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Parikh vectors
6QVD_1 6TFM_1 6FYF_1 Letter Amino acid
50 6 17 F Phenylalanine
71 12 30 P Proline
18 10 5 C Cysteine
40 7 32 R Arginine
15 3 13 N Asparagine
77 9 46 G Glycine
47 4 16 I Isoleucine
113 13 46 L Leucine
28 5 10 M Methionine
53 7 28 T Threonine
73 8 59 A Alanine
26 7 15 Y Tyrosine
13 2 9 W Tryptophan
73 5 28 V Valine
41 8 29 D Aspartic acid
62 12 20 E Glutamic acid
25 2 13 H Histidine
42 6 10 K Lycine
76 4 27 S Serine
45 8 11 Q Glutamine 

6QVD_1|Chains A, B|Chloride channel protein 1|Homo sapiens (9606)
>6TFM_1|Chains A, B, C, D|Frizzled-8|Mus musculus (10090)
>6FYF_1|Chains A, B, C, D|Putative FAD-dependent oxygenase EncM|Streptomyces maritimus (115828)
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 \(w=f(c)\)
6QVD , Knot 355 988 0.82 40 308 863 
MEQSRSQQRGGEQSWWGSDPQYQYMPFEHCTSYGLPSENGGLQHRLRKDAGPRHNVHPTQIYGHHKEQFSDREQDIGMPKKTGSSSTVDSKDEDHYSKCQDCIHRLGQVVRRKLGEDGIFLVLLGLLMALVSWSMDYVSAKSLQAYKWSYAQMQPSLPLQFLVWVTFPLVLILFSALFCHLISPQAVGSGIPEMKTILRGVVLKEYLTMKAFVAKVVALTAGLGSGIPVGKEGPFVHIASICAAVLSKFMSVFCGVYEQPYYYSDILTVGCAVGVGCCFGTPLGGVLFSIEVTSTYFAVRNYWRGFFAATFSAFVFRVLAVWNKDAVTITALFRTNFRMDFPFDLKELPAFAAIGICCGLLGAVFVYLHRQVMLGVRKHKALSQFLAKHRLLYPGIVTFVIASFTFPPGMGQFMAGELMPREAISTLFDNNTWVKHAGDPESLGQSAVWIHPRVNVVIIIFLFFVMKFWMSIVATTMPIPCGGFMPVFVLGAAFGRLVGEIMAMLFPDGILFDDIIYKILPGGYAVIGAAALTGAVSHTVSTAVICFELTGQIAHILPMMVAVILANMVAQSLQPSLYDSIIQVKKLPYLPDLGWNQLSKYTIFVEDIMVRDVKFVSASYTYGELRTLLQTTTVKTLPLVDSKDSMILLGSVERSELQALLQRHLCPERRLRAAQEMARKLSELPYDGKARLAGEGLPGAPPGRPESFAFVDEDEDEDLSGKSELPPSLALHPSTTAPLSPEEPNGPLPGHKQQPEAPEPAGQRPSIFQSLLHCLLGRARPTKKKTTQDSTDLVDNMSPEEIEAWEQEQLSQPVCFDSCCIDQSPFQLVEQTTLHKTHTLFSLLGLHLAYVTSMGKLRGVLALEELQKAIEGHTKSGVQLRPPLASFRNTTSTRKSTGAPPSSAENWNLPEDRPGATGTGDVIAASPETPVPSPSPEPPLSLAPGKVEGELEELELVESPGLEEELADILQGPSLRSTDEEDEDELIL
6TFM , Knot 70 138 0.83 40 111 135 
ETGASAKELACQEITVPLCKGIGYEYTYMPNQFNHDTQDEAGLEVHQFWPLVEIQCSPDLKFFLCSMYTPICLEDYKKPLPPCRSVCERAKAGCAPLMRQYGFAWPDRMRCDRLPEQGNPDTLCMDYERGTLEVLFQG
6FYF , Knot 186 464 0.82 40 226 434 
MQFPQLDPATLAAFSAAFRGELIWPSDADYDEARRIWNGTIDRRPALIARCTSTPDVVAAVSFARKSGLLVAVRGGGHSMAGHSVCDGGIVIDLSLMNSIKVSRRLRRARAQGGCLLGAFDTATQAHMLATPAGMVSHTGLGGLVLGGGFGWLSRKYGLSIDNLTSVEIVTADGGVLTASDTENPDLFWAVRGGGGNFGVVTAFEFDLHRVGPVRFASTYYSLDEGPQVIRAWRDHMATAPDELTWALYLRLAPPLPELPADMHGKPVICAMSCWIGDPHEGERQLESILHAGKPHGLTKATLPYRALQAYSFPGAVVPDRIYTKSGYLNELSDEATDTVLEHAADIASPFTQLELLYLGGAVARVPDDATAYPNRQSPFVTNLAAAWMDPTEDARHTAWAREGYRALAGHLSGGYVNFMNPGEADRTREAYGAAKFERLQGVKAKYDPTNLFRLNQNIPPSSP

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 \(c\).

\(|P_{f(6QVD_1)}(2) \setminus P_{f(6TFM_1)}(2)|=218\), \(|P_{f(6TFM_1)}(2) \setminus P_{f(6QVD_1)}(2)|=21\). 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 1:1000000001100011100100001110000001110001110001000111000101001010000010000001111000100001000000000000001001101100011001111111111111101010010100101001001010101110111110111111110111001101011101110100110111100010101111011110111101111100111101101011110011011011000100000110110111110011011111110101000011100010111110101111011111000110101110001010111010011111111100111111110100011111000011001110001101111011110101111110111101110011001100001100110100110011110101011111111111011101110011110111111111111110111011111110111100110011111011111111011100010011101010101101111111111101110010101000110100110110111001000011100111001011010000101001100001001111000001111101000010111000101000101100110010011001010111011111111010011110000000101000111011101000111010010111110000101101110010110011001110101000000000001100101001011000010011010000100011011000010000011011110110100110101111100100110100001101011110100000000001111001001011000111010101111010011101010111011110101010010110011100011011011010000000000111
Pair \(Z_2\) Length of longest common subsequence
6QVD_1,6TFM_1 239 3
6QVD_1,6FYF_1 148 4
6TFM_1,6FYF_1 195 3

Newick tree

 
[
	6TFM_1:11.45,
	[
		6QVD_1:74,6FYF_1:74
	]:44.45
]

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 \((0.85)(0.8)(\frac{1126 }{\log_{20} 1126}-\frac{138}{\log_{20}138})=269.\)
Status Protein1 Protein2 d d1/2
Query variables 6QVD_1 6TFM_1 334 190
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]