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Parikh vectors
7NUZ_1 9DWG_1 6SLX_1 Letter Amino acid
36 6 20 S Serine
19 6 12 V Valine
14 4 15 D Aspartic acid
5 7 33 E Glutamic acid
11 7 10 I Isoleucine
5 2 9 M Methionine
14 12 24 L Leucine
6 4 5 F Phenylalanine
22 10 10 T Threonine
17 3 10 Y Tyrosine
17 1 8 N Asparagine
5 0 2 C Cysteine
8 13 17 K Lycine
9 6 7 P Proline
4 2 3 H Histidine
2 0 2 W Tryptophan
33 19 27 A Alanine
12 18 13 R Arginine
7 8 9 Q Glutamine
33 7 17 G Glycine 

7NUZ_1|Chain A|Proteinase K|Parengyodontium album (37998)
>9DWG_1|Chains A, E|Histone H3.2|Homo sapiens (9606)
>6SLX_1|Chain A|14-3-3 protein sigma|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 \(w=f(c)\)
7NUZ , Knot 120 279 0.80 40 170 266 
AAQTNAPWGLARISSTSPGTSTYYYDESAGQGSCVYVIDTGIEASHPEFEGRAQMVKTYYYSSRDGNGHGTHCAGTVGSRTYGVAKKTQLFGVKVLDDNGSGQYSTIIAGMDFVASDKNNRNCPKGVVASLSLGGGYSSSVNSAAARLQSSGVMVAVAAGNNNADARNYSPASEPSVCTVGASDRYDRRSSFSNYGSVLDIFGPGTDILSTWIGGSTRSISGTSMATPHVAGLAAYLMTLGKTTAASACRYIADTANKGDLSNIPFGTVNLLAYNNYQA
9DWG , Knot 65 135 0.78 36 102 127 
ARTKQTARKSTGGKAPRKQLATKAARKSAPATGGVKKPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEASEAYLVGLFEDTNLAAIHAKRVTIMPKDIQLARRIRGERA
6SLX , Knot 114 253 0.83 40 170 244 
GAMGSMERASLIQKAKLAEQAERYEDMAAFMKGAVEKGEELSCEERNLLSVAYKNVVGGQRAAWRVLSSIEQKSNEEGSEEKGPEVREYREKVETELQGVCDTVLGLLDSHLIKEAGDAESRVFYLKMKGDYYRYLAEVATGDDKKRIIDSARSAYQEAMDISKKEMPPTNPIRLGLALNFSVFHYEIANSPEEAISLAKTTFDEAMADLHTLSEDSYKDSTLIMQLLRDNLTLWTADNAGEEGGEAPQEPQS

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 \(c\).

\(|P_{f(7NUZ_1)}(2) \setminus P_{f(9DWG_1)}(2)|=111\), \(|P_{f(9DWG_1)}(2) \setminus P_{f(7NUZ_1)}(2)|=43\). 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 1:110001111110100001100000000011010010110011010010101010110000000001010100011011000011100001111011000101000011111011100000000101111010111100001001110100011111111100010100001100101001110000000001000101101111100110011110000101001101011111101101100011010001100100101001111010111000001
Pair \(Z_2\) Length of longest common subsequence
7NUZ_1,9DWG_1 154 3
7NUZ_1,6SLX_1 156 3
9DWG_1,6SLX_1 138 3

Newick tree

 
[
	7NUZ_1:80.13,
	[
		9DWG_1:69,6SLX_1:69
	]:11.13
]

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 \((0.85)(0.8)(\frac{414 }{\log_{20} 414}-\frac{135}{\log_{20}135})=83.8\)
Status Protein1 Protein2 d d1/2
Query variables 7NUZ_1 9DWG_1 104 76.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]