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Parikh vectors
7HTC_1 5KHD_1 6VNW_1 Letter Amino acid
19 7 1 R Arginine
23 11 9 L Leucine
7 1 5 M Methionine
6 0 1 F Phenylalanine
28 3 7 T Threonine
19 7 2 D Aspartic acid
4 0 1 C Cysteine
21 6 8 E Glutamic acid
14 3 9 K Lycine
9 6 3 P Proline
7 1 0 W Tryptophan
8 3 1 Y Tyrosine
11 9 3 A Alanine
13 3 2 H Histidine
15 4 3 I Isoleucine
21 6 2 S Serine
22 7 3 V Valine
12 2 0 N Asparagine
15 7 8 Q Glutamine
21 5 1 G Glycine 

7HTC_1|Chains A, B|Oleoyl-acyl carrier protein thioesterase 1, chloroplastic|Arabidopsis thaliana (3702)
>5KHD_1|Chains A, B[auth R]|DNA-binding protein|Streptomyces venezuelae (953739)
>6VNW_1|Chain A[auth H]|Bardet-Biedl syndrome 18 protein|Bos taurus (9913)
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 \(w=f(c)\)
7HTC , Knot 131 295 0.84 40 189 276 
MGSLTEDGLSYKEKFVVRSYEVGSNKTATVETIANLLQEVGCNHAQSVGFSTDGFATTTTMRKLHLIWVTARMHIEIYKYPAWGDVVEIETWCQSEGRIGTRRDWILKDSVTGEVTGRATSKWVMMNQDTRRLQKVSDDVRDEYLVFCPQEPRLAFPEENNRSLKKIPKLEDPAQYSMIGLKPRRADLDMNQHVNNVTYIGWVLESIPQEIVDTHELQVITLDYRRECQQDDVVDSLTTTTSEIGGTNGSATSGTQGHNDSQFLHLLRLSGDGQEINRGTTLWRKKPSSHHHHHH
5KHD , Knot 49 91 0.81 36 78 88 
GSHMEPPPKLVLDLERLAHVPQEKAGPLQRYAATIQSQRGDYNGKVLSIRQDDLRTLAVIYDQSPSVLTEQLISWGVLDADARRAVAHEEN
6VNW , Knot 38 69 0.77 36 58 66 
MAETKSMFREVLPKQGQLYVEDITTMVLCKPKLLPLKSLTLEKLEKMQQAAQDTIHQQEMTEKEQKITH

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 \(c\).

\(|P_{f(7HTC_1)}(2) \setminus P_{f(5KHD_1)}(2)|=142\), \(|P_{f(5KHD_1)}(2) \setminus P_{f(7HTC_1)}(2)|=31\). 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 1:1101000110000011100001100001010011011001100010011100011100001001011110101010100011110110100100001011000011100010101010100011110000001001000100001110100101111000000100110100110001111010010101000100100111110011001100001011010000000000110010000001110010100100100000110110101010010010011000100000000
Pair \(Z_2\) Length of longest common subsequence
7HTC_1,5KHD_1 173 3
7HTC_1,6VNW_1 181 3
5KHD_1,6VNW_1 106 3

Newick tree

 
[
	7HTC_1:97.52,
	[
		5KHD_1:53,6VNW_1:53
	]:44.52
]

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 \((0.85)(0.8)(\frac{386 }{\log_{20} 386}-\frac{91}{\log_{20}91})=90.9\)
Status Protein1 Protein2 d d1/2
Query variables 7HTC_1 5KHD_1 116 74.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]