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Parikh vectors
9DJT_1 2LER_1 6QKZ_1 Letter Amino acid
21 0 59 A Alanine
26 0 40 Q Glutamine
7 0 10 H Histidine
22 0 47 T Threonine
25 2 72 S Serine
21 0 60 V Valine
11 1 37 N Asparagine
16 4 13 C Cysteine
12 0 73 G Glycine
38 1 71 L Leucine
8 0 24 M Methionine
22 0 55 E Glutamic acid
26 0 57 I Isoleucine
12 1 46 F Phenylalanine
9 0 15 W Tryptophan
19 1 48 R Arginine
20 0 48 D Aspartic acid
25 1 54 K Lycine
21 0 32 P Proline
12 0 36 Y Tyrosine 

9DJT_1|Chains A, D|Protein cereblon|Homo sapiens (9606)
>2LER_1|Chain A|Conotoxin pc16a|Conus pictus (1042615)
>6QKZ_1|Chains A, C|GluA1|Rattus norvegicus (10116)
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 \(w=f(c)\)
9DJT , Knot 161 373 0.85 40 221 361 
RTLHDDDSCQVIPVLPQVMMILIPGQTLPLQLFHPQEVSMVRNLIQKDRTFAVLAYSNVQEREAQFGTTAEIYAYREEQDFGIEIVKVKAIGRQRFKVLELRTQSDGIQQAKVQILPECVLPSTMSAVQLESLNKCQIFPSKPVSREDQCSYKWWQKYQKRKFHCANLTSWPRWLYSLYDAETLMDRIKKQLREWDENLKDDSLPSNPIDFSYRVAACLPIDDVLRIQLLKIGSAIQRLRCELDIMNKCTSLCCKQCQETEITTKNEIFSLSLCGPMAAYVNPHGYVHETLTVYKACNLNLIGRPSTEHSWFPGYAWTVAQCKICASHIGWKFTATKKDMSPQKFWGLTRSALLPTIPDTEDEISPDKVILCL
2LER , Knot 8 11 0.58 14 9 9 
SCSCKRNFLCC
6QKZ , Knot 336 897 0.85 40 318 833 
ADYKDDDDKNFPNNIQIGGLFPNQQSQEHAAFRFALSQLTEPPKLLPQIDIVNISDSFEMTYRFCSQFSKGVYAIFGFYERRTVNMLTSFCGALHVCFITPSFPVDTSNQFVLQLRPELQEALISIIDHYKWQTFVYIYDADRGLSVLQRVLDTAAEKNWQVTAVNILTTTEEGYRMLFQDLEKKKERLVVVDCESERLNAILGQIVKLEKNGIGYHYILANLGFMDIDLNKFKESGANVTGFQLVNYTDTIPARIMQQWRTSDSRDHTRVDWKRPKYTSALTYDGVKVMAEAFQSLRRQRIDISRRGNAGDCLANPAVPWGQGIDIQRALQQVRFEGLTGNVQFNEKGRRTNYTLHVIEMKHDGIRKIGYWNEDDKFVPAATDAQAGGDNSSVQNRTYIVTTILEDPYVMLKKNANQFEGNDRYEGYCVELAAEIAKHVGYSYRLEIVSDGKYGARDPDTKAWNGMVGELVYGRADVAVAPLTITLVREEVIDFSKPFMSLGISIMIKKPQKSKPGVFSFLDPLAYEIWMCIVFAYIGVSVVLFLVSRFSPYEWHSEEFEEGRDQTTSDQSNEFGIFNSLWFSLGAFMQQGCDISPRSLSGRIVGGVWWFFTLIIISSYTANLAAFLTVERMVSPIESAEDLAKQTEIAYGTLEAGSTKEFFRRSKIAVFEKMWTYMKSAEPSVFVRTTEEGMIRVRKSKGKYAYLLESTMNEYIEQRKPCDTMKVGGNLDSKGYGIATPKGSALRGPVNLAVLKLSEQGVLDKLKSKWWYDKGECGSKDSGSKDKTSALSLSNVAGVFYILIGGLGLAMLVALIEFCYKSRSESKRMKGFCLIPQQSINEAIRTSTLPRNSGAGASGGGGSGENGRVVSQDFPKSMQSIPCMSHSSGMPLGATGL

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 \(c\).

\(|P_{f(9DJT_1)}(2) \setminus P_{f(2LER_1)}(2)|=214\), \(|P_{f(2LER_1)}(2) \setminus P_{f(9DJT_1)}(2)|=2\). 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 1:0010000000111111011111111001110110100101100110000011111000100001011001010100000011101101011100010110100000110010101110011100101101001000011100110000000001100000001001010011011001001001100100010010001000011001101000111011100110101101101100100010110000010000000001000001101010111110101010100010100100101110100000111101101100010100111010100001010011110001111011000001010011101
Pair \(Z_2\) Length of longest common subsequence
9DJT_1,2LER_1 216 3
9DJT_1,6QKZ_1 173 4
2LER_1,6QKZ_1 317 2

Newick tree

 
[
	2LER_1:14.42,
	[
		9DJT_1:86.5,6QKZ_1:86.5
	]:61.92
]

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 \((0.85)(0.8)(\frac{384 }{\log_{20} 384}-\frac{11}{\log_{20}11})=122.\)
Status Protein1 Protein2 d d1/2
Query variables 9DJT_1 2LER_1 156 80
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]