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Parikh vectors
6DPO_1 2EGJ_1 8EHG_1 Letter Amino acid
11 6 20 I Isoleucine
2 12 7 F Phenylalanine
5 4 19 P Proline
6 0 3 W Tryptophan
6 8 15 R Arginine
6 5 14 N Asparagine
15 11 26 K Lycine
2 4 4 M Methionine
8 6 21 S Serine
5 9 12 Y Tyrosine
9 12 22 V Valine
7 6 14 D Aspartic acid
3 2 16 Q Glutamine
3 4 11 H Histidine
10 4 22 T Threonine
0 2 8 C Cysteine
11 5 30 G Glycine
10 10 34 L Leucine
8 6 42 A Alanine
15 12 24 E Glutamic acid 

6DPO_1|Chain A|Ribonuclease H|Bacillus halodurans (86665)
>2EGJ_1|Chains A, B|Hypothetical protein aq_1494|Aquifex aeolicus (63363)
>8EHG_1|Chains A, B, C, D|Fructose-bisphosphate aldolase A|Oryctolagus cuniculus (9986)
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 \(w=f(c)\)
6DPO , Knot 70 142 0.81 38 112 139 
GSHMAKEEIIWESLSVDVGSQGNPGIVEYKGVDTKTGEVLFEREPIPIGTNNMGEFLAIVHGLRYLKERNSRKPIYSDSQTAIKWVKDKKAKSTLVRNEETALIWKLVDEAEEWLNTHTYETPILKWQTDKWGAIKADYGRK
2EGJ , Knot 66 128 0.83 38 106 123 
MPFIYRRRVQFYETDAQGIVHHSNYFRYFEEARGEFLRSKGFPYSKMRDMGLEVVLLNAYCEYKKPLFYDDVFEVHLNLEELSRFTFTFSYIVFKEDIAVAKANTKHCMVKNGKIVSIPKEVLEVLKD
8EHG , Knot 159 364 0.85 40 207 346 
MPHSHPALTPEQKKELSDIAHRIVAPGKGILAADESTGSIAKRLQSIGTENTEENRRFYRQLLLTADDRVNPCIGGVILFHETLYQKADDGRPFPQVIKSKGGVVGIKVDKGVVPLAGTNGETTTQGLDGLSERCAQYKKDGADFAKWRCVLKIGEHTPSALAIMENANVLARYASICQQNGIVPIVEPEILPDGDHDLKRCQYVTEKVLAAVYKALSDHHIYLEGTLLKPNMVTPGHACTQKYSHEEIAMATVTALRRTVPPAVTGVTFLSGGQSEEEASINLNAINKCPLLKPWALTFSYGRALQASALKAWGGKKENLKAAQEEYVKRALANSLACQGKYTPSGQAGAAASESLFISNHAY

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 \(c\).

\(|P_{f(6DPO_1)}(2) \setminus P_{f(2EGJ_1)}(2)|=72\), \(|P_{f(2EGJ_1)}(2) \setminus P_{f(6DPO_1)}(2)|=66\). 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 1:1001100011100101011001011110001100001011100011111000110111110110010000000110000001101100001000110000011110110010011000000011101000011110100100
Pair \(Z_2\) Length of longest common subsequence
6DPO_1,2EGJ_1 138 4
6DPO_1,8EHG_1 177 3
2EGJ_1,8EHG_1 181 4

Newick tree

 
[
	8EHG_1:95.36,
	[
		6DPO_1:69,2EGJ_1:69
	]:26.36
]

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 \((0.85)(0.8)(\frac{270 }{\log_{20} 270}-\frac{128}{\log_{20}128})=44.5\)
Status Protein1 Protein2 d d1/2
Query variables 6DPO_1 2EGJ_1 55 51.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]