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Parikh vectors
1WTV_1 6FYO_1 6FNV_1 Letter Amino acid
3 16 12 T Threonine
0 4 1 W Tryptophan
0 21 8 R Arginine
0 9 11 Q Glutamine
0 34 3 L Leucine
0 24 7 K Lycine
0 7 7 M Methionine
0 19 5 S Serine
0 21 11 V Valine
0 24 7 E Glutamic acid
0 23 4 I Isoleucine
0 17 3 F Phenylalanine
0 9 10 N Asparagine
1 16 13 G Glycine
0 21 5 H Histidine
3 15 9 A Alanine
0 23 5 D Aspartic acid
1 9 2 C Cysteine
0 14 5 P Proline
0 13 12 Y Tyrosine 

1WTV_1|Chains A[auth B], B[auth C]|5'-D(*GP*TP*AP*AP*TP*TP*AP*C)-3'|
>6FYO_1|Chain A|Dual specificity protein kinase CLK1|Homo sapiens (9606)
>6FNV_1|Chain A|Major prion protein|Odocoileus hemionus (9872)
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 \(w=f(c)\)
1WTV , Knot 5 8 0.43 8 6 6 
GTAATTAC
6FYO , Knot 146 339 0.83 40 209 328 
GPHLICQSGDVLSARYEIVDTLGEGAFGKVVECIDHKAGGRHVAVKIVKNVDRYCEAARSEIQVLEHLNTTDPNSTFRCVQMLEWFEHHGHICIVFELLGLSTYDFIKENGFLPFRLDHIRKMAYQICKSVNFLHSNKLTHTDLKPENILFVQSDYTEAYNPKIKRDERTLINPDIKVVDFGSATYDDEHHSTLVSTRHYRAPEVILALGWSQPCDVWSIGCILIEYYLGFTVFPTHDSKEHLAMMERILGPLPKHMIQKTRKRKYFHHDRLDWDEHSSAGRYVSRRCKPLKEFMLSQDVEHERLFDLIQKMLEYDPAKRITLREALKHPFFDLLKKSI
6FNV , Knot 71 140 0.83 40 111 133 
GQGGTHSQWNKPSKPKTNMKHVAGAAAAGAVVGGLGGYMLGSAMSRPLIHFGNDYEDRYYRENMYRYPNQVYYRPVDQYNNQNTFVHDCVNITVKQHTVTTTTKGENFTETDIKMMERVVEQMCITQYQRESQAYYQRGA

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 \(c\).

\(|P_{f(1WTV_1)}(2) \setminus P_{f(6FYO_1)}(2)|=3\), \(|P_{f(6FYO_1)}(2) \setminus P_{f(1WTV_1)}(2)|=206\). 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 1:10110010
Pair \(Z_2\) Length of longest common subsequence
1WTV_1,6FYO_1 209 2
1WTV_1,6FNV_1 111 2
6FYO_1,6FNV_1 186 4

Newick tree

 
[
	6FYO_1:10.63,
	[
		1WTV_1:55.5,6FNV_1:55.5
	]:54.13
]

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 \((0.85)(0.8)(\frac{347 }{\log_{20} 347}-\frac{8}{\log_{20}8})=113.\)
Status Protein1 Protein2 d d1/2
Query variables 1WTV_1 6FYO_1 142 72
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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