Domain > blog.mcbryan.co.uk

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Whois

Property	Value
Name	Tony McBryan
Address	40 Hamilton Gardens
Zip Code	United Kingdom
City	Armadale
State	EH48 2JA
NameServer	ns-1539.awsdns-00.co.uk 205.251.198.3
Created	2005-07-13 00:00:00
Changed	2016-06-18 00:00:00
Expires	2017-07-13 00:00:00
Registrar	Gandi

DNS Resolutions

Date	IP Address
2015-05-05	64.233.191.121 (ClassC)
2024-11-17	172.217.14.243 (ClassC)

HTTP/1.1 200 OKContent-Type: text/html; charsetUTF-8Expires: Sun, 17 Nov 2024 04:39:28 GMTDate: Sun, 17 Nov 2024 04:39:28 GMTCache-Control: private, max-age0Last-Modified: Wed, 28 Aug 2024 12:34:57 GMTX-Content-Type-Options: nosniffX-XSS-Protection: 1; modeblockServer: GSEAccept-Ranges: noneVary: Accept-EncodingTransfer-Encoding: chunked

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classcap-left>/div>div classcap-right>/div>/div>div classfauxborder-left content-fauxborder-left>div classfauxborder-right content-fauxborder-right>/div>div classcontent-inner>header>div classheader-outer>div classheader-cap-top cap-top>div classcap-left>/div>div classcap-right>/div>/div>div classfauxborder-left header-fauxborder-left>div classfauxborder-right header-fauxborder-right>/div>div classregion-inner header-inner>div classheader section idheader>div classwidget Header data-version1 idHeader1>div idheader-inner>div classtitlewrapper>h1 classtitle>McBryans Musings/h1>/div>div classdescriptionwrapper>p classdescription>span>Computational Biology, Bioinformatics and Other Things/span>/p>/div>/div>/div>/div>/div>/div>div classheader-cap-bottom cap-bottom>div classcap-left>/div>div classcap-right>/div>/div>/div>/header>div classtabs-outer>div classtabs-cap-top cap-top>div classcap-left>/div>div classcap-right>/div>/div>div classfauxborder-left tabs-fauxborder-left>div classfauxborder-right tabs-fauxborder-right>/div>div classregion-inner tabs-inner>div classtabs no-items section idcrosscol>/div>div classtabs no-items section idcrosscol-overflow>/div>/div>/div>div classtabs-cap-bottom cap-bottom>div classcap-left>/div>div classcap-right>/div>/div>/div>div classmain-outer>div classmain-cap-top cap-top>div classcap-left>/div>div classcap-right>/div>/div>div classfauxborder-left main-fauxborder-left>div classfauxborder-right main-fauxborder-right>/div>div classregion-inner main-inner>div classcolumns fauxcolumns>div classfauxcolumn-outer fauxcolumn-center-outer>div classcap-top>div classcap-left>/div>div classcap-right>/div>/div>div classfauxborder-left>div classfauxborder-right>/div>div classfauxcolumn-inner>/div>/div>div classcap-bottom>div classcap-left>/div>div classcap-right>/div>/div>/div>div classfauxcolumn-outer fauxcolumn-left-outer>div classcap-top>div classcap-left>/div>div classcap-right>/div>/div>div classfauxborder-left>div classfauxborder-right>/div>div classfauxcolumn-inner>/div>/div>div classcap-bottom>div classcap-left>/div>div classcap-right>/div>/div>/div>div classfauxcolumn-outer fauxcolumn-right-outer>div classcap-top>div classcap-left>/div>div classcap-right>/div>/div>div classfauxborder-left>div classfauxborder-right>/div>div classfauxcolumn-inner>/div>/div>div classcap-bottom>div classcap-left>/div>div classcap-right>/div>/div>/div>!-- corrects IE6 width calculation -->div classcolumns-inner>div classcolumn-center-outer>div classcolumn-center-inner>div classmain section idmain>div classwidget Blog data-version1 idBlog1>div classblog-posts hfeed>          div classdate-outer>        h2 classdate-header>span>Tuesday, 18 March 2014/span>/h2>          div classdate-posts>        div classpost-outer>div classpost hentry itempropblogPost itemscopeitemscope itemtypehttp://schema.org/BlogPosting>meta contenthttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPdIP9I8CbJiPDCWP3V8vx6zx3rVUeios7YMH-_AebBa8CoQx2ikHbPi4UQjK3395vMYvaNGIrRqr09f_dQXwPFEowDHGyeWSPyFdbZj7qrKNWES_o87Hc4_pYwu2dJsmASknUn76tX9uX/s1600/DSC07179.jpg itempropimage_url/>meta content5657701209880344284 itempropblogId/>meta content2102504493250284507 itemproppostId/>a name2102504493250284507>/a>h3 classpost-title entry-title itempropname>a hrefhttp://blog.mcbryan.co.uk/2014/03/belkin-hi-speed-usb-20-7-port-hub.html>Fixing an Overheating USB Hub/a>/h3>div classpost-header>div classpost-header-line-1>/div>/div>div classpost-body entry-content idpost-body-2102504493250284507 itempropdescription articleBody>So Ive had a a hrefhttp://www.belkin.com/us/p/P-F5U237/>Belkin F5U237v1 USB 2.0 7-port powered hub/a> for quite some time.  Its a pretty nice little hub to have; I especially like the top USB ports and the fact that I can charge USB devices from it without needing the computer turned on.br />br />However, occasionally Ive noticed it stops working entirely when I either (i) plug lots of stuff into it for a long time, or, (ii) when Im doing something fairly intensive across it for a prolonged period of time (large file transfers to portable USB disks etc).br />br />This hub has long since passed its warranty and I didnt particularly feel like shelling out for a new one when this is fine 95% of the time.  However, I did notice that gets really hot to the touch just before it stops working.br />br />Anyway, lets open it up:br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPdIP9I8CbJiPDCWP3V8vx6zx3rVUeios7YMH-_AebBa8CoQx2ikHbPi4UQjK3395vMYvaNGIrRqr09f_dQXwPFEowDHGyeWSPyFdbZj7qrKNWES_o87Hc4_pYwu2dJsmASknUn76tX9uX/s1600/DSC07179.jpg imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height214 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPdIP9I8CbJiPDCWP3V8vx6zx3rVUeios7YMH-_AebBa8CoQx2ikHbPi4UQjK3395vMYvaNGIrRqr09f_dQXwPFEowDHGyeWSPyFdbZj7qrKNWES_o87Hc4_pYwu2dJsmASknUn76tX9uX/s1600/DSC07179.jpg width320 />/a>/div>br />The screws are under the four little feet on the base.  After they are out the entire thing just snaps apart without any problem.  Its made up of just one circuit board, which isnt secured to the case, so its pretty hard to break anything.  The visor at the front, covering the LEDs, will fall out so make sure you dont lose it.br />br />The majority of the heat seems to be coming from the power transistor on the left (labelled UTC 2N2955) with a smaller amount coming from the diagonally mounted chip on the right.  As the transistor heats up the amount of power it will be able to disipate will decrease - my guess is that the hub gets hot enough that the transistor cant cope with the load any more and it all stops working.br />br />The internals dont look great for cooling.  Its an enclosed area with no airflow and a plastic shell acting as an insulator.  Letting it breathe a little bit should help.br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf_W3cyJB8wh8zrWB9K0TQMwz3WeBGVZy-oCLpbZiAjbLrYdlvfS0Q9HvR2zqSVKfwmAOZo0R5lI_P-TsPReXScLuboT3oQIFIm4Mj2uhjv0kR0lz61J7m3nvStXFzhtrz7F3WnDI0wVno/s1600/DSC07182.jpg imageanchor1 stylemargin-bottom: 1em;>img border0 height145 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf_W3cyJB8wh8zrWB9K0TQMwz3WeBGVZy-oCLpbZiAjbLrYdlvfS0Q9HvR2zqSVKfwmAOZo0R5lI_P-TsPReXScLuboT3oQIFIm4Mj2uhjv0kR0lz61J7m3nvStXFzhtrz7F3WnDI0wVno/s1600/DSC07182.jpg width200 />/a>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPaFfI_n0m95GYq6-_o7v27ux5jttoQaghRxc9hRNyxJga2ZJvpQilkSM3C2Fv-HvjVmuDfAwZmAaVtZNxvJG-mnnzKYXN1rQqNEz_2bbPMSk9GAYE58WornRpbU5lp1qr7oHcAsTCInVJ/s1600/DSC07181.jpg imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height145 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPaFfI_n0m95GYq6-_o7v27ux5jttoQaghRxc9hRNyxJga2ZJvpQilkSM3C2Fv-HvjVmuDfAwZmAaVtZNxvJG-mnnzKYXN1rQqNEz_2bbPMSk9GAYE58WornRpbU5lp1qr7oHcAsTCInVJ/s1600/DSC07181.jpg width200 />/a>/div>br />Excuse the terrible drill work - I started trying to do this just using a masonry drill bit which didnt go terribly well - switched to a tile bit to do the slightly nicer holes.  Function over form anyway! The aim here is just to punch some holes in the plastic shell to let hot air out and, hopefully, cooler air in near the two hottest components.  This should keep the whole unit a little cooler.br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFfF4lxhoMFugTJmANq395SnxBUNrrxO0ATXn_zr6H_ms17RA_ZwuF6Gp-X3DiKDhXf06tRXetr5A73gNsVXSQl4SBPtvZjnFhCBr5qyFprUAFY2mldU1B9c1DF3i_hQzOH63BHVBaqRFw/s1600/DSC07186.jpg imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height214 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFfF4lxhoMFugTJmANq395SnxBUNrrxO0ATXn_zr6H_ms17RA_ZwuF6Gp-X3DiKDhXf06tRXetr5A73gNsVXSQl4SBPtvZjnFhCBr5qyFprUAFY2mldU1B9c1DF3i_hQzOH63BHVBaqRFw/s1600/DSC07186.jpg width320 />/a>/div>br />Putting it all back together, remembering to put the LED visor in, it doesnt look too bad; even with my poor drilling work.  Its actually even less noticable in practice as I artificially lit the scene for the camera - this sits behind my monitor in the shade where the holes are virtually invisible.br />br />Importantly, the hub runs a lot cooler to the touch which has hopefully solved my problem (at the very least its not done it yet despite some fairly extensive testing).  If you do something like this on your own hub I imagine itll void any warranty you might have.div styleclear: both;>/div>/div>div classpost-footer>div classpost-footer-line post-footer-line-1>span classpost-author vcard>Posted byspan classfn itempropauthor itemscopeitemscope itemtypehttp://schema.org/Person>meta contenthttps://www.blogger.com/profile/14143519988774162737 itempropurl/>a hrefhttps://www.blogger.com/profile/14143519988774162737 relauthor titleauthor profile>span itempropname>Tony McBryan/span>/a>/span>/span>span classpost-timestamp>atmeta contenthttp://blog.mcbryan.co.uk/2014/03/belkin-hi-speed-usb-20-7-port-hub.html itempropurl/>a classtimestamp-link hrefhttp://blog.mcbryan.co.uk/2014/03/belkin-hi-speed-usb-20-7-port-hub.html relbookmark titlepermanent link>abbr classpublished itempropdatePublished title2014-03-18T16:38:00Z>16:38/abbr>/a>/span>span classpost-comment-link>a classcomment-link hrefhttp://blog.mcbryan.co.uk/2014/03/belkin-hi-speed-usb-20-7-port-hub.html#comment-form onclick>No comments:  /a>/span>span classpost-icons>span classitem-control blog-admin pid-535916799>a hrefhttps://www.blogger.com/post-edit.g?blogID5657701209880344284&postID2102504493250284507&frompencil titleEdit Post>img alt classicon-action height18 srchttps://resources.blogblog.com/img/icon18_edit_allbkg.gif width18/>/a>/span>/span>div classpost-share-buttons goog-inline-block>a classgoog-inline-block share-button sb-email hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID2102504493250284507&targetemail target_blank titleEmail This>span classshare-button-link-text>Email This/span>/a>a classgoog-inline-block share-button sb-blog hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID2102504493250284507&targetblog onclickwindow.open(this.href, _blank, height270,width475); return false; target_blank titleBlogThis!>span classshare-button-link-text>BlogThis!/span>/a>a classgoog-inline-block share-button sb-twitter hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID2102504493250284507&targettwitter target_blank titleShare to X>span classshare-button-link-text>Share to X/span>/a>a classgoog-inline-block share-button sb-facebook hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID2102504493250284507&targetfacebook onclickwindow.open(this.href, _blank, height430,width640); return false; target_blank titleShare to Facebook>span classshare-button-link-text>Share to Facebook/span>/a>a classgoog-inline-block share-button sb-pinterest hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID2102504493250284507&targetpinterest target_blank titleShare to Pinterest>span classshare-button-link-text>Share to Pinterest/span>/a>/div>/div>div classpost-footer-line post-footer-line-2>span classpost-labels>Labels:a hrefhttp://blog.mcbryan.co.uk/search/label/7%20port%20hub reltag>7 port hub/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/belkin reltag>belkin/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/F5U237v1 reltag>F5U237v1/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/hardware reltag>hardware/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/hardware%20hacking reltag>hardware hacking/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/overheating reltag>overheating/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/usb reltag>usb/a>/span>/div>div classpost-footer-line post-footer-line-3>span classpost-location>/span>/div>/div>/div>/div>          /div>/div>                  div classdate-outer>        h2 classdate-header>span>Monday, 25 November 2013/span>/h2>          div classdate-posts>        div classpost-outer>div classpost hentry itempropblogPost itemscopeitemscope itemtypehttp://schema.org/BlogPosting>meta contenthttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglRG8U9uTZ0SUbJfk3WB18h8SOS60ZC641YaTNGlS4-JmnPzr734zyKgAsV8aks9n-sojrteYGwdJcHdCYvrDuaH0NTt-OS4ucQu4chnecFXW30ne1vlZjMskrs_uN8mu4Ab-3bxHi04ur/s640/summary.png itempropimage_url/>meta content5657701209880344284 itempropblogId/>meta content5161250857968100872 itemproppostId/>a name5161250857968100872>/a>h3 classpost-title entry-title itempropname>a hrefhttp://blog.mcbryan.co.uk/2013/11/cellular-senescence-and-methylation.html>Cellular Senescence and Genome Wide Methylation Analysis/a>/h3>div classpost-header>div classpost-header-line-1>/div>/div>div classpost-body entry-content idpost-body-5161250857968100872 itempropdescription articleBody>Recently we conducted a study into the pattern of methylation within senescent cells.br />br />h4>Senescence/h4>Senescence is the permanent halt of proliferation associated with cellular stresses including DNA damage, damaged or short telomeres and oxidative stress.  