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Parikh vectors
3GGR_1 8DOZ_1 2WEI_1 Letter Amino acid
16 4 14 R Arginine
6 10 9 N Asparagine
17 7 22 E Glutamic acid
38 15 25 L Leucine
6 2 6 M Methionine
17 7 13 F Phenylalanine
0 5 3 W Tryptophan
4 11 14 Y Tyrosine
12 8 18 D Aspartic acid
10 5 6 C Cysteine
17 18 16 G Glycine
7 3 13 H Histidine
12 14 27 K Lycine
24 36 18 S Serine
18 20 12 V Valine
24 11 12 A Alanine
10 12 8 P Proline
11 9 9 Q Glutamine
9 4 26 I Isoleucine
12 20 16 T Threonine 

3GGR_1|Chain A|Cell cycle checkpoint control protein RAD9A|Homo sapiens (9606)
>8DOZ_1|Chains A, C|Fab 2C7, heavy chain Fd fragment|Mus musculus (10090)
>2WEI_1|Chain A|CALMODULIN-DOMAIN PROTEIN KINASE 1, PUTATIVE|CRYPTOSPORIDIUM PARVUM IOWA II (353152)
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 \(w=f(c)\)
3GGR , Knot 124 270 0.85 38 171 261 
MKCLVTGGNVKVLGKAVHSLSRIGDELYLEPLEDGLSLRTVNSSRSAYACFLFAPLFFQQYQAATPGQDLLRCKILMKSFLSVFRSLAMLEKTVEKCCISLNGRSSRLVVQLHCKFGVRKTHNLSFQDCESLQAVFDPASCPHMLRAPARVLGEAVLPFSPALAEVTLGIGRGRRVILRSYHEEEADSTAKAMVTEMCLGEEDFQQLQAQEGVAITFCLKEFRGLLSFAESANLNLSIHFDAPGRPAIFTIKDSLLDGHFVLATLSDTDS
8DOZ , Knot 98 221 0.79 40 145 207 
EVQLQQSGPELVKPGSSVKISCKGSGYTFTDYNMEWVKQSHGKSLEWIGVINPNNRFTSYNQNFRGKATLTVDKSSSTAYMDLRSLTSEDSAVYFCAGSRWYQYDYWGQGTTLTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHAPSNTKVDKKVEPKSCD
2WEI , Knot 127 287 0.83 40 178 274 
MHHHHHHSSGRENLYFQGTFAERYNIVCMLGKGSFGEVLKCKDRITQQEYAVKVINKASAKNKDTSTILREVELLKKLDHPNIMKLFEILEDSSSFYIVGELYTGGELFDEIIKRKRFSEHDAARIIKQVFSGITYMHKHNIVHRDLKPENILLESKEKDCDIKIIDFGLSTCFQQNTKMKDRIGTAYYIAPEVLRGTYDEKCDVWSAGVILYILLSGTPPFYGKNEYDILKRVETGKYAFDLPQWRTISDDAKDLIRKMLTFHPSLRITATQCLEHPWIQKYSSEE

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 \(c\).

\(|P_{f(3GGR_1)}(2) \setminus P_{f(8DOZ_1)}(2)|=99\), \(|P_{f(8DOZ_1)}(2) \setminus P_{f(3GGR_1)}(2)|=73\). 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 1:100110110101110110010011001010110011010010000010101111111100001101100110001110011011001111000100001010100001110100011100000101000001011101100101101110111011111011110101111010011100000001000101110010110001001010011110101001011101100101010101011101111010001101011110100000
Pair \(Z_2\) Length of longest common subsequence
3GGR_1,8DOZ_1 172 3
3GGR_1,2WEI_1 171 3
8DOZ_1,2WEI_1 175 3

Newick tree

 
[
	8DOZ_1:87.16,
	[
		3GGR_1:85.5,2WEI_1:85.5
	]:1.66
]

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 \((0.85)(0.8)(\frac{491 }{\log_{20} 491}-\frac{221}{\log_{20}221})=78.0\)
Status Protein1 Protein2 d d1/2
Query variables 3GGR_1 8DOZ_1 99 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]