Wheat is probably the most important crop in the world, yet it has one of the most challenging genomes. Bread wheat is a hexaploid, with three complete genomes termed A, B and D in the nucleus of each cell. Each of these genomes is almost twice of the human genome and consists of around 5,500 million letters. Several groups around the world are working towards sequencing wheat. Details of individual efforts can be found on the wiki below.
Genome sequencing projects can be generally divided into whole genome shotgun (WGS) methods or BAC by BAC methods.
WGS attempts to sequence the genome in one go, by generating a large amount of sequence data and then assembling this to produce a representation of the string of letters which make up the genome. WGS has the benefit in that it is quick and relatively inexpensive, but it is often confounded by the inability to stitch the individual sequence reads together, resulting in a poor quality assembly. This is particularly problematic for polyploids, where more than one genome is present in each cell, or where there is a substantial quantity of repetitive sequences. Wheat is a polyploid with 3 genomes, each of which is 80% repetitive, making WGS unattractive.
The alternative BAC by BAC approach requires breaking the genome down to relatively small pieces (c. 120 kbp), ordering these as a minimal tiling path, then sequencing each of the BACs in the tiling path. While sequence assembly or repetitive regions remains problematic, this approach offers the potential to produce the best quality finished genome. However, BAC by BAC sequencing of wheat is hugely expensive, time consuming and is still not guaranteed to produce a complete genome due to some regions being underrepresented in BAC libraries.
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WheatGenome.info: An integrated database and portal for wheat genome information. Kaitao Lai, Paul J Berkman, Michal Tadeusz Lorenc, Christopher Duran, Lars Smits, Sahana Manoli, Jiri Stiller, David Edwards. Plant and Cell Physiology (2012) 53(2): e2.