{"id":4950,"date":"2018-08-07T15:20:24","date_gmt":"2018-08-07T15:20:24","guid":{"rendered":"http:\/\/41j.com\/blog\/?p=4950"},"modified":"2018-08-08T01:18:57","modified_gmt":"2018-08-08T01:18:57","slug":"sequencing-with-mixtures-of-three-bases","status":"publish","type":"post","link":"https:\/\/41j.com\/blog\/2018\/08\/sequencing-with-mixtures-of-three-bases\/","title":{"rendered":"Sequencing with Mixtures of Three Bases"},"content":{"rendered":"

\"\"<\/a><\/p>\n

A previous post discussed Cygnus’ approach to sequencing<\/a>, using mixtures of bases and multiple reads of the same template. Centrillion also have a patent that appears to cover a related approach.<\/p>\n

The Cygnus approach, as described in their paper uses mixtures of 2 bases. I thought it might be interesting to work through corrections using mixtures of 3 bases. It’s possible this is covered somewhere in their supplementary info, or huge 200+ page patent. I’ve not checked and this is just for fun.<\/p>\n

There are 4 possible sets of 3 different base types: ATG, ATC, TGC and AGC. The difference between each of these sets is clearly a single base (3 bases out of ATGC in the set, and 1 left out).<\/p>\n

To recap on the previous post, a template is exposed to alternating sets (mixtures) of bases, and we measure incorporation intensity and learn how many bases incorporate (as in the same for a normal single channel unterminated sequencing chemistry). In order to process the entire strand the sets we alternate between must contain all base types. For the sets of 3 base types this is no problem, any pair of sets will contain all four base types and differ by only a single base type.<\/p>\n

There are 6 possible pairings:<\/p>\n

a ATG,ATC<\/p>\n

b ATG,TGC<\/p>\n

c ATG,AGC<\/p>\n

d ATC,TGC<\/p>\n

e ATC,AGC<\/p>\n

f TGC,AGC<\/p>\n

We could vary the order of the pairs. But we don’t really need to. Working through all possible 2bp repeats [1] it’s clear that we can accurate resolve all sequences using 3 out of the 6 alternating pairs.<\/p>\n

In all cases, one pairing supplies the base transition information. For example for the repeat ATATAT this is group f above. This is the only pairing that blocks incorporation between A and T transitions. Each pairing blocks on transitions between one of the six possible transition types (G<->C A<->T A<->G A<->C T<->G T<->C). To accurately resolve all sequences, all pairings are therefore required. In the example 2bp repeats, one pairing provides the “transition” information and 2 other pairings are required to resolve the sequence to one of the four bases.<\/p>\n

You therefore need to sequence each template six times. However, at any given base information from only 3 of the “mixture sequences” is required to resolve the strand. The other 3 sequences provide redundant information for error correction. This information could be used in a number of ways (either masking likely errored bases, taking a majority vote, or using this information in a more complex error correction model).<\/p>\n

How much sequencing does this require as compared to standard single base sequencing?<\/p>\n

Well, there will always be degenerate sequences, both in this scheme and the Cygnus approach. These sequences will require very slightly more sequencing than using a normal single base incorporation system.<\/p>\n

However we can simulate the number of cycles required (a cycle being the incorporation of a single base type, or a single mixture type). I quickly threw some code together to do this [2]. Assuming this hastily thrown together code is correct the single base incorporation scheme requires 1.481 cycles per base (or ~2.7 bases incorporated per set of 4 bases). The mix of 3 scheme described above requires 1.4905 cycles per base.<\/p>\n

So, if you just go by this, there’s very little overhead.<\/p>\n

One downside of the base mixture incorporations is that the sequencing system has to cope with longer homopolymers (or rather runs of 1 of 3 different base types). Again this is true of the approach described here, and the Cygnus system. What issues this causes, will depend on the error profile of the underlying technology.<\/p>\n

While I’ve discussed mixtures of 3 bases here, it might also be interesting to look at combinations of mixtures of 2 and 3 bases. For example you might have set pairs of ATG, and ATC. Then a set of CA and GT to resolve the ambiguity (this could be extended to create a complete sequencing system).<\/p>\n

