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Parikh vectors
1SLF_1 7YOZ_1 1GMG_1 Letter Amino acid
6 3 1 Y Tyrosine
19 18 5 A Alanine
7 1 3 N Asparagine
5 7 7 E Glutamic acid
0 3 2 M Methionine
6 0 0 W Tryptophan
3 6 1 P Proline
12 6 3 S Serine
6 4 7 D Aspartic acid
2 3 2 H Histidine
3 7 2 I Isoleucine
7 12 10 L Leucine
6 13 3 K Lycine
4 18 4 R Arginine
0 2 2 C Cysteine
16 8 2 G Glycine
8 6 0 V Valine
4 8 3 Q Glutamine
2 4 2 F Phenylalanine
19 10 4 T Threonine 

1SLF_1|Chains A[auth B], B[auth D]|STREPTAVIDIN|Streptomyces avidinii (1895)
>7YOZ_1|Chains A, C, E, G|Histone H3.1|Homo sapiens (9606)
>1GMG_1|Chains A, B|REGULATORY PROTEIN ROP|ESCHERICHIA COLI (562)
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 \(w=f(c)\)
1SLF , Knot 64 135 0.77 36 94 128 
DPSKDSKAQVSAAEAGITGTWYNQLGSTFIVTAGADGALTGTYESAVGNAESRYVLTGRYDSAPATDGSGTALGWTVAWKNNYRNAHSATTWSGQYVGGAEARINTQWLLTSGTTEANAWKSTLVGHDTFTKVKP
7YOZ , Knot 68 139 0.80 38 107 131 
GSHMARTKQTARKSTGGKAPRKQLATKAARKSAPATGGVKKPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEACEAYLVGLFEDTNLCAIHAKRVTIMPKDIQLARRIRGERA
1GMG , Knot 36 63 0.79 36 53 60 
MTKQEKTALNMARFIRSQTLTLLEKLNELDPDEQADICESLHDHADELYRSCLARFGDDGENL

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 \(c\).

\(|P_{f(1SLF_1)}(2) \setminus P_{f(7YOZ_1)}(2)|=59\), \(|P_{f(7YOZ_1)}(2) \setminus P_{f(1SLF_1)}(2)|=72\). 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 1:010000010101101110101000110011101110111010000111010000110100001110010101111011100000010010010100111101010001110010001011000111000100101
Pair \(Z_2\) Length of longest common subsequence
1SLF_1,7YOZ_1 131 5
1SLF_1,1GMG_1 119 3
7YOZ_1,1GMG_1 118 3

Newick tree

 
[
	1SLF_1:63.71,
	[
		1GMG_1:59,7YOZ_1:59
	]:4.71
]

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 \((0.85)(0.8)(\frac{274 }{\log_{20} 274}-\frac{135}{\log_{20}135})=43.3\)
Status Protein1 Protein2 d d1/2
Query variables 1SLF_1 7YOZ_1 52 50.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]