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Parikh vectors
6KPQ_1 7FTA_1 4ZCT_1 Letter Amino acid
2 15 17 K Lycine
1 8 4 F Phenylalanine
4 15 10 S Serine
3 12 12 T Threonine
4 12 14 V Valine
3 11 8 A Alanine
7 11 19 D Aspartic acid
0 3 1 C Cysteine
0 9 7 Q Glutamine
5 16 8 G Glycine
3 7 4 M Methionine
3 5 5 P Proline
1 9 10 N Asparagine
7 9 16 E Glutamic acid
0 6 5 H Histidine
1 0 9 Y Tyrosine
3 8 5 R Arginine
2 25 11 I Isoleucine
3 13 12 L Leucine
1 1 3 W Tryptophan 

6KPQ_1|Chain A|Serine protease subunit NS2B|Zika virus (64320)
>7FTA_1|Chains A, B, C, D|Syntenin-1|Homo sapiens (9606)
>4ZCT_1|Chain A|Cholinephosphate cytidylyltransferase|Plasmodium falciparum (36329)
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 \(w=f(c)\)
6KPQ , Knot 32 53 0.80 34 49 51 
MTGKSVDMYIERAGDITWEKDAEVTGNSPRLDVALDESGDFSLVEEDGPPMRE
7FTA , Knot 90 195 0.81 38 132 183 
SMAEIKQGIREVILCKDQDGKIGLRLKSIDNGIFVQLVQANSPASLVGLRFGDQVLQINGENCAGWSSDKAHKVLKQAFGEKITMTIRDRPFERTITMHKDSTGHVGFIFKNGKITSIVKDSSAARNGLLTEHNICEINGQNVIGLKDSQIADILSTSGTVVTITIMPAFIFEHIIKRMAPSIMKSLMDHTIPEV
4ZCT , Knot 84 180 0.80 40 133 169 
GHMAVPDDDDDDDNSNDESEYESSQMDSEKNKGSIKNSKNVVIYADGVYDMLHLGHMKQLEQAKKLFENTTLIVGVTSDNETKLFKGQVVQTLEERTETLKHIRWVDEIISPCPWVVTPEFLEKYKIDYVAHDDIPYANNQKEDIYAWLKRAGKFKATQRTEGVSTTDLIVRILKNYEDY

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 \(c\).

\(|P_{f(6KPQ_1)}(2) \setminus P_{f(7FTA_1)}(2)|=27\), \(|P_{f(7FTA_1)}(2) \setminus P_{f(6KPQ_1)}(2)|=110\). 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 1:10100101010011010100010101001010111000101011000111100
Pair \(Z_2\) Length of longest common subsequence
6KPQ_1,7FTA_1 137 3
6KPQ_1,4ZCT_1 148 3
7FTA_1,4ZCT_1 157 3

Newick tree

 
[
	4ZCT_1:78.70,
	[
		6KPQ_1:68.5,7FTA_1:68.5
	]:10.20
]

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 \((0.85)(0.8)(\frac{248 }{\log_{20} 248}-\frac{53}{\log_{20}53})=64.4\)
Status Protein1 Protein2 d d1/2
Query variables 6KPQ_1 7FTA_1 78 50
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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