Maybe that’s another fun project for another time.<\/p>\n

Notes<\/h2>\n

[1]<\/p>\n

\"\"<\/a><\/p>\n

[2]<\/p>\n

\r\n#include <iostream>\r\n#include <vector>\r\n#include <math.h>\r\n#include <stdlib.h>\r\n\r\nusing namespace std;\r\n\r\n\/\/ Multiple base incorporations\r\nstring s1 = "ATG";\r\nstring s2 = "ATC";\r\nstring s3 = "TGC";\r\nstring s4 = "AGC";\r\n\r\nint mix_incorp(string temp,vector<string> pair) {\r\n\r\n  int p=0;\r\n  int cycles=0;\r\n  for(int n=0;n<temp.size();) {\r\n  \r\n    for(;;) {\r\n      bool ad=false;\r\n      if(temp[n] == pair[p][0]) {n++; ad=true;}\r\n      if(temp[n] == pair[p][1]) {n++; ad=true;}\r\n      if(temp[n] == pair[p][2]) {n++; ad=true;}\r\n      if(ad==false) break;\r\n    }\r\n\r\n    cycles++; \r\n    if(p==0) p=1; else p=0;\r\n  }\r\n\r\n  return cycles;\r\n\r\n}\r\n\r\nint main() {\r\n\r\n  string temp;\r\n\r\n  \/\/ generate random sequence\r\n  for(int n=0;n<10000;n++) {\r\n    int r = rand()%4;\r\n    if(r == 0) temp += "A";\r\n    if(r == 1) temp += "T";\r\n    if(r == 2) temp += "G";\r\n    if(r == 3) temp += "C";\r\n  }\r\n\r\n  cout << "Sequence: " << temp << endl;\r\n\r\n  \/\/ Single base incorps\r\n  string order="ATGC";\r\n  int pos=0;\r\n  int cycle_count=0;\r\n  for(int n=0;n<temp.size();) {\r\n\r\n    for(;temp[n] == order[pos];) n++;\r\n   \r\n    pos++;\r\n    cycle_count++;\r\n    if(pos == order.size()) pos=0;\r\n  }\r\n  cout << "Average cycles per base, single base incorps: " << ((float)cycle_count)\/((float)temp.size()) << endl;\r\n\r\n \r\n  \/\/ Super ugly code, but functional...\r\n  vector<vector<string> > pairs(6);\r\n  pairs[0].push_back(s1); \r\n  pairs[0].push_back(s2); \r\n  pairs[1].push_back(s1); \r\n  pairs[1].push_back(s3); \r\n  pairs[2].push_back(s1); \r\n  pairs[2].push_back(s4); \r\n  pairs[3].push_back(s2); \r\n  pairs[3].push_back(s3); \r\n  pairs[4].push_back(s2); \r\n  pairs[4].push_back(s4); \r\n  pairs[5].push_back(s3); \r\n  pairs[5].push_back(s4); \r\n  \r\n  int total=0;\r\n  for(int n=0;n<6;n++) {\r\n\r\n    int count = mix_incorp(temp,pairs[n]);\r\n    total+=count;\r\n  }\r\n  cout << "Average cycles per base, mixture incorps: " << ((float)total)\/((float)temp.size()) << endl;\r\n}\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
A previous post discussed Cygnus’ approach to sequencing, using mixtures of bases and multiple reads of the same template. Centrillion also have a patent that appears to cover a related approach. The Cygnus approach, as described in their paper uses mixtures of 2 bases. I thought it might be interesting to work through corrections using […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-4950","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p1RRoU-1hQ","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/posts\/4950","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/comments?post=4950"}],"version-history":[{"count":6,"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/posts\/4950\/revisions"}],"predecessor-version":[{"id":5046,"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/posts\/4950\/revisions\/5046"}],"wp:attachment":[{"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/media?parent=4950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/categories?post=4950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/41j.com\/blog\/wp-json\/wp\/v2\/tags?post=4950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}