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Parikh vectors
8GOG_1 1FXX_1 1STS_1 Letter Amino acid
4 31 4 R Arginine
16 19 16 G Glycine
2 20 2 H Histidine
7 47 7 L Leucine
4 20 3 Q Glutamine
0 11 0 M Methionine
16 49 17 A Alanine
5 38 4 D Aspartic acid
2 21 4 K Lycine
8 13 9 S Serine
19 23 19 T Threonine
6 9 6 W Tryptophan
7 29 7 V Valine
7 27 7 N Asparagine
0 5 0 C Cysteine
5 30 5 E Glutamic acid
3 21 3 I Isoleucine
2 24 2 F Phenylalanine
1 28 2 P Proline
7 17 6 Y Tyrosine 

8GOG_1|Chains A, B|Streptavidin|Streptomyces avidinii (1895)
>1FXX_1|Chain A|EXONUCLEASE I|Escherichia coli (562)
>1STS_1|Chains A[auth B], B[auth D]|STREPTAVIDIN|Streptomyces avidinii (1895)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
8GOG , Knot 56 121 0.74 36 85 117 
DQAGITGTWYNQLGSTFIVTAGADGALTGTYESAVGNAESRYVLTGRYDSAPATDGSGTALGWTVAWKNNYRNAHSATTWSGQYVGGAEARINTQWLLTYGTTEANAWESTLVGHDTFTKV
1FXX , Knot 200 482 0.85 40 242 452 
MMNDGKQQSTFLFHDYETFGTHPALDRPAQFAAIRTDSEFNVIGEPEVFYCKPADDYLPQPGAVLITGITPQEARAKGENEAAFAARIHSLFTVPKTCILGYNNVRFDDEVTRNIFYRNFYDPYAWSWQHDNSRWDLLDVMRACYALRPEGINWPENDDGLPSFRLEHLTKANGIEHSNAHDAMADVYATIAMAKLVKTRQPRLFDYLFTHRNKHKLMALIDVPQMKPLVHVSGMFGAWRGNTSWVAPLAWHPENRNAVIMVDLAGDISPLLELDSDTLRERLYTAKTDLGDNAAVPVKLVHINKCPVLAQANTLRPEDADRLGINRQHCLDNLKILRENPQVREKVVAIFAEAEPFTPSDNVDAQLYNGFFSDADRAAMKIVLETEPRNLPALDITFVDKRIEKLLFNYRARNFPGTLDYAEQQRWLEHRRQVFTPEFLQGYADELQMLVQQYADDKEKVALLKALWQYADEIVEHHHHHH
1STS , Knot 57 123 0.74 36 85 116 
AEAGITGTWYNQLGSTFIVTAGADGALTGTYESAVGNAESRYVLTGRYDSAPATDGSGTALGWTVAWKNNYRNAHSATTWSGQYVGGAEARINTQWLLTSGTTEANAWKSTLVGHDTFTKVKP

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(8GOG_1)}(2) \setminus P_{f(1FXX_1)}(2)|=25\), \(|P_{f(1FXX_1)}(2) \setminus P_{f(8GOG_1)}(2)|=182\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:0011101010001100111011101110100001110100001101000011100101011110111000000100100101001111010100011100100010110001110001001
Pair \(Z_2\) Length of longest common subsequence
8GOG_1,1FXX_1 207 3
8GOG_1,1STS_1 8 97
1FXX_1,1STS_1 203 3

Newick tree

 
[
	1FXX_1:11.33,
	[
		8GOG_1:4,1STS_1:4
	]:11.33
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{603 }{\log_{20} 603}-\frac{121}{\log_{20}121})=140.\)
Status Protein1 Protein2 d d1/2
Query variables 8GOG_1 1FXX_1 183 112.5
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]