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Parikh vectors
1YJC_1 5DSB_1 8YLS_1 Letter Amino acid
11 0 17 D Aspartic acid
15 0 29 L Leucine
10 0 11 K Lycine
13 0 24 T Threonine
3 0 3 W Tryptophan
30 0 27 V Valine
9 0 14 Q Glutamine
13 0 11 I Isoleucine
4 0 17 F Phenylalanine
32 5 26 G Glycine
4 0 10 M Methionine
38 0 16 S Serine
11 0 11 Y Tyrosine
14 0 13 P Proline
38 0 17 A Alanine
2 0 11 R Arginine
16 0 21 N Asparagine
1 4 12 C Cysteine
5 0 9 E Glutamic acid
6 0 7 H Histidine 

1YJC_1|Chain A|SUBTILISIN 8397+1|Bacillus amyloliquefaciens (1390)
>5DSB_1|Chains A, B|5'-D(*CP*CP*GP*GP*CP*GP*5HCP*CP*GP*G)-3'|synthetic construct (32630)
>8YLS_1|Chain A|3C-like proteinase nsp5|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
1YJC , Knot 115 275 0.78 40 148 254 
AQSVPYGVSQIKAPALHSQGYTGSNVKVAVIDSGIDSSHPDLKVAGGASFVPSETNPFQDNNSHGTHVAGTVAALDNSIGVLGVAPSASLYAVKVLGADGSGQYSWIINGIEWAIANNMDVINMSLGGPSGSAALKAAVDKAVASGVVVVAAAGNEGTSGSSSTVGYPAKYPSVIAVGAVDSSNQRASFSSVGPELDVMAPGVSICSTLPGNKYGAYSGTSMASPHVAGAAALILSKHPNWTNTQVRSSLENTTTYLGDSFYYGKGLINVQAAAQ
5DSB , Knot 5 10 0.38 6 6 7 
CCGGCGXCGG
8YLS , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ

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 \(c\).

\(|P_{f(1YJC_1)}(2) \setminus P_{f(5DSB_1)}(2)|=147\), \(|P_{f(5DSB_1)}(2) \setminus P_{f(1YJC_1)}(2)|=5\). 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 1:10011011001011110001001001011110011000010101111101110000110000001001110111100011111111010101101111010100011101101111001011010111101011101110011101111111110010010000110110010111111100000010100111010111111010001110001100100110101111111110001010000100010000001100100101110101110
Pair \(Z_2\) Length of longest common subsequence
1YJC_1,5DSB_1 152 2
1YJC_1,8YLS_1 178 3
5DSB_1,8YLS_1 198 2

Newick tree

 
[
	8YLS_1:99.44,
	[
		1YJC_1:76,5DSB_1:76
	]:23.44
]

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 \((0.85)(0.8)(\frac{285 }{\log_{20} 285}-\frac{10}{\log_{20}10})=93.8\)
Status Protein1 Protein2 d d1/2
Query variables 1YJC_1 5DSB_1 114 59
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]