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Parikh vectors
5UHV_1 6GQD_1 7QQN_1 Letter Amino acid
3 5 4 C Cysteine
12 24 29 E Glutamic acid
11 7 30 I Isoleucine
12 39 39 L Leucine
15 21 28 V Valine
5 10 14 N Asparagine
9 25 29 R Arginine
9 26 17 Q Glutamine
2 17 5 H Histidine
6 12 10 F Phenylalanine
8 24 29 S Serine
12 17 21 T Threonine
10 35 26 A Alanine
14 19 30 D Aspartic acid
11 16 31 G Glycine
10 12 36 K Lycine
4 11 9 M Methionine
4 35 7 P Proline
0 12 1 W Tryptophan
9 13 19 Y Tyrosine 

5UHV_1|Chain A|GTPase NRas|Homo sapiens (9606)
>6GQD_1|Chain A|Galactose-1-phosphate uridylyltransferase|Homo sapiens (9606)
>7QQN_1|Chains A, B[auth C]|Gamma-1-syntrophin,Annexin A2|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 \(w=f(c)\)
5UHV , Knot 79 166 0.81 38 127 164 
MTEYKLVVVGAGGVGKSALTIQLIQNHFVDEYDPTIEDSYRKQVVIDGETCLLDILDTAGQEEYSAMRDQYMRTGEGFLCVFAINNSKSFADINLYREQIKRVKDSDDVPMVLVGNKCDLPTRTVDTKQAHELAKSYGIPFIETSAKTRQGVEDAFYTLVREIRQY
6GQD , Knot 160 380 0.83 40 222 364 
SMSRSGTDPQQRQQASEADAAYTPFLANDHQHIRYNPLQDEWVLVSAHRMKRPWQGQVEPQLLKTVPRHDPLNPLCPGAIRANGEVNPQYDSTFLFDNDFPALQPDAPSPGPSDHPLFQAKSARGVCKVMCFHPWSDVTLPLMSVPEIRAVVDAWASVTEELGAQYPWVQIFENKGAMMGCSNPHPHCQVWASSFLPDIAQREERSQQAYKSQHGEPLLMEYSRQELLRKERLVLTSEHWLVLVPFWATWPYQTLLLPRRHVRRLPELTPAERDDLASIMKKLLTKYDNLFETSFPYSMGWHGAPTGSEAGANWDHWQLHAHYYPPLLRSATVRKFMVGYEMLAQAQRDLTPEQAAERLRALPEVHYHLGQKDRETATIA
7QQN , Knot 173 414 0.84 40 215 391 
GSHMGGERTVTIRRQTVGGFGLSIKGGAEHNIPVVVSKISKEQRAELSGLLFIGDAILQINGINVRKCRHEEVVQVLRNAGEEVTLTVSFLKRAPGSAYGSVKAYTNFDAERDALNIETAIKTKGVDEVTIVNILTNRSNEQRQDIAFAYQRRTKKELASALKSALSGHLETVILGLLKTPAQYDASELKASMKGLGTDEDSLIEIICSRTNQELQEINRVYKEMYKTDLEKDIISDTSGDFRKLMVALAKGRRAEDGSVIDYELIDQDARDLYDAGVKRKGTDVPKWISIMTERSVPHLQKVFDRYKSYSPYDMLESIRKEVKGDLENAFLNLVQCIQNKPLYFADRLYDSMKGKGTRDKVLIRIMVSRSEVDMLKIRSEFKRKYGKSLYYYIQQDTKGDYQKALLYLCGGDD

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 \(c\).

\(|P_{f(5UHV_1)}(2) \setminus P_{f(6GQD_1)}(2)|=51\), \(|P_{f(6GQD_1)}(2) \setminus P_{f(5UHV_1)}(2)|=146\). 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 1:1000011111111110011010110001100001010000000111010001101100110000011000010010111011110000011010100001001000001111111000011000100001001100011111000100001100110011001000
Pair \(Z_2\) Length of longest common subsequence
5UHV_1,6GQD_1 197 3
5UHV_1,7QQN_1 152 4
6GQD_1,7QQN_1 175 4

Newick tree

 
[
	6GQD_1:98.21,
	[
		5UHV_1:76,7QQN_1:76
	]:22.21
]

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 \((0.85)(0.8)(\frac{546 }{\log_{20} 546}-\frac{166}{\log_{20}166})=110.\)
Status Protein1 Protein2 d d1/2
Query variables 5UHV_1 6GQD_1 144 102
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]