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Parikh vectors
7MHQ_1 6NKR_1 7YGP_1 Letter Amino acid
3 1 0 W Tryptophan
17 18 1 A Alanine
26 22 4 G Glycine
29 26 0 L Leucine
13 14 0 P Proline
24 19 2 T Threonine
21 12 0 N Asparagine
11 23 0 I Isoleucine
11 35 0 K Lycine
10 8 0 M Methionine
11 19 0 R Arginine
11 12 0 Y Tyrosine
27 18 0 V Valine
7 9 0 H Histidine
17 14 0 F Phenylalanine
16 21 0 S Serine
17 21 0 D Aspartic acid
12 3 4 C Cysteine
14 13 0 Q Glutamine
9 27 0 E Glutamic acid 

7MHQ_1|Chain A|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>6NKR_1|Chain A|DNA polymerase beta|Homo sapiens (9606)
>7YGP_1|Chain A|DNA (5'-D(*GP*GP*AP*CP*CP*TP*(OHU)P*GP*GP*TP*CP*C)-3')|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 \(w=f(c)\)
7MHQ , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
6NKR , Knot 147 335 0.85 40 199 322 
MSKRKAPQETLNGGITDMLTELANFEKNVSQAIHKYNAYRKAASVIAKYPHKIKSGAEAKKLPGVGTKIAEKIDEFLATGKLRKLEKIRQDDTSSSINFLTRVSGIGPSAARKFVDEGIKTLEDLRKNEDKLNHHQRIGLKYFGDFEKRIPREEMLQMQDIVLNEVKKVDSEYIATVCGSFRRGAESSGDMDVLLTHPSFTSESTKQPKLLHQVVEQLQKVHFITDTLSKGETKFMGVCQLPSKNDEKEYPHRRIDIRLIPKDQYYCGVLYFTGSDIFNKNMRAHALEMGFTINEYTIRPLGVTGVAGEPLPVDSEKDIFDYIQWKYREPKDRSE
7YGP , Knot 7 12 0.48 10 9 10 
GGACCTXGGTCC

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 \(c\).

\(|P_{f(7MHQ_1)}(2) \setminus P_{f(6NKR_1)}(2)|=83\), \(|P_{f(6NKR_1)}(2) \setminus P_{f(7MHQ_1)}(2)|=86\). 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
7MHQ_1,6NKR_1 169 4
7MHQ_1,7YGP_1 197 2
6NKR_1,7YGP_1 202 2

Newick tree

 
[
	7YGP_1:10.34,
	[
		7MHQ_1:84.5,6NKR_1:84.5
	]:19.84
]

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 \((0.85)(0.8)(\frac{641 }{\log_{20} 641}-\frac{306}{\log_{20}306})=93.1\)
Status Protein1 Protein2 d d1/2
Query variables 7MHQ_1 6NKR_1 119 112.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]