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Parikh vectors
3HFF_1 7QQT_1 1UAM_1 Letter Amino acid
24 19 26 G Glycine
9 0 13 I Isoleucine
0 0 8 M Methionine
5 0 14 P Proline
0 0 5 Y Tyrosine
14 0 16 V Valine
14 0 13 S Serine
8 0 13 T Threonine
12 29 18 A Alanine
7 0 4 N Asparagine
10 0 14 D Aspartic acid
5 0 20 H Histidine
9 0 31 L Leucine
11 0 14 K Lycine
2 15 3 C Cysteine
12 0 23 E Glutamic acid
4 0 16 R Arginine
3 0 11 Q Glutamine
3 0 7 F Phenylalanine
1 0 5 W Tryptophan 

3HFF_1|Chain A|Superoxide dismutase [Cu-Zn]|Homo sapiens (9606)
>7QQT_1|Chain A|FANCF sgRNA|synthetic construct (32630)
>1UAM_1|Chain A|tRNA (Guanine-N(1)-)-methyltransferase|Haemophilus influenzae (727)
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 \(w=f(c)\)
3HFF , Knot 71 153 0.77 36 109 149 
ATKAVAVLKGDGPVQGIINFEQKESNGPVKVWGSIKGLTEGLHGFHVHEEEDNTAGCTSAGPSFNPLSRKSGGPKDEERSVGSLGNVTADKDGVADVSIEDSVISLSGDHAIIGRTLVVHEKADDLGKGGNEESTKTGNAGSRLACGVIGIAQ
7QQT , Knot 27 84 0.47 8 16 44 
GGGGAAUCCCUUCUGCAGCACCGUUUUAGAGCUAGAAAUAGCAAGUUAAAAUAAGGCUAGUCCGUUAUCAACUUGAAAAAGUGA
1UAM , Knot 121 274 0.82 40 178 258 
MGSSHHHHHHSSGLVPRGSHMWIGVISLFPEMFKAITEFGVTGRAVKHNLLKVECWNPRDFTFDKHKTVDDRPYGGGPGMLMMVQPLRDAIHTAKAAAGEGAKVIYLSPQGRKLDQGGVTELAQNQKLILVCGRYEGIDERLIQTEIDEEWSIGDYVLTGGELPAMTLIDAVARFIPGVLGKQASAEEDSFADGLLDCPHYTRPEVLEGLTVPPVLMSGHHEEIRKWRLKQSLQRTWLRRPELLEGLALTDEQRKLLKEAQAEHNSLEHHHHHH

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 \(c\).

\(|P_{f(3HFF_1)}(2) \setminus P_{f(7QQT_1)}(2)|=104\), \(|P_{f(7QQT_1)}(2) \setminus P_{f(3HFF_1)}(2)|=11\). 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 1:100111110101110111010000001110111010110011011010000000110001110101100001110000001101101010001110101000110101001111001110001001101100000001011001101111110
Pair \(Z_2\) Length of longest common subsequence
3HFF_1,7QQT_1 115 3
3HFF_1,1UAM_1 165 4
7QQT_1,1UAM_1 184 4

Newick tree

 
[
	1UAM_1:95.27,
	[
		3HFF_1:57.5,7QQT_1:57.5
	]:37.77
]

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 \((0.85)(0.8)(\frac{237 }{\log_{20} 237}-\frac{84}{\log_{20}84})=49.6\)
Status Protein1 Protein2 d d1/2
Query variables 3HFF_1 7QQT_1 65 44.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]