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Parikh vectors
8UUQ_1 5JJN_1 4PHP_1 Letter Amino acid
1 6 0 W Tryptophan
2 11 0 Y Tyrosine
6 28 4 G Glycine
1 11 0 F Phenylalanine
1 0 7 C Cysteine
5 1 0 Q Glutamine
9 15 0 I Isoleucine
13 33 0 L Leucine
11 29 0 V Valine
10 11 0 R Arginine
1 9 0 D Aspartic acid
10 10 0 S Serine
8 16 2 T Threonine
3 8 0 E Glutamic acid
4 10 0 P Proline
3 8 0 H Histidine
5 2 0 K Lycine
5 6 0 M Methionine
7 31 3 A Alanine
7 3 0 N Asparagine 

8UUQ_1|Chains A, C[auth D], E[auth F]|Fusion glycoprotein F0|Measles virus strain Ichinose-B95a (645098)
>5JJN_1|Chains A, C|Sensory rhodopsin-2|Natronomonas pharaonis (2257)
>4PHP_1|Chain A[auth T]|DNA (5'-D(*CP*CP*GP*AP*CP*TP*GP*CP*GP*CP*AP*TP*CP*AP*GP*C)-3')|synthetic construct (32630)
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 \(w=f(c)\)
8UUQ , Knot 58 112 0.81 40 95 110 
MGLKVNVSAIFMAVLLTLQTPTGQIHWGNLSKIGVVGIGSASYKVMTRSSHQSLVIKLMPNITLLNNCTRVEIAEYRRLLRTVLEPIRDALNAMTQNIRPVQSVASSRRHKR
5JJN , Knot 104 248 0.77 38 133 228 
VGLTTLFWLGAIGMLVGTLAFAWAGRDAGSGERRYYVTLVGISGIAAVAYVVMALGVGWVPVAERTVFAPRYIDWILTTPLIVYFLGLLAGLDSREFGIVITLNTVVMLAGFAGAMVPGIERYALFGMGAVAFLGLVYYLVGPMTESASQRSSGIKSLYVRLRNLTVILWAIYPFIWLLGPPGVALLTPTVDVALIVYLDLVTKVGFGFIALDAAATLRAEHGESLAGVDTDAPAVADENSHHHHHHH
4PHP , Knot 9 16 0.52 8 11 14 
CCGACTGCGCATCAGC

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 \(c\).

\(|P_{f(8UUQ_1)}(2) \setminus P_{f(5JJN_1)}(2)|=50\), \(|P_{f(5JJN_1)}(2) \setminus P_{f(8UUQ_1)}(2)|=88\). 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 1:1110101011111111010010101011010011111110100011000000011101110101100000101100001100110110011011000101100110000000
Pair \(Z_2\) Length of longest common subsequence
8UUQ_1,5JJN_1 138 3
8UUQ_1,4PHP_1 102 2
5JJN_1,4PHP_1 138 2

Newick tree

 
[
	5JJN_1:74.03,
	[
		8UUQ_1:51,4PHP_1:51
	]:23.03
]

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 \((0.85)(0.8)(\frac{360 }{\log_{20} 360}-\frac{112}{\log_{20}112})=76.2\)
Status Protein1 Protein2 d d1/2
Query variables 8UUQ_1 5JJN_1 91 67
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]