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Parikh vectors
7ASU_1 5KGK_1 5MTY_1 Letter Amino acid
49 8 19 K Lycine
21 3 11 M Methionine
55 18 20 S Serine
28 7 19 T Threonine
12 5 4 C Cysteine
46 11 15 Q Glutamine
18 11 12 H Histidine
22 18 22 I Isoleucine
54 22 22 V Valine
39 21 19 R Arginine
19 6 14 N Asparagine
35 20 15 G Glycine
70 31 43 L Leucine
43 15 17 P Proline
8 7 5 W Tryptophan
20 7 15 Y Tyrosine
51 9 25 A Alanine
39 19 27 D Aspartic acid
59 24 23 E Glutamic acid
20 14 13 F Phenylalanine 

7ASU_1|Chain A|DNA-directed RNA polymerase III subunit RPC5|Homo sapiens (9606)
>5KGK_1|Chain A|Serine/threonine-protein kinase pim-1|Homo sapiens (9606)
>5MTY_1|Chain A|Mitogen-activated protein kinase 14|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 \(w=f(c)\)
7ASU , Knot 271 708 0.83 40 275 661 
MANEEDDPVVQEIDVYLAKSLAEKLYLFQYPVRPASMTYDDIPHLSAKIKPKQQKVELEMAIDTLNPNYCRSKGEQIALNVDGACADETSTYSSKLMDKQTFCSSQTTSNTSRYAAALYRQGELHLTPLHGILQLRPSFSYLDKADAKHREREAANEAGDSSQDEAEDDVKQITVRFSRPESEQARQRRVQSYEFLQKKHAEEPWVHLHYYGLRDSRSEHERQYLLCPGSSGVENTELVKSPSEYLMMLMPPSQEEEKDKPVAPSNVLSMAQLRTLPLADQIKILMKNVKVMPFANLMSLLGPSIDSVAVLRGIQKVAMLVQGNWVVKSDILYPKDSSSPHSGVPAEVLCRGRDFVMWKFTQSRWVVRKEVATVTKLCAEDVKDFLEHMAVVRINKGWEFILPYDGEFIKKHPDVVQRQHMLWTGIQAKLEKVYNLVKETMPKKPDAQSGPAGLVCGDQRIQVAKTKAQQNHALLERELQRRKEQLRVPAVPPGVRIKEEPVSEEGEEDEEQEAEEEPMDTSPSGLHSKLANGLPLGRAAGTDSFNGHPPQGCASTPVARELKAFVEATFQRQFVLTLSELKRLFNLHLASLPPGHTLFSGISDRMLQDTVLAAGCKQILVPFPPQTAASPDEQKVFALWESGDMSDQHRQVLLEIFSKNYRVRRNMIQSRLTQECGEDLSKQEVDKVLKDCCVSYGGMWYLKGTVQS
5KGK , Knot 122 276 0.82 40 176 259 
EKEPLESQYQVGPLLGSGGFGSVYSGIRVSDNLPVAIKHVEKDRISDWGELPNGTRVPMEVVLLKKVSSGFSGVIRLLDWFERPDSFVLILERPEPVQDLFDFITERGALQEELARSFFWQVLEAVRHCHNCGVLHRDIKDENILIDLNRGELKLIDFGSGALLKDTVYTDFDGTRVYSPPEWIRYHRYHGRSAAVWSLGILLYDMVCGDIPFEHDEEIIRGQVFFRQRVSSECQHLIRWCLALRPSDRPTFEEIQNHPWMQDVLLPQETAEIHLH
5MTY , Knot 159 360 0.86 40 224 346 
MSQERPTFYRQELNKTIWEVPERYQNLSPVGSGAYGSVCAAFDTKTGLRVAVKKLSRPFQSIIHAKRTYRELRLLKHMKHENVIGLLDVFTPARSLEEFNDVYLVTHLMGADLNNIVKCQKLTDDHVQFLIYQILRGLKYIHSADIIHRDLKPSNLAVNEDCELKILDFGLARHTDDEMTGYVATRWYRAPEIMLNWMHYNQTVDIWSVGCIMAELLTGRTLFPGTDHIDQLKLILRLVGTPGAELLKKISSESARNYIQSLTQMPKMNFANVFIGANPLAVDLLEKMLVLDSDKRITAAQALAHAYFAQYHDPDDEPVADPYDQSFESRDLLIDEWKSLTYDEVISFVPPPLDQEEMES

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 \(c\).

\(|P_{f(7ASU_1)}(2) \setminus P_{f(5KGK_1)}(2)|=143\), \(|P_{f(5KGK_1)}(2) \setminus P_{f(7ASU_1)}(2)|=44\). 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 1:110000011100101011001100101100110110100001101010101000010101110010100000010011101011010000000001100001000000000000111100010101011011101010100100101000000110011000000100010010101001000010000100001100001001110100011000000000001101100110000110010001111111000000001111001101101001111001011100101111101101111010011110110011111010111000110100000100111101100100111101000011100011010010100100110011110100110111100101100010110000111011010100100110001100101001111110100010110001000011100010000001011111111010001100010000000100011000101100011011111011100010101101010011100101110101000111010010011010110111100110110001100011111000111111100110100001111100101000000111011000001000110001000010010000100110000100111101010100
Pair \(Z_2\) Length of longest common subsequence
7ASU_1,5KGK_1 187 4
7ASU_1,5MTY_1 153 4
5KGK_1,5MTY_1 182 4

Newick tree

 
[
	5KGK_1:96.94,
	[
		7ASU_1:76.5,5MTY_1:76.5
	]:20.44
]

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 \((0.85)(0.8)(\frac{984 }{\log_{20} 984}-\frac{276}{\log_{20}276})=190.\)
Status Protein1 Protein2 d d1/2
Query variables 7ASU_1 5KGK_1 244 168
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]