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Parikh vectors
1WJN_1 6LAX_1 6BWW_1 Letter Amino acid
3 0 15 N Asparagine
3 0 27 I Isoleucine
17 0 53 L Leucine
6 0 31 P Proline
15 0 33 S Serine
2 15 4 C Cysteine
7 0 23 K Lycine
2 0 8 M Methionine
1 0 37 F Phenylalanine
1 0 1 W Tryptophan
8 18 33 G Glycine
2 0 27 T Threonine
2 0 13 Y Tyrosine
6 0 30 V Valine
0 11 22 A Alanine
4 0 36 R Arginine
3 0 24 D Aspartic acid
7 0 16 Q Glutamine
8 0 27 E Glutamic acid
0 0 12 H Histidine 

1WJN_1|Chain A|Tubulin-folding protein TBCE|Mus musculus (10090)
>6LAX_1|Chains A, E[auth B]|RNA (55-MER)|Bifidobacterium angulatum (1683)
>6BWW_1|Chain A|Cytochrome P450 2B4|Oryctolagus cuniculus (9986)
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 \(w=f(c)\)
1WJN , Knot 48 97 0.75 36 75 91 
GSSGSSGQLLTLKIKCSNQPERQILEKQLPDSMTVQKVKGLLSRLLKVPVSELLLSYESSKMPGREIELENDLQPLQFYSVENGDCLLVRWSGPSSG
6LAX , Knot 21 55 0.51 8 16 36 
GGCAUCGUGCCUCGCAUUGCACUCCGCGGGGCGAUAAGUCCUGAAAAGGGAUGUC
6BWW , Knot 191 472 0.83 40 237 443 
MAKKTSSKGKLPPGPSPLPVLGNLLQMDRKGLLRSFLRLREKYGDVFTVYLGSRPVVVLCGTDAIREALVDQAEAFSGRGKIAVVDPIFQGYGVIFANGERWRALRRFSLATMRDFGMGKRSVEERIQEEARCLVEELRKSKGALLDNTLLFHSITSNIICSIVFGKRFDYKDPVFLRLLDLFFQSFSLISSFSSQVFELFPGFLKYFPGTHRQIYRNLQEINTFIGQSVEKHRATLDPSNPRDFIDVYLLRMEKDKSDPSSEFHHQNLILTVLSLFFAGTETTSTTLRYGFLLMLKYPHVTERVQKEIEQVIGSHRPPALDDRAKMPYTDAVIHEIQRLGDLIPFGVPHTVTKDTQFRGYVIPKNTEVFPVLSSALHDPRYFETPNTFNPGHFLDANGALKRNEGFMPHSLGKRICLGEGIARTELFLFFTTILQNFSIASPVPPEDIDLTPRESGVGNVPPSYQIRFLAR

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 \(c\).

\(|P_{f(1WJN_1)}(2) \setminus P_{f(6LAX_1)}(2)|=75\), \(|P_{f(6LAX_1)}(2) \setminus P_{f(1WJN_1)}(2)|=16\). 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 1:1001001011010100000100011000110010100101110011011100111000000111001010001011010010010011101011001
Pair \(Z_2\) Length of longest common subsequence
1WJN_1,6LAX_1 91 1
1WJN_1,6BWW_1 206 4
6LAX_1,6BWW_1 247 2

Newick tree

 
[
	6BWW_1:12.64,
	[
		1WJN_1:45.5,6LAX_1:45.5
	]:83.14
]

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 \((0.85)(0.8)(\frac{152 }{\log_{20} 152}-\frac{55}{\log_{20}55})=33.6\)
Status Protein1 Protein2 d d1/2
Query variables 1WJN_1 6LAX_1 46 32.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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