Senescence dates back to the a hrefhttp://en.wikipedia.org/wiki/Hayflick_limit target_blank>Hayflick limit/a> and, while there are no definitive markers, cells typically become large and flat and can be identified by the presence of a hrefhttp://en.wikipedia.org/wiki/Senescence-associated_beta-galactosidase target_blank>SA-β-GAL/a>, a hrefhttp://www.ncbi.nlm.nih.gov/pubmed/17377503 target_blank>SAHF/a> and a hrefhttp://genesdev.cshlp.org/content/24/22/2463.full target_blank>tumour suppression networks/a> (i.e. p53 / p16).br />br />Senescence is thought to be a tumour suppression mechanism, through blocking clonal proliferation of cancer cells, and a promoter of ageing via an a hrefhttp://www.ncbi.nlm.nih.gov/pubmed/10911963 target_blank>inflammaging/a> phenotype.  Cancer cells must somehow bypass senescence in order to continue proliferating.br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglRG8U9uTZ0SUbJfk3WB18h8SOS60ZC641YaTNGlS4-JmnPzr734zyKgAsV8aks9n-sojrteYGwdJcHdCYvrDuaH0NTt-OS4ucQu4chnecFXW30ne1vlZjMskrs_uN8mu4Ab-3bxHi04ur/s1600/summary.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height249 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglRG8U9uTZ0SUbJfk3WB18h8SOS60ZC641YaTNGlS4-JmnPzr734zyKgAsV8aks9n-sojrteYGwdJcHdCYvrDuaH0NTt-OS4ucQu4chnecFXW30ne1vlZjMskrs_uN8mu4Ab-3bxHi04ur/s640/summary.png width640 />/a>/div>br />h4>Methylation  /h4>We were interested in studying genome-wide DNA methylation patterns within senescence.  DNA methylation is the addition of a a hrefhttp://en.wikipedia.org/wiki/Methyl_group target_blank>Methyl group/a> to specific DNA bases.  In mammals this is restricted to the cytosine nucleotide (C) within DNA.  Methylation is largely localised at CpGs (a cytosine nucleotide followed by a guamine nucleotide) within the genome.br />br />In order to study DNA methylation we use whole genome sequencing combined with bisulphite treatment.  Bisulphite treatment of DNA converts unmethylated cytosines into uracil - when we apply a process known as polymerase chain reaction (PCR) to the DNA before sequencing this is then further converted into thymine.  Methylated cytosines are unaffected.  Therefore, when sequencing a methylated cytosine will be read as a cytosine while an unmethylated cytosine will be read as a thymine.  As such when we sequence the DNA we can then deduce, via comparison with the human reference genome, which cytosine nucleotides were originally methylated and which were unmethylated.br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfcgn30XMZmOynqcMbDAwWkeDduxUin_me_ziV0MQl_2iLJUY4etQiDR4JsCW4M8Kxgu2kWo5W1A_edTUTowv91YbgO6gUbB95jaSbblgNDwbJglUz9Tbrcw-XsfkEW4qW9lQZ6UX0W1RN/s1600/bisulphite.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height138 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfcgn30XMZmOynqcMbDAwWkeDduxUin_me_ziV0MQl_2iLJUY4etQiDR4JsCW4M8Kxgu2kWo5W1A_edTUTowv91YbgO6gUbB95jaSbblgNDwbJglUz9Tbrcw-XsfkEW4qW9lQZ6UX0W1RN/s400/bisulphite.png width400 />/a>/div>br />h4>Loss of Methylation at Late Replicating Regions/h4>We sequenced three replicates of proliferating and replicative senescent cells (IMR90 cell culture). Our first observation was that there was a general loss of methylation (hypo-methylation) within the cells and that this loss was focused at regions of the genome which were only partially methylated (as opposed to completely unmethylated or fully methylated).  Further investigation highlighted a relationship with the regions losing methylation and late replicating regions of the genome.  i.e. regions of the genome where DNA is replicated later on during the cell cycle1.br />br />h4>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRaTuVTwMsoq6r6qI7ycFhkLfFx0JkgxpSn8MBxlaicKqxOVCEYpTdk5HpbRcIFGiDvakyYrAk-ezkUhD7_I0ffAC5vcx6XYrtribdoYp7fXKodCYpx0Stucp3TTGwaSaj0jeCPCCE0QB3/s1600/methlaterep.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height304 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRaTuVTwMsoq6r6qI7ycFhkLfFx0JkgxpSn8MBxlaicKqxOVCEYpTdk5HpbRcIFGiDvakyYrAk-ezkUhD7_I0ffAC5vcx6XYrtribdoYp7fXKodCYpx0Stucp3TTGwaSaj0jeCPCCE0QB3/s640/methlaterep.png width640 />/a> /h4>br />h4>Focal Hypermethylation/h4>We observed that methylation does not globally regulate gene expression changes but we did detect a subset of genes with very similar patterns in terms of methylation changes and which were coregulated at the expression level.  In these genes we observed focal increase in methylation (hyper-methylation) at the regions adjacent to islands of high CpG content and that these genes were frequently associated with cell cycle functions.br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje-CsKeu5OCzxhubn7VBid1OfM4eEbqh5bsV8tPT0c1SBhM3LDDUasob7OErx-ZPw45xkHDwXwirIaa61aDlXmU3UFMqvBcqcT4gpkJjL1y4nyftqPrZOlWk-sALeso5rj0l9KRf7gKSzM/s1600/hyper-average.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height166 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje-CsKeu5OCzxhubn7VBid1OfM4eEbqh5bsV8tPT0c1SBhM3LDDUasob7OErx-ZPw45xkHDwXwirIaa61aDlXmU3UFMqvBcqcT4gpkJjL1y4nyftqPrZOlWk-sALeso5rj0l9KRf7gKSzM/s320/hyper-average.png width320 />/a>/div>br />h4>Relationship to Cancer/h4>Surprisingly, considering the role of senescence as a tumour i>suppression /i>mechanism, we discovered that the methylation changes in senescence were very similar to the methylation changes that had previously been described in cancers2,3,4.br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhobn3nHKRdbyzrDqVcN7bpptO564eE7fSTGtd4qevlKXi81KwRR9BMVo0HJPB3pyXyyCF8qLQ-HvESzwyDocrYoNOjQnQHnj26ZGZbbthloxo-Eby0dfUN8tKIkXiwNBk-eqz2AovxSotB/s1600/methcancer.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height314 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhobn3nHKRdbyzrDqVcN7bpptO564eE7fSTGtd4qevlKXi81KwRR9BMVo0HJPB3pyXyyCF8qLQ-HvESzwyDocrYoNOjQnQHnj26ZGZbbthloxo-Eby0dfUN8tKIkXiwNBk-eqz2AovxSotB/s640/methcancer.png width640 />/a>/div>br />h4>Origins/h4>We discovered that the origin of the loss of methylation appeared to be due to mislocalisation of the DNMT1 a hrefhttp://en.wikipedia.org/wiki/Methyltransferase target_blank>methyltransferase/a> which is responsible for propagating the original methylation pattern of DNA at replication.  Specifically we noticed that foci of the DNMT1 protein are lost in old cycling cells and that these foci had previously been linked to late replicating regions5.br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8ZCUtY_APFFvgh9Yvg4fpbaDlC8DTwC-HeKs3OWS4QplHhRDm02H-bwdGicylzbXLWuXI6MY7q0u7J2exK1PZpGjp5RKiHXEipqGnqbkLPQ4VSsDFTmC_ttV8_Bi80bV0AiL-rYYA4iFY/s1600/dnmt1.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height180 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8ZCUtY_APFFvgh9Yvg4fpbaDlC8DTwC-HeKs3OWS4QplHhRDm02H-bwdGicylzbXLWuXI6MY7q0u7J2exK1PZpGjp5RKiHXEipqGnqbkLPQ4VSsDFTmC_ttV8_Bi80bV0AiL-rYYA4iFY/s320/dnmt1.png width320 />/a>/div>h4>Bypassing Senescence/h4>Finally, we bypassed senescence via the introduction of a hrefhttp://en.wikipedia.org/wiki/SV40_large_T_antigen target_blank>SV40 T antigen/a> into the cells in order to deactivate tumour suppression networks.  This allows the cells to continue proliferating, for a period of time, beyond the usual senescence time limit.  When we did this we made the same measurements of DNA methylation as before and found that the methylation changes that occur on the path to senescence are retained in the bypass cells.br />br />div classseparator styleclear: both; text-align: center;>/div>div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicEOQC68d08jkzuV2NaqdZ5l-R8QaLXDgYLPiZFHH2f3L5gl_TP3QRqGyAxGNF8WhHSumcVIt-8-yg2wJkJUasLSBHMVabuE4gltvUUWwWn7oCwzV43S8bz-nlQkh6AalP6OzNvIAByo5g/s1600/bypass.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height147 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicEOQC68d08jkzuV2NaqdZ5l-R8QaLXDgYLPiZFHH2f3L5gl_TP3QRqGyAxGNF8WhHSumcVIt-8-yg2wJkJUasLSBHMVabuE4gltvUUWwWn7oCwzV43S8bz-nlQkh6AalP6OzNvIAByo5g/s400/bypass.png width400 />/a>/div>br />h4>Conclusion  /h4>We therefore conclude that the failure of DNMT1 to methylate late replicating regions in near senescent cells may be the origin of the same methylation patterns found in cancer cells.  Furthermore, given the similarities, it may be possible that these changes may lead cells to be more susceptible to transformation into cancer cells.br />br />br />div classseparator styleclear: both; text-align: center;>/div>div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHnuuzy17pHCcW9tHVy0N13xNlyeMXRXjGq_Jvvd0eUWl5Hg3BMJeV5doHEwaG4f4888OcKpYdW5zvIjJp2jJoAGxSYVaIfQ_cDgk-NNEzQahKsDyST3kCO4YLlXW0tSJ54UAV_YwN3N3O/s1600/conclusion.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height218 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHnuuzy17pHCcW9tHVy0N13xNlyeMXRXjGq_Jvvd0eUWl5Hg3BMJeV5doHEwaG4f4888OcKpYdW5zvIjJp2jJoAGxSYVaIfQ_cDgk-NNEzQahKsDyST3kCO4YLlXW0tSJ54UAV_YwN3N3O/s400/conclusion.png width400 />/a>/div>br />br />The full paper is available online from a hrefhttp://www.nature.com/ncb/journal/vaop/ncurrent/full/ncb2879.html target_blank>Nature Cell Biology/a>, is discussed by a a hrefhttp://www.cancerresearchuk.org/cancer-info/news/archive/pressrelease/2013-11-24-ageing-cells-could-be-ticking-cancer-time-bomb target_blank>CRUK press release/a> and the raw data is available from a hrefhttp://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?accGSE48580 target_blank>GEO GSE48580/a>.br />br />h4>References/h4>br />1 R. S. Hansen et al., Sequencing newly replicated DNA reveals widespread plasticity in human replication timing, PNAS, 2010.br />br />2 K. D. Hansen et al., Increased methylation variation in epigenetic domains across cancer types, Nature Genetics, 2011.br />br />3 B. P. Berman et al., Regions of focal DNA hypermethylation and long-range hypomethylation in colorectal cancer coincide with nuclear lamina–associated domains, Nature Genetics, 2012.br />br />4 G. C. Hon et al., Global DNA hypomethylation coupled to repressive chromatin domain formation and gene silencing in breast cancer. Genome Research, 2012.br />br />5 L. Schermelleh  et al., Dynamics of Dnmt1 interaction with the replication machinery and its role in postreplicative maintenance of DNA methylation. Nucleic Acids Res, 2007.div styleclear: both;>/div>/div>div classpost-footer>div classpost-footer-line post-footer-line-1>span classpost-author vcard>Posted byspan classfn itempropauthor itemscopeitemscope itemtypehttp://schema.org/Person>span itempropname>McBryan/span>/span>/span>span classpost-timestamp>atmeta contenthttp://blog.mcbryan.co.uk/2013/11/cellular-senescence-and-methylation.html itempropurl/>a classtimestamp-link hrefhttp://blog.mcbryan.co.uk/2013/11/cellular-senescence-and-methylation.html relbookmark titlepermanent link>abbr classpublished itempropdatePublished title2013-11-25T16:27:00Z>16:27/abbr>/a>/span>span classpost-comment-link>a classcomment-link hrefhttp://blog.mcbryan.co.uk/2013/11/cellular-senescence-and-methylation.html#comment-form onclick>1 comment:  /a>/span>span classpost-icons>span classitem-control blog-admin pid-213027344>a hrefhttps://www.blogger.com/post-edit.g?blogID5657701209880344284&postID5161250857968100872&frompencil titleEdit Post>img alt classicon-action height18 srchttps://resources.blogblog.com/img/icon18_edit_allbkg.gif width18/>/a>/span>/span>div classpost-share-buttons goog-inline-block>a classgoog-inline-block share-button sb-email hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5161250857968100872&targetemail target_blank titleEmail This>span classshare-button-link-text>Email This/span>/a>a classgoog-inline-block share-button sb-blog hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5161250857968100872&targetblog onclickwindow.open(this.href, _blank, height270,width475); return false; target_blank titleBlogThis!