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Parikh vectors
2YVB_1 8WIX_1 6QFJ_1 Letter Amino acid
7 6 6 D Aspartic acid
8 15 6 L Leucine
6 9 7 K Lycine
3 8 2 F Phenylalanine
6 1 0 W Tryptophan
6 11 9 V Valine
7 2 5 T Threonine
3 4 2 Y Tyrosine
2 8 11 E Glutamic acid
12 5 2 G Glycine
1 12 1 H Histidine
6 6 11 I Isoleucine
2 6 3 P Proline
10 13 4 S Serine
11 5 4 R Arginine
14 4 2 N Asparagine
8 4 0 C Cysteine
3 2 3 Q Glutamine
2 4 1 M Methionine
12 17 5 A Alanine 

2YVB_1|Chain A|Lysozyme C|Gallus gallus (9031)
>8WIX_1|Chain A|Hemoglobin subunit alpha|Alligator mississippiensis (8496)
>6QFJ_1|Chains A, B, C, D, E, F|Magnetosome membrane protein MamB, putative Co/Zn/Cd cation transporter. Cation diffusion facilitator family|Desulfamplus magnetovallimortis (1246637)
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 \(w=f(c)\)
2YVB , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL
8WIX , Knot 71 142 0.82 40 109 138 
MVLSMEDKSNVKAIWGKASGHLEEYGAEALERMFCAYPQTKIYFPHFDMSHNSAQIRAHGKKVFSALHEAVNHIDDLPGALCRLSELHAHSLRVDPVNFKFLAHCVLVVFAIHHPSALSPEIHASLDKFLCAVSAVLTSKYR
6QFJ , Knot 46 84 0.80 36 72 81 
SHMEDYIEAIANVLEKTPSISDVKDIIARELGQVLEFEIDLYVPPDITVTTGERIKKEVNQIIKEIVDRKSTVKVRLFAAQEEL

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 \(c\).

\(|P_{f(2YVB_1)}(2) \setminus P_{f(8WIX_1)}(2)|=76\), \(|P_{f(8WIX_1)}(2) \setminus P_{f(2YVB_1)}(2)|=81\). 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 1:011100011111000110000100110110110100010001000000100001110100011000100110001001100111000101010010011001011011111000001001011101001
Pair \(Z_2\) Length of longest common subsequence
2YVB_1,8WIX_1 157 3
2YVB_1,6QFJ_1 142 3
8WIX_1,6QFJ_1 131 3

Newick tree

 
[
	2YVB_1:77.70,
	[
		6QFJ_1:65.5,8WIX_1:65.5
	]:12.20
]

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 \((0.85)(0.8)(\frac{271 }{\log_{20} 271}-\frac{129}{\log_{20}129})=44.4\)
Status Protein1 Protein2 d d1/2
Query variables 2YVB_1 8WIX_1 58 56
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]