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Parikh vectors
6EAX_1 5JPV_1 1TMB_1 Letter Amino acid
15 1 1 I Isoleucine
14 7 5 L Leucine
14 5 3 K Lycine
34 6 3 S Serine
10 5 1 Y Tyrosine
14 6 1 A Alanine
16 6 0 N Asparagine
4 12 6 E Glutamic acid
25 13 4 G Glycine
2 2 0 M Methionine
6 14 3 D Aspartic acid
8 8 1 P Proline
10 7 2 T Threonine
4 11 0 W Tryptophan
17 10 0 V Valine
2 8 3 R Arginine
12 7 1 C Cysteine
10 6 0 Q Glutamine
3 7 0 H Histidine
3 4 2 F Phenylalanine 

6EAX_1|Chain A|Cationic trypsin|Bos taurus (9913)
>5JPV_1|Chains A, B|Asialoglycoprotein receptor 1|Homo sapiens (9606)
>1TMB_1|Chain A[auth L]|ALPHA-THROMBIN (SMALL SUBUNIT)|Homo sapiens (9606)
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 \(w=f(c)\)
6EAX , Knot 101 223 0.81 40 140 216 
IVGGYTCGANTVPYQVSLNSGYHFCGGSLINSQWVVSAAHCYKSGIQVRLGEDNINVVEGNEQFISASKSIVHPSYNSNTLNNDIMLIKLKSAASLNSRVASISLPTSCASAGTQCLISGWGNTKSSGTSYPDVLKCLKAPILSDSSCKSAYPGQITSNMFCAGYLEGGKDSCQGDSGGPVVCSGKLQGIVSWGSGCAQKNKPGVYTKVCNYVSWIKQTIASN
5JPV , Knot 74 145 0.84 40 118 142 
MGSERTCCPVNWVEHERSCYWFSRSGKAWADADNYCRLEDAHLVVVTSWEEQKFVQHHIGPVNTWMGLHDQNGPWKWVDGTDYETGFKNWRPEQPDDWYGHGLGGGEDCAHFTDDGRWNDDVCQRPYRWVCETELDKASQEPPLL
1TMB , Knot 24 36 0.79 28 34 34 
TFGSGEADCGLRPLFEKKSLEDKTERELLESYIDGR

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 \(c\).

\(|P_{f(6EAX_1)}(2) \setminus P_{f(5JPV_1)}(2)|=101\), \(|P_{f(5JPV_1)}(2) \setminus P_{f(6EAX_1)}(2)|=79\). 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 1:1111000110011001010010010110110001110110000011010110001011010001101000110100000010001111010011010001101011000101100011011100000100010110010111100000001011010001101101011000001001111100101011101101010000111000100010110001100
Pair \(Z_2\) Length of longest common subsequence
6EAX_1,5JPV_1 180 3
6EAX_1,1TMB_1 156 3
5JPV_1,1TMB_1 118 3

Newick tree

 
[
	6EAX_1:91.08,
	[
		1TMB_1:59,5JPV_1:59
	]:32.08
]

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 \((0.85)(0.8)(\frac{368 }{\log_{20} 368}-\frac{145}{\log_{20}145})=67.5\)
Status Protein1 Protein2 d d1/2
Query variables 6EAX_1 5JPV_1 88 73.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]