>span classshare-button-link-text>BlogThis!/span>/a>a classgoog-inline-block share-button sb-twitter hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5161250857968100872&targettwitter target_blank titleShare to X>span classshare-button-link-text>Share to X/span>/a>a classgoog-inline-block share-button sb-facebook hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5161250857968100872&targetfacebook onclickwindow.open(this.href, _blank, height430,width640); return false; target_blank titleShare to Facebook>span classshare-button-link-text>Share to Facebook/span>/a>a classgoog-inline-block share-button sb-pinterest hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5161250857968100872&targetpinterest target_blank titleShare to Pinterest>span classshare-button-link-text>Share to Pinterest/span>/a>/div>/div>div classpost-footer-line post-footer-line-2>span classpost-labels>Labels:a hrefhttp://blog.mcbryan.co.uk/search/label/bisulfite reltag>bisulfite/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bisulphite reltag>bisulphite/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bsseq reltag>bsseq/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bypass reltag>bypass/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/cancer reltag>cancer/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/dnmt1 reltag>dnmt1/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/geo reltag>geo/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/imr90 reltag>imr90/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/late%20replicating%20regions reltag>late replicating regions/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/methylation reltag>methylation/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/nature%20cell%20biology reltag>nature cell biology/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/ncb reltag>ncb/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/next%20generation%20sequencing reltag>next generation sequencing/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/ngs reltag>ngs/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/replicative%20senescence reltag>replicative senescence/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/senescence reltag>senescence/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/sv40 reltag>sv40/a>/span>/div>div classpost-footer-line post-footer-line-3>span classpost-location>/span>/div>/div>/div>/div>          /div>/div>                  div classdate-outer>        h2 classdate-header>span>Friday, 1 November 2013/span>/h2>          div classdate-posts>        div classpost-outer>div classpost hentry itempropblogPost itemscopeitemscope itemtypehttp://schema.org/BlogPosting>meta content5657701209880344284 itempropblogId/>meta content1856668406146901060 itemproppostId/>a name1856668406146901060>/a>h3 classpost-title entry-title itempropname>a hrefhttp://blog.mcbryan.co.uk/2013/11/what-is-replicate-anyway.html>What is a replicate anyway?/a>/h3>div classpost-header>div classpost-header-line-1>/div>/div>div classpost-body entry-content idpost-body-1856668406146901060 itempropdescription articleBody>In science we perform replication as the primary way of ensuring reproducibility.  This is one of the key principles.  Science only advances through consensus - initially within a single lab and later within the scientific community at large.br />br />However,  there are lots of different ways the replicates can be performed in any given experiment and the choice depends on exactly what experimental conditions you are trying to control for.br />br />In this post I will argue there is a hierarchy of replication which should be considered when planning any scientific experiment.  For the purposes of this post I will use experiments within the molecular biology domain to illustrate my points but I believe it is applicable into other fields.br />br />b>Technical replicates/b>br />br />Technical replicates are aimed at solving the problem of inaccurate measuring devices.  No measuring device is perfect and they will produce slightly different answers each time you use them.br />br />A typical example of technical replication might be to measure the RNA abundance of a particular gene three times on a single sample.  Subsequently this allows you to make a higher confidence estimate of the actual abundance of the sample - specifically it allows you to actually estimate the degree of error in the measurement. i.e. How accurate is your gene expression abundance measurement anyway?br />br />b>Experimental replicates/b>br />br />Experimental replicates are used to detect the degree of variation that is introduced by a particular instance of an experiment.  If any given experiment is repeated on a different day it will have slightly different results from the original.  Experimental replicates are there to figure out exactly how big an effect this has on your experimental observations.  Experimental replicates may well be performed on the same tissue sample or cell line if the aim is to show the effect of a particular treatment is consistent for a sample.br />br />Examples of things that might influence how well an experiment replicates on different days might include environmental effects such as ambient temperature, the experimenters mood (and subsequently how careful they were) or how many interruptions they had and when they were.br />br />b>Biological replicates/b>br />br />Next up is biological replication which aims to show that the experimental observation is generalisable to more than a specific tissue sample or cell line.  For this we need to show that the effect holds across multiple different samples.br />br />The more different the samples are the stronger the case that can be made.  For example if an effect is shown to be consistent across a population of genetically identical mice this is not as strong as showing that the effect is the same in another different strain of mouse.  Even stronger would be using different rodents or even a completely different species altogether.br />br />b>Experimenter replicates/b>br />br />Each experimenter introduces their own variation via differences in skill, patience and familiarity with a given assay.  Replication by multiple people shows that the result can be obtained by a different person using the same protocol, reagents and equipment as the original experiment.br />br />For complicated or tricky experiments it is often common for a researcher to visit a lab which has the experiment working in order to learn first-hand the techniques used by the original experimenter to enable them to be able to reproduce an experiment on their own.br />br />b>Method replicates/b>br />br />Finally, another approach to confirming your results is to use a different method entirely.  In most high impact papers it is often the case that an important observation may be shown in multiple different ways and in multiple model systems in order to demonstrate its robustness.br />br />One simple example might be to show the change in regulation of a gene or pathway via detection using a whole genome screen (RNA-seq/microarray), quantitative RNA abundance (qRT-PCR), protein abundance (western blot) and via changes in localisation within the tissue (immunohistochemistry).  These methods may therefore be complimentary to one another and tell the same story but share little otherwise in common.  This may be extended to show the effect in a variety of tissues or model systems.br />b>br />/b>b>Laboratory replicates/b>br />br />Laboratory replicates are the gold standard of experimental replication and are used to demonstrate that the results of an experiment can be replicated by the scientific community at large.  When results are replicated by many different laboratories they come as close to the label of truth that science can reasonably apply.br />br />Variation between labs and institutes can be induced by apparently minor differences in protocol, equipment, reagents, regulations, behaviour, strains of model system, batches of the same reagent and suppliers of equipment.br />br />b>Summary/b>br />br />As you move up the replication hierarchy, the number of confounding variables will increase - your experiment will be less controlled.  But the results will be more generalisable and robust.  Ultimately the strength of your observation should exceed the noise introduced by any of the confounding variables weve discussed above in order to be accepted by the scientific community. Otherwise it just goes down in history as unreproducible.br />br />But how easy should it be to reproduce results?  Methods sections may be incomplete and this not necessarily the authors fault; journals frequently impose word limits which may preclude full detail.  Reagents used may no longer be available and the replacement may not work in the same way.  And there is just as much chance that the original experiment is correct and the replication is wrong as there is of the reverse.  For a more in depth discussion see a hrefhttp://genesgonewild.blogspot.co.uk/2013/10/how-easy-should-it-be-to-replicate.html target_blank>this post/a> by span classpost-author vcard>span classfn itempropauthor itemscopeitemscope itemtypehttp://schema.org/Person>span itempropname>Ian Dworkin./span>/span>/span>br />br />It is good to see endeavours such as the a hrefhttp://blog.scienceexchange.com/2013/10/reproducibility-initiative-receives-1-3m-grant-to-validate-50-landmark-cancer-studies/ target_blank>reproducibility initiative/a> set out to independently reproduce important papers.  In addition important papers will be reproduced simply because other labs will want to build on previous published results and will discover problems in reproducing it while they try to extend it.br />br />This does, however, leave one problem.  Small papers, with less ground-breaking results, published in low-tier journals are less likely to be reproduced by other labs - they may not be as interesting for other labs to build on. As such their results may live on in science as a dogma that may persist for many years.  It is unclear to me how to address this final issue as there are currently very few incentives for scientists to reproduce results for their own sake.div styleclear: both;>/div>/div>div classpost-footer>div classpost-footer-line post-footer-line-1>span classpost-author vcard>Posted byspan classfn itempropauthor itemscopeitemscope itemtypehttp://schema.org/Person>span itempropname>McBryan/span>/span>/span>span classpost-timestamp>atmeta contenthttp://blog.mcbryan.co.uk/2013/11/what-is-replicate-anyway.html itempropurl/>a classtimestamp-link hrefhttp://blog.mcbryan.co.uk/2013/11/what-is-replicate-anyway.html relbookmark titlepermanent link>abbr classpublished itempropdatePublished title2013-11-01T16:12:00Z>16:12/abbr>/a>/span>span classpost-comment-link>a classcomment-link hrefhttp://blog.mcbryan.co.uk/2013/11/what-is-replicate-anyway.html#comment-form onclick>No comments:  /a>/span>span classpost-icons>span classitem-control blog-admin pid-213027344>a hrefhttps://www.blogger.com/post-edit.g?blogID5657701209880344284&postID1856668406146901060&frompencil titleEdit Post>img alt classicon-action height18 srchttps://resources.blogblog.com/img/icon18_edit_allbkg.gif width18/>/a>/span>/span>div classpost-share-buttons goog-inline-block>a classgoog-inline-block share-button sb-email hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID1856668406146901060&targetemail target_blank titleEmail This>span classshare-button-link-text>Email This/span>/a>a classgoog-inline-block share-button sb-blog hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID1856668406146901060&targetblog onclickwindow.open(this.href, _blank, height270,width475); return false; target_blank titleBlogThis!>span classshare-button-link-text>BlogThis!