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Parikh vectors
8VRV_1 1LKO_1 6RGZ_1 Letter Amino acid
5 4 2 C Cysteine
12 22 27 E Glutamic acid
5 2 1 M Methionine
19 14 9 F Phenylalanine
26 5 8 P Proline
18 7 16 S Serine
16 7 17 N Asparagine
34 7 10 T Threonine
8 6 7 Y Tyrosine
10 14 15 R Arginine
15 6 18 D Aspartic acid
26 15 14 G Glycine
10 8 5 H Histidine
23 11 29 L Leucine
14 27 12 A Alanine
7 12 21 I Isoleucine
8 11 18 K Lycine
4 2 2 W Tryptophan
26 6 22 V Valine
20 5 5 Q Glutamine 

8VRV_1|Chains A, B|Capsid protein|Norovirus GII.4 (489821)
>1LKO_1|Chain A|Rubrerythrin all-iron(II) form|Desulfovibrio vulgaris (881)
>6RGZ_1|Chains A, B|Sensor histidine kinase|Thermotoga maritima (2336)
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 \(w=f(c)\)
8VRV , Knot 131 306 0.81 40 182 290 
KPFTVPILTVEEMTNSRFPIPLEKLFTGPSGAFVVQPQNGRCTTDGVLLGTTQLSPVNICTFRGDVTHIAGTQEYTMNLASQNWNNYDPTEEIPAPLGTPDFVGKIQGVLTQTTRGDGSTRGHKATVSTGSVHFTPKLGSVQFSTDTSNDFETGQNTKFTPVGVVQDGSTTHQNEPQQWVLPDYSGRDSHNVHLAPAVAPTFPGEQLLFFRSTMPGCSGYPNMNLDCLLPQEWVQHFYQEAAPAQSDVALLRFVNPDTGRVLFECKLHKSGYVTVAHTGQHDLVIPPNGYFRFDSWVNQFYTLAPM
1LKO , Knot 87 191 0.79 40 136 184 
MKSLKGSRTEKNILTAFAGESQARNRYNYFGGQAKKDGFVQISDIFAETADQEREHAKRLFKFLEGGDLEIVAAFPAGIIADTHANLIASAAGEHHEYTEMYPSFARIAREEGYEEIARVFASIAVAEEFHEKRFLDFARNIKEGRVFLREQATKWRCRNCGYVHEGTGAPELCPACAHPKAHFELLGINW
6RGZ , Knot 111 258 0.79 40 168 246 
VENVTESKELERLKRIDRMKTEFIANISHELRTPLTAIKAYAETIYNSLGELDLSTLKEFLEVIIDQSNHLENLLNELLDFSRLERKSLQINREKVDLCDLVESAVNAIKEFASSHNVNVLFESNVPCPVEAYIDPTRIRQVLLNLLNNGVKYSKKDAPDKYVKVILDEKDGGVLIIVEDNGIGIPDHAKDRIFEQFYRVDSSLTYEVPGTGLGLAITKEIVELHGGRIWVESEVGKGSRFFVWIPKDRAGEDNRQDN

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 \(c\).

\(|P_{f(8VRV_1)}(2) \setminus P_{f(1LKO_1)}(2)|=114\), \(|P_{f(1LKO_1)}(2) \setminus P_{f(8VRV_1)}(2)|=68\). 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 1:011011110100100001111100110110111110100100000111110001011010010101001110000010110001000010001111110101110101110000010100010010100101010101101010000000100100001011111001000000010011110001000001011111110111001111000111001010101001110011001000111100011110110100101110001000101011001000111110101010011001001111
Pair \(Z_2\) Length of longest common subsequence
8VRV_1,1LKO_1 182 3
8VRV_1,6RGZ_1 188 4
1LKO_1,6RGZ_1 146 4

Newick tree

 
[
	8VRV_1:98.15,
	[
		1LKO_1:73,6RGZ_1:73
	]:25.15
]

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 \((0.85)(0.8)(\frac{497 }{\log_{20} 497}-\frac{191}{\log_{20}191})=88.9\)
Status Protein1 Protein2 d d1/2
Query variables 8VRV_1 1LKO_1 112 91
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]