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Parikh vectors
1ZSE_1 7YUA_1 6XRA_1 Letter Amino acid
0 11 76 I Isoleucine
0 1 63 K Lycine
0 7 14 M Methionine
0 18 107 S Serine
0 33 42 R Arginine
0 11 64 Q Glutamine
0 14 79 F Phenylalanine
0 25 60 P Proline
0 17 97 T Threonine
7 38 81 A Alanine
0 33 62 D Aspartic acid
0 37 109 L Leucine
0 36 97 V Valine
0 12 88 N Asparagine
0 19 51 E Glutamic acid
4 27 93 G Glycine
0 16 19 H Histidine
0 6 14 W Tryptophan
0 8 54 Y Tyrosine
4 7 40 C Cysteine

1ZSE_1|Chain A[auth R]|RNA HAIRPIN|null
>7YUA_1|Chains A, B, C, D|Transglycosylse|Marinactinospora thermotolerans (531310)
>6XRA_1|Chains A, B, C|Spike glycoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
1ZSE , Knot 10 20 0.50 8 12 15
AUGCAUGUCUAAGACAGCAU
7YUA , Knot 157 376 0.82 40 197 351
MSGRDISTAVVVTTISDGGFLDRLAPALRDAGARLIVIPDRNTGPALFAACERHRRLGLDVVCPSVAEQQDLLERLAVPDLIPYHSDNRRNVGYLMAWMEGFDVIVSMDDDNLPTTDDFVERHQVVCQGPRTQPVTASSDGWFNNCALLEVEPTEVFPRGFPFHARPAHAQARTSVCERPADVRINAGLWLGDPDVDAITRLAVRPNALAHSGGSVVLAEGTWCPVNSQNTAVHRDALPAYYFLRMGQPVDGVPMERFGDIFSGYFVQVCAQHLGHAVRFGDPVVEHPRNEHDLLDDLHKEVPAVRLLDDILDHLRDHPLEGGDYLETYESLSYALQEIAERVNGRAWSPDARAFLHRSAHLMRSWTGALRTVAGT
6XRA , Knot 461 1310 0.84 40 341 1121
MFVFLVLLPLVSSQCVNLTTRTQLPPAYTNSFTRGVYYPDKVFRSSVLHSTQDLFLPFFSNVTWFHAIHVSGTNGTKRFDNPVLPFNDGVYFASTEKSNIIRGWIFGTTLDSKTQSLLIVNNATNVVIKVCEFQFCNDPFLGVYYHKNNKSWMESEFRVYSSANNCTFEYVSQPFLMDLEGKQGNFKNLREFVFKNIDGYFKIYSKHTPINLVRDLPQGFSALEPLVDLPIGINITRFQTLLALHRSYLTPGDSSSGWTAGAAAYYVGYLQPRTFLLKYNENGTITDAVDCALDPLSETKCTLKSFTVEKGIYQTSNFRVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFNFNGLTGTGVLTESNKKFLPFQQFGRDIADTTDAVRDPQTLEILDITPCSFGGVSVITPGTNTSNQVAVLYQDVNCTEVPVAIHADQLTPTWRVYSTGSNVFQTRAGCLIGAEHVNNSYECDIPIGAGICASYQTQTNSPRRARSVASQSIIAYTMSLGAENSVAYSNNSIAIPTNFTISVTTEILPVSMTKTSVDCTMYICGDSTECSNLLLQYGSFCTQLNRALTGIAVEQDKNTQEVFAQVKQIYKTPPIKDFGGFNFSQILPDPSKPSKRSFIEDLLFNKVTLADAGFIKQYGDCLGDIAARDLICAQKFNGLTVLPPLLTDEMIAQYTSALLAGTITSGWTFGAGAALQIPFAMQMAYRFNGIGVTQNVLYENQKLIANQFNSAIGKIQDSLSSTASALGKLQDVVNQNAQALNTLVKQLSSNFGAISSVLNDILSRLDKVEAEVQIDRLITGRLQSLQTYVTQQLIRAAEIRASANLAATKMSECVLGQSKRVDFCGKGYHLMSFPQSAPHGVVFLHVTYVPAQEKNFTTAPAICHDGKAHFPREGVFVSNGTHWFVTQRNFYEPQIITTDNTFVSGNCDVVIGIVNNTVYDPLQPELDSFKEELDKYFKNHTSPDVDLGDISGINASVVNIQKEIDRLNEVAKNLNESLIDLQELGKYEQYIKWPWYIWLGFIAGLIAIVMVTIMLCCMTSCCSCLKGCCSCGSCCKFDEDDSEPVLKGVKLHYTLESGGGSAWSHPQFEKGGGSGGGSGGSSAWSHPQFEK

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 \(c\).

\(|P_{f(1ZSE_1)}(2) \setminus P_{f(7YUA_1)}(2)|=7\), \(|P_{f(7YUA_1)}(2) \setminus P_{f(1ZSE_1)}(2)|=192\). 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 1:10101010001111011010
Pair \(Z_2\) Length of longest common subsequence
1ZSE_1,7YUA_1 199 3
1ZSE_1,6XRA_1 343 3
7YUA_1,6XRA_1 178 5

Newick tree

 
[
	1ZSE_1:15.51,
	[
		7YUA_1:89,6XRA_1:89
	]:64.51
]

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 \((0.85)(0.8)(\frac{396 }{\log_{20} 396}-\frac{20}{\log_{20}20})=121.\)
Status Protein1 Protein2 d d1/2
Query variables 1ZSE_1 7YUA_1 153 79.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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