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Parikh vectors
6CJW_1 5LVY_1 8FMZ_1 Letter Amino acid
9 10 6 Y Tyrosine
30 9 18 L Leucine
14 14 17 K Lycine
23 15 15 S Serine
17 9 20 D Aspartic acid
13 2 4 C Cysteine
11 1 4 H Histidine
16 10 6 P Proline
20 6 16 A Alanine
17 2 20 R Arginine
9 7 13 N Asparagine
19 7 17 I Isoleucine
5 2 5 M Methionine
4 1 3 W Tryptophan
16 8 7 Q Glutamine
28 1 16 E Glutamic acid
22 18 17 G Glycine
14 4 14 F Phenylalanine
7 17 14 T Threonine
22 11 14 V Valine 

6CJW_1|Chain A|MAP kinase-interacting serine/threonine-protein kinase 2|Homo sapiens (9606)
>5LVY_1|Chain A|Adhesin protein|Escherichia coli O111:H21 (660582)
>8FMZ_1|Chain A[auth B]|MiniGq|Escherichia coli (562)
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 \(w=f(c)\)
6CJW , Knot 139 316 0.84 40 204 307 
GSTDSFSGRFEDVYQLQEDVLGEGAHARVQTCINLITSQEYAVKIIEKQPGHIRSRVFREVEMLYQCQGHRNVLELIEFFEEEDRFYLVFEKMRGGSILSHIHKRRHFNELEASVVVQDVASALDFLHNKGIAHRDLKPENILCEHPNQVSPVKICDFGLGSGIKLNGDCSPISTPELLTPCGSAEYMAPEVVEAFSEEASIYDKRCDLWSLGVILYILLSGYPPFVGRCGSDCGWDRGEACPACQNMLFESIQEGKYEFPDKDWAHISCAAKDLISKLLVRDAKQRLSAAQVLQHPWVQGCAPENTLPTPMVLQR
5LVY , Knot 73 154 0.79 40 112 148 
NSCSLSISSPDPVTYTIPTDKGDKYINFKLDVPDPRCKALGGTVYFWGADTRDGKLVMKKGQDKYTLMTTYGGAVQQQLGGGYGYYHVSQKTPPQTISGVVSKNVGYKPGQYTVELTGFFSLNDNKQANPTPSSLTSKAAGKNIVSSTGTITIS
8FMZ , Knot 109 246 0.81 40 167 234 
MGSTVSAEDKAAAERSKMIDKNLREDGEKARRTLRLLLLGADNSGKSTIVKQMRILHGGSGGSGGTSGIFETKFQVDKVNFHMFDVGGQRDERRKWIQCFNDVTAIIFVVDSSDYNRLQEALNDFKSIWNNRWLRTISVILFLNKQDLLAEKVLAGKSKIEDYFPEFARYTTPEDATPEPGEDPRVTRAKYFIRKEFVDISTASGDGRHICYPHFTCAVDTENARRIFNDCKDIILQMNLREYNLV

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 \(c\).

\(|P_{f(6CJW_1)}(2) \setminus P_{f(5LVY_1)}(2)|=143\), \(|P_{f(5LVY_1)}(2) \setminus P_{f(6CJW_1)}(2)|=51\). 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
6CJW_1,5LVY_1 194 3
6CJW_1,8FMZ_1 191 3
5LVY_1,8FMZ_1 171 3

Newick tree

 
[
	6CJW_1:99.57,
	[
		8FMZ_1:85.5,5LVY_1:85.5
	]:14.07
]

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 \((0.85)(0.8)(\frac{470 }{\log_{20} 470}-\frac{154}{\log_{20}154})=93.3\)
Status Protein1 Protein2 d d1/2
Query variables 6CJW_1 5LVY_1 120 89
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]