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Parikh vectors
7YVG_1 8BSC_1 2EPX_1 Letter Amino acid
12 0 1 W Tryptophan
79 42 1 A Alanine
96 28 8 G Glycine
72 22 3 I Isoleucine
105 29 1 L Leucine
62 17 4 K Lycine
80 12 1 F Phenylalanine
92 23 3 T Threonine
60 18 0 D Aspartic acid
30 5 2 C Cysteine
64 15 1 Q Glutamine
50 27 3 E Glutamic acid
11 12 0 M Methionine
103 16 8 S Serine
55 10 3 Y Tyrosine
85 9 1 N Asparagine
28 6 2 H Histidine
42 20 2 R Arginine
67 10 3 P Proline
95 18 0 V Valine 

7YVG_1|Chains A, B, C|Spike glycoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
>8BSC_1|Chains A, B, C, D, E, F, G|DNA repair protein RAD51 homolog 1|Homo sapiens (9606)
>2EPX_1|Chain A|Zinc finger protein 28 homolog|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 \(w=f(c)\)
7YVG , Knot 455 1288 0.84 40 332 1108 
MFVFLVLLPLVSSQCVNLITRTQLPPAYTNSFTRGVYYPDKVFRSSVLHSTQDLFLPFFSNVTWFHAIHVSGTNGTKRFDNPVLPFNDGVYFASTEKSNIIRGWIFGTTLDSKTQSLLIVNNATNVVIKVCEFQFCNDPFLDVYYHKNNKSWMESEFRVYSSANNCTFEYVSQPFLMDLEGKQGNFKNLREFVFKNIDGYFKIYSKHTPINLGRDLPQGFSALEPLVDLPIGINITRFQTLLALHRSYLTPGDSSSGWTAGAAAYYVGYLQPRTFLLKYNENGTITDAVDCALDPLSETKCTLKSFTVEKGIYQTSNFRVQPTESIVRFPNITNLCPFDEVFNATRFASVYAWNRKRISNCVADYSVLYNFAPFFAFKCYGVSPTKLNDLCFTNVYADSFVIRGNEVSQIAPGQTGNIADYNYKLPDDFTGCVIAWNSNKLDSKVGGNYNYRYRLFRKSNLKPFERDISTEIYQAGNKPCNGVAGVNCYFPLQSYGFRPTYGVGHQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFNFNGLTGTGVLTESNKKFLPFQQFGRDIADTTDAVRDPQTLEILDITPCSFGGVSVITPGTNTSNQVAVLYQGVNCTEVPVAIHADQLTPTWRVYSTGSNVFQTRAGCLIGAEYVNSSYECDIPIGAGICASYQTQTKSHGSASSVASQSIIAYTMSLGAENSVAYSNNSIAIPTNFTISVTTEILPVSMTKTSVDCTMYICGDSTECSNLLLQYGSFCTQLKRALTGIAVEQDKNTQEVFAQVKQIYKTPPIKYFGGFNFSQILPDPSKPSKRSPIEDLLFNKVTLADAGFIKQYGDCLGDIAARDLICAQKFNGLTVLPPLLTDEMIAQYTSALLAGTITSGWTFGAGPALQIPFPMQMAYRFNGIGVTQNVLYENQKLIANQFNSAIGKIQDSLSSTPSALGKLQDVVNHNAQALNTLVKQLSSKFGAISSVLNDILSRLDPPEAEVQIDRLITGRLQSLQTYVTQQLIRAAEIRASANLAATKMSECVLGQSKRVDFCGKGYHLMSFPQSAPHGVVFLHVTYVPAQEKNFTTAPAICHDGKAHFPREGVFVSNGTHWFVTQRNFYEPQIITTDNTFVSGNCDVVIGIVNNTVYDPLQPELDSFKEELDKYFKNHTSPDVDLGDISGINASVVNIQKEIDRLNEVAKNLNESLIDLQELGKYEQGSGYIPEAPRDGQAYVRKDGEWVFLSTFLSGLEVLFQGPGGWSHPQFEKGGGSGGGSGGSAWSHPQFEKGGSHHHHHHHH
8BSC , Knot 144 339 0.82 38 191 323 
MAMQMQLEANADTSVEEESFGPQPISRLEQCGINANDVKKLEEAGFHTVEAVAYAPKKELINIKGISEAKADKILAEAAKLVPMGFTTATEFHQRRSEIIQITTGSKELDKLLQGGIETGSITEMFGEFRTGKTQICHTLAVTCQLPIDRGGGEGKAMYIDTEGTFRPERLLAVAERYGLSGSDVLDNVAYARAFNTDHQTQLLYQASAMMVESRYALLIVDSATALYRTDYSGRGELSARQMHLARFLRMLLRLADEFGVAVVITNQVVAQVDGAAMFAADPKKPIGGNIIAHASTTRLYLRKGRGETRICKIYDSPCLPEAEAMFAINADGVGDAKD
2EPX , Knot 26 47 0.71 34 35 42 
GSSGSSGTGKKPYECIECGKAFIQNTSLIRHWRYYHTGEKPSGPSSG

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 \(c\).

\(|P_{f(7YVG_1)}(2) \setminus P_{f(8BSC_1)}(2)|=155\), \(|P_{f(8BSC_1)}(2) \setminus P_{f(7YVG_1)}(2)|=14\). 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 1:1111111111100001011000011110000100110010011000110000011111100101101101010010001001111100110110000001101111100100000011110010011101001010001110100000000110001010001000010010011110101001010010011100101010100000110110011011011011101111101001001111000010110000110111110011010100111000001010011001101100000010010100110000010101000110110100101100110100110101100001000110001100111111100011010010010100101001110100100111100101100000110010101111000010001110000000110000101100010001001100100111110001110001101001110010011110101101110101100000110000101010110101110000001111001100110000110010010110101001111011011000000111100110000111110100101010100010011000110111100100000001111111010000000001010011000111001011100011000001111001010100011110100001000101010000000111001010001001101111000000001110100100011100111101001110100100001100111001011011110001001101110011010010110111111000111000011111010011011111110111110110010111100011000001110010011101000100010111010011000101100110010001111001100110010110101010011010100100010001101101010101110010001110000101010100110110011011111010011100001001111000101011001111001001110000100101100000110100011111100010011010100100010001000001010110101101011010001001001100100011010011000010101101100101010001011110011011011101111100101001110111011011001010011000000000
Pair \(Z_2\) Length of longest common subsequence
7YVG_1,8BSC_1 169 4
7YVG_1,2EPX_1 301 3
8BSC_1,2EPX_1 188 3

Newick tree

 
[
	2EPX_1:13.42,
	[
		7YVG_1:84.5,8BSC_1:84.5
	]:51.92
]

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 \((0.85)(0.8)(\frac{1627 }{\log_{20} 1627}-\frac{339}{\log_{20}339})=329.\)
Status Protein1 Protein2 d d1/2
Query variables 7YVG_1 8BSC_1 418 262.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]