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Parikh vectors
7TKA_1 2AWU_1 1LPH_1 Letter Amino acid
2 11 0 K Lycine
6 2 0 F Phenylalanine
6 8 1 V Valine
1 3 2 Y Tyrosine
10 7 0 A Alanine
1 4 0 D Aspartic acid
1 0 4 C Cysteine
0 9 0 H Histidine
3 3 0 M Methionine
2 3 0 P Proline
1 1 0 R Arginine
9 10 2 I Isoleucine
5 6 2 S Serine
0 0 0 W Tryptophan
2 4 2 N Asparagine
1 2 2 Q Glutamine
1 7 2 E Glutamic acid
10 12 1 G Glycine
12 8 2 L Leucine
3 5 1 T Threonine 

7TKA_1|Chains A[auth 0], B[auth 1], C[auth 2], D[auth 3], E[auth 4], F[auth 5], G[auth 6], H[auth 7], I[auth 8], J[auth 9]|ATP synthase subunit 9, mitochondrial|Saccharomyces cerevisiae (4932)
>2AWU_1|Chains A, B|Synapse-associated protein 97|Rattus norvegicus (10116)
>1LPH_1|Chains A, C|INSULIN|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 \(w=f(c)\)
7TKA , Knot 40 76 0.76 36 57 72 
MQLVLAAKYIGAGISTIGLLGAGIGIAIVFAALINGVSRNPSIKDTVFPMAILGFALSEATGLFCLMVSFLLLFGV
2AWU , Knot 52 105 0.76 36 82 100 
MEKIMEIKLIKGPKGLGFSIAGGVGNQHIPGDNSIYVTKIIEGGAAHKDGKLQIGDKLLAVNSVGLEEVTHEEAVTALKNTSDFVYLKVAKPTSMYISRHHHHHH
1LPH , Knot 15 21 0.72 22 20 19 
GIVEQCCTSICSLYQLENYCN

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 \(c\).

\(|P_{f(7TKA_1)}(2) \setminus P_{f(2AWU_1)}(2)|=36\), \(|P_{f(2AWU_1)}(2) \setminus P_{f(7TKA_1)}(2)|=61\). 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 1:1011111001111100111111111111111111011000101000111111111110010111011101111111
Pair \(Z_2\) Length of longest common subsequence
7TKA_1,2AWU_1 97 3
7TKA_1,1LPH_1 69 2
2AWU_1,1LPH_1 96 2

Newick tree

 
[
	2AWU_1:52.03,
	[
		7TKA_1:34.5,1LPH_1:34.5
	]:17.53
]

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 \((0.85)(0.8)(\frac{181 }{\log_{20} 181}-\frac{76}{\log_{20}76})=35.1\)
Status Protein1 Protein2 d d1/2
Query variables 7TKA_1 2AWU_1 43 37
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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