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Parikh vectors
4AFZ_1 2VMB_1 4LHF_1 Letter Amino acid
13 8 4 V Valine
9 2 0 H Histidine
12 3 5 I Isoleucine
11 5 1 F Phenylalanine
3 0 4 W Tryptophan
15 12 7 A Alanine
7 1 0 C Cysteine
21 15 9 L Leucine
5 4 4 Y Tyrosine
14 10 6 R Arginine
9 2 2 N Asparagine
14 6 7 K Lycine
20 7 9 G Glycine
4 5 5 M Methionine
15 4 6 P Proline
14 10 5 S Serine
15 6 4 T Threonine
8 6 5 D Aspartic acid
9 7 3 Q Glutamine
8 10 5 E Glutamic acid 

4AFZ_1|Chains A, B|CHYMASE|HOMO SAPIENS (9606)
>2VMB_1|Chains A, B|GENERAL SECRETION PATHWAY PROTEIN F|VIBRIO CHOLERAE (666)
>4LHF_1|Chain A|Regulatory protein cox|Enterobacteria phage P2 (10679)
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 \(w=f(c)\)
4AFZ , Knot 111 226 0.88 40 172 221 
IIGGTECKPHSRPYMAYLEIVTSNGPSKFCGGFLIRRNFVLTAAHCAGRSITVTLGAHNITEEEDTWQKLEVIKQFRHPKYNTSTLHHDIMLLKLKEKASLTLAVGTLPFPSQFNFVPPGRMCRVAGWGRTGVLKPGSDTLQEVKLRLMDPQACSHFRDFDHNLQLCVGNPRKTKSAFKGDSGGPLLCAGVAQGIVSYGRSDAKPPAVFTRISHYRPWINQILQAN
2VMB , Knot 63 123 0.82 38 103 121 
MGFAFKRGISTPDLALITRQLATLVQSGMPLEECLRAVAEQSEKPRIRTMLVAVRAKVTEGYTLSDSLGDYPHVFDELFRSMVAAGEKSGHLDSVLERLADYAENRQKMRSKLQQASENLYFQ
4LHF , Knot 51 91 0.84 36 78 88 
MSKQVTLMTDAIPYQEFAKLIGKSTGAVRRMIDKGKLPVIDMTDPQSASGRAGEYWVYLPAWNNGLKLAYESRPKEIRDGWLMWLGLGEPR

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 \(c\).

\(|P_{f(4AFZ_1)}(2) \setminus P_{f(2VMB_1)}(2)|=120\), \(|P_{f(2VMB_1)}(2) \setminus P_{f(4AFZ_1)}(2)|=51\). 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 1:1111000010001011010110001100101111100011101100110010101110010000001001011001001000000100011110100010101111011110010111110100111110011101100010010101101010001001000101011010000011010011111011110111001000101111100100001110011010
Pair \(Z_2\) Length of longest common subsequence
4AFZ_1,2VMB_1 171 3
4AFZ_1,4LHF_1 160 3
2VMB_1,4LHF_1 139 3

Newick tree

 
[
	4AFZ_1:86.77,
	[
		4LHF_1:69.5,2VMB_1:69.5
	]:17.27
]

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 \((0.85)(0.8)(\frac{349 }{\log_{20} 349}-\frac{123}{\log_{20}123})=69.3\)
Status Protein1 Protein2 d d1/2
Query variables 4AFZ_1 2VMB_1 91 68.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]