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Parikh vectors
6UWE_1 6JCU_1 7UKM_1 Letter Amino acid
41 22 61 D Aspartic acid
44 28 83 G Glycine
10 9 17 H Histidine
15 4 12 W Tryptophan
15 16 54 Y Tyrosine
3 6 40 C Cysteine
21 28 48 E Glutamic acid
19 30 76 I Isoleucine
33 27 97 T Threonine
47 21 96 V Valine
34 29 79 A Alanine
25 19 60 K Lycine
31 19 60 P Proline
22 23 99 S Serine
16 17 14 M Methionine
18 12 77 F Phenylalanine
17 18 42 R Arginine
17 12 88 N Asparagine
13 11 62 Q Glutamine
30 26 108 L Leucine 

6UWE_1|Chains A, B, C, D|thiocyanate dehydrogenase|Thioalkalivibrio paradoxus ARh 1 (713585)
>6JCU_1|Chains A, C|Actin, alpha skeletal muscle|Oryctolagus cuniculus (9986)
>7UKM_1|Chains A, D[auth B], G[auth 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 \(w=f(c)\)
6UWE , Knot 193 471 0.84 40 241 444 
GAMGKYVKVQDFYDQLGKYVLVAPGKFSGTVAATDLSTGWTMAWLAAWNYGDTCPIMHHMAAFPSPDPYKEFEFVVNTQGGKNLFIYGVPVTVEDPGEGMKIYRIKYDGTRMNLQRDAAEVSGLGLGVHVTITPEADGYAVGDGQKDICAEFDRETDMVRYAWAFDWDPNVKDLKRAWLDGGTMTIKRLKPTLPGGRYDLQGSKGNKIDWELVPGGELAIEDGKVSGDRPLHSVANDALVFDPRGKWAVASMRLPGVCVVFDRENQVPVAVLAGPKGTPSQFQLVKVDDDTWTVDIPEVISAGHQAGFSPDGQSFLFMNSLRQNNIMVWDSSNHDDPTTWEKKAVVESPDWRGAYPNTFHMVFTPDAKKIYVTMWWPSPTPNGIAVIDAVNWEVLKEVDLGPDMHTLAITYDGKFVVGTLSGYQNTASAIVVMETETDEVLGFLPSPMGHHDNVIVPRTLEDLRISRSTTT
6JCU , Knot 160 377 0.84 40 220 362 
MCDEDETTALVCDNGSGLVKAGFAGDDAPRAVFPSIVGRPRHQGVMVGMGQKDSYVGDEAQSKRGILTLKYPIEHGIITNWDDMEKIWHHTFYNELRVAPEEHPTLLTEAPLNPKANREKMTQIMFETFNVPAMYVAIQAVLSLYASGRTTGIVLDSGDGVTHNVPIYEGYALPHAIMRLDLAGRDLTDYLMKILTERGYSFVTTAEREIVRDIKEKLCYVALDFENEMATAASSSSLEKSYELPDGQVITIGNERFRCPETLFQPSFIGMESAGIHETTYNSIMKCDIDIRKDLYANNVMSGGTTMYPGIADRMQKEITALAPSTMKIKIIAPPERKYSVWIGGSILASLSTFQQMWITKQEYDEAGPSIVHRKCF
7UKM , Knot 453 1273 0.84 40 338 1105 
MFVFLVLLPLVSSQCVNLTTRTQLPPAYTNSFTRGVYYPDKVFRSSVLHSTQDLFLPFFSNVTWFHAIHVSGTNGTKRFDNPVLPFNDGVYFASTEKSNIIRGWIFGTTLDSKTQSLLIVNNATNVVIKVCEFQFCNDPFLGVYYHKNNKSWMESEFRVYSSANNCTFEYVSQPFLMDLEGKQGNFKNLREFVFKNIDGYFKIYSKHTPINLVRDLPQGFSALEPLVDLPIGINITRFQTLLALHRSYLTPGDSSSGWTAGAAAYYVGYLQPRTFLLKYNENGTITDAVDCALDPLSETKCTLKSFTVEKGIYQTSNFRVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFNFNGLTGTGVLTESNKKFLPFQQFGRDIADTTDAVRDPQTLEILDITPCSFGGVSVITPGTNTSNQVAVLYQGVNCTEVPVAIHADQLTPTWRVYSTGSNVFQTRAGCLIGAEHVNNSYECDIPIGAGICASYQTQTNSPRRARSVASQSIIAYTMSLGAENSVAYSNNSIAIPTNFTISVTTEILPVSMTKTSVDCTMYICGDSTECSNLLLQYGSFCTQLNRALTGIAVEQDKNTQEVFAQVKQIYKTPPIKDFGGFNFSQILPDPSKPSKRSFIEDLLFNKVTLADAGFIKQYGDCLGDIAARDLICAQKFNGLTVLPPLLTDEMIAQYTSALLAGTITSGWTFGAGAALQIPFAMQMAYRFNGIGVTQNVLYENQKLIANQFNSAIGKIQDSLSSTASALGKLQDVVNQNAQALNTLVKQLSSNFGAISSVLNDILSRLDPPEAEVQIDRLITGRLQSLQTYVTQQLIRAAEIRASANLAATKMSECVLGQSKRVDFCGKGYHLMSFPQSAPHGVVFLHVTYVPAQEKNFTTAPAICHDGKAHFPREGVFVSNGTHWFVTQRNFYEPQIITTDNTFVSGNCDVVIGIVNNTVYDPLQPELDSFKEELDKYFKNHTSPDVDLGDISGINASVVNIQKEIDRLNEVAKNLNESLIDLQELGKYEQYIKWPWYIWLGFIAGLIAIVMVTIMLCCMTSCCSCLKGCCSCGSCCKFDEDDSEPVLKGVKLHYT

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 \(c\).

\(|P_{f(6UWE_1)}(2) \setminus P_{f(6JCU_1)}(2)|=91\), \(|P_{f(6JCU_1)}(2) \setminus P_{f(6UWE_1)}(2)|=70\). 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 1:111100101001000110011111101010111001001101111111001000111001111101010001011100011001110111101001101101001000100101000110101111110101010101011101000101010000011001111010101001001110110101001010111100010100100101011111011100101010011001100111101010111101011110111000001111111110101001011010000101011011011001110101001111001000011110000000100100011100101011010010111010100101011110101011111011010110010111010011100010111101010000101111100000011111101110000111100100101000000
Pair \(Z_2\) Length of longest common subsequence
6UWE_1,6JCU_1 161 4
6UWE_1,7UKM_1 151 4
6JCU_1,7UKM_1 160 4

Newick tree

 
[
	6JCU_1:81.77,
	[
		6UWE_1:75.5,7UKM_1:75.5
	]:6.27
]

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 \((0.85)(0.8)(\frac{848 }{\log_{20} 848}-\frac{377}{\log_{20}377})=126.\)
Status Protein1 Protein2 d d1/2
Query variables 6UWE_1 6JCU_1 161 144
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]