><span style=\"font-weight: 400\"> (Manders et al., 1993)<\/span><span style=\"font-weight: 400\">. <\/span><span style=\"font-weight: 400\">MOC has a range of 0 &#8211; 1 and <\/span><span style=\"font-weight: 400\">R<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> and G<\/span><span style=\"font-weight: 400\">i <\/span><span style=\"font-weight: 400\">have a range of -1 &#8211; +1. The limitation to this equation is that the ratio of values can result in ambiguous numbers. Therefore, the numerator and denominator can be split up in such a way to account for the ambiguity. <\/span><span style=\"font-weight: 400\">\u00a0From this we get two coefficients: M1 (fraction of red fluorescence in areas with green fluorescence) and M2 (fraction of green fluorescence in areas with red fluorescence) \u00a0(Manders et al., 1993). <\/span><span style=\"font-weight: 400\">M1 = (\u2211<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">R<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">,colocal) \/ \u2211<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">R<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> where <\/span><i><span style=\"font-weight: 400\">R<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">,colocal<\/span><span style=\"font-weight: 400\"> = <\/span><i><span style=\"font-weight: 400\">R<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> if <\/span><i><span style=\"font-weight: 400\">G<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> &gt; 0 and <\/span><i><span style=\"font-weight: 400\">R<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">,colocal<\/span><span style=\"font-weight: 400\"> = 0 if <\/span><i><span style=\"font-weight: 400\">G<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> = 0 and <\/span><span style=\"font-weight: 400\">M2 = (\u2211<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">G<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">,colocal) \/ \u2211<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">G<\/span><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> where <\/span><i><span style=\"font-weight: 400\">G<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">,colocal<\/span><span style=\"font-weight: 400\"> = <\/span><i><span style=\"font-weight: 400\">G<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> if <\/span><i><span style=\"font-weight: 400\">R<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> &gt; 0 and <\/span><i><span style=\"font-weight: 400\">G<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\">,colocal<\/span><span style=\"font-weight: 400\"> = 0 if <\/span><i><span style=\"font-weight: 400\">R<\/span><\/i><span style=\"font-weight: 400\">i<\/span><span style=\"font-weight: 400\"> = 0 (Manders et al., 1993). The larger MOC, M1, and M2 are the stronger the evidence for co-localization of the proteins within a cell. In my thesis, MOC, M1, and M2, will be gathered for each cell to determine whether or not Split Discs are co-localizing with other specific proteins. <\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">References:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400\">Dunn, K. W., Kamocka, M. M., &amp; McDonald, J. H. (2011). A practical guide to evaluating colocalization in biological microscopy. <\/span><i><span style=\"font-weight: 400\">American Journal of Physiology &#8211; Cell Physiology<\/span><\/i><span style=\"font-weight: 400\">, 300(4), C723\u2013C742. <\/span><a href=\"http:\/\/doi.org\/10.1152\/ajpcell.00462.2010\"><span style=\"font-weight: 400\">http:\/\/doi.org\/10.1152\/ajpcell.00462.2010<\/span><\/a><\/p>\n<p><span style=\"font-weight: 400\">Manders, E. M., Verbeek, F. J. &amp; Aten, J. A. (1993). Measurement of co\u2010localization of objects in dual\u2010colour confocal images. <\/span><i><span style=\"font-weight: 400\">Journal of Microscopy<\/span><\/i><span style=\"font-weight: 400\">, 169, 375-382. doi:<\/span><a href=\"https:\/\/doi.org\/10.1111\/j.1365-2818.1993.tb03313.x\"><span style=\"font-weight: 400\">10.1111\/j.1365-2818.1993.tb03313.x<\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>One aspect of my thesis is exploring co-localization of Split Discs with other proteins in drosophila cells. In order to do this, not only does wet lab work need to be accomplished, but mathematical analysis (in this case using Mander\u2019s coefficient). Fluorescence microscopy does not have the ability to see whether or not two molecules &hellip; <a href=\"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/2018\/10\/03\/manders-coefficient\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Mander&#8217;s Coefficient&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1912,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-81","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/posts\/81","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/users\/1912"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/comments?post=81"}],"version-history":[{"count":1,"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/posts\/81\/revisions"}],"predecessor-version":[{"id":82,"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/posts\/81\/revisions\/82"}],"wp:attachment":[{"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/media?parent=81"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/categories?post=81"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.reed.edu\/bytes-of-the-apple\/wp-json\/wp\/v2\/tags?post=81"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}