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Parikh vectors
7JZT_1 3VQI_1 9FQP_1 Letter Amino acid
7 13 17 R Arginine
11 8 12 Q Glutamine
24 18 25 I Isoleucine
19 18 23 K Lycine
10 13 9 N Asparagine
21 20 21 D Aspartic acid
18 22 17 S Serine
4 11 13 Y Tyrosine
20 11 20 A Alanine
2 4 6 C Cysteine
6 15 26 E Glutamic acid
18 14 21 G Glycine
7 6 13 M Methionine
9 11 8 F Phenylalanine
32 12 19 P Proline
25 10 13 T Threonine
2 9 6 W Tryptophan
18 26 22 V Valine
13 5 14 H Histidine
31 28 33 L Leucine 

7JZT_1|Chains A, B, C, D|Matrix protein VP40|Zaire ebolavirus (strain Mayinga-76) (128952)
>3VQI_1|Chains A, B, C, D, E|Atg5|Kluyveromyces marxianus (4911)
>9FQP_1|Chain A|Epidermal growth factor receptor|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 \(w=f(c)\)
7JZT , Knot 128 297 0.81 40 176 276 
MAHHHHHHVDDDDKGDTPSNPLRPIADDTIDHASHTPGSVSSAFILEAMVNVISGPKVLMKQIPIWLPLGVADQKTYSFDSTTAAIMLASYTITHFGKATNPLVRVNRLGPGIPDHPLRLLRIGNQAFLQEFVLPPVQLPQYFTFDLTALKLITQPLPAATWTDDTPTGSNGALRPGISFHPKLRPILLPNKSGKKGNSADLTSPEKIQAIMTSLQDFKIVPIDPTKNIMGIEVPETLVHKLTGKKVTSKNGQPIIPVLLPKYIGLDPVAPGDLTMVITQDCDTCHSPASLPAVIEK
3VQI , Knot 124 274 0.84 40 180 268 
GPHMEELRERVWNGTINVEVVVSDAIVVPNTTLADKSCHIVMLRDAYLGFYLPTVVRKLADTIKVPYESDYRNWWFEYNGEGVPWEYPCGVLFDLLNKKRKKQGNELDDTSLQMWELQLCHGDKYPRGILPLVDGHSQIKDYWRHQWKQACFILNGSAKRIMSLSIPDFENFWVSILSRNRSDFMAVRSKLFSMNKAKSLPVRVWTSNYAVLQPTVPVTDKELSVAELLDSIKLSSDGVKSVIIQGIDVSIEDNIFELYDIFASIDGFLYLVTK
9FQP , Knot 148 338 0.85 40 216 329 
MSGEAPNQALLRILKETEFKKIKVLGSGAFGTVYKGLWIPEGEKVKIPVAIKELREATSPKANKEILDEAYVMASVDNPGNPHVCRLLGICLTSTVQLITQLMPFGCLLDYVREHKDNIGSQYLLNWCVQIAKGMNYLEDRRLVHRDLAARNVLVKTPQHVKITDFGLAKLLGAEEKEYHAEGGKVPIKWMALESILHRIYTHQSDVWSYGVTVWELMTFGSKPYDGIPASEISSILEKGERLPQPPICTIDVYMIMRKCWMIDADSRPKFRELIIEFSKMARDPQRYLVIQGDERMHLPSPTDSNFYRALMDEEDMDDVVDADEYLIPQQGHHHHHH

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 \(c\).

\(|P_{f(7JZT_1)}(2) \setminus P_{f(3VQI_1)}(2)|=92\), \(|P_{f(3VQI_1)}(2) \setminus P_{f(7JZT_1)}(2)|=96\). 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 1:110000001000001001001101110001001000110100111101110110110111001111111111000000100001111110001001101001110100111111001101101100111001111110110010101011011001111101000010100111011101010101111100010010010100100101110010010111101000111101100110010100100001011111111001110111110101110000000001101111100
Pair \(Z_2\) Length of longest common subsequence
7JZT_1,3VQI_1 188 4
7JZT_1,9FQP_1 168 6
3VQI_1,9FQP_1 184 4

Newick tree

 
[
	3VQI_1:95.81,
	[
		7JZT_1:84,9FQP_1:84
	]:11.81
]

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 \((0.85)(0.8)(\frac{571 }{\log_{20} 571}-\frac{274}{\log_{20}274})=83.8\)
Status Protein1 Protein2 d d1/2
Query variables 7JZT_1 3VQI_1 104 103.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]