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Parikh vectors
6CJH_1 6GCW_1 8UFF_1 Letter Amino acid
9 9 0 N Asparagine
22 15 6 G Glycine
4 5 0 W Tryptophan
9 10 0 Y Tyrosine
14 12 0 F Phenylalanine
16 14 0 P Proline
23 19 0 S Serine
7 14 2 T Threonine
17 19 0 R Arginine
17 12 0 D Aspartic acid
19 18 0 I Isoleucine
30 27 0 L Leucine
13 8 0 C Cysteine
11 5 0 H Histidine
14 16 0 K Lycine
22 16 0 V Valine
20 16 8 A Alanine
16 10 0 Q Glutamine
28 20 0 E Glutamic acid
5 11 0 M Methionine 

6CJH_1|Chain A|MAP kinase-interacting serine/threonine-protein kinase 2|Homo sapiens (9606)
>6GCW_1|Chains A, B|Focal adhesion kinase 1|Gallus gallus (9031)
>8UFF_1|Chain A[auth C]|DNA (5'-D(*AP*AP*TP*AP*AP*AP*AP*GP*GP*AP*AP*GP*TP*GP*GP*G)-3')|synthetic construct (32630)
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 \(w=f(c)\)
6CJH , Knot 139 316 0.84 40 204 307 
GSTDSFSGRFEDVYQLQEDVLGEGAHARVQTCINLITSQEYAVKIIEKQPGHIRSRVFREVEMLYQCQGHRNVLELIEFFEEEDRFYLVFEKMRGGSILSHIHKRRHFNELEASVVVQDVASALDFLHNKGIAHRDLKPENILCEHPNQVSPVKICDFGLGSGIKLNGDCSPISTPELLTPCGSAEYMAPEVVEAFSEEASIYDKRCDLWSLGVILYILLSGYPPFVGRCGSDCGWDRGEACPACQNMLFESIQEGKYEFPDKDWAHISCAAKDLISKLLVRDAKQRLSAAQVLQHPWVQGCAPENTLPTPMVLQR
6GCW , Knot 125 276 0.84 40 185 266 
STRDYEIQRERIELGRCIGEGQFGDVHQGIYMSPENPAMAVAIKTCKNCTSDSVREKFLQEALTMRQFDHPHIVKLIGVITENPVWIIMELCTLGELRSFLQVRKFSLDLASLILYAYQLSTALAYLESKRFVHRDIAARNVLVSATDCVKLGDFGLSRYMEDSTYYKASKGKLPIKWMAPESINFRRFTSASDVWMFGVCMWEILMHGVKPFQGVKNNDVIGRIENGERLPMPPNCPPTLYSLMTKCWAYDPSRRPRFTELKAQLSTILEEEKLQ
8UFF , Knot 7 16 0.40 6 8 12 
AATAAAAGGAAGTGGG

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 \(c\).

\(|P_{f(6CJH_1)}(2) \setminus P_{f(6GCW_1)}(2)|=89\), \(|P_{f(6GCW_1)}(2) \setminus P_{f(6CJH_1)}(2)|=70\). 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 1:1000010101001001000111011010100010110000011011000110100011001011000010001101101100000101110010110110010000010010101110011011011000111000101001100010010110100111101101010001100101101010100111011011000101000000110111110111010111110010001100101011000111001001000110001101001100110011100100010110110011101011000110111100
Pair \(Z_2\) Length of longest common subsequence
6CJH_1,6GCW_1 159 4
6CJH_1,8UFF_1 206 2
6GCW_1,8UFF_1 187 2

Newick tree

 
[
	8UFF_1:10.89,
	[
		6CJH_1:79.5,6GCW_1:79.5
	]:24.39
]

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 \((0.85)(0.8)(\frac{592 }{\log_{20} 592}-\frac{276}{\log_{20}276})=88.8\)
Status Protein1 Protein2 d d1/2
Query variables 6CJH_1 6GCW_1 110 102.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]