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Parikh vectors
8KFH_1 3MFQ_1 7YPR_1 Letter Amino acid
17 24 15 A Alanine
7 9 1 Q Glutamine
12 14 26 G Glycine
3 8 2 M Methionine
8 11 6 F Phenylalanine
3 2 0 W Tryptophan
4 11 5 Y Tyrosine
4 4 8 R Arginine
6 20 13 D Aspartic acid
3 11 9 N Asparagine
9 11 18 I Isoleucine
19 27 18 L Leucine
5 11 10 P Proline
7 19 15 S Serine
8 24 13 V Valine
0 0 2 C Cysteine
16 28 3 E Glutamic acid
13 8 8 H Histidine
21 25 6 K Lycine
5 15 16 T Threonine 

8KFH_1|Chains A, B|Myoglobin|Physeter catodon (9755)
>3MFQ_1|Chains A, B, C|High-affinity zinc uptake system protein znuA|Streptococcus suis (391295)
>7YPR_1|Chains A, B, C, D, E, F|Superoxide dismutase [Cu-Zn]|Ramazzottius varieornatus (947166)
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 \(w=f(c)\)
8KFH , Knot 83 170 0.83 38 122 164 
MWSHPQFEKENLYFQGKVLSEGEWQLVLHVWAKVEADVAGHGQDILIRLFKSHPETLEKFDRFKHLKTEAEMKASEDLKKHGVTVLTALGAILKKKGHHEAELKPLAQSHATKHKIPIKYLEFISEAIIHVLHSRHPGNFGADAQGAMNKALELFRKDIAAKYKELGYQG
3MFQ , Knot 125 282 0.83 38 171 271 
TEGSSKPRVAVTTSFLNDMVYQLAGDEVERDLLIPAGEDPHLYVAKSSDLSKLQKADLVLYHGLHFEGKMVEALEKTGVAVSKNFNAKDLNTMDEDGEEIVDPHFWFSIPLYKSAVAVASEELQKLLPAKAEMIQKNTEKYQAQLDDLHAWVEKELSVIPKESRYLVTPHDAFNYFAASYDFTLYAPQGVSTDSEVANSDMIETVNLIIDHNIKAIFTESTTNPERMKKLQEAVKAKGGQVEVVTGEGKELFSDSLAPEGEEGDTFIDMYKHNVKLMVKYLK
7YPR , Knot 92 194 0.83 38 132 189 
MTRPLALIIFLVAILTNTDPSRSDAGSDPVNYLFRGPVTAVAAIAGEGEHAGIKGSLTFLQKSLDGRTVINGTISGLPEGKHGLHIHDSGDMTKGCYITTAKGHLNPFNLSHGAPSDSARHVGDLGNIYADDTGISVINLTDTVISLFPTPAFVIGRILVIHTTYDDLGRGGSPVSKVNGNAGGRLACGIISYV

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 \(c\).

\(|P_{f(8KFH_1)}(2) \setminus P_{f(3MFQ_1)}(2)|=52\), \(|P_{f(3MFQ_1)}(2) \setminus P_{f(8KFH_1)}(2)|=101\). 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 1:11001010000101010110010101110111010101110100111011000100100100100100010101000100011011011111100010001010111000100001110010110011101100001101110101110011011000111000011001
Pair \(Z_2\) Length of longest common subsequence
8KFH_1,3MFQ_1 153 3
8KFH_1,7YPR_1 154 3
3MFQ_1,7YPR_1 145 4

Newick tree

 
[
	8KFH_1:78.11,
	[
		3MFQ_1:72.5,7YPR_1:72.5
	]:5.61
]

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 \((0.85)(0.8)(\frac{452 }{\log_{20} 452}-\frac{170}{\log_{20}170})=83.1\)
Status Protein1 Protein2 d d1/2
Query variables 8KFH_1 3MFQ_1 105 82
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]