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Parikh vectors
4OGH_1 5KDT_1 4XXB_1 Letter Amino acid
13 7 3 M Methionine
17 13 8 F Phenylalanine
28 21 13 L Leucine
8 5 3 H Histidine
4 3 1 W Tryptophan
15 8 7 Q Glutamine
11 18 6 N Asparagine
5 7 4 C Cysteine
14 21 16 K Lycine
13 12 17 R Arginine
11 15 8 D Aspartic acid
12 17 14 E Glutamic acid
9 25 19 G Glycine
15 16 15 I Isoleucine
12 11 5 P Proline
17 15 7 S Serine
5 21 7 T Threonine
15 11 10 A Alanine
19 28 9 V Valine
7 11 6 Y Tyrosine 

4OGH_1|Chain A|Androgen receptor|Homo sapiens (9606)
>5KDT_1|Chain A|Glutamate receptor ionotropic, NMDA 2A|Homo sapiens (9606)
>4XXB_1|Chain A|60S ribosomal protein L11|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 \(w=f(c)\)
4OGH , Knot 121 250 0.89 40 185 243 
QPIFLNVLEAIEPGVVCAGHDNNQPDSFAALLSSLNELGERQLVHVVKWAKALPGFRNLHVDDQMAVIQYSWMGLMVFAMGWRSFTNVNSAMLYFAPDLVFNEYRMHKSRMYSQCVRMRHLSQEFGWLQITPQEFLCMKALLLFSIIPVDGLKNQKFFDELRMNYIKELDRIIACKRKNPTSCSRRFYQLTKLLDSVQPIARELHQFAFDLLIKSHMVSVDFPEMMAEIISVQVPKILSGKVKPIYFHTQ
5KDT , Knot 128 285 0.84 40 184 275 
GSPDDNHLSIVTLEEAPFVIVEDIDPLTETCVRNTVPCRKFVKINNSTNEGMNVKKCCKGFCIDILKKLSRTVKFTYDLYLVTNGKHGKKVNNVWNGMIGEVVYQRAVMAVGSLTINEERSEVVDFSVPFVETGISVMVSRGTQVTGLSDKKFQRPHDYSPPFRFGTVPNGSTERNIRNNYPYMHQYMTKFNQKGVEDALVSLKTGKLDAFIYDAAVLNYKAGRDEGCKLVTIGSGYIFATTGYGIALQKGSPWKRQIDLALLQFVGDGEMEELETLWLTGICHN
4XXB , Knot 85 178 0.82 40 131 171 
MAQDQGEKENPMRELRIRKLCLNICVGESGDRLTRAAKVLEQLTGQTPVFSKARYTVRSFGIRRNEKIAVHCTVRGAKAEEILEKGLKVREYELRKNNFSDTGNFGFGIQEHIDLGIKYDPSIGIYGLDFYVVLGRPGFSIADKKRRTGCIGAKHRISKEEAMRWFQQKYDGIILPGK

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 \(c\).

\(|P_{f(4OGH_1)}(2) \setminus P_{f(5KDT_1)}(2)|=90\), \(|P_{f(5KDT_1)}(2) \setminus P_{f(4OGH_1)}(2)|=89\). 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 1:0111101101101111011000001001111100100110001101101101111100101000111100011111111111001001001110111011100001000010000101001000111101010011010111110111101100001100101001001001110000010000001001001100101110010011101110001101011011101101011011010101101000
Pair \(Z_2\) Length of longest common subsequence
4OGH_1,5KDT_1 179 3
4OGH_1,4XXB_1 174 3
5KDT_1,4XXB_1 181 3

Newick tree

 
[
	5KDT_1:90.97,
	[
		4OGH_1:87,4XXB_1:87
	]:3.97
]

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 \((0.85)(0.8)(\frac{535 }{\log_{20} 535}-\frac{250}{\log_{20}250})=81.2\)
Status Protein1 Protein2 d d1/2
Query variables 4OGH_1 5KDT_1 104 99.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]