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Parikh vectors
6IHB_1 4OEZ_1 6OAR_1 Letter Amino acid
4 9 10 G Glycine
1 8 10 H Histidine
2 17 11 F Phenylalanine
10 17 11 S Serine
4 15 10 Q Glutamine
7 15 11 I Isoleucine
7 14 7 K Lycine
0 13 4 M Methionine
6 12 5 P Proline
2 13 8 R Arginine
0 5 2 C Cysteine
6 12 12 E Glutamic acid
8 28 14 L Leucine
2 7 5 Y Tyrosine
5 11 7 N Asparagine
7 11 12 D Aspartic acid
11 6 11 T Threonine
1 4 3 W Tryptophan
7 19 13 V Valine
4 14 12 A Alanine 

6IHB_1|Chain A[auth R]|Dyslexia-associated protein KIAA0319-like protein|Homo sapiens (9606)
>4OEZ_1|Chain A|Androgen receptor|Homo sapiens (9606)
>6OAR_1|Chains A, C, E, G|RNA-dependent RNA polymerase|Kupe virus (498356)
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 \(w=f(c)\)
6IHB , Knot 48 94 0.77 36 76 91 
KNRPPIAIVSPQFQEISLPTTSTVIDGSQSTDDDKIVQYHWEELKGPLREEKISEDTAILKLSKLVPGNYTFSLTVVDSDGATNSTTANLTVNK
4OEZ , Knot 121 250 0.89 40 185 243 
QPIFLNVLEAIEPGVVCAGHDNNQPDSFAALLSSLNELGERQLVHVVKWAKALPGFRNLHVDDQMAVIQYSWMGLMVFAMGWRSFTNVNSAMLYFAPDLVFNEYRMHKSRMYSQCVRMRHLSQEFGWLQITPQEFLCMKALLLFSIIPVDGLKNQKFFDELRMNYIKELDRIIACKRKNPTSCSRRFYQLTKLLDSVQPIARELHQFTFDLLIKSHMVSVDFPEMMAEIISVQVPKILSGKVKPIYFHTQ
6OAR , Knot 90 178 0.87 40 144 171 
MDFLDSLIWERVVDDQYVTNPTFCISDYFEIVRQPGDGNCFYHSIAELFFDVKTPFSFRKVKEHLRLAADAFYDTEPEAIGTGVTKEEYIQAAMKDNEWGGSLEASMLSKQLQITIILWVVNQTEQVTAAIKFGPGRVSTALNLMHVGRTHFDALRVINQLEDNQLQSRSGSHHHHHH

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 \(c\).

\(|P_{f(6IHB_1)}(2) \setminus P_{f(4OEZ_1)}(2)|=34\), \(|P_{f(4OEZ_1)}(2) \setminus P_{f(6IHB_1)}(2)|=143\). 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 1:0001111110101001011000011010000000011000100101110000100001110100111100010101100011000001010100
Pair \(Z_2\) Length of longest common subsequence
6IHB_1,4OEZ_1 177 3
6IHB_1,6OAR_1 144 3
4OEZ_1,6OAR_1 163 4

Newick tree

 
[
	4OEZ_1:89.00,
	[
		6IHB_1:72,6OAR_1:72
	]:17.00
]

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 \((0.85)(0.8)(\frac{344 }{\log_{20} 344}-\frac{94}{\log_{20}94})=77.8\)
Status Protein1 Protein2 d d1/2
Query variables 6IHB_1 4OEZ_1 105 70
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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