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Parikh vectors
7GGF_1 5JKE_1 5IXU_1 Letter Amino acid
16 15 4 S Serine
17 14 11 A Alanine
11 8 9 R Arginine
21 10 2 N Asparagine
9 21 7 E Glutamic acid
17 9 5 F Phenylalanine
7 7 8 H Histidine
10 8 4 M Methionine
3 6 4 W Tryptophan
11 8 6 Y Tyrosine
14 8 7 Q Glutamine
26 12 6 G Glycine
11 6 5 I Isoleucine
11 21 2 K Lycine
13 9 6 P Proline
17 15 7 D Aspartic acid
12 10 2 C Cysteine
29 26 8 L Leucine
24 12 6 T Threonine
27 21 8 V Valine 

7GGF_1|Chain A|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>5JKE_1|Chains A, C|Izumo sperm-egg fusion protein 1|Homo sapiens (9606)
>5IXU_1|Chain A|Uncharacterized protein|Burkholderia xenovorans (strain LB400) (266265)
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 \(w=f(c)\)
7GGF , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
5JKE , Knot 113 246 0.84 40 173 237 
RSPWCVICDPSVVLALKSLEKDYLPGHLDAKHHKAMMERVENAVKDFQELSLNEDAYMGVVDEATLQKGSWSLLKDLKRITDSDVKGDLFVKELFWMLHLQKETFATYVARFQKEAYCPNKCGVMLQTLIWCKNCKKEVHACRKSYDCGERNVEVPQMEDMILDCELNWHQASEGLTDYSFYRVWGNNTETLVSKGKEATLTKPMVGPEDAGSYRCELGSVNSSPATIINFHVTVLPKEFLEVLFQ
5IXU , Knot 60 117 0.81 40 96 112 
MAHHHHHHMRGEDNMLVEMRTYRITAGKVPEFLKIYQDEGLGIITQYARLRGCWTQDSGTLNSVVFWWAYDDYSHRAAQRERLAADPQWQAFTPRIVPYLEHQESVFLVPAAFCPDV

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 \(c\).

\(|P_{f(7GGF_1)}(2) \setminus P_{f(5JKE_1)}(2)|=101\), \(|P_{f(5JKE_1)}(2) \setminus P_{f(7GGF_1)}(2)|=78\). 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
7GGF_1,5JKE_1 179 3
7GGF_1,5IXU_1 192 3
5JKE_1,5IXU_1 177 3

Newick tree

 
[
	7GGF_1:94.19,
	[
		5JKE_1:88.5,5IXU_1:88.5
	]:5.69
]

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 \((0.85)(0.8)(\frac{552 }{\log_{20} 552}-\frac{246}{\log_{20}246})=87.0\)
Status Protein1 Protein2 d d1/2
Query variables 7GGF_1 5JKE_1 111 99.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]