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Parikh vectors
7QCO_1 8AQD_1 6HYF_1 Letter Amino acid
7 2 3 F Phenylalanine
16 3 7 P Proline
12 20 6 T Threonine
17 8 12 L Leucine
0 0 1 C Cysteine
4 7 7 Q Glutamine
5 6 1 K Lycine
14 9 10 V Valine
17 23 3 A Alanine
15 21 10 G Glycine
3 6 2 W Tryptophan
5 5 8 E Glutamic acid
12 10 5 N Asparagine
8 7 4 D Aspartic acid
1 2 8 H Histidine
12 4 3 I Isoleucine
3 2 2 M Methionine
8 12 10 S Serine
5 6 4 Y Tyrosine
8 5 7 R Arginine 

7QCO_10|Chains FA[auth L], J[auth S], QA[auth l], U[auth s]|Photosystem I reaction center subunit XI|Chroococcidiopsis sp. TS-821 (1378066)
>8AQD_1|Chain A|Streptavidin|Streptomyces avidinii (1895)
>6HYF_1|Chains A, B, C, D|Integrin beta-4|Rattus norvegicus (10116)
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 \(w=f(c)\)
7QCO , Knot 79 172 0.78 38 122 166 
MAQAIDASKNRPSDPRNQEVVYPSRRDPQIGNLETPINNSSLVKWFINNLPAYRPGITPLRRGLEVGMAHGYWLLGPFAKLGPLRDTDVANIAGLLATLGMVVISTLAVSLYAATDPPKPVATVTVPNPPDTFDTTEGWNTFASGFLIGGVGGAVVAYFILANIELIQNIFK
8AQD , Knot 74 158 0.79 38 108 152 
ASMTGGQQMGRDEAGITGTWYNQLGSTFIVTAGADGALTGTYESAVGNAESRYVLTGRYDSAPATDGSGTALGWTVAWKNNYRNAHSATTWSGQYVGGAEARINTQWLLTSGTTEANAWKSTLVGHDTFTKVKPSAASIDAAKKAGVNNGNPLDAVQQ
6HYF , Knot 57 113 0.79 40 85 108 
MHHHHHHSSGVDLGTENLYFQSPDTPTRLVFSALGPTSLKVSWQEPQCDRALLGYSVEYQLLNGGEMHRLNIPNPGQTSVVVEDLLPNHSYVFRVRAQSQEGWGREREGVITI

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 \(c\).

\(|P_{f(7QCO_1)}(2) \setminus P_{f(8AQD_1)}(2)|=73\), \(|P_{f(8AQD_1)}(2) \setminus P_{f(7QCO_1)}(2)|=59\). 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 1:1101101000010010000110100001011010011000011011100111001110110011011110101111111011110000110111111011111100111010110011011101011011001000011001101111111111111011110101100110
Pair \(Z_2\) Length of longest common subsequence
7QCO_1,8AQD_1 132 4
7QCO_1,6HYF_1 145 3
8AQD_1,6HYF_1 149 3

Newick tree

 
[
	6HYF_1:75.84,
	[
		7QCO_1:66,8AQD_1:66
	]:9.84
]

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 \((0.85)(0.8)(\frac{330 }{\log_{20} 330}-\frac{158}{\log_{20}158})=52.3\)
Status Protein1 Protein2 d d1/2
Query variables 7QCO_1 8AQD_1 63 59.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]