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Parikh vectors
3ZBD_1 1YKZ_1 7GKW_1 Letter Amino acid
5 11 11 R Arginine
6 6 11 K Lycine
1 7 24 T Threonine
6 3 11 Y Tyrosine
6 14 21 N Asparagine
6 2 9 E Glutamic acid
7 12 26 G Glycine
6 6 11 I Isoleucine
3 2 10 M Methionine
5 10 16 S Serine
0 6 3 W Tryptophan
3 12 17 A Alanine
9 7 17 D Aspartic acid
4 3 14 Q Glutamine
7 1 7 H Histidine
11 8 29 L Leucine
5 3 17 F Phenylalanine
4 8 12 C Cysteine
5 2 13 P Proline
14 6 27 V Valine 

3ZBD_1|Chains A, B|NON-STRUCTURAL PROTEIN 1|PORCINE TRANSMISSIBLE GASTROENTERITIS CORONAVIRUS (11151)
>1YKZ_1|Chain A[auth X]|Lysozyme C|Gallus gallus (9031)
>7GKW_1|Chains A, B|3C-like proteinase|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 \(w=f(c)\)
3ZBD , Knot 59 113 0.82 38 87 105 
MAHHHHHHMSSKQFKILVNEDYQVNVPSLPIRDVLQEIKYCYRNGFEGYVFVPEYCRDLVDCDRKDHYVIGVLGNGVSDLKPVLLTEPSVMLQGFIVRANCNGVLEDFDLKIA
1YKZ , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL
7GKW , 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 \(c\).

\(|P_{f(3ZBD_1)}(2) \setminus P_{f(1YKZ_1)}(2)|=62\), \(|P_{f(1YKZ_1)}(2) \setminus P_{f(3ZBD_1)}(2)|=79\). 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 1:11000000100001011100000101101110011001000000110101111000001100000000111111011001011110010111011110100011100101011
Pair \(Z_2\) Length of longest common subsequence
3ZBD_1,1YKZ_1 141 3
3ZBD_1,7GKW_1 181 3
1YKZ_1,7GKW_1 178 4

Newick tree

 
[
	7GKW_1:95.31,
	[
		3ZBD_1:70.5,1YKZ_1:70.5
	]:24.81
]

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 \((0.85)(0.8)(\frac{242 }{\log_{20} 242}-\frac{113}{\log_{20}113})=41.1\)
Status Protein1 Protein2 d d1/2
Query variables 3ZBD_1 1YKZ_1 52 49
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]