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Parikh vectors
8IVG_1 8VTZ_1 5LNI_1 Letter Amino acid
19 7 16 S Serine
6 0 11 W Tryptophan
12 0 2 C Cysteine
12 9 17 I Isoleucine
9 2 5 M Methionine
10 1 10 Q Glutamine
35 10 30 G Glycine
22 14 31 L Leucine
4 12 10 K Lycine
20 3 16 T Threonine
28 12 22 V Valine
24 5 24 R Arginine
16 2 8 N Asparagine
17 6 21 D Aspartic acid
4 2 17 F Phenylalanine
16 4 22 P Proline
17 2 6 Y Tyrosine
20 9 54 A Alanine
14 13 24 E Glutamic acid
10 0 13 H Histidine 

8IVG_1|Chain A|Kelch-like ECH-associated protein 1|Homo sapiens (9606)
>8VTZ_1|Chains A, B|Methionyl-tRNA synthetase beta subunit|Aquifex aeolicus (63363)
>5LNI_1|Chain A|NADH:flavin oxidoreductase|Pseudomonas putida (303)
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 \(w=f(c)\)
8IVG , Knot 128 315 0.78 40 175 270 
LHKPTQVMPCRAPKVGRLIYTAGGYFRQSLSYLEAYNPSDGTWLRLADLQVPRSGLAGCVVGGLLYAVGGRNNSPDGNTDSSALDCYNPMTNQWSPCAPMSVPRNRIGVGVIDGHIYAVGGSHGCIHHNSVERYEPERDEWHLVAPMLTRRIGVGVAVLNRLLYAVGGFDGTNRLNSAECYYPERNEWRMITAMNTIRSGAGVCVLHNCIYAAGGYDGQDQLNSVERYDVETETWTFVAPMKHRRSALGITVHQGRIYVLGGYDGHTFLDSVECYDPDTDTWSEVTRMTSGRSGVGVAVTMEPCRKQIDQQNCTC
8VTZ , Knot 56 113 0.78 34 86 109 
GPMEEKALIGIEDFLKVDLRVAKVLSAERVEGSEKLLKLTLSLGDEERTVVAGIAKYYTPEELVGKKIVIVANLKPRKIFGIESQGMILAASDGENLSVIVPDRDVKEGAKLS
5LNI , Knot 156 359 0.85 40 207 346 
SALFEPYTLKDVTLRNRIAIPPMCQYMAEDGMINDWHHVHLAGLARGGAGLLVVEATAVAPEGRITPGCAGIWSDAHAQAFVPVVQAIKAAGSVPGIQIAHAGRKASANRPWEGDDHIAADDTRGWETIAPSAIAFGAHLPKVPREMTLDDIARVKQDFVDAARRARDAGFEWIELHFAHGFLGQSFFSEHSNKRTDAYGGSFDNRSRFLLETLAAVREVWPENLPLTARFGVLEYDGRDEQTLEESIELARRFKAGGLDLLSVSVGFTIPDTNIPWGPAFMGPIAERVRREAKLPVTSAWGFGTPQLAEAALQANQLDLVSVGRAHLADPHWAYFAAKELGVEKASWTLPAPYAHWLE

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 \(c\).

\(|P_{f(8IVG_1)}(2) \setminus P_{f(8VTZ_1)}(2)|=127\), \(|P_{f(8VTZ_1)}(2) \setminus P_{f(8IVG_1)}(2)|=38\). 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 1:100100111001101101100111010001001010010010110110101100111101111110111100001010000011000011000101011101100011111101010111100101000010000100001011111100011111111001101111101000100100001000010110110010011110110001011110010001001000010000101111100000111101001010111100100110010000100001001001001001111110101000010000000
Pair \(Z_2\) Length of longest common subsequence
8IVG_1,8VTZ_1 165 3
8IVG_1,5LNI_1 182 4
8VTZ_1,5LNI_1 159 4

Newick tree

 
[
	8IVG_1:89.17,
	[
		8VTZ_1:79.5,5LNI_1:79.5
	]:9.67
]

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 \((0.85)(0.8)(\frac{428 }{\log_{20} 428}-\frac{113}{\log_{20}113})=95.2\)
Status Protein1 Protein2 d d1/2
Query variables 8IVG_1 8VTZ_1 113 77
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]