/span>/a>a classgoog-inline-block share-button sb-twitter hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID1856668406146901060&targettwitter target_blank titleShare to X>span classshare-button-link-text>Share to X/span>/a>a classgoog-inline-block share-button sb-facebook hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID1856668406146901060&targetfacebook onclickwindow.open(this.href, _blank, height430,width640); return false; target_blank titleShare to Facebook>span classshare-button-link-text>Share to Facebook/span>/a>a classgoog-inline-block share-button sb-pinterest hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID1856668406146901060&targetpinterest target_blank titleShare to Pinterest>span classshare-button-link-text>Share to Pinterest/span>/a>/div>/div>div classpost-footer-line post-footer-line-2>span classpost-labels>Labels:a hrefhttp://blog.mcbryan.co.uk/search/label/biological%20replicate reltag>biological replicate/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/experimental%20replicate reltag>experimental replicate/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/experimenter%20replicate reltag>experimenter replicate/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/laboratory%20replicate reltag>laboratory replicate/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/method%20replicate reltag>method replicate/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/replication reltag>replication/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/reproducibility reltag>reproducibility/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/technical%20replicate reltag>technical replicate/a>/span>/div>div classpost-footer-line post-footer-line-3>span classpost-location>/span>/div>/div>/div>/div>          /div>/div>                  div classdate-outer>        h2 classdate-header>span>Tuesday, 16 July 2013/span>/h2>          div classdate-posts>        div classpost-outer>div classpost hentry itempropblogPost itemscopeitemscope itemtypehttp://schema.org/BlogPosting>meta content5657701209880344284 itempropblogId/>meta content5994593849262595865 itemproppostId/>a name5994593849262595865>/a>h3 classpost-title entry-title itempropname>a hrefhttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-bisulphite-sequencing.html>The G Test and Bisulphite Sequencing DMRs/a>/h3>div classpost-header>div classpost-header-line-1>/div>/div>div classpost-body entry-content idpost-body-5994593849262595865 itempropdescription articleBody>center>b>This is Part 4 in a series on Bisulphite Sequencing.br />You can return to a hrefhttp://blog.mcbryan.co.uk/2013/07/bisulphite-sequencing-simple.html>Part 3 (Bisulphite Sequencing Simple Visualisation)/a>./b>/center>br />br />Okay, so we have our bisulphite sequencing data on the UCSC genome browser.  Lets assume we have two conditions CondA and CondB, and we have two replicates of each condition.  We can see what appear to be changes from our visual inspection on the browser. Now what?br />br />Well, we probably want to compute differentially methylated regions.  With 1 replicate of each thats fairly straight forward for categorical data like the bisulphite seq data we have - we use a hrefhttp://en.wikipedia.org/wiki/Fisher%27s_exact_test>fishers exact test/a>.  With replicates a simple approach is just to pool the two replicates together and do our fishers exact test on the pooled data, but this doesnt give us a very good idea of whats going on if the two replicates disagree for a given region.br />br />Instead we use the G-test which can be calculated for any given contingency table with the following formula:br />br />$$$$ G  2 \sum_{i0}^{r} \sum_{j0}^{c} {O_{i,j} \ln(O_{i,j}/E_{i,j}) } $$$$br />Where, $$$r$$$ and $$$c$$$ are the number of rows and columns in the contingency table, $$$O_{i,j}$$$ and $$$E_{i,j}$$$ are the Observed and Expected values for cell $$$i,j$$$ in the table.  Ive detailed how to implement the G-test for a 2x2 contingency table in Python a hrefhttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-python.html>previously/a>.br />br />The main selling point of the G-test, over a regular chi-square test, is that the G value is additive.  Consider the following:br />br />table aligncenter border1>tbody>tr>th>G-test 1/th>th>G-test 2/th>/tr>tr>td>table aligncenter border0 styleheight: 78px; width: 245px;>tbody>tr>th styletext-align: center;>/th>th styletext-align: center;>A/th>th styletext-align: center;>B/th>th>G-value/th>/tr>tr>   th styletext-align: center;>C/th>   td styletext-align: center;>100/td>   td styletext-align: center;>70/td>  td rowspan2 styletext-align: center;> 7.1/td>   /tr>tr>   th styletext-align: center;>D/th>   td styletext-align: center;>35/td>   td styletext-align: center;>50/td>   /tr>/tbody>/table>/td>td>table aligncenter border0 styleheight: 78px; width: 245px;>tbody>tr>th styletext-align: center;>/th>th styletext-align: center;>A/th>th styletext-align: center;>B/th>th>G-value/th>/tr>tr>   th styletext-align: center;>C/th>   td styletext-align: center;>200/td>   td styletext-align: center;>140/td>  td rowspan2 styletext-align: center;> 14.2/td>   /tr>tr>   th styletext-align: center;>D/th>   td styletext-align: center;>70/td>   td styletext-align: center;>100/td>   /tr>/tbody>/table>/td>/tr>/tbody>/table>br />br />To find out where we have differential regions we first partition the genome into 2kb windows.  There are large regions of the genome where there are no CpGs or, alternatively, where we have no sequencing coverage - we will skip those regions.  We align our windows such that each window starts at an individual CpG and stops at the last CpG within 2kb of the start position.br />br />b>Pooled G/b>br />br />We first compute a Pooled G which is the G-test performed on the pooled replicates.  The contingency table would consist of columns representing each condition and rows representing methylated and unmethylated counts.  The number of degrees of freedom is equal to $$$(R-1) \cdot (C-1)$$$ so as we are doing a single 2x2 contingency table this will always be equal to 1.br />br />pre classbrush: python;>def pooledG(lmeth,lunmeth,rmeth,runmeth):       dof  1    pooledg  gtest(lmeth,lunmeth,rmeth,runmeth)    return pooledg, dof, GtoP(pooledg,dof)/pre>br />br />b>Total G/b>br />br />We then compute a G-value for each individual replicate and add them together.  Each G-test we do adds 1 to the total number of degrees of freedom.br />br />pre classbrush: python;>def totalG(data):    dof  0    totalg  0    for lmeth,lunmeth,rmeth,runmeth in data:            totalg + gtest(lmeth,lunmeth,rmeth,runmeth)            dof+1     return totalg, dof, GtoP(totalg,dof)/pre>br />br />b>Heterogeneous G/b>br />br />If each of our three replicates reproduce exactly then Pooled G will be identical to Total G (due to the additive nature of G-test results).  However, if the ratios are not identical then they will not match.  The difference between the Total G-value and the Pooled G-value is the heterogeneous G-value and tells us if the difference between our replicates is significant (i.e. our replicates are not all doing the same thing.br />br />pre classbrush: python;>def heterogenousG(totalg,totaldof,pooledg,pooleddof):    heteroG  totalg-pooledg    heterodof  totaldof-pooleddof    return heteroG,heterodof,GtoP(heteroG,totaldof-pooleddof)/pre>br />br />b>Putting it all together/b>br />br />Now, we can iterate through a file summarising the number of methylated and unmethylated reads at each CpG (described in a a hrefhttp://blog.mcbryan.co.uk/2013/02/post-processing-bismark-bisulphite.html>previous post/a>) and compute the Pooled, Total and Heterogenous G-values (and corresponding p-values) for each genomic window.pre classbrush: python;>import getoptimport sysimport csvfrom itertools import izip_longestfrom itertools import izipfrom memoized import memoized# sudo easy_install mpmathimport mpmath#mpmath.mp.dps  20 # decimal digits of precision@memoizeddef mpmathcdf(g,df,dps10):    mpmath.mp.dps  dps        x,k  mpmath.mpf(g), mpmath.mpf(df)    cdf  mpmath.gammainc(k/2, 0, x/2, regularizedTrue)        # floating point precision insufficient, use more precision    if cdf  1.0:        if dps > 4000:            return cdf # give up after a certain point        else:            cdf  mpmathcdf(g,df,dps*2)    return cdfdef GtoP(g,df):    assert g > 0, g    return float(1-mpmathcdf(g,df))import math@memoizeddef flnf(f):    return f*math.log(f) if f>0.5 else 0@memoizeddef gtest(a,b,c,d):    row1  a+b    row2  c+d    col1  a+c    col2  b+d        total  flnf(a+b+c+d)    celltotals  flnf(a)+flnf(b)+flnf(c)+flnf(d)    rowtotals  flnf(row1)+flnf(row2)    coltotals  flnf(col1)+flnf(col2)        # abs is necessary to account for float precision errors when doing the subtraction    return abs(2*((celltotals + total)-(rowtotals+coltotals)))# extract the pooled meth counts from the sampledef pooledMethCounts(data,covs,compare):    lmethtotal  0    lunmethtotal  0    rmethtotal  0    runmethtotal  0        if len(compare)2:        # if we are given covariates to use        covleft, covright  compare            for cov, (meth,unmeth) in izip(covs,grouper(2,data)): # extract in pairs of meth/unmeth            if cov  covleft:                lmethtotal + meth                lunmethtotal + unmeth            elif cov  covright:                rmethtotal + meth                runmethtotal + unmeth    else:        # if we have not been given them, assume that each adjacent sample (which is one pair) is one replicate        for lmeth,lunmeth,rmeth,runmeth in grouper(4,data): # extract in quads (2 pairs) representing one replicate            lmethtotal + lmeth            lunmethtotal + lunmeth            rmethtotal + rmeth            runmethtotal + runmeth            return lmethtotal,lunmethtotal,rmethtotal,runmethtotal# extract individual replicate counts from the sample and return as a list of (lmeth,lunmeth,rmeth,runmeth)# where l and r refer to the left and right cov in the compare array# if compare array is empty assume that data is formatted as:# lmeth1,lunmeth1,rmeth1,runmeth1,lmeth2,lunmeth2,rmeth2,runmeth2 etcdef covReplicateMethCounts(data,covs,compare):    if len(compare)2:        covleft, covright  compare                lreplicates          rreplicates              for cov, (meth,unmeth) in izip(covs,grouper(2,data)): # extract in pairs of meth/unmeth            if cov  covleft:                lreplicates.append((meth,unmeth))            elif cov  covright:                rreplicates.append((meth,unmeth))        #return (lmeth,lunmeth,rmeth,runmeth),(),(),...            return (a,b,c,d) for (a,b),(c,d) in izip(lreplicates,rreplicates)    else:        # assume that each pair of samples (i.e. 4 columns) in the input is one replicate        # in this case our input file is in the right order and we just need to split it up.        return grouper(4,data)# total G: at least some of the data is different# 1 degree of freedom per replicate (i.e. 3 in total), add Gs from each seperate testdef totalG(data,covs,compare):    dof  0    totalg  0    for lmeth,lunmeth,rmeth,runmeth in covReplicateMethCounts(data,covs,compare): # extract in quads (2 pairs)            totalg + gtest(lmeth,lunmeth,rmeth,runmeth)            dof+1     assert totalg > 0    return totalg, dof, GtoP(totalg,dof)# pooled G: the data as a whole is different# 1 degree of freedom, pool results from all replicates and do 1 2x2 tabledef pooledG(data,covs,compare):        lmeth,lunmeth,rmeth,runmeth  pooledMethCounts(data,covs,compare)        dof  1        pooledg  gtest(lmeth,lunmeth,rmeth,runmeth)        assert pooledg > 0        return pooledg, dof, GtoP(pooledg,dof)# there is evidence that they are significantly different from each other# heterogeneity G: total G - pooled G, df  3-1  2def heterogeneityG(totalg,totaldof,pooledg,pooleddof):    heteroG  max(totalg-pooledg,0)    heterodof  totaldof-pooleddof    return heteroG,heterodof,GtoP(heteroG,totaldof-pooleddof)def grouper(n, iterable, fillvalueNone):    grouper(3, ABCDEFG, x) --> ABC DEF Gxx    args  iter(iterable) * n    return izip_longest(fillvaluefillvalue, *args)def unpackLine(chrm,coord,*data):    return chrm.strip(), int(coord), int(d) for d in datadef extractLine(line):    chrm,coord,data  unpackLine(*line)    if not chrm.startswith(chr):        chrm  chr+chrm    return (chrm,coord,data)    if __name__  __main__:    try:        opts, args  getopt.getopt(sys.argv1:, , combined,cov,compare)    except getopt.GetoptError, err:        # print help information and exit:        print str(err) # will print something like option -a not recognized        sys.exit(2)        infile  None    covs  None    compare  None        for o, a in opts:        if o--combined:            infile  a            print combined, a        elif o--cov:            covs  a.split(,)            print covs        elif o--compare:            compare  a.split(,)            print compare            assert len(compare)2        assert infile ! None        # we either have compare and covs or neither    assert compare  None or len(compare)2    if compare  None: assert covs  None    if len(compare)2: assert covs ! None        methfile  csv.reader(open(infile, r), delimiter\t)        # ---        # windows        if compare ! None:        leftcov,rightcov  compare        windows  csv.writer(open(infile+.+leftcov+-vs-+rightcov+.windows.bedGraph,w),delimiter\t)        percent  csv.writer(open(infile+.