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Parikh vectors
2BDR_1 6QJG_1 7MAU_1 Letter Amino acid
8 6 16 S Serine
13 5 27 V Valine
12 15 26 G Glycine
10 11 11 I Isoleucine
10 4 17 F Phenylalanine
10 5 13 P Proline
14 2 7 H Histidine
7 1 10 M Methionine
11 9 17 A Alanine
11 7 11 R Arginine
11 4 17 D Aspartic acid
6 4 14 Q Glutamine
8 4 21 N Asparagine
12 10 9 E Glutamic acid
4 4 11 K Lycine
9 3 24 T Threonine
1 0 12 C Cysteine
15 8 29 L Leucine
1 0 3 W Tryptophan
2 2 11 Y Tyrosine 

2BDR_1|Chains A, B|Ureidoglycolate hydrolase|Pseudomonas putida (160488)
>6QJG_1|Chains A, B, C, D|Disks large homolog 4|Homo sapiens (9606)
>7MAU_1|Chains A, B|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
2BDR , Knot 83 175 0.81 40 126 168 
MRTLMIEPLTKEAFAQFGDVIETDGSDHFMINNGSTMRFHKLATVETAEPEDKAIISIFRADAQDMPLTVRMLERHPLGSQAFIPLLGNPFLIVVAPVGDAPVSGLVRAFRSNGRQGVNYHRGVWHHPVLTIEKRDDFLVVDRSGSGNNCDEHYFTEEQMLILNPHQLEHHHHHH
6QJG , Knot 52 104 0.77 36 85 101 
MGLGEEDIPREPRRIVIHRGSTGLGFNIVGGEPGEGIFISFILAGGPADLSGELRKGDQILSVNGVDLRNASHEQAAIALKNAGQTVTIIAQYKPEEYSRFEAK
7MAU , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ

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 \(c\).

\(|P_{f(2BDR_1)}(2) \setminus P_{f(6QJG_1)}(2)|=91\), \(|P_{f(6QJG_1)}(2) \setminus P_{f(2BDR_1)}(2)|=50\). 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 1:1001110110001110110110001000111001001010011010010100011101101010011101011000111001111111011111111110111011101100010011000011100111010000011110001010000000100001111010010000000
Pair \(Z_2\) Length of longest common subsequence
2BDR_1,6QJG_1 141 3
2BDR_1,7MAU_1 192 4
6QJG_1,7MAU_1 183 4

Newick tree

 
[
	7MAU_1:10.34,
	[
		2BDR_1:70.5,6QJG_1:70.5
	]:29.84
]

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 \((0.85)(0.8)(\frac{279 }{\log_{20} 279}-\frac{104}{\log_{20}104})=55.3\)
Status Protein1 Protein2 d d1/2
Query variables 2BDR_1 6QJG_1 71 56
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]