Ciro Santilli @cirosantilli 35

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Group of even permutations.

Note that odd permutations don't form a subgroup of the symmetric group like the even permutations do, because the composition of two odd permutations is an even permutation.

A quantum circuit which when fed with input $|00⟩$ produces the Bell state.

In Qiskit at: qiskit/hello.py.

UniProt entry: www.uniprot.org/uniprot/P00561.

NCBI entry: www.ncbi.nlm.nih.gov/gene/945803.

The second gene in the E. Coli K-12 MG1655 genome. Part of the E. Coli K-12 MG1655 operon thrLABC.

Part of a reaction that produces threonine.

This protein is an enzyme. The UniProt entry clearly shows the chemical reactions that it catalyses. In this case, there are actually two! It can either transforming the metabolite:Also interestingly, we see that both of those reaction require some extra energy to catalyse, one needing adenosine triphosphate and the other nADP+.

TODO: any mention of how much faster it makes the reaction, numerically?

Since this is an enzyme, it would also be interesting to have a quick search for it in the KEGG entry starting from the organism: www.genome.jp/pathway/eco01100+M00022 We type in the search bar "thrA", it gives a long list, but the last entry is our "thrA". Selecting it highlights two pathways in the large graph, so we understand that it catalyzes two different reactions, as suggested by the protein name itself (fused blah blah). We can now hover over:Note that common cofactor are omitted, since we've learnt from the UniProt entry that this reaction uses ATP.

If we can now click on the L-Homoserine edge, it takes us to: www.genome.jp/entry/eco:b0002+eco:b3940. Under "Pathway" we see an interesting looking pathway "Glycine, serine and threonine metabolism": www.genome.jp/pathway/eco00260+b0002 which contains a small manually selected and extremely clearly named subset of the larger graph!

But looking at the bottom of this subgraph (the UI is not great, can't Ctrl+F and enzyme names not shown, but the selected enzyme is slightly highlighted in red because it is in the URL www.genome.jp/pathway/eco00260+b0002 vs www.genome.jp/pathway/eco00260) we clearly see that thrA, thrB and thrC for a sequence that directly transforms "L-aspartate 4-semialdehyde" into "Homoserine" to "O-Phospho-L-homoserine" and finally tothreonine. This makes it crystal clear that they are not just located adjacently in the genome by chance: they are actually functionally related, and likely controlled by the same transcription factor: when you want one of them, you basically always want the three, because you must be are lacking threonine. TODO find transcription factor!

The UniProt entry also shows an interactive browser of the tertiary structure of the protein. We note that there are currently two sources available: X-ray crystallography and AlphaFold. To be honest, the AlphaFold one looks quite off!!!

By inspecting the FASTA for the entire genome, or by using the NCBI open reading frame tool, we see that this gene lies entirely in its own open reading frame, so it is quite boring

From the FASTA we see that the very first three Codons at position 337 arewhere ATG is the start codon, and CGA GTG should be the first two that actually go into the protein:

ecocyc.org/gene?orgid=ECOLI&id=ASPKINIHOMOSERDEHYDROGI-MONOMER mentions that the enzime is most active as protein complex with four copies of the same protein:TODO image?

Parent/predecessor of ASML.

The degree of some algebraic structure is some parameter that describes the structure. There is no universal definition valid for all structures, it is a per structure type thing.

This is particularly useful when talking about structures with an infinite number of elements, but it is sometimes also used for finite structures.

Examples: