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Parikh vectors
9HDN_1 6YIG_1 8CQP_1 Letter Amino acid
12 0 0 C Cysteine
7 1 0 H Histidine
17 6 0 F Phenylalanine
11 6 8 R Arginine
21 7 18 N Asparagine
11 5 8 I Isoleucine
29 10 25 L Leucine
17 7 24 D Aspartic acid
14 7 18 Q Glutamine
10 2 1 M Methionine
13 6 8 P Proline
16 10 9 S Serine
3 1 8 W Tryptophan
9 3 33 E Glutamic acid
11 5 19 K Lycine
24 3 0 T Threonine
11 2 48 Y Tyrosine
27 5 0 V Valine
17 13 44 A Alanine
26 10 21 G Glycine 

9HDN_1|Chains A, B, C, D|3C-like proteinase nsp5|Severe acute respiratory syndrome coronavirus 2 (2697049)
>6YIG_1|Chain A|Calcium-binding EF hand family protein|Arabidopsis thaliana (3702)
>8CQP_1|Chains A, B, C|Monomer|synthetic construct (32630)
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 \(w=f(c)\)
9HDN , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
6YIG , Knot 56 109 0.80 38 88 107 
GGMAGQNPNMDQFEAYFKRADLDGDGRISGAEAVGFFQGSGLSKQVLAQIWSLSDRSHSGFLDRQNFYNSLRLVTVAQSKRDLTPEIVNAALNTPAAAKIPPPKINLSA
8CQP , Knot 28 292 0.18 30 38 46 
GAMGSAEAWYNLGNAYYKQGDYDEAIEYYQKALELDPRSAEAWYNLGNAYYKQGDYDEAIEYYQKALELDPRSAEAWYNLGNAYYKQGDYDEAIEYYQKALELDPRSAEAWYNLGNAYYKQGDYDEAIEYYQKALELDPRSAEAWYNLGNAYYKQGDYDEAIEYYQKALELDPRSAEAWYNLGNAYYKQGDYDEAIEYYQKALELDPRSAEAWYNLGNAYYKQGDYDEAIEYYQKALELDPRSAEAWYNLGNAYYKQGDYDEAIEYYQKALELDPRSAEAKGNLGNAKQKQG

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 \(c\).

\(|P_{f(9HDN_1)}(2) \setminus P_{f(6YIG_1)}(2)|=149\), \(|P_{f(6YIG_1)}(2) \setminus P_{f(9HDN_1)}(2)|=41\). 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 1:011001111010101011010010001011110011001001100000110100001110000001110110101011100100011010100101001000110101100101110001010110001101010101011010010111010000101001001011011011001010101111000010111000010101111101111010011100100010010111100000110000101111101001111101010100110011010011101110001011011000011010
Pair \(Z_2\) Length of longest common subsequence
9HDN_1,6YIG_1 190 3
9HDN_1,8CQP_1 194 3
6YIG_1,8CQP_1 94 3

Newick tree

 
[
	9HDN_1:10.48,
	[
		6YIG_1:47,8CQP_1:47
	]:60.48
]

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 \((0.85)(0.8)(\frac{415 }{\log_{20} 415}-\frac{109}{\log_{20}109})=92.9\)
Status Protein1 Protein2 d d1/2
Query variables 9HDN_1 6YIG_1 119 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]