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Parikh vectors
6NBG_1 5DRJ_1 2JZT_1 Letter Amino acid
22 13 12 V Valine
10 12 11 R Arginine
10 9 7 Q Glutamine
9 15 3 M Methionine
14 20 8 S Serine
11 9 9 P Proline
7 4 0 Y Tyrosine
1 4 0 C Cysteine
13 13 6 I Isoleucine
23 48 15 L Leucine
7 7 6 F Phenylalanine
11 13 7 H Histidine
11 14 2 K Lycine
11 9 3 N Asparagine
10 13 11 D Aspartic acid
15 15 9 E Glutamic acid
17 10 7 G Glycine
28 15 12 A Alanine
12 11 9 T Threonine
0 3 5 W Tryptophan 

6NBG_1|Chains A, B, C, D, E, F|Glucosamine-6-phosphate deaminase|Klebsiella pneumoniae (573)
>5DRJ_1|Chains A, B|Estrogen receptor|Homo sapiens (9606)
>2JZT_1|Chain A|Putative thiol-disulfide isomerase and thioredoxin|Salmonella typhimurium LT2 (99287)
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 \(w=f(c)\)
6NBG , Knot 114 242 0.86 38 169 235 
SNAMKMIVTEDYEEMSLVASHHVLGYITAPRRVNLAVTAGSTPKRMYEHLTAAVKGKAFYDRVHYYNFDEIPFRGQSREGVTISNLRQLFFTPAQIKEENIHKLTLDNAAQHDRQLEEAGGLDLMVLGLGADGHFCGNLPNTTRFHDQTVEVPIHGEMIALIANSEMGGDISAVPNSYVTMGPRSVMAAKNLLLIVSGAAKAHALKQVVEGPVSVQVPASVLKLHPSLVIIADKAAAAELQQ
5DRJ , Knot 117 257 0.84 40 165 246 
IKRSKKNSLALSLTADQMVSALLDAEPPILYSEYDPTRPFSEASMMGLLTNLADRELVHMINWAKRVPGFVDLTLHDQVHLLECAWLEILMIGLVWRSMEHPGKLLFAPNLLLDRNQGKCVEGMVEIFDMLLATSSRFRMMNLQGEEFVCLKSIILLNSGVYTFLSSTLKSLEEKDHIHRVLDKITDTLIHLMAKAGLTLQQQHQRLAQLLLILSHIRHMSNKGMEHLYSMKCKNVVPLSDLLLEMLDAHRLHAPTS
2JZT , Knot 70 142 0.81 36 107 133 
MANDTPFSALWQRLLTRGWQPVEASTVDDWIKRVGDGVILLSSDPRRTPEVSDNPVMIAELLREFPQFDWQVAVADLEQSEAIGDRFNVRRFPATLVFTDGKLRGALSGIHPWAELLTLMRSIVDTPAAQETVQLEHHHHHH

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 \(c\).

\(|P_{f(6NBG_1)}(2) \setminus P_{f(5DRJ_1)}(2)|=80\), \(|P_{f(5DRJ_1)}(2) \setminus P_{f(6NBG_1)}(2)|=76\). 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 1:00110111000000101110001110101100101110110010010001011101011000100001001110100001101001001110110100001001010011000001001111011111111010101011000010000101110101111110001110101110001011100111100111110111010110011011101011101101010111110011110100
Pair \(Z_2\) Length of longest common subsequence
6NBG_1,5DRJ_1 156 4
6NBG_1,2JZT_1 146 3
5DRJ_1,2JZT_1 158 3

Newick tree

 
[
	5DRJ_1:80.25,
	[
		6NBG_1:73,2JZT_1:73
	]:7.25
]

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 \((0.85)(0.8)(\frac{499 }{\log_{20} 499}-\frac{242}{\log_{20}242})=73.8\)
Status Protein1 Protein2 d d1/2
Query variables 6NBG_1 5DRJ_1 91 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]