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Parikh vectors
6PSP_1 5FBX_1 6OTA_1 Letter Amino acid
11 5 1 A Alanine
1 2 4 C Cysteine
15 7 1 I Isoleucine
5 12 3 P Proline
15 8 0 T Threonine
10 3 1 R Arginine
7 12 2 N Asparagine
8 1 0 H Histidine
18 13 1 L Leucine
5 9 0 Q Glutamine
8 5 0 M Methionine
3 5 0 F Phenylalanine
6 2 1 S Serine
1 3 0 W Tryptophan
3 7 0 Y Tyrosine
13 6 1 D Aspartic acid
19 8 0 E Glutamic acid
14 2 1 G Glycine
18 12 0 K Lycine
20 5 0 V Valine 

6PSP_1|Chains A, B, C, D, E, F|Adenylate kinase|Methanotorris igneus (2189)
>5FBX_1|Chain A|Bromodomain-containing protein 4|Homo sapiens (9606)
>6OTA_1|Chain A|Alpha-conotoxin TxIA|Conus textile (6494)
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 \(w=f(c)\)
6PSP , Knot 88 200 0.77 40 133 185 
MKNKVVVVTGVPGVGGTTLTQKTIEKLKEEGIEYKMVNFGTVMFEVAKEEGLVEDRDQMRKLDPDTQKRIQKLAGRKIAEMAKESNVIVDTHSTVKTPKGYLAGLPIWVLEELNPDIIVIVETSSDEILMRRLGDATRNRDIELTSDIDEHQFMNRCAAMAYGVLTGATVKIIKNRDGLLDKAVEELISVLKLEHHHHHH
5FBX , Knot 66 127 0.84 40 110 123 
SMNPPPPETSNPNKPKRQTNQLQYLLRVVLKTLWKHQFAWPFQQPVDAVKLNLPDYYKIIKTPMDMGTIKKRLENNYYWNAQECIQDFNTMFTNCYIYNKPGDDIVLMAEALEKLFLQKINELPTEE
6OTA , Knot 13 16 0.75 20 15 14 
GCCSRPPCIANNPDLC

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 \(c\).

\(|P_{f(6PSP_1)}(2) \setminus P_{f(5FBX_1)}(2)|=86\), \(|P_{f(5FBX_1)}(2) \setminus P_{f(6PSP_1)}(2)|=63\). 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 1:10001111011111110010000100100011000110110111011000111000001001010000010011100110110000111000001001010111111111001010111110000001110011010000010100010000110001111011101101011000011100110011011010000000
Pair \(Z_2\) Length of longest common subsequence
6PSP_1,5FBX_1 149 4
6PSP_1,6OTA_1 142 3
5FBX_1,6OTA_1 115 2

Newick tree

 
[
	6PSP_1:77.19,
	[
		6OTA_1:57.5,5FBX_1:57.5
	]:19.69
]

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 \((0.85)(0.8)(\frac{327 }{\log_{20} 327}-\frac{127}{\log_{20}127})=61.6\)
Status Protein1 Protein2 d d1/2
Query variables 6PSP_1 5FBX_1 75 63
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]