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Parikh vectors
3FFG_1 7NQP_1 1JJF_1 Letter Amino acid
5 3 5 H Histidine
6 7 16 P Proline
9 2 2 C Cysteine
19 33 10 E Glutamic acid
12 5 10 F Phenylalanine
7 8 22 N Asparagine
9 9 6 Q Glutamine
20 10 15 T Threonine
4 2 4 W Tryptophan
8 10 14 Y Tyrosine
13 27 21 A Alanine
17 17 11 K Lycine
22 17 31 G Glycine
13 10 19 I Isoleucine
13 24 23 L Leucine
5 9 3 M Methionine
11 20 18 S Serine
16 12 14 V Valine
14 13 11 R Arginine
11 15 13 D Aspartic acid 

3FFG_1|Chain A|Coagulation factor X, heavy chain|Homo sapiens (9606)
>7NQP_1|Chain A|14-3-3 protein sigma|Homo sapiens (9606)
>1JJF_1|Chain A|ENDO-1,4-BETA-XYLANASE Z|Clostridium thermocellum (1515)
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 \(w=f(c)\)
3FFG , Knot 109 234 0.84 40 171 226 
IVGGQECKDGECPWQALLINEENEGFCGGTILSEFYILTAAHCLYQAKRFKVRVGDRNTEQEEGGEAVHEVEVVIKHNRFTKETYDFDIAVLRLKTPITFRMNVAPACLPERDWAESTLMTQKTGIVSGFGRTHEKGRQSTRLKMLEVPYVDRNSCKLSSSFIITQNMFCAGYDTKQEDACQGDSGGPHVTRFKDTYFVTGIVSWGEGCARKGKYGIYTKVTAFLKWIDRSMKT
7NQP , Knot 114 253 0.83 40 170 244 
GAMGSMERASLIQKAKLAEQAERYEDMAAFMKGAVEKGEELSCEERNLLSVAYKNVVGGQRAAWRVLSSIEQKSNEEGSEEKGPEVREYREKVETELQGVCDTVLGLLDSHLIKEAGDAESRVFYLKMKGDYYRYLAEVATGDDKKRIIDSARSAYQEAMDISKKEMPPTNPIRLGLALNFSVFHYEIANSPEEAISLAKTTFDEAMADLHTLSEDSYKDSTLIMQLLRDNLTLWTADNAGEEGGEAPQEPQS
1JJF , Knot 124 268 0.86 40 179 257 
LVTISSTSAASLPTMPPSGYDQVRNGVPRGQVVNISYFSTATNSTRPARVYLPPGYSKDKKYSVLYLLHGIGGSENDWFEGGGRANVIADNLIAEGKIKPLIIVTPNTNAAGPGIADGYENFTKDLLNSLIPYIESNYSVYTDREHRAIAGLSMGGGQSFNIGLTNLDKFAYIGPISAAPNTYPNERLFPDGGKAAREKLKLLFIACGTNDSLIGFGQRVHEYCVANNINHVYWLIQGGGHDFNVWKPGLWNFLQMADEAGLTRDGNT

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 \(c\).

\(|P_{f(3FFG_1)}(2) \setminus P_{f(7NQP_1)}(2)|=90\), \(|P_{f(7NQP_1)}(2) \setminus P_{f(3FFG_1)}(2)|=89\). 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 1:111100000100110111100000110110110010110110010010010101100000000110110010111000010000001011110100110101011110110001100011000011101110000010000010110110100000010001110001101100000001001001110100100001101110110101001001100010111011000100
Pair \(Z_2\) Length of longest common subsequence
3FFG_1,7NQP_1 179 6
3FFG_1,1JJF_1 180 3
7NQP_1,1JJF_1 173 3

Newick tree

 
[
	3FFG_1:90.80,
	[
		7NQP_1:86.5,1JJF_1:86.5
	]:4.30
]

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 \((0.85)(0.8)(\frac{487 }{\log_{20} 487}-\frac{234}{\log_{20}234})=72.9\)
Status Protein1 Protein2 d d1/2
Query variables 3FFG_1 7NQP_1 93 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]