+leftcov+-vs-+rightcov+.percent.windows.bedGraph,w),delimiter\t)    else:        windows  csv.writer(open(infile+.windows.bedGraph,w),delimiter\t)        percent  csv.writer(open(infile+.percent.windows.bedGraph,w),delimiter\t)        windowSize  2000        currentWindowPos  None    currentChr  None        cs  0    dataCount  None        def writeWindow(chrm,pos,epos):        global dataCount        global cs        global windows        global percent                lmethCount,lunmethCount,rmethCount,runmethCount  pooledMethCounts(dataCount,covs,compare)                if (lmethCount + lunmethCount)  0 or (rmethCount + runmethCount)  0:            print Unprintable window:,chrm, pos, epos, lmethCount, lunmethCount, rmethCount, runmethCount            return                lPercentage  (float(lmethCount)/float(lmethCount+lunmethCount)) * 100.0        rPercentage  (float(rmethCount)/float(rmethCount+runmethCount)) * 100.0                total,totaldof,totalp  totalG(dataCount,covs,compare)        pooled,pooleddof,pooledp  pooledG(dataCount,covs,compare)        hetero,heterodof,heterop  heterogeneityG(total,totaldof,pooled,pooleddof)                windows.writerow(chrm,pos,epos+1,1 if rPercentage > lPercentage else -1,totalp,pooledp,heterop,cs)                percent.writerow(chrm,pos,epos+1,lPercentage,rPercentage)                         dataCount  None        cs  0    lastCoordCounted  None    # the actual work here    for line in methfile:                chrm,coord,data  extractLine(line)        if currentChr  None:            currentChr  chrm            currentWindowPos  coord            lastCoordCounted  coord        else:            # always write a window if we change chrm            if chrm ! currentChr:                writeWindow(currentChr,currentWindowPos,lastCoordCounted)                currentChr  chrm                currentWindowPos  coord                            # write a window if the next cpg is outside the current window            elif coord - currentWindowPos > windowSize:                writeWindow(currentChr,currentWindowPos,lastCoordCounted)                currentChr  chrm                currentWindowPos  coord                            # otherwise dont write any window (the current cpg is in the window)                ####        # add data to existing data count        ####        if dataCount  None:            dataCount  data        else:            for index,d in enumerate(data):                dataCountindex + d        lastCoordCounted  coord                # inc number of cs counted        cs + 1            # after we write a window there is always at least one unmeasured coord after it so we have one more window to write    writeWindow(currentChr,currentWindowPos,lastCoordCounted)/pre>br />br />Note that the above script relies upon the a hrefhttp://wiki.python.org/moin/PythonDecoratorLibrary#Memoize>Memoized decorator/a>.br />br />Executed as:br />br />pre classbrush: bash;>python replicatesGTest.py \--combined Conditions.1.and.2.CpG_context.aggregate \--cov Condition1,Condition2,Condition1,Condition2,Condition1,Condition2--compare Condition1,Condition2 /pre>br />br />Where --cov lists the order of the conditions in the file and --cov indicates which conditions should be compared.br />br />For each window, this script outputs a tab separated file containing the chromosome,start and stop position of the window,1 if it is increasing otherwise -1 and p-values for computed from the Total, Pooled ahd Hetero G computations as well as the number of methylation sites considered in the window.br />br />Note that the p-values generated are uncorrected for multiple testing and should be FDR corrected.  Ive a hrefhttp://blog.mcbryan.co.uk/2013/01/false-discovery-rates-and-large-files.html>previously described/a> a suitable approach for large files such as these.br />br />Differentially methylated regions can then be defined as regions of adjacent windows with a FDR adjusted p-value less than or equal to a fixed level (i.e. 0.05 FDR) that change in the same direction.div styleclear: both;>/div>/div>div classpost-footer>div classpost-footer-line post-footer-line-1>span classpost-author vcard>Posted byspan classfn itempropauthor itemscopeitemscope itemtypehttp://schema.org/Person>span itempropname>McBryan/span>/span>/span>span classpost-timestamp>atmeta contenthttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-bisulphite-sequencing.html itempropurl/>a classtimestamp-link hrefhttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-bisulphite-sequencing.html relbookmark titlepermanent link>abbr classpublished itempropdatePublished title2013-07-16T14:34:00+01:00>14:34/abbr>/a>/span>span classpost-comment-link>a classcomment-link hrefhttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-bisulphite-sequencing.html#comment-form onclick>No comments:  /a>/span>span classpost-icons>span classitem-control blog-admin pid-213027344>a hrefhttps://www.blogger.com/post-edit.g?blogID5657701209880344284&postID5994593849262595865&frompencil titleEdit Post>img alt classicon-action height18 srchttps://resources.blogblog.com/img/icon18_edit_allbkg.gif width18/>/a>/span>/span>div classpost-share-buttons goog-inline-block>a classgoog-inline-block share-button sb-email hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5994593849262595865&targetemail target_blank titleEmail This>span classshare-button-link-text>Email This/span>/a>a classgoog-inline-block share-button sb-blog hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5994593849262595865&targetblog onclickwindow.open(this.href, _blank, height270,width475); return false; target_blank titleBlogThis!>span classshare-button-link-text>BlogThis!/span>/a>a classgoog-inline-block share-button sb-twitter hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5994593849262595865&targettwitter target_blank titleShare to X>span classshare-button-link-text>Share to X/span>/a>a classgoog-inline-block share-button sb-facebook hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5994593849262595865&targetfacebook onclickwindow.open(this.href, _blank, height430,width640); return false; target_blank titleShare to Facebook>span classshare-button-link-text>Share to Facebook/span>/a>a classgoog-inline-block share-button sb-pinterest hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5994593849262595865&targetpinterest target_blank titleShare to Pinterest>span classshare-button-link-text>Share to Pinterest/span>/a>/div>/div>div classpost-footer-line post-footer-line-2>span classpost-labels>Labels:a hrefhttp://blog.mcbryan.co.uk/search/label/bisulfite reltag>bisulfite/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bisulfite%20sequencing reltag>bisulfite sequencing/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bisulphite reltag>bisulphite/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bisulphite%20sequencing reltag>bisulphite sequencing/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bs-seq reltag>bs-seq/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bsseq reltag>bsseq/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/differentially%20methylated%20regions reltag>differentially methylated regions/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/DMR reltag>DMR/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/fdr reltag>fdr/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/g%20test reltag>g test/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/g-test reltag>g-test/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/methylation reltag>methylation/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/ngs reltag>ngs/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/p-value reltag>p-value/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/python reltag>python/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/statistics reltag>statistics/a>/span>/div>div classpost-footer-line post-footer-line-3>span classpost-location>/span>/div>/div>/div>/div>          /div>/div>                  div classdate-outer>        h2 classdate-header>span>Tuesday, 9 July 2013/span>/h2>          div classdate-posts>        div classpost-outer>div classpost hentry itempropblogPost itemscopeitemscope itemtypehttp://schema.org/BlogPosting>meta content5657701209880344284 itempropblogId/>meta content5148735681642524482 itemproppostId/>a name5148735681642524482>/a>h3 classpost-title entry-title itempropname>a hrefhttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-python.html>The G-Test and Python/a>/h3>div classpost-header>div classpost-header-line-1>/div>/div>div classpost-body entry-content idpost-body-5148735681642524482 itempropdescription articleBody>The a hrefhttp://en.wikipedia.org/wiki/G-test>G-Test/a> is a statistical test which can be used much like a chi-squared test.  It is defined as:$$$$ G  2 \sum_{i0}^{r} \sum_{j0}^{c} {O_{i,j} \ln(O_{i,j}/E_{i,j}) } $$$$Where, $$$r$$$ and $$$c$$$ are the number of rows and columns in the contingency table and $$$O_{i,j}$$$ and $$$E_{i,j}$$$ are the Observed and Expected values for cell $$$i,j$$$ in the table.br />br />To make a straightforward implementation for it in Python we first do a bit of math.  For a 2x2 contingency table:br />br />$$$ G  2 \Bigg({O_{1,1} \ln(\frac{O_{1,1}}{E_{1,1}})}  + {O_{1,2} \ln(\frac{O_{1,2}}{E_{1,2}})} + {O_{2,1} \ln(\frac{O_{2,1}}{E_{2,1}})}  + {O_{2,2} \ln(\frac{O_{2,2}}{E_{2,2}})}  \Bigg) $$$ br />br />Expand via log equivalences:br />br />table>tr>td>$$$ G  2 \Bigg( $$$/td>td>$$$  \bigg( {O_{1,1} \ln(O_{1,1}) -  O_{1,1} \ln(E_{1,1})} \bigg)  + \bigg( {O_{1,2} \ln(O_{1,2}) -  O_{1,2} \ln(E_{1,2})} \bigg) $$$/td>/tr>tr>td>/td>td> $$$ + \bigg( {O_{2,1} \ln(O_{2,1}) -  O_{2,1} \ln(E_{2,1})} \bigg)  + \bigg( {O_{2,2} \ln(O_{2,2}) -  O_{2,2} \ln(E_{2,2})} \bigg)  \Bigg) $$$/td>/tr>/table>br />br />Group Observed vs Expected together:br />br />table>tr>td>$$$ G  2 \Bigg( $$$/td>td>$$$  \bigg( O_{1,1} \ln(O_{1,1}) +                     O_{1,2} \ln(O_{1,2}) +                     O_{2,1} \ln(O_{2,1}) +                     O_{2,2} \ln(O_{1,2}) \bigg)$$$/td>/tr>tr>td>/td>td> $$$ - \bigg(                         O_{1,1} \ln(E_{1,1})  +                         O_{1,2} \ln(E_{1,2})  +                         O_{2,1} \ln(E_{2,1})  +                         O_{2,2} \ln(E_{2,2}) \Bigg) $$$/td>/tr>/table>br />br />For a 2x2 contingency table; $$$E_{i,j}  \frac{T_{i} \cdot T_{j}}{T} $$$, where $$$T_{i}$$$ and $$$T_{j}$$$ are the totals for the row and column of cell $$$E_{i,j}$$$ and $$$T$$$ is the total for all cells in the table.  Specifically,$$$$ \ln(E_{1,1})  \ln \Bigg( \frac{ (O_{1,1}+O_{1,2}) \cdot (O_{1,1}+O_{2,1}) }{ O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} } \Bigg) $$$$$$$$ \ln(E_{1,2})  \ln \Bigg( \frac{ (O_{1,1}+O_{1,2}) \cdot (O_{1,2}+O_{2,2}) }{ O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} } \Bigg) $$$$$$$$ \ln(E_{2,1})  \ln \Bigg( \frac{ (O_{2,1}+O_{2,2}) \cdot (O_{1,1}+O_{2,1}) }{ O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} } \Bigg) $$$$$$$$ \ln(E_{2,2})  \ln \Bigg( \frac{ (O_{2,1}+O_{2,2}) \cdot (O_{1,2}+O_{2,2}) }{ O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} } \Bigg) $$$$br />We then substitute these into our equation for G.br />table>tr>td>$$$ G  2 \Bigg( $$$/td>td>$$$\bigg( O_{1,1} \ln(O_{1,1}) +                          O_{1,2} \ln(O_{1,2}) +                         O_{2,1} \ln(O_{2,1}) +                         O_{2,2} \ln(O_{1,2}) \bigg) - $$$/td>/tr>tr>td>/td>td> $$$                   \bigg(                         O_{1,1} \ln \Big( \frac{ (O_{1,1}+O_{1,2}) \cdot (O_{1,1}+O_{2,1}) }{ O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} } \Big)  +                         O_{1,2} \ln \Big( \frac{ (O_{1,1}+O_{1,2}) \cdot (O_{1,2}+O_{2,2}) }{ O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} } \Big)  + $$$/td>/tr>tr>td>/td>td> $$$    O_{2,1} \ln \Big( \frac{ (O_{2,1}+O_{2,2}) \cdot (O_{1,1}+O_{2,1}) }{ O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} } \Big)  +                         O_{2,2} \ln \Big( \frac{ (O_{2,1}+O_{2,2}) \cdot (O_{1,2}+O_{2,2}) }{ O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} } \Big)                   \bigg)            \Bigg) $$$/td>/tr>/table>br />Another log equivalence gives us this:br />table>tr>td>$$$ G  2 \Bigg( $$$ /td>td>$$$\bigg( O_{1,1} \ln(O_{1,1}) +                          O_{1,2} \ln(O_{1,2}) +                         O_{2,1} \ln(O_{2,1}) +                         O_{2,2} \ln(O_{1,2}) \bigg) - $$$/td>/tr>tr>td>/td>td> $$$                   \bigg(                         O_{1,1} \ln (  (O_{1,1}+O_{1,2}) \cdot (O_{1,1}+O_{2,1}) ) - O_{1,1} \ln ( O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} )  + $$$/td>/tr>tr>td>/td>td> $$$    O_{1,2} \ln (  (O_{1,1}+O_{1,2}) \cdot (O_{1,2}+O_{2,2}) ) - O_{1,2} \ln ( O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} )  + $$$/td>/tr>tr>td>/td>td> $$$    O_{2,1} \ln (  (O_{2,1}+O_{2,2}) \cdot (O_{1,1}+O_{2,1}) ) - O_{2,1} \ln ( O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} )  + $$$/td>/tr>tr>td>/td>td> $$$    O_{2,2} \ln (  (O_{2,1}+O_{2,2}) \cdot (O_{1,2}+O_{2,2}) ) - O_{2,2} \ln ( O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} )                   \bigg)            \Bigg) $$$/td>/tr>/table>br />Group common factor of $$$\ln ( O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2} )$$$:br />table>tr>td>$$$ G  2 \Bigg( $$$/td>td>$$$ \bigg( O_{1,1} \ln(O_{1,1}) +                          O_{1,2} \ln(O_{1,2}) +                         O_{2,1} \ln(O_{2,1}) +                         O_{2,2} \ln(O_{1,2}) \bigg) +$$$/td>/tr>tr>td>/td>td> $$$                   \bigg( (O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2}) \cdot \ln(O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2})                                              \bigg) - $$$/td>/tr>tr>td>/td>td> $$$                   \bigg(                         O_{1,1} \ln \big(  (O_{1,1}+O_{1,2}) \cdot (O_{1,1}+O_{2,1}) \big) +                         O_{1,2} \ln \big(  (O_{1,1}+O_{1,2}) \cdot (O_{1,2}+O_{2,2}) \big) + $$$/td>/tr>tr>td>/td>td> $$$    O_{2,1} \ln \big(  (O_{2,1}+O_{2,2}) \cdot (O_{1,1}+O_{2,1}) \big) +                         O_{2,2} \ln \big(  (O_{2,1}+O_{2,2}) \cdot (O_{1,2}+O_{2,2}) \big)                   \bigg)            \Bigg) $$$/td>/tr>/table>br />More log equivalences:br />table>tr>td>$$$ G  2 \Bigg( $$$/td>td>$$$ \bigg( O_{1,1} \ln(O_{1,1}) +                          O_{1,2} \ln(O_{1,2}) +                         O_{2,1} \ln(O_{2,1}) +                         O_{2,2} \ln(O_{1,2}) \bigg) + $$$/td>/tr>tr>td>/td>td> $$$                     \bigg( (O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2}) \cdot \ln(O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2})                                              \bigg) -$$$/td>/tr>tr>td>/td>td> $$$                    \bigg(                         O_{1,1} \ln (O_{1,1}+O_{1,2}) +                         O_{1,1} \ln (O_{1,1}+O_{2,1}) +                         O_{1,2} \ln (O_{1,1}+O_{1,2}) +                         O_{1,2} \ln (O_{1,2}+O_{2,2}) + $$$/td>/tr>tr>td>/td>td> $$$    O_{2,1} \ln (O_{2,1}+O_{2,2}) +                         O_{2,1} \ln (O_{1,1}+O_{2,1}) +                          O_{2,2} \ln (O_{2,1}+O_{2,2}) +                         O_{2,2} \ln (O_{1,2}+O_{2,2})                   \bigg)            \Bigg) $$$/td>/tr>/table>br />Group common factors of $$$\ln (O_{1,1}+O_{1,2})$$$, $$$\ln (O_{1,1}+O_{2,1})$$$ etc. Yielding:br />table>tr>td>$$$ G  2 \Bigg( $$$/td>td>$$$ \bigg( O_{1,1} \ln(O_{1,1}) +                          O_{1,2} \ln(O_{1,2}) +                         O_{2,1} \ln(O_{2,1}) +                         O_{2,2} \ln(O_{1,2}) \bigg) $$$/td>/tr>tr>td>/td>td> $$$ +                   \bigg( (O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2}) \cdot \ln(O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2})                                              \bigg) $$$/td>/tr>tr>td>/td>td> $$$ -                   \bigg(                         (O_{1,1} + O_{1,2}) \ln (O_{1,1}+O_{1,2}) +                         (O_{2,1} + O_{2,2}) \ln (O_{2,1}+O_{2,2})                   \bigg) $$$/td>/tr>tr>td>/td>td> $$$ -                   \bigg(                         (O_{1,1} + O_{2,1}) \ln (O_{1,1}+O_{2,1}) +                         (O_{1,2} + O_{2,2}) \ln (O_{1,2}+O_{2,2})                   \bigg)            \Bigg) $$$/td>/tr>/table>br />We can then summarise the four parts of the above equation as follows:br />$$$$ celltotals  O_{1,1} \ln(O_{1,1}) +                          O_{1,2} \ln(O_{1,2}) +                         O_{2,1} \ln(O_{2,1}) +                         O_{2,2} \ln(O_{1,2}) $$$$$$$$ total  (O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2}) \ln(O_{1,1} + O_{1,2} + O_{2,1} + O_{2,2})  $$$$$$$$ rowtotals  (O_{1,1} + O_{1,2}) \ln (O_{1,1}+O_{1,2}) +                         (O_{2,1} + O_{2,2}) \ln (O_{2,1}+O_{2,2}) $$$$$$$$ columntotals  (O_{1,1} + O_{2,1}) \ln (O_{1,1}+O_{2,1}) +                         (O_{1,2} + O_{2,2}) \ln (O_{1,2}+O_{2,2}) $$$$where:$$$$ G  2 \big(celltotals + total - (rowtotals + columntotals) \big) $$$$If we assign $$$a  O_{1,1}, b  O_{1,2}, c  O_{2,1}, d  O_{2,2}$$$ then we can then implement as follows in Python:br />br />pre classbrush: python;>import mathdef flnf(f):    return f*math.log(f) if f>0.5 else 0def gtest(a,b,c,d):    row1  a+b    row2  c+d    col1  a+c    col2  b+d        total  flnf(a+b+c+d)    celltotals  flnf(a)+flnf(b)+flnf(c)+flnf(d)    rowtotals  flnf(row1)+flnf(row2)    coltotals  flnf(col1)+flnf(col2)        return 2*(celltotals + total-(rowtotals+coltotals))/pre>br />br />We then probably want to convert our G-value into a P-value.  The G-test approximates a chi squared distribution and has the same number of degrees of freedom.br />br />If the calculated a hrefhttps://en.wikipedia.org/wiki/Chi-squared_distribution#Cumulative_distribution_function>chi-squared distribution cumulative distribution function/a> is equal to exactly 1 (i.e. a p-value of exactly 0) then we increase the precision and try again.  This means that we can find the correct order of magnitude for our p-value (which is good for when we FDR correct these p-values later on) while minimising the number of calculations we need to do (the majority of conversions dont need 4000 decimal places computed). ($$$g$$$ is the G-value and $$$df$$$ is the degrees of freedom - 1 for a 2x2 table).br />br />pre classbrush: python;>import mpmathdef mpmathcdf(g,df,dps10):    mpmath.mp.dps  dps        x,k  mpmath.mpf(g), mpmath.mpf(df)    cdf  mpmath.gammainc(k/2, 0, x/2, regularizedTrue)        # floating point precision insufficient, use more precision    if cdf  1.0:        if dps > 4000:            return cdf # give up after a certain point        else:            cdf  mpmathcdf(g,df,dps*2)    return cdfdef GtoP(g,df):    assert g > 0, g    return float(1-mpmathcdf(g,df))/pre>br />br />b>Update:/b>br />br />Following on from the comments below Ive written up a generalised version of the G-test for any sized contingency table which uses the trick from above.  Ive not proven explicitly that this is necessarily generalisable for any sized table but Im pretty sure it is.pre classbrush: python;>def gtest(a):    rowtotals      coltotals  0*len(a0)    cells      for row in a:        rowtotals.append(sum(row))        for index,col in enumerate(row):            coltotalsindex + col            cells.append(col)    return 2*(math.fsum(flnf(x) for x in cells) + flnf(sum(cells)) - ( math.fsum(flnf(x) for x in rowtotals) + math.fsum(flnf(x) for x in coltotals) ))/pre>br />For a table with 2 columns and 3 rows this can then be called as follows:br />pre>gtest(268,807,       199,759,       42,184)> 7.300817075862142/pre>br />Again, because Ive not proven this will always work it should, of course, be used at your own risk.  That said, the same technique is used for up to 10 columns and 50 rows in the a hrefhttp://udel.edu/~mcdonald/statgtestind.xls>G-test spreadsheet/a> at the a hrefhttp://udel.edu/~mcdonald/statgtestind.html>Handbook for Biological Statistics/a> so its probably safe at least that far.div styleclear: both;>/div>/div>div classpost-footer>div classpost-footer-line post-footer-line-1>span classpost-author vcard>Posted byspan classfn itempropauthor itemscopeitemscope itemtypehttp://schema.org/Person>span itempropname>McBryan/span>/span>/span>span classpost-timestamp>atmeta contenthttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-python.html itempropurl/>a classtimestamp-link hrefhttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-python.html relbookmark titlepermanent link>abbr classpublished itempropdatePublished title2013-07-09T12:04:00+01:00>12:04/abbr>/a>/span>span classpost-comment-link>a classcomment-link hrefhttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-python.html#comment-form onclick>5 comments:  /a>/span>span classpost-icons>span classitem-control blog-admin pid-213027344>a hrefhttps://www.blogger.com/post-edit.g?blogID5657701209880344284&postID5148735681642524482&frompencil titleEdit Post>img alt classicon-action height18 srchttps://resources.blogblog.com/img/icon18_edit_allbkg.gif width18/>/a>/span>/span>div classpost-share-buttons goog-inline-block>a classgoog-inline-block share-button sb-email hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5148735681642524482&targetemail target_blank titleEmail This>span classshare-button-link-text>Email This/span>/a>a classgoog-inline-block share-button sb-blog hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5148735681642524482&targetblog onclickwindow.open(this.href, _blank, height270,width475); return false; target_blank titleBlogThis!>span classshare-button-link-text>BlogThis!/span>/a>a classgoog-inline-block share-button sb-twitter hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5148735681642524482&targettwitter target_blank titleShare to X>span classshare-button-link-text>Share to X/span>/a>a classgoog-inline-block share-button sb-facebook hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5148735681642524482&targetfacebook onclickwindow.open(this.href, _blank, height430,width640); return false; target_blank titleShare to Facebook>span classshare-button-link-text>Share to Facebook/span>/a>a classgoog-inline-block share-button sb-pinterest hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5148735681642524482&targetpinterest target_blank titleShare to Pinterest>span classshare-button-link-text>Share to Pinterest/span>/a>/div>/div>div classpost-footer-line post-footer-line-2>span classpost-labels>Labels:a hrefhttp://blog.mcbryan.co.uk/search/label/contingency%20table reltag>contingency table/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/cumulative%20distribution%20function reltag>cumulative distribution function/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/expected%20value reltag>expected value/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/g%20test reltag>g test/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/g-test reltag>g-test/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/gtest reltag>gtest/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/observed%20value reltag>observed value/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/p-value reltag>p-value/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/python reltag>python/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/shortcut reltag>shortcut/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/statistics reltag>statistics/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/stats reltag>stats/a>/span>/div>div classpost-footer-line post-footer-line-3>span classpost-location>/span>/div>/div>/div>/div>          /div>/div>                  div classdate-outer>        h2 classdate-header>span>Monday, 8 July 2013/span>/h2>          div classdate-posts>        div classpost-outer>div classpost hentry itempropblogPost itemscopeitemscope itemtypehttp://schema.org/BlogPosting>meta contenthttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyZGqFp-pwKfynro9y9AzqJw-xwyMr0YO2Sp3jz3ZU_BazsGqYqkp-0gh-PpH7iE0heWLq1DUD5ffacdmJMghwZvb4OhYIUR7FrdO3n5m4uWzDM_1nGqLdJkwWnf0yeTAnBrgslLrfvvok/s320/overlaytracks.png itempropimage_url/>meta content5657701209880344284 itempropblogId/>meta content5379218744208837827 itemproppostId/>a name5379218744208837827>/a>h3 classpost-title entry-title itempropname>a hrefhttp://blog.mcbryan.co.uk/2013/07/bisulphite-sequencing-simple.html>Bisulphite Sequencing Simple Visualisation (Multiple Samples)/a>/h3>div classpost-header>div classpost-header-line-1>/div>/div>div classpost-body entry-content idpost-body-5379218744208837827 itempropdescription articleBody>center>b>This is Part 3 in a series on Bisulphite Sequencing.br />You can return to a hrefhttp://blog.mcbryan.co.uk/2013/02/the-binomial-distribution-python-and.html>Part 2 (Using the Binomial Distribution in Bisulphite Sequencing)/a>./b> or skip to b>a hrefhttp://blog.mcbryan.co.uk/2013/07/the-g-test-and-bisulphite-sequencing.html>Part 4 (The G Test and Bisulphite Sequencing DMRs)/a>./b>/center>br />br />Jumping back to bisulphite sequencing analysis for a bit.  After we have summarised our data by individual CpG we probably want to do something useful with it.br />br />First up, lets just display it on the a hrefhttp://genome.ucsc.edu/ target_blank>UCSC genome browser/a>.  When we display bisulphite sequening data on UCSC we probably want something like this below: br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyZGqFp-pwKfynro9y9AzqJw-xwyMr0YO2Sp3jz3ZU_BazsGqYqkp-0gh-PpH7iE0heWLq1DUD5ffacdmJMghwZvb4OhYIUR7FrdO3n5m4uWzDM_1nGqLdJkwWnf0yeTAnBrgslLrfvvok/s1600/overlaytracks.