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Parikh vectors
6SNB_1 2WYX_1 6OXQ_1 Letter Amino acid
12 5 1 Y Tyrosine
23 15 6 V Valine
3 1 2 C Cysteine
11 11 13 I Isoleucine
20 10 6 P Proline
21 14 0 S Serine
4 3 2 W Tryptophan
20 11 4 R Arginine
15 15 4 N Asparagine
12 5 2 M Methionine
15 4 2 F Phenylalanine
30 25 8 T Threonine
26 34 3 A Alanine
14 12 5 Q Glutamine
11 12 4 E Glutamic acid
19 17 13 G Glycine
5 4 1 H Histidine
14 28 12 L Leucine
9 16 7 K Lycine
14 14 4 D Aspartic acid 

6SNB_1|Chain A|Capsid protein VP1|Coxsackievirus A10 (42769)
>2WYX_1|Chain A|BETA-LACTAMSE TOHO-1|ESCHERICHIA COLI (511693)
>6OXQ_1|Chains A, B|Protease NL4-3|Human immunodeficiency virus 1 (11676)
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 \(w=f(c)\)
6SNB , Knot 133 298 0.84 40 192 291 
GDPVEDIIHDALSSTVRRAITSGQDVNTAAGTAPSSHRLETGRVPALQAAETGATSNATDENMIETRCVMNRNGVLEATISHFFSRSGLVGVVNLTDGGTDTTGYAVWDIDIMGFVQLRRKCEMFTYMRFNAEFTFVTTTENGEARPFMLQYMYVPPGAPKPTGRDAFQWQTATNPSVFVKLTDPPAQVSVPFMSPASAYQWFYDGYPTFGQHPETSNTTYGQCPNNMMGTFAVRVVSRVASQLKLQTRVYMKLKHVRAWIPRPIRSQPYLLKNFPNYDSSKITYSARDRASIKQANM
2WYX , Knot 114 256 0.82 40 164 244 
VQQQLEALEKSSGGRLGVALINTADNSQILYRADERFAMCSTSKVMAAAAVLKQSESDKHLLNQRVEIKKSDLVNYNPIAEKHVNGTMTLAELGAAALQYSDNTAMNKLIAHLGGPDKVTAFARSLGDETFRLDRTAPTLNTAIPGDPRDTTTPLAMAQTLKNLTLGKALAETQRAQLVTWLKGNTTGSASIRAGLPKSWVVGDKTGSGDYGTTNDIAVIWPENHAPLVLVTYFTQPEQKAENRNDILAAAAKIVT
6OXQ , Knot 52 99 0.80 38 79 94 
PQITLWKRPLVTIKIGGQLKEALLDTGADDTVLEEMNLPGRWKPKMIGGIGGFIKVRQYDQILIEICGHKAIGTVLVGPTPVNIIGRNLLTQIGCTLNF

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 \(c\).

\(|P_{f(6SNB_1)}(2) \setminus P_{f(2WYX_1)}(2)|=100\), \(|P_{f(2WYX_1)}(2) \setminus P_{f(6SNB_1)}(2)|=72\). 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 1:1011001100110001001100100100111011000010010111101100110001000011000011000111010100110001111110100110000101110101111101000001100101010101100000101011110010111111010100110100100101110100111010111101101001100101011001000000010010011101110110011001010001010100101111011000101100110000001000100010100101
Pair \(Z_2\) Length of longest common subsequence
6SNB_1,2WYX_1 172 3
6SNB_1,6OXQ_1 185 3
2WYX_1,6OXQ_1 157 3

Newick tree

 
[
	6SNB_1:92.63,
	[
		2WYX_1:78.5,6OXQ_1:78.5
	]:14.13
]

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 \((0.85)(0.8)(\frac{554 }{\log_{20} 554}-\frac{256}{\log_{20}256})=84.6\)
Status Protein1 Protein2 d d1/2
Query variables 6SNB_1 2WYX_1 110 100.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]