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Parikh vectors
8FCL_1 7EOJ_1 3MNH_1 Letter Amino acid
63 19 22 G Glycine
10 0 12 H Histidine
40 0 18 S Serine
32 0 12 T Threonine
13 0 8 Y Tyrosine
12 18 1 C Cysteine
26 0 11 Q Glutamine
68 0 13 E Glutamic acid
53 0 17 V Valine
59 0 9 I Isoleucine
47 0 23 K Lycine
3 0 7 W Tryptophan
58 0 7 R Arginine
20 0 2 M Methionine
43 0 17 P Proline
69 0 26 L Leucine
31 0 12 F Phenylalanine
65 4 14 A Alanine
32 0 10 N Asparagine
62 0 19 D Aspartic acid 

8FCL_1|Chains A, B, C, D, E, F|Transitional endoplasmic reticulum ATPase|Homo sapiens (9606)
>7EOJ_1|Chain A|Pepper (49-MER)|synthetic construct (32630)
>3MNH_1|Chain A|Carbonic anhydrase 2|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 \(w=f(c)\)
8FCL , Knot 295 806 0.81 40 279 705 
MASGADSKGDDLSTAILKQKNRPNRLIVDEAINEDNSVVSLSQPKMDELQLFRGDTVLLKGKKRREAVCIVLSDDTCSDEKIRMNRVVRNNLRVRLGDVISIQPCPDVKYGKRIHVLPIDDTVEGITGNLFEVYLKPYFLEAYRPIRKGDIFLVRGGMRAVEFKVVETDPSPYCIVAPDTVIHCEGEPIKREDEEESLNEVGYDDIGGCRKQLAQIKEMVELPLRHPALFKAIGVKPPRGILLYGPPGTGKTLIARAVANETGAFFFLINGPEIMSKLAGESESNLRKAFEEAEKNAPAIIFIDELDAIAPKREKTHGEVERRIVSQLLTLMDGLKQRAHVIVMAATNRPNSIDPALRRFGRFDREVDIGIPDATGRLEILQIHTKNMKLADDVDLEQVANETHGHVGADLAALCSEAALQAIRKKMDLIDLEDETIDAEVMNSLAVTMDDFRWALSQSNPSALRETVVEVPQVTWEDIGGLEDVKRELQELVQYPVEHPDKFLKFGMTPSKGVLFYGPPGCGKTLLAKAIANECQANFISIKGPELLTMWFGESEANVREIFDKARQAAPCVLFFDELDSIAKARGGNIGDGGGAADRVINQILTEMDGMSTKKNVFIIGATNRPDIIDPAILRPGRLDQLIYIPLPDEKSRVAILKANLRKSPVAKDVDLEFLAKMTNGFSGADLTEICQRACKLAIRESIESEIRRERERQTNPSAMEVEEDDPVPEIRRDHFEEAMRFARRSVSDNDIRKYEMFAQTLQQSRGFGSFRFPSGNQGGAGPSQGSGGGTGGSVYTEDNDDDLYG
7EOJ , Knot 15 49 0.39 8 15 28 
GGCGCACUGGCGCUGCGCCUUCGGGCGCCAAUCGUAGCGUGUCGGCGCC
3MNH , Knot 112 260 0.79 40 177 249 
MSHHWGYGKHNGPEHWHKDFPIAKGERQSPVDIDTHTAKYDPSLKPLSVSYDQATSLRILNNGHAFNVEFDDSQDKAVLKGGPLDGTYRLIQFHFHWGSLDGQGSEHTVDKKKYAAELHLVHWNTKYGDFGKAVQQPDGLAVLGIFLKVGSAKPGLQKVVDVLDSIKTAGKSADFTNFDPRGLLPESLDYWTYPGSLTTPPLLECVTWIVLKEPISVSSEQVLKFRKLNFNGEGEPEELMVDNWRPAQPLKNRQIKASFK

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 \(c\).

\(|P_{f(8FCL_1)}(2) \setminus P_{f(7EOJ_1)}(2)|=273\), \(|P_{f(7EOJ_1)}(2) \setminus P_{f(8FCL_1)}(2)|=9\). 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 1:11011000100100111000001001110011000001101001010010110100111010000011011100000000010100110001010110110101010100100101111000101101011010101011010011001011110111011010110001010011110011000101100000000100110001110000110100110111001111011110110111101111010011101110001111111011011001110000010011001000111111100101111000000101000110011011011000101111110001001011100110100010111101010101101000010110010100110000101110111100011101100010110100001010110011101001011100001011000110110101001111001000100110011001001101110100111101111010011101110000101101011011011110001010011001001110111100100110101101101111100110011001011000001111110001011011110110100110111100000111101010001110010101110100110110100100010011100010001000000000101101000011101000010011011000100001000011100100001110101101001111100101110110100000000101
Pair \(Z_2\) Length of longest common subsequence
8FCL_1,7EOJ_1 282 3
8FCL_1,3MNH_1 166 4
7EOJ_1,3MNH_1 186 2

Newick tree

 
[
	7EOJ_1:12.32,
	[
		8FCL_1:83,3MNH_1:83
	]:46.32
]

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 \((0.85)(0.8)(\frac{855 }{\log_{20} 855}-\frac{49}{\log_{20}49})=232.\)
Status Protein1 Protein2 d d1/2
Query variables 8FCL_1 7EOJ_1 292 152.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]