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Parikh vectors
6JJT_1 1PUI_1 6EWW_1 Letter Amino acid
3 3 2 W Tryptophan
7 4 11 Y Tyrosine
7 13 13 D Aspartic acid
12 13 8 G Glycine
11 6 10 I Isoleucine
9 13 19 S Serine
15 12 9 T Threonine
3 12 11 R Arginine
6 14 26 E Glutamic acid
4 15 20 K Lycine
7 6 6 F Phenylalanine
8 7 4 P Proline
7 16 12 V Valine
5 15 13 Q Glutamine
1 3 2 H Histidine
1 7 7 M Methionine
15 25 24 L Leucine
18 17 23 A Alanine
10 9 9 N Asparagine
0 0 3 C Cysteine 

6JJT_1|Chains A, B, C, D|PhnH|Penicillium herquei (69774)
>1PUI_1|Chains A, B|Probable GTP-binding protein engB|Escherichia coli (562)
>6EWW_1|Chains A, B, C, D|14-3-3 protein zeta/delta|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 \(w=f(c)\)
6JJT , Knot 71 149 0.79 38 109 141 
MKFTYLVSLAAFAVTALGSRPTPPNLEFLFSANLTKGPAYIYDQSDAQIKALQTLTGGIIAGPNFDGTVIGGTALSTRGADGTIRADAHYLIQTSDGANILVTESAAIPYVAVLFDTSSEKYNWLNNVTAWGTPPNLNEINFLEYWQIE
1PUI , Knot 95 210 0.80 38 145 203 
MTNLNYQQTHFVMSAPDIRHLPSDTGIEVAFAGRSNAGKSSALNTLTNQKSLARTSKTPGRTQLINLFEVADGKRLVDLPGYGYAEVPEEMKRKWQRALGEYLEKRQSLQGLVVLMDIRHPLKDLDQQMIEWAVDSNIAVLVLLTKADKLASGARKAQLNMVREAVLAFNGDVQVETFSSLKKQGVDKLRQKLDTWFSEMQPVEETQDGE
6EWW , Knot 106 232 0.83 40 153 224 
GHMDKNELVQKAKLAEQAERYDDMAACMKSVTEQGAELSNEERNLLSVAYKNVVGARRSSWRVVSSIEQKTEGAEKKQQMAREYREKIETELRDICNDVLSLLEKFLIPNASQAESKVFYLKMKGDYYRYLAEVAAGDDKKGIVDQSQQAYQEAFEISKKEMQPTHPIRLGLALNFSVFYYEILNSPEKACSLAKTAFDEAIAELDTLSEESYKDSTLIMQLLRDNLTLWTS

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 \(c\).

\(|P_{f(6JJT_1)}(2) \setminus P_{f(1PUI_1)}(2)|=60\), \(|P_{f(1PUI_1)}(2) \setminus P_{f(6JJT_1)}(2)|=96\). 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 1:10100110111111011100101101011101010011101000001010110010111111101010111101100011010101010011000011011100011110111110000000011001011101101001011001010
Pair \(Z_2\) Length of longest common subsequence
6JJT_1,1PUI_1 156 3
6JJT_1,6EWW_1 152 3
1PUI_1,6EWW_1 142 4

Newick tree

 
[
	6JJT_1:78.90,
	[
		6EWW_1:71,1PUI_1:71
	]:7.90
]

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 \((0.85)(0.8)(\frac{359 }{\log_{20} 359}-\frac{149}{\log_{20}149})=63.6\)
Status Protein1 Protein2 d d1/2
Query variables 6JJT_1 1PUI_1 79 67
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]