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Parikh vectors
6XDT_1 3ERV_1 2VZX_1 Letter Amino acid
4 14 12 N Asparagine
11 19 19 K Lycine
7 11 12 F Phenylalanine
7 9 13 P Proline
11 14 9 S Serine
3 11 11 Y Tyrosine
13 22 17 V Valine
9 12 14 T Threonine
3 6 8 R Arginine
1 2 3 C Cysteine
1 11 6 Q Glutamine
7 17 19 G Glycine
10 8 14 H Histidine
0 14 10 I Isoleucine
1 2 3 W Tryptophan
21 10 9 A Alanine
8 13 13 D Aspartic acid
4 18 16 E Glutamic acid
18 17 17 L Leucine
2 6 6 M Methionine 

6XDT_1|Chains A, C|Hemoglobin subunit alpha|Homo sapiens (9606)
>3ERV_1|Chain A|putative C39-like peptidase|Bacillus anthracis (1392)
>2VZX_1|Chains A, B, C, D, E, F, G, H|Green fluorescent protein|Dendronephthya sp. SSAL-2002 (191210)
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 \(w=f(c)\)
6XDT , Knot 69 141 0.80 38 99 137 
VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHFDLSHGSAQVKGHGKKVADALTNAVAHVDDMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHLPAEFTPAVHASLDKFLASVSTVLTSKYR
3ERV , Knot 111 236 0.85 40 169 230 
MSLNGITKYVEKLTFFNIQSGKQVEFNRDEKVILSNVPFIQQLPELDRGCEVTSLAMMLQYAGITVDKMKLANEIKKVDFMNDGVRGNPNEGFVGNIYTFSESGYGVYHGPLFQLAKKYLPNKAVDLTGKSIEELYKSVKAGQPVVIITNATFAPLDEDEFTTWETNNGDVSITYNEHCVVLIGYDQESVYIRDPLKDSLDVKVPREKFEQAWVQMGSQAISYVKRSKEGHHHHHH
2VZX , Knot 108 231 0.84 40 166 224 
MNLIKEDMRVKVHMEGNVNGHAFVIEGEGKGKPYEGTQTANLTVKEGAPLPFSYDILTTAVHYGNRVFTKYPEDIPDYFKQSFPEGYSWERTMTFEDKGICTIRSDISLEGDCFFQNVRFKGTNFPPNGPVMQKKTLKWEPSTEKLHVRDGLLVGNINMALLLEGGGHYLCDFKTTYKAKKVVQLPDAHFVDHRIEILGNDSDYNKVKLYEHAVARYSPLPSQVWHHHHHH

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 \(c\).

\(|P_{f(6XDT_1)}(2) \setminus P_{f(3ERV_1)}(2)|=54\), \(|P_{f(3ERV_1)}(2) \setminus P_{f(6XDT_1)}(2)|=124\). 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 1:110110000101111011101100110110011101100000110101001010101010011011001110100110110110010100101011010110001110111011101011101010011101001100000
Pair \(Z_2\) Length of longest common subsequence
6XDT_1,3ERV_1 178 3
6XDT_1,2VZX_1 155 3
3ERV_1,2VZX_1 169 6

Newick tree

 
[
	3ERV_1:89.65,
	[
		6XDT_1:77.5,2VZX_1:77.5
	]:12.15
]

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 \((0.85)(0.8)(\frac{377 }{\log_{20} 377}-\frac{141}{\log_{20}141})=71.4\)
Status Protein1 Protein2 d d1/2
Query variables 6XDT_1 3ERV_1 92 73
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]