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Parikh vectors
1TZL_1 6LKC_1 7RMD_1 Letter Amino acid
15 19 7 Y Tyrosine
40 65 5 A Alanine
28 34 3 R Arginine
36 17 5 F Phenylalanine
44 29 12 P Proline
16 24 5 M Methionine
45 36 8 T Threonine
9 8 3 W Tryptophan
41 40 5 V Valine
31 26 12 N Asparagine
39 23 6 D Aspartic acid
41 47 2 G Glycine
26 24 7 I Isoleucine
29 26 9 Q Glutamine
35 36 8 E Glutamic acid
14 15 1 H Histidine
9 5 2 C Cysteine
44 50 13 L Leucine
30 25 12 K Lycine
50 38 2 S Serine 

1TZL_1|Chains A, B, C, D, E, F, G, H|pyranose oxidase|Peniophora sp. SG (204723)
>6LKC_1|Chains A, B|Polyunsaturated fatty acid synthase PfaD|Shewanella piezotolerans (strain WP3 / JCM 13877) (225849)
>7RMD_1|Chain A|Bromodomain-containing protein 4|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 \(w=f(c)\)
1TZL , Knot 244 622 0.84 40 283 584 
STSSSDPFFNFAKSSFRSAAAQKASASSLPPLPGPDKKVPGMDIKYDVVIVGSGPIGCTYARELVGAGYKVAMFDIGEIDSGLKIGAHKKNTVEYQKNIDKFVNVIQGQLMSVSVPVNTLVVDTLSPTSWQASTFFVRNGSNPEQDPLRNLSGQAVTRVVGGMSTHWTCATPRFDREQRPLLVKDDADADDAEWDRLYTKAESYFQTGTDQFKESIRHNLVLNKLAEEYKGQRDFQQIPLAATRRSPTFVEWSSANTVFDLQNRPNTDAPEERFNLFPAVACERVVRNALNSEIESLHIHDLISGDRFEIKADVYVLTAGAVHNTQLLVNSGFGQLGRPNPTNPPELLPSLGSYITEQSLVFCQTVMSTELIDSVKSDMTIRGTPGELTYSVTYTPGASTNKHPDWWNEKVKNHMMQHQEDPLPIPFEDPEPQVTTLFQPSHPWHTQIHRDAFSYGAVQQSIDSRLIVDWRFFGRTEPKEENKLWFSDKITDAYNMPQPTFDFRFPAGRTSKEAEDMMTDMCVMSAKIGGFLPGSLPQFMEPGLVLHLGGTHRMGFDEKEDNCCVNTDSRVFGFKNLFLGGCGNIPTAYGANPTLTAMSLAIKSCEYIKQNFTPSPFTSEAQ
6LKC , Knot 230 587 0.83 40 264 542 
MGSSHHHHHHSSGLVPRGSHMASMTGGQQMGRGSEFELRRQACGRMNPTTTNEMLSPWPWLVTDTNISFDVTVMEQQLRDFSRGCYVVNHNEKGVGIAQTAELVADQAANSNSLPVAAFTPALGTESLGDSNFRRVHGVKYAYYAGAMANGISSEELVIALGQAGILCSFGAAGLIPSRVEKAINRIQAALPNGPYMFNLIHSPSEPALERGSVELFLKHKVRTVEASAFLGLTPQIVYYRAAGLSRDAQGNIVVANKVIAKVSRTEVAEKFMMPAPAKMLQKLVDEGSITPEQMELAQLVPMADDITAEADSGGHTDNRPLVTLLPTILALKEEIQTKYQYPTPIRVGCGGGVGTPDAALATFNMGAAYIVTGSVNQACVEAGASEHTRKLLSTTEMADVTMAPAADMFEMGVKLQVVKRGTLFPMRANKLYELYTRYDSIEAIPADEREKLEKQVFRSTLDDIWAGTVAHFNERDPKQIERATDNPKRKMALIFRWYLGLSSRWSNSGETGREMDYQIWAGPALGAFNQWAKGSYLDNYQERNAVDVAKHLMYGAAYLNRVNSLTSQGVKLPTQLLRWKPTQRMA
7RMD , Knot 66 127 0.84 40 110 123 
SMNPPPPETSNPNKPKRQTNQLQYLLRVVLKTLWKHQFAWPFQQPVDAVKLNLPDYYKIIKTPMDMGTIKKRLENNYYWNAQECIQDFNTMFTNCYIYNKPGDDIVLMAEALEKLFLQKINELPTEE

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 \(c\).

\(|P_{f(1TZL_1)}(2) \setminus P_{f(6LKC_1)}(2)|=78\), \(|P_{f(6LKC_1)}(2) \setminus P_{f(1TZL_1)}(2)|=59\). 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 1:0000001110110001001110010100111111100011110100011111011110001001111100111101101001101110000010000010011011010110101110011100101001010011100100100011001010110011111000100101010000011110001010010100100010001001000100010001110011000010001001111100001011010010011010001000110001011111100011001100010010100110100101010101101111000011100111011010100110111011001000011100011000110010001010101101000100011100000101100010001100000111111001010100110100110001000110011100010001110101110001000001110001001001101010101111000001001100101101011111110110110111110111000111000000001000001111001111101011010110101011011100000100010101100010
Pair \(Z_2\) Length of longest common subsequence
1TZL_1,6LKC_1 137 4
1TZL_1,7RMD_1 229 3
6LKC_1,7RMD_1 212 3

Newick tree

 
[
	7RMD_1:12.10,
	[
		1TZL_1:68.5,6LKC_1:68.5
	]:52.60
]

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 \((0.85)(0.8)(\frac{1209 }{\log_{20} 1209}-\frac{587}{\log_{20}587})=159.\)
Status Protein1 Protein2 d d1/2
Query variables 1TZL_1 6LKC_1 207 198
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]