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height62 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyZGqFp-pwKfynro9y9AzqJw-xwyMr0YO2Sp3jz3ZU_BazsGqYqkp-0gh-PpH7iE0heWLq1DUD5ffacdmJMghwZvb4OhYIUR7FrdO3n5m4uWzDM_1nGqLdJkwWnf0yeTAnBrgslLrfvvok/s320/overlaytracks.png width320 /> /a>/div>div classseparator styleclear: both; text-align: center;>br />/div>div classseparator styleclear: both; text-align: left;>We also want to filter out low confidence CpGs (those with less than a certain number of reads). bismarkToBedGraph does something pretty much like this./div>div classseparator styleclear: both; text-align: left;>br />/div>div classseparator styleclear: both; text-align: left;>However, it is important that when we filter a particular CpG from any given sample we should also filter it from the other samples displayed at the same time - otherwise we give a misleading indication that there is 0% methylation in the filtered sample and a non-negative amount of methylation in the unfiltered sample./div>div classseparator styleclear: both; text-align: left;>br />/div>div classseparator styleclear: both; text-align: left;>To address this I made a short script that can take multiple replicates/samples of bisulphite sequencing data, summarised by individual CpGs, and output bedGraph files such that the same CpGs are always reported based on coverage./div>div classseparator styleclear: both; text-align: left;>br />/div>pre classbrush: python;>import getoptimport sysimport csvfrom itertools import izip_longestclass CommentException(Exception):    passdef grouper(n, iterable, fillvalueNone):    grouper(3, ABCDEFG, x) --> ABC DEF Gxx    args  iter(iterable) * n    return izip_longest(fillvaluefillvalue, *args)def unpackLine(chrm,coord,*data):    return chrm.strip(), int(coord), int(d) for d in datadef extractLine(line):    if line0.startswith(#):        raise CommentException()    chrm,coord,data  unpackLine(*line)    if not chrm.startswith(chr):        chrm  chr+chrm    return (chrm,coord,data)    if __name__  __main__:    try:        opts, args  getopt.getopt(sys.argv1:, , combined,suffixes)    except getopt.GetoptError, err:        # print help information and exit:        print str(err) # will print something like option -a not recognized        sys.exit(2)        infile  None    suffixes  None    rightsuffix  None        for o, a in opts:        if o--combined:            infile  a            print combined, a        elif o--suffixes:            suffixes  a.split(,)            print Suffix, suffixes        assert infile ! None    assert suffixes ! None        methfile  csv.reader(open(infile, r), delimiter\t)        files  {}        for suffix in suffixes:        percentage  csv.writer(open(infile+-+suffix+.percent.bedGraph,w),delimiter\t)        coverage  csv.writer(open(infile+-+suffix+.coverage.bedGraph,w),delimiter\t)        filessuffix(percentage,coverage)        # ---    # for each    # coverage    # percentage        minReadsForPercentage  5    minSamplesWithCoverage  1    for line in methfile:        try:            (chrm,coord,data)  extractLine(line)        except CommentException:            continue                percentages          coverages                  for meth,unmeth in grouper(2,data):            coverage  meth + unmeth            if coverage  0:                percentage  0            else:                           percentage  (float(meth)/float(meth+unmeth)) * 100.0            percentages.append(percentage)            coverages.append(coverage)            satisfycoveragecriteria  0        for coverage in coverages:            if coverage > minReadsForPercentage:                satisfycoveragecriteria + 1        if satisfycoveragecriteria < minSamplesWithCoverage:            continue        for index,(percentage,coverage) in enumerate(izip_longest(percentages,coverages)):                        percentfile,coveragefile  filessuffixesindex            percentfile.writerow(chrm,coord,coord+1,percentage)            coveragefile.writerow(chrm,coord,coord+1,coverage)            /pre>br />Executed as:br />br />pre classbrush: bash;>python bisulphiteToBedGraph.py \--combined Samples.1.and.2.CpG_context.aggregate \--suffixes Sample1,Sample2,Sample3,Sample4 /pre>br />You can then use a hrefhttp://hgdownload.cse.ucsc.edu/admin/exe/>bedGraphToBigWig/a> to create bigWig files suitable for UCSC custom track / track hubs.div styleclear: both;>/div>/div>div classpost-footer>div classpost-footer-line post-footer-line-1>span classpost-author vcard>Posted byspan classfn itempropauthor itemscopeitemscope itemtypehttp://schema.org/Person>span itempropname>McBryan/span>/span>/span>span classpost-timestamp>atmeta contenthttp://blog.mcbryan.co.uk/2013/07/bisulphite-sequencing-simple.html itempropurl/>a classtimestamp-link hrefhttp://blog.mcbryan.co.uk/2013/07/bisulphite-sequencing-simple.html relbookmark titlepermanent link>abbr classpublished itempropdatePublished title2013-07-08T15:06:00+01:00>15:06/abbr>/a>/span>span classpost-comment-link>a classcomment-link hrefhttp://blog.mcbryan.co.uk/2013/07/bisulphite-sequencing-simple.html#comment-form onclick>No comments:  /a>/span>span classpost-icons>span classitem-control blog-admin pid-213027344>a hrefhttps://www.blogger.com/post-edit.g?blogID5657701209880344284&postID5379218744208837827&frompencil titleEdit Post>img alt classicon-action height18 srchttps://resources.blogblog.com/img/icon18_edit_allbkg.gif width18/>/a>/span>/span>div classpost-share-buttons goog-inline-block>a classgoog-inline-block share-button sb-email hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5379218744208837827&targetemail target_blank titleEmail This>span classshare-button-link-text>Email This/span>/a>a classgoog-inline-block share-button sb-blog hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5379218744208837827&targetblog onclickwindow.open(this.href, _blank, height270,width475); return false; target_blank titleBlogThis!>span classshare-button-link-text>BlogThis!/span>/a>a classgoog-inline-block share-button sb-twitter hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5379218744208837827&targettwitter target_blank titleShare to X>span classshare-button-link-text>Share to X/span>/a>a classgoog-inline-block share-button sb-facebook hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5379218744208837827&targetfacebook onclickwindow.open(this.href, _blank, height430,width640); return false; target_blank titleShare to Facebook>span classshare-button-link-text>Share to Facebook/span>/a>a classgoog-inline-block share-button sb-pinterest hrefhttps://www.blogger.com/share-post.g?blogID5657701209880344284&postID5379218744208837827&targetpinterest target_blank titleShare to Pinterest>span classshare-button-link-text>Share to Pinterest/span>/a>/div>/div>div classpost-footer-line post-footer-line-2>span classpost-labels>Labels:a hrefhttp://blog.mcbryan.co.uk/search/label/bedGraph reltag>bedGraph/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bismark reltag>bismark/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bisulfite reltag>bisulfite/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bisulfite%20sequencing reltag>bisulfite sequencing/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bisulphite reltag>bisulphite/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bisulphite%20sequencing reltag>bisulphite sequencing/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bs-seq reltag>bs-seq/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/bsseq reltag>bsseq/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/genome%20browser reltag>genome browser/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/methylation reltag>methylation/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/next%20generation%20sequencing reltag>next generation sequencing/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/python reltag>python/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/UCSC reltag>UCSC/a>,a hrefhttp://blog.mcbryan.co.uk/search/label/visualisation reltag>visualisation/a>/span>/div>div classpost-footer-line post-footer-line-3>span classpost-location>/span>/div>/div>/div>/div>          /div>/div>                  div classdate-outer>        h2 classdate-header>span>Wednesday, 19 June 2013/span>/h2>          div classdate-posts>        div classpost-outer>div classpost hentry itempropblogPost itemscopeitemscope itemtypehttp://schema.org/BlogPosting>meta contenthttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOV2pGzUOcnehGFfgApWcjZIsE4U2uky1iE1lNhPUBmXJr3xyx_cNkSXSUI1KR_yJamNb8Ta6iFxndemP7iLxVuTzowIefyVzhkS3EPffH18pbcV8fMmPopXZci54W7BZ2tBcFlGLoX603/s320/standardcurve.png itempropimage_url/>meta content5657701209880344284 itempropblogId/>meta content6224761136227837231 itemproppostId/>a name6224761136227837231>/a>h3 classpost-title entry-title itempropname>a hrefhttp://blog.mcbryan.co.uk/2013/06/qpcr-normalisation.html>qPCR normalisation/a>/h3>div classpost-header>div classpost-header-line-1>/div>/div>div classpost-body entry-content idpost-body-6224761136227837231 itempropdescription articleBody>This post will discuss the normalisation of qPCR results using both the Delta Delta CT (Livak) and Standard Curve (Pfaffl) methods as applied to qPCR of RNA and ChIP.  It will also discuss some of the common pitfalls when considering replicates of qPCR data.br />br />While this isnt a cutting edge technique, the motivation for this post is the number of qPCR spreadsheets I see that do this wrongly.br />br />h2>Delta Delta CT /h2>br />The Livak method is more commonly known as the Delta Delta CT (ΔΔCT). The Delta Delta CT method makes one important assumption about the PCR, namely, the amplification efficiencies of the reference control gene and the target gene of interest must be approximately equal.  Specifically Delta Delta CT assumes that each PCR cycle will exactly double the amount of material in your sample (amplification efficiency  100%).br />br />$$$ ΔΔCT  ΔCT (treated sample) - ΔCT (untreated sample) $$$br />br />where $$$ ΔCT(sample)  CT(target) - CT(ref) $$$, thereforebr />br />$$$ ΔΔCT  (CT(target,untreated) - CT(ref,untreated)) - (CT(target,treated) - CT(ref,treated)) $$$br />br />wherebr />br />$$$CT(target,untreated)$$$  CT value of gene of interest in untreated samplebr />$$$CT(ref,untreated)$$$  CT value of control gene in untreated samplebr />$$$CT(target,treated)$$$  CT value of gene of interest in treated samplebr />$$$CT(ref,treated)$$$   CT value of control gene in treated samplebr />br />We can then calculate the ratio of our target gene in our treated sample relative to our untreated sample by taking $$$2^{ΔΔCT}$$$.br />br />A quick worked example:br />br />table aligncenter border1>tbody>tr>td>/td>th>Untreated/th>th>Treated/th>/tr>tr>th>Ref Gene/th>td styletext-align: center;>16.17/td>td styletext-align: center;>15.895/td>/tr>tr>th>Target Gene/th>td styletext-align: center;>21.225/td>td styletext-align: center;>19.763/td>/tr>/tbody>/table>br />br />$$$$ΔΔCT  (CT(target,untreated) - CT(ref,untreated)) - (CT(target,treated) - CT(ref,treated))$$$$br />$$$$ΔΔCT  (21.225 - 16.17) - (19.763 - 15.895)$$$$br />$$$$ΔΔCT  (5.055) - (3.868)$$$$br />$$$$ΔΔCT  1.187$$$$br />$$$$2^{ΔΔCT}  2^{1.187}  2.277$$$$br />br />So our gene of interest is increased by 2.277 times in our treated sample versus our untreated sample.br />br />The exact order that you do the subtraction in actually doesnt make a huge difference and youll probably see other people do it slightly differently.  Consider these possibilities:br />br />b>ΔUntreated vs ΔTreated/b>br />br />$$$ΔΔCT  (CT(target,untreated) - CT(ref,untreated)) - (CT(target,treated) - CT(ref,treated))$$$br />$$$ΔΔCT  (21.225 - 16.17) - (19.763 - 15.895)$$$br />$$$ΔΔCT  1.187$$$br />br />$$$ΔΔCT  (CT(ref,treated) - CT(target,treated)) - (CT(ref,untreated) - CT(target,untreated))$$$br />$$$ΔΔCT  (15.895 - 19.763) - (16.17 - 21.225)$$$br />$$$ΔΔCT  1.187$$$br />br />$$$ΔΔCT  (CT(ref,untreated) - CT(target,untreated)) - (CT(ref,treated) - CT(target,treated))$$$br />$$$ΔΔCT  (16.17 - 21.225) - (15.895 - 19.763)$$$br />$$$ΔΔCT  -1.187$$$br />br />$$$ΔΔCT  (CT(target,treated) - CT(ref,treated)) - (CT(target,untreated) - CT(ref,untreated))$$$br />$$$ΔΔCT  (19.763 - 15.895) - (21.225 - 16.17)$$$br />$$$ΔΔCT  -1.187$$$br />br />br />b>ΔReference Gene vs ΔTarget Gene/b>br />br />br />$$$ΔΔCT  (CT(target,untreated) - CT(target,treated)) - (CT(ref,untreated) - CT(ref,treated))$$$br />$$$ΔΔCT  (21.225 - 19.763) - (16.17 - 15.895)$$$br />$$$ΔΔCT  1.187$$$br />br />$$$ΔΔCT  (CT(ref,treated) - CT(ref,untreated)) - (CT(target,treated) - CT(target,untreated))$$$br />$$$ΔΔCT  (15.895 - 16.17) - (19.763 - 21.225)$$$br />$$$ΔΔCT  1.187$$$br />br />$$$ΔΔCT  (CT(ref,untreated) - CT(ref,treated)) - (CT(target,untreated) - CT(target,treated))$$$br />$$$ΔΔCT  (16.17 - 15.895) - (21.225 - 19.763)$$$br />$$$ΔΔCT  -1.187$$$br />br />$$$ΔΔCT  (CT(target,treated) - CT(target,untreated)) - (CT(ref,treated) - CT(ref,untreated))$$$br />$$$ΔΔCT  (19.763 - 21.225) - (15.895 - 16.17)$$$br />$$$ΔΔCT  -1.187$$$br />br />As long as you stay consistent with the two ΔCT subtractions (i.e. always subtract treated from untreated, or reference gene from control gene, or vice versa) then the magnitude of the ΔΔCT part will always be the same.  