What is the "best" assembly for the popular model organisms:
- human (GRCh37 and GRCh38 are obvious, I'd pick whatever bwakit uses)
- mouse (GRCm37/GRCm38, OK)
but what about non-human/mouse ones?
- fruit fly
- E. coli
- any other idea?
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I will answer one of the points – E.coli.
TL;DR Bacteria, and in particular E.coli, are highly variable and there is usually no single best assembly. Large scale WGS studies should come with multiple assemblies for individual monophyletic clusters.
Long answer: Whereas a single reference sequence can make sense for human or mice (to a certain extent), bacteria are not the case. The variability between them even within a single species can be enormous and various lineages can contain very different genes. This is the reason why biologists usually distinguish a core genome consisting of the genes shared among a vast majority (typically 95%) of individuals within a given phylogenetic clade, (i.e., of those genes which are essential for this clade – imagine a CPU and RAM in a computer), and an accessory genome consisting of the other, unnecessary, genes – imagine a joystick in our analogy). The size of the accessory genome can vary a lot for different bacteria. For instance, Escherichia coli is said to have an open accessory genome (i.e., much bigger than the core genome; imagine a Raspberry-PI and all the extension kits) whereas Chlamydia trachomatis has a closed accessory genome (i.e., small compared to the core genome; imagine an ATM).
For species having a small accessory genome, a single reference might be sufficient. However, if a core genome is large, we can use either pan-genomes, or multiple references. The word pan-genome tends to be used for different things: the computational biologists usually use it as a representation of all genomic content in a certain phylogenetic clade (which can be mathematically modeled using finite automata, hence as graphs) whereas some biologists define it as a concatenation of all (core and accessory) genes from the clade (without considering SNPs, etc.). Unfortunately, methods for graph references (especially for read mapping) are still not sufficiently developed, therefore, researchers still have to resort to reference sequence-based methods and use either concatenated genes or multiple reference sequences.
When particular bacterial species are studied using massive whole-genome sequencing of many isolates, researchers usually cluster the isolates to monophyletic sequence clusters and infer a special reference sequence for each of these clusters (see, e.g., this example for the pneumococcus). All of the inferred references should be then published together with the paper or in a separate data paper (see, e.g., the sequences from the previous example).
Disclaimer: I am not a biologist. If anything in this post is too simplified or incorrect, please, leave me a comment and I will try to fix it. I tried to make this text accessible for my younger self.
If the programs you are using allow for it, take the most recent available genome, as it will be most likely to have the fewest errors.
Many of the well-known model organisms have an official release site (e.g. flybase for drosophila, wormbase for nematodes) from which genomes are fairly promptly propagated through to larger public databases, of which the most well-known are probably Ensembl and RefSeq Genome. There's usually enough cross-talk between the large data repositories that it doesn't matter all that much where the source is, as long as it is at least a few months since the last genome release.
The "best" assembly depends on the species. For more common species, Ensembl/UCSC/NCBI has their own version that corresponds to the most popular assembly. Usually the actual genetic sequence is identical across all of them, but the chromosome names and gene annotations will vary. If those three sources agree for a species, there is a "standard" reference.
For fruit fly specifically, FlyBase Consortium/Berkeley Drosophila Genome Project is the gold standard. Other species have their own organizations.