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Parikh vectors
6JDA_1 2WIZ_1 7UZO_1 Letter Amino acid
41 13 7 A Alanine
8 0 5 H Histidine
7 11 3 F Phenylalanine
12 7 8 P Proline
3 2 4 W Tryptophan
6 4 4 Y Tyrosine
10 10 8 R Arginine
15 4 5 D Aspartic acid
8 1 6 C Cysteine
14 3 4 Q Glutamine
29 13 6 G Glycine
3 3 1 M Methionine
15 5 2 T Threonine
24 12 7 V Valine
13 14 8 E Glutamic acid
19 5 3 I Isoleucine
13 12 5 K Lycine
9 5 2 S Serine
14 2 4 N Asparagine
28 13 9 L Leucine 

6JDA_1|Chain A|N-acetylmannosamine kinase|Pasteurella multocida (747)
>2WIZ_1|Chains A, B|ARCHAEAL HJC|ARCHAEOGLOBUS FULGIDUS DSM 4304 (224325)
>7UZO_1|Chain A|Parathyroid hormone/parathyroid hormone-related peptide receptor|Homo sapiens (9606)
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 \(w=f(c)\)
6JDA , Knot 126 291 0.81 40 174 272 
MRCLALDIGGTKIASAIVTDGKIEQRQQIATPQADAANAMHDTLANILALYAGQFDYVAVASTGIINHGVLTALNPKNLGGLAEFPLKESIARHTDKPIGLLNDVQAAACAEYKDEDKNAVQNFVFITVSTGVGGGIILERRLLTEPNGVAGHIGHTLADPNGPVCGCGRVGCVEAVAAGRAIEAVSSQWNPPCTPKQAFELFRKNDEKATALIQRSASAIANLIADLVIGLDVQKVVVGGSVGLAEGYLPLVKQYLNTMPHFYHCTVEQARHGQDAGLLGAAWWVADCLK
2WIZ , Knot 68 139 0.80 38 106 135 
GTMGKSKGTRFERDLLVELWKAGFAAIRVAGSGVSPFPCPDIVAGNGRTYLAIEVKMRKELPLYLSADEVEQLVTFARGFGAEAYVALKLPRKKWRFFPVQMLERTEKNFKIDESVYPLGLEIAEVAGKFFQERFGEKV
7UZO , Knot 54 101 0.82 40 91 99 
DVMTKEEQIFLLHRAQAQCEKRLKEVLQRPAGRPCLPEWDHILCWPLGAPGEVVAVPCPDYIYDFNHKGHAYRRCDRNGSWELVPGHNRTWANYSECVKFL

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 \(c\).

\(|P_{f(6JDA_1)}(2) \setminus P_{f(2WIZ_1)}(2)|=113\), \(|P_{f(2WIZ_1)}(2) \setminus P_{f(6JDA_1)}(2)|=45\). 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 1:100111011100110111001010000011010101101100011011110110100111100111001110110100111110111000110000011111001011101000000001100111101001111111100011001011110110011010111010101101011111011011000101100100110110000001011100010111011101111101001111101111010111100010011010000100100100111111111110010
Pair \(Z_2\) Length of longest common subsequence
6JDA_1,2WIZ_1 158 3
6JDA_1,7UZO_1 189 3
2WIZ_1,7UZO_1 145 4

Newick tree

 
[
	6JDA_1:91.44,
	[
		2WIZ_1:72.5,7UZO_1:72.5
	]:18.94
]

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 \((0.85)(0.8)(\frac{430 }{\log_{20} 430}-\frac{139}{\log_{20}139})=87.0\)
Status Protein1 Protein2 d d1/2
Query variables 6JDA_1 2WIZ_1 109 80
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]