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Parikh vectors
1TCO_1 6TED_1 1XJC_1 Letter Amino acid
9 3 3 M Methionine
17 1 6 S Serine
18 3 4 Y Tyrosine
25 4 9 D Aspartic acid
12 4 0 C Cysteine
24 1 1 F Phenylalanine
18 3 6 T Threonine
19 6 6 K Lycine
4 0 7 W Tryptophan
22 3 20 V Valine
24 1 17 A Alanine
20 1 4 N Asparagine
10 4 4 Q Glutamine
21 2 13 G Glycine
41 1 20 L Leucine
20 4 9 P Proline
18 7 14 R Arginine
25 4 14 E Glutamic acid
11 1 9 H Histidine
17 5 3 I Isoleucine 

1TCO_1|Chain A|SERINE/THREONINE PHOSPHATASE B2|Bos taurus (9913)
>6TED_12|Chain L|Uncharacterized protein|Sus scrofa (9823)
>1XJC_1|Chain A|MobB protein homolog|Geobacillus stearothermophilus (1422)
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 \(w=f(c)\)
1TCO , Knot 163 375 0.85 40 227 367 
VKAVPFPPSHRLTAKEVFDNDGKPRVDILKAHLMKEGRLEETVALRIITEGASILRQEKNLLDIDAPVTVCGDIHGQFFDLMKLFEVGGSPANTRYLFLGDYVDRGYFSIECVLYLWALKILYPKTLFLLRGNHECRHLTEYFTFKQECKIKYSERVYDACMDAFDCLPLAALMNQQFLCVHGGLSPEINTLDDIRKLDRFKEPPAYGPMCDILWSDPLEDFGNEKTQEHFTHNTVRGCSYFYSYPAVCEFLQHNNLLSILRAHEAQDAGYRMYRKSQTTGFPSLITIFSAPNYLDVYNNKAAVLKYENNVMNIRQFNCSPHPYWLPNFMDVFTWSLPFVGEKVTEMLVNVLNICSDDELGSEEDGFDGATAAAR
6TED , Knot 35 58 0.81 38 53 56 
MDTQKDVQPPKQQPMIYICGECHTENEIKSRDPIRCRECGYRIMYKKRTKRLVVFDAR
1XJC , Knot 81 169 0.82 38 121 163 
SNAMNVWQVVGYKHSGKTTLMEKWVAAAVREGWRVGTVKHHGHGGEPARPEGVDSVRHERAGAVATAVEGDGLLQLHLRRPLWRLDDVLALYAPLRLDLVLVEGYKQERHPKVVLVRSEEDWASLQHLANIRAVIAWEPLEGPLAHPVFSLADDDEYIPWLMNEVRTRT

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 \(c\).

\(|P_{f(1TCO_1)}(2) \setminus P_{f(6TED_1)}(2)|=196\), \(|P_{f(6TED_1)}(2) \setminus P_{f(1TCO_1)}(2)|=22\). 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 1:101111110001010011000101010110101100101000111011001101100000110101110101010101101101101110110000111100100101010011011110110100111101000000100010100000100000100101011001111111000110101110101001001001001001110111001110011001100000001000010100010001110011000011011010010011001000000011101101101100101000011110000011010010001010111011011010111110010011101101000001100001101101110
Pair \(Z_2\) Length of longest common subsequence
1TCO_1,6TED_1 218 3
1TCO_1,1XJC_1 186 4
6TED_1,1XJC_1 142 2

Newick tree

 
[
	1TCO_1:10.57,
	[
		1XJC_1:71,6TED_1:71
	]:38.57
]

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 \((0.85)(0.8)(\frac{433 }{\log_{20} 433}-\frac{58}{\log_{20}58})=116.\)
Status Protein1 Protein2 d d1/2
Query variables 1TCO_1 6TED_1 148 85
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]