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Parikh vectors
7TRB_1 4QKI_1 3FGU_1 Letter Amino acid
10 0 23 M Methionine
13 7 19 F Phenylalanine
9 11 42 G Glycine
13 8 25 A Alanine
11 8 27 D Aspartic acid
3 6 12 C Cysteine
23 7 48 E Glutamic acid
17 10 16 H Histidine
31 7 42 L Leucine
10 4 9 P Proline
2 7 3 W Tryptophan
9 4 13 N Asparagine
10 2 37 V Valine
15 9 16 Q Glutamine
15 7 17 I Isoleucine
15 8 25 K Lycine
16 12 31 S Serine
14 7 23 T Threonine
5 4 12 Y Tyrosine
10 7 30 R Arginine 

7TRB_1|Chains A, B|Bile acid receptor|Homo sapiens (9606)
>4QKI_1|Chains A, B|C-type lectin domain family 2 member D|Homo sapiens (9606)
>3FGU_1|Chain A|Glucokinase|Homo sapiens (9606)
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 \(w=f(c)\)
7TRB , Knot 111 251 0.81 40 165 237 
MGSSHHHHHHSSGETVRFQGHMELTPDQQTLLHFIMDSYNKQRMPQEITNKILKEAFSAEENFLILTEMATNHVQVLVEFTKKLPGFQTLDHEDQIALLKGSAVEAMFLRSAEIFNKKLPSGHSDLLEARIRNSGISDEYITPMFSFYKSIGELKMTQEEYALLTAIVILSPDRQYIKDREAVEKLQEPLLDVLQKLCKIHQPENPQHFACLLGRLTELRTFNHHHAEMLMSWRVNDHKFTPLLCEIWDVQ
4QKI , Knot 65 135 0.78 38 107 126 
ITGQAACPESWIGFQRKCFYFSDDTKNWTSSQRFCDSQDADLAQVESFQELNFLLRYKGPSDHWIGLSREQGQPWKWINGTEWTRQFPILGAGECAYLNDKGASSARCYTERKWICSKSDIHVGTKHHHHHHHHG
3FGU , Knot 192 470 0.83 40 241 440 
MGHHHHHHENLYFQGMKKEKVEQILAEFQLQEEDLKKVMRRMQKEMDRGLRLETHEEASVKMLPTYVRSTPEGSEVGDFLSLDLGGTNFRVMLVKVGEGEEGQWSVKTKHQMYSIPEDAMTGTAEMLFDYISECISDFLDKHQMKHKKLPLGFTFSFPVRHEDIDKGILLNWTKGFKASGAEGNNVVGLLRDAIKRRGDFEMDVVAMVNDTVATMISCYYEDHQCEVGMIVGTGCNACYMEEMQNVELVEGDEGRMCVNTEWGAFGDSGELDEFLLEYDRLVDESSANPGQQLYEKLIGGKYMGELVRLVLLRLVDENLLFHGEASEQLRTRGAFETRFVSQVESDTGDRKQIYNILSTLGLRPSTTDCDIVRRACESVSTRAAHMCSAGLAGVINRMRESRSEDVMRITVGVDGSVYKLHPSFKERFHASVRRLTPSCEITFIESEEGSGRGAALVSAVACKKACMLGQ

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 \(c\).

\(|P_{f(7TRB_1)}(2) \setminus P_{f(4QKI_1)}(2)|=120\), \(|P_{f(4QKI_1)}(2) \setminus P_{f(7TRB_1)}(2)|=62\). 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 1:11000000000010010101010101000011011100000001100100011001101000111100110001011101000111100100000111101011011110010110001101000110101000110000101110100011010100000111011111010000100001100100111011001001001001001101110100100100001011101010000101110011010
Pair \(Z_2\) Length of longest common subsequence
7TRB_1,4QKI_1 182 6
7TRB_1,3FGU_1 172 6
4QKI_1,3FGU_1 208 6

Newick tree

 
[
	4QKI_1:10.32,
	[
		7TRB_1:86,3FGU_1:86
	]:15.32
]

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 \((0.85)(0.8)(\frac{386 }{\log_{20} 386}-\frac{135}{\log_{20}135})=75.9\)
Status Protein1 Protein2 d d1/2
Query variables 7TRB_1 4QKI_1 97 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]