The only thing that will change is the sign.br />br />This is why youll see some people will calculate the expression ratio as $$$2^{ΔΔCT}$$$ and others will do it as $$$2^{-ΔΔCT}$$$.  The difference is basically just how they set up their initial equation - effectively which direction they are comparing the samples.br />br />To see why Delta Delta CT actually works we have to consider whats actually going on under the hood.br />br />The absolute amount of material that we obtain through PCR for each sample for each primer pair is inversely proportional to $$$2^{CT}$$$.  We normalise our genes to a reference gene within each sample to ensure that we dont have any systematic errors due to differences between each sample (an internal control).br />br />So the ratio of target gene to reference gene in each sample is therefore $$$2^{CT(target)} / 2^{CT(ref)}$$$.br />br />However, because $$$\frac{b^c}{b^d}  b^{c-d}$$$ we can rewrite this as $$$2^{CT(target) - CT(ref)}$$$.br />br />We then calculate the ratio between our two sample by calculating the quotient between the ratio of target gene to reference gene between the two samples as such:br />br />$$$$Ratio  {2^{CT(target,untreated) - CT(ref,untreated)} \over 2^{CT(target,treated) - CT(ref,treated)}}$$$$br />br />which by the same identity rule we applied before equals our ΔΔCT equation:br />br />$$$(CT(target,untreated) - CT(ref,untreated)) - (CT(target,treated) - CT(ref,treated))$$$.br />br />br />h2>Standard Curve/h2>An improvement to the Delta Delta CT method was introduced by Pfaffl to account for PCR efficiency curves deviating from the theoretical 100% efficient reaction.br />br />To measure how efficient our PCR is for a given amplicon we run a template dilution series and see how closely our idealised PCR compares to real life.br />br />If we run a dilution series of (0.25, 0.5, 1, 2) we would expect that there would be a one CT difference between each sample in the ideal 100% efficient reaction as shown:br />br />table aligncenter>tbody>tr>th styletext-align: center;>CT Value/th>th styletext-align: center;>Concentration/th>/tr>tr>td styletext-align: center;>36/td>td styletext-align: center;>0.25/td>/tr>tr>td styletext-align: center;>35/td>td styletext-align: center;>0.5/td>/tr>tr>td styletext-align: center;>34/td>td styletext-align: center;>1/td>/tr>tr>td styletext-align: center;>33/td>td styletext-align: center;>2/td>/tr>/tbody>/table>br />However, if our actual measured CT values indicate a larger difference then our PCR reaction has been less efficient than we hoped.br />br />table aligncenter>tbody>tr>th styletext-align: center;>CT Value/th>th styletext-align: center;>Concentration/th>/tr>tr>td styletext-align: center;>36/td>td styletext-align: center;>0.25/td>/tr>tr>td styletext-align: center;>34.9/td>td styletext-align: center;>0.5/td>/tr>tr>td styletext-align: center;>33.8/td>td styletext-align: center;>1/td>/tr>tr>td styletext-align: center;>32.7/td>td styletext-align: center;>2/td>/tr>/tbody>/table>br />We can work out exactly how much less efficient by comparing the CT values and the log of the Concentration.br />br />We can do this on any log scale you like although commonly itll be done on either $$$log_2$$$ or $$$log_{10}$$$ scales.  The result will come out the same either way.  We will use $$$log_2$$$ from now on since it fits well with the property of PCR doublings.br />br />div classseparator styleclear: both; text-align: center;>a hrefhttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOV2pGzUOcnehGFfgApWcjZIsE4U2uky1iE1lNhPUBmXJr3xyx_cNkSXSUI1KR_yJamNb8Ta6iFxndemP7iLxVuTzowIefyVzhkS3EPffH18pbcV8fMmPopXZci54W7BZ2tBcFlGLoX603/s1600/standardcurve.png imageanchor1 stylemargin-left: 1em; margin-right: 1em;>img border0 height182 srchttps://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOV2pGzUOcnehGFfgApWcjZIsE4U2uky1iE1lNhPUBmXJr3xyx_cNkSXSUI1KR_yJamNb8Ta6iFxndemP7iLxVuTzowIefyVzhkS3EPffH18pbcV8fMmPopXZci54W7BZ2tBcFlGLoX603/s320/standardcurve.png width320 />/a>/div>br />br />What we are interested in is the slope of the trend line.  In the case above the slope is -1.1.  We can then work out the efficiency of the reaction asbr />br />$$$Efficency  2^{-1/slope}  2^{-1/-1.1}  1.878$$$br />br />Therefore, for each PCR reaction we generate 1.878 copies of our template rather than, the theoretical, 2 copies in the ideal case.  The Efficiency is often then represented as a scale between 0-1 which is obtainable by subtracting 1 from the calculated efficiency above.br />br />If we do a standard curve for each primer set we have (reference gene and target gene) then we can incorporate them into our Delta Delta CT equation to get:br />br />$$$$Ratio  {Efficency(Target)^{CT(target,untreated) - CT(target,treated)} \over Efficency(Ref)^{CT(ref,untreated) - CT(ref,treated)}}$$$$br />br />Note that the order of subtraction matters more here as we make sure that the the exponent of each calculated efficiency contains only the CTs which were produced by that primer pair. br />br />h2>ChIP-PCR/h2>Unlike in RT-PCR for gene expression quantitation, ChIP-PCR will use a single primer pair per region of interest.  However, we will then usually also include an Input sample which the ChIP sample is compared with.br />br />Input usually comprises a huge amount of DNA so it is usually necessary to take a subset of the Input as our actual sample to PCR.  The amount that is actually used may be between 1% and 10%.br />br />To account for this we should apply an a hrefhttp://www.invitrogen.com/site/us/en/home/Products-and-Services/Applications/epigenetics-noncoding-rna-research/Chromatin-Remodeling/Chromatin-Immunoprecipitation-ChIP/chip-analysis.html target_blank>input adjustment/a>.  This involves calculating a dilution factor which is equal to $$$1/ {Fraction Input}$$$.  For example if you have 1% input then your dilution factor (DF) is 1/0.01  100.  We then calculate our CT correction factor by calculating $$$log_{Efficiency}(Dilution Factor)$$$.br />br />Worked example:  5% input is a DF of 1/0.05  20.  For the standard curve described above this is a CT correction of $$$log_{1.878}(20)  4.75$$$.  This is then subtracted from each of the Input CTs before continuing as per the Standard Curve approach described above.br />br />Because we only have a single primer pair we can use the same efficiency for the PCR throughout which allows us to simplify the Standard Curve approach to $$$Efficiency^{ΔΔCT}$$$.br />br />Often youll want to represent your result as a percent of input and this can be calculated for each condition as $$$Efficiency^{ΔCT}$$$.br />br />h2>Replicates & Error Propagation/h2>One place that a number of mistakes seem to creep in is the treatment of replicates within PCR experiments.br />br />The most frequent mistake Ive seen is the use of the wrong type of mean when calculating the average ratio.  The key fact to remember is to always use the arithmetic mean on anything on a linear scale and always to use the geometric mean on anything on an exponential scale.br />br />More concisely, if its CT values (or differences thereof), then use an arithmetic mean.  If its concentration values (anything that is $$$Efficiency^{CT}$$$) then use the geometric mean.br />br />I also frequently encounter incorrect treatment of error bars.  Often people will take the standard deviation (or standard error) of concentration data, or ratios, and depict them directly in their bar charts.  However, these metrics assume normally distributed data which is only the case for the CT values themselves, not the ratios or concentrations.  Briefly, if your y axis on your chart is linear scale and your error bars are the same on both sides then this is wrong.br />br />Finally we should deal with error propagation.  The error in your experiment is composed of the errors of $$$(Untreated,Ref) + (Untreated,Target) + (Treated,Ref) + (Treated,Target)$$$.  This error will usually be more than the error implied by taking the standard error of the ΔΔCT values for each replicate.  However, for uncorrelated variables we can propagate additive errors using the formula:br />br />$$$Error(a+b)  \sqrt{ Error(a)^2 + Error(b)^2 }$$$br />br />This works well for delta delta CT as the error is just the product of multiple additive errors.  However, for standard curve approaches we also have error from the Efficiency values we calculated for our curve and this cant be expressed as an additive factor.br />br />Instead we need to use a a hrefhttp://www.gene-quantification.de/avery-rel-pcr-errors.pdf target_blank>Taylor series/a> to propogate the error.  This allows for all six sources of variance (4x CTs + 2x Efficiencies) to be included in the final error calculation.br />br />h2>Control Gene Choice/h2>One final factor is the choice of a suitable housekeeping gene as a control.  If you choose a reference housekeeping gene that changes wildly in between your untreated and treated samples then the results of your target gene compared to this gene will be wrong.br />br />One approach to reduce the effect of this is to use the geometric mean of multiple housekeeping genes as your reference instead of choosing one.  Even still, its important to carefully choose your reference genes for stability in your particular experiment.br />br />h2>Software/h2>Another approach is just to use some of the software thats out there already.  One thats well used is a hrefhttp://www.gene-quantification.de/rest-2009.html target_blank>REST/a> 2009 which supports virtually anything youll want to do.  Similarly there are open source solutions such as a hrefhttp://pyqpcr.sourceforge.net/ target_blank>pyQPCR/a>.  If you are willing to pay money you can also use something like a hrefhttp://www.biomcc.com/genex-software.html target_blank>GenEx/a>.br />br />If you do decide to make your own spreadsheet you should, at the very least, confirm that the answers you get from there are the same as the answers that you get from these programs.br />br />Ive uploaded a a hrefhttp://www.mcbryan.co.uk/blog/PCR.xls target_blank>spreadsheet/a> which illustrates most of the things Ive talked about in this post.  It has examples for calculating standard curves, ΔΔCT, Standard Curve and Input Correction for ChIP-PCR.  It also has worked examples for error propagation for both ΔΔCT (via simple additive error propagation) and for Standard Curves (via a taylor series).br />br />Realistically though, for almost all cases, and particularly anything rtPCR related, I recommend using something off the shelf like REST 2009.  There arent many reasons you need to make your own spreadsheets - unless of course you are trying to explain how PCR normalisation works in a blog post.br />br />Note that Ive previously had errors in this spreadsheet myself.  I take this as a sign of just how easy it is to make these mistakes and also a reminder that there could well be errors still lurking in this sheet (and in any other spreadsheet or software youve used). Thanks most recently to Duncan Brian (UCL) for highlighting that the SE from the Taylor Series I took from REST384 was inversely correlated to the SE of the individual components. Ive updated the sheet to include both the taylor series which matches the output of REST 384 and also the Taylor series described in the Gene Quantification Platform.br />br />h2>Referencescite class_Rm>/cite>/h2>div idgs_cit0>Gene Quantification Platform, Real Time PCR amended, A useful new approach? Statistical problems? a hrefhttp://www.gene-quantification.com/avery-rel-pcr-errors.pdf>http://www.gene-quantification.com/avery-rel-pcr-errors.pdf/a>, Last Accessed 2017.br />br />Livak, Kenneth J., and Thomas D. Schmittgen. Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the $$$2^{-ΔΔCT}$$$ Method. i>Methods/i> 25.4 (2001)./div>br />Pfaffl, Michael W. A new mathematical model for relative quantification in real-time RT–PCR. i>Nucleic Acids Research/i> 29.9 (2001).br />br />div idgs_cit0>Vandesompele, Jo, et al. 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