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Parikh vectors
6VJC_1 6IQE_1 4XXU_1 Letter Amino acid
7 0 0 C Cysteine
25 10 12 E Glutamic acid
11 6 3 H Histidine
14 10 8 Q Glutamine
9 1 10 P Proline
6 0 4 W Tryptophan
18 2 7 Y Tyrosine
7 2 9 N Asparagine
10 5 10 I Isoleucine
32 5 21 L Leucine
17 1 3 M Methionine
14 2 11 F Phenylalanine
36 4 24 V Valine
43 15 42 A Alanine
13 5 7 R Arginine
25 0 16 D Aspartic acid
16 4 18 G Glycine
26 9 22 K Lycine
9 4 16 S Serine
24 2 14 T Threonine 

6VJC_1|Chains A, B|Farnesyl pyrophosphate synthase|Leishmania major (5664)
>6IQE_1|Chain A|Prohibitin-2|Homo sapiens (9606)
>4XXU_1|Chains A, B|Molybdate-binding periplasmic protein|Escherichia coli (strain K12) (83333)
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 \(w=f(c)\)
6VJC , Knot 153 362 0.83 40 205 344 
MAHMERFQKVYEEVQEFLLGDAEKRFEMDVHRKGYLKSMMDTTCLGGKYNRGLCVVDVAEAMAKDTQMDAAAMERVLHDACVCGWMIEMLQAHFLVEDDIMDHSKTRRGKPCWYLHPGVTAQVAINDGLILLAWATQMALHYFADRPFLAEVLRVFHDVDLTTYIGQLYDVTSMVDSAKLDAKVAHANTTDYVEYTPFNHRRIVVYKTAYYTYWLPLVMGLLVSGTLEKVDKKATHKVAMVMGEYFQVQDDVMDCFTPPEKLGKIGTDIEDAKCSWLAVTFLTTAPAEKVAEFKANYGSTDPAAVAVIKQLYTEQNLLARFEEYEKAVVAEVEQLIAALEAQNAAFAASVKVLWSKTYKRQK
6IQE , Knot 43 87 0.73 34 61 80 
GSFSREYTAAVEAKQVAQQEAQRAQFLVEKAKQEQRQKIVQAEGEAEAAKMLGEALSKNPGYIKLRKIRAAQNISKTIALEHHHHHH
4XXU , Knot 109 257 0.78 38 154 247 
MARKWLNLFAGAALSFAVAGNALADEGKITVFAAASLTNAMQDIATQFKKEKGVDVVSSFASSSTLARQIEAGAPADLFISADQKWMDYAVDKKAIDTATRQTLLGNSLVVVAPKASVQKDFTIDSKTNWTSLLNGGRLAVGDPEHVPAGIYAKEALQKLGAWDTLSPKLAPAEDVRGALALVERNEAPLGIVYGSDAVASKGVKVVATFPEDSHKKVEYPVAVVEGHNNATVKAFYDYLKGPQAAEIFKRYGFTIK

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 \(c\).

\(|P_{f(6VJC_1)}(2) \setminus P_{f(6IQE_1)}(2)|=163\), \(|P_{f(6IQE_1)}(2) \setminus P_{f(6VJC_1)}(2)|=19\). 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 1:11010010010001001111010001010100010100110000111000011011011011100001011110011001010111101101011100011000000010101010111010111001111111100111001100111101101100101000110100100110010101011010000010001100001110001000011111111110101001000100011111100101000110010110011011001001000111101100111001101010010001111111001000001110100000111101001111101001111101011100000000
Pair \(Z_2\) Length of longest common subsequence
6VJC_1,6IQE_1 182 4
6VJC_1,4XXU_1 171 5
6IQE_1,4XXU_1 147 3

Newick tree

 
[
	6VJC_1:92.70,
	[
		4XXU_1:73.5,6IQE_1:73.5
	]:19.20
]

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 \((0.85)(0.8)(\frac{449 }{\log_{20} 449}-\frac{87}{\log_{20}87})=110.\)
Status Protein1 Protein2 d d1/2
Query variables 6VJC_1 6IQE_1 137 82.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]