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Parikh vectors
3RIH_1 8VKK_1 6DZE_1 Letter Amino acid
36 91 1 G Glycine
16 67 2 P Proline
19 105 1 S Serine
31 93 0 V Valine
14 41 4 R Arginine
13 59 0 D Aspartic acid
7 64 1 Q Glutamine
3 30 0 C Cysteine
16 52 0 E Glutamic acid
24 105 0 L Leucine
10 11 0 M Methionine
6 78 3 F Phenylalanine
20 93 0 T Threonine
1 12 0 W Tryptophan
39 80 0 A Alanine
8 28 0 H Histidine
14 73 2 I Isoleucine
7 85 1 N Asparagine
4 63 1 K Lycine
5 54 0 Y Tyrosine

3RIH_1|Chains A, B, C, D|short chain dehydrogenase or reductase|Mycobacterium abscessus (561007)
>8VKK_1|Chains A, B, C|Spike glycoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
>6DZE_1|Chain A|CPfox7|synthetic construct (36630)
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 \(w=f(c)\)
3RIH , Knot 120 293 0.77 40 159 274
MAHHHHHHMGTLEAQTQGPGSMLVVESAEPAERKVMFDLSARSVLVTGGTKGIGRGIATVFARAGANVAVAARSPRELSSVTAELGELGAGNVIGVRLDVSDPGSCADAARTVVDAFGALDVVCANAGIFPEARLDTMTPEQLSEVLDVNVKGTVYTVQACLAPLTASGRGRVILTSSITGPVTGYPGWSHYGASKAAQLGFMRTAAIELAPRGVTVNAILPGNILTEGLVDMGEEYISGMARSIPMGMLGSPVDIGHLAAFLATDEAGYITGQAIVVDGGQVLPESPDAVNP
8VKK , Knot 454 1284 0.84 40 331 1109
MFVFLVLLPLVSSQCVNLITRTQSYTNSFTRGVYYPDKVFRSSVLHSTQDLFLPFFSNVTWFHAIHVSGTNGTKRFDNPALPFNDGVYFASTEKSNIIRGWIFGTTLDSKTQSLLIVNNATNVVIKVCEFQFCNDPFLDVYQKNNKSWMESEFRVYSSANNCTFEYVSQPFLMDLEGKEGNFKNLREFVFKNIDGYFKIYSKHTPINLERDLPQGFSALEPLVDLPIGINITRFQTLLALHRSYLTPVDSSSGWTAGAAAYYVGYLQPRTFLLKYNENGTITDAVDCALDPLSETKCTLKSFTVEKGIYQTSNFRVQPTESIVRFPNITNLCPFHEVFNATTFASVYAWNRKRISNCVADYSVIYNFAPFFAFKCYGVSPTKLNDLCFTNVYADSFVIRGNEVSQIAPGQTGNIADYNYKLPDDFTGCVIAWNSNKLDSKPSGNYNYLYRLFRKSKLKPFERDISTEIYQAGNKPCNGVAGPNCYSPLQSYGFRPTYGVGHQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFNFNGLTGTGVLTESNKKFLPFQQFGRDIADTTDAVRDPQTLEILDITPCSFGGVSVITPGTNTSNQVAVLYQGVNCTEVPVAIHADQLTPTWRVYSTGSNVFQTRAGCLIGAEYVNNSYECDIPIGAGICASYQTQTKSHGSASSVASQSIIAYTMSLGAENSVAYSNNSIAIPTNFTISVTTEILPVSMTKTSVDCTMYICGDSTECSNLLLQYGSFCTQLKRALTGIAVEQDKNTQEVFAQVKQIYKTPPIKYFGGFNFSQILPDPSKPSKRSPIEDLLFNKVTLADAGFIKQYGDCLGDIAARDLICAQKFNGLTVLPPLLTDEMIAQYTSALLAGTITSGWTFGAGPALQIPFPMQMAYRFNGIGVTQNVLYENQKLIANQFNSAIGKIQDSLSSTPSALGKLQDVVNHNAQALNTLVKQLSSKFGAISSVLNDILSRLDPPEAEVQIDRLITGRLQSLQTYVTQQLIRAAEIRASANLAATKMSECVLGQSKRVDFCGKGYHLMSFPQSAPHGVVFLHVTYVPAQEKNFTTAPAICHDGKAHFPREGVFVSNGTHWFVTQRNFYEPQIITTDNTFVSGNCDVVIGIVNNTVYDPLQPELDSFKEELDKYFKNHTSPDVDLGDISGINASVVNIQKEIDRLNEVAKNLNESLIDLQELGKYEQGSGYIPEAPRDGQAYVRKDGEWVLLSTFLGRSLEVLFQGPGHHHHHHHHSAWSHPQFEKGGGSGGGGSGGSAWSHPQFEK
6DZE , Knot 11 16 0.63 18 14 14
GSRRFRFPPKIIFNQR

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 \(c\).

\(|P_{f(3RIH_1)}(2) \setminus P_{f(8VKK_1)}(2)|=12\), \(|P_{f(8VKK_1)}(2) \setminus P_{f(3RIH_1)}(2)|=184\). 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 1:11000000110101000111011110010110001110101001110110011101110111011101111100100100101011011110111101010011001011001101111101101011111010100101001001101010101001010111101010101110001011101011100011001101111001110111011010111110110011101100010111001111111011011011111100011010101111011011100101101
Pair \(Z_2\) Length of longest common subsequence
3RIH_1,8VKK_1 196 6
3RIH_1,6DZE_1 167 2
8VKK_1,6DZE_1 319 3

Newick tree

 
[
	8VKK_1:14.04,
	[
		3RIH_1:83.5,6DZE_1:83.5
	]:61.54
]

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 \((0.85)(0.8)(\frac{1577 }{\log_{20} 1577}-\frac{293}{\log_{20}293})=331.\)
Status Protein1 Protein2 d d1/2
Query variables 3RIH_1 8VKK_1 419 254.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]