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Parikh vectors
1OZT_1 7CSW_1 8AVE_1 Letter Amino acid
14 3 11 V Valine
4 0 2 C Cysteine
7 3 10 H Histidine
0 5 3 M Methionine
4 4 3 F Phenylalanine
1 1 2 W Tryptophan
5 5 8 P Proline
10 6 19 S Serine
10 14 6 A Alanine
11 5 10 D Aspartic acid
25 6 15 G Glycine
9 8 10 I Isoleucine
11 2 7 K Lycine
8 4 12 T Threonine
0 3 3 Y Tyrosine
5 7 4 R Arginine
7 4 5 N Asparagine
3 4 12 Q Glutamine
10 8 5 E Glutamic acid
9 9 24 L Leucine 

1OZT_1|Chains A[auth G], B[auth H], C[auth I], D[auth J], E[auth K], F[auth L], G[auth M], H[auth N]|Superoxide dismutase [Cu-Zn]|Homo sapiens (9606)
>7CSW_1|Chains A, B|HTH cro/C1-type domain-containing protein|Pseudomonas aeruginosa PAO1 (208964)
>8AVE_1|Chains A, C|Leptin|Homo sapiens (9606)
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 \(w=f(c)\)
1OZT , Knot 72 153 0.79 36 114 148 
ATKAVCVLKGDGPVQGIINFEQKESNGPVKVWGSIKGLTEGLHGFRVHEFGDNTAGCTSAGPHFNPLSRKHGGPKDEERHVGDLGNVTADKDGVADVSIEDSVISLSGDHCIIGRTLVVHEKADDLGKGGNEESTKTGNAGSRLACGVIGIAQ
7CSW , Knot 52 101 0.79 38 85 99 
MATNGMRPIHPGEILRDEFLMEFDISPAALARALKVSAPTVNDIVREQRGISADMAIRLGRYFDTSAQFWMNLQSEYSLATAYAANGKQIEHEIEPLLAHG
8AVE , Knot 77 171 0.77 40 116 161 
AHHHHHHPGGPGSENLYFQGGSTGGVPIQKVQDDTKTLIKTIVTRINDISHTQSVSSKQKVTGLDFIPGLHPILTLSKMDQTLAVYQQILTSMPSRNVIQISNDLENLRDLLHVLAFSKSCHLPWASGLETLDSLGGVLEASGYSTEVVALSRLQGSLQDMLWQLDLSPGC

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 \(c\).

\(|P_{f(1OZT_1)}(2) \setminus P_{f(7CSW_1)}(2)|=89\), \(|P_{f(7CSW_1)}(2) \setminus P_{f(1OZT_1)}(2)|=60\). 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 1:100110110101110111010000001110111010110011011010011000110001110101100001110000001101101010001110101000110101000111001110001001101100000001011001101111110
Pair \(Z_2\) Length of longest common subsequence
1OZT_1,7CSW_1 149 3
1OZT_1,8AVE_1 144 3
7CSW_1,8AVE_1 139 3

Newick tree

 
[
	1OZT_1:74.47,
	[
		8AVE_1:69.5,7CSW_1:69.5
	]:4.97
]

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 \((0.85)(0.8)(\frac{254 }{\log_{20} 254}-\frac{101}{\log_{20}101})=48.8\)
Status Protein1 Protein2 d d1/2
Query variables 1OZT_1 7CSW_1 63 52
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]