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Parikh vectors
1EAU_1 7FTL_1 6UYT_1 Letter Amino acid
10 18 5 I Isoleucine
3 43 9 K Lycine
7 11 2 P Proline
22 28 5 S Serine
7 4 0 W Tryptophan
15 12 6 Q Glutamine
25 14 8 G Glycine
4 32 11 E Glutamic acid
7 18 3 D Aspartic acid
8 10 0 C Cysteine
6 8 3 H Histidine
18 41 6 L Leucine
11 11 3 Y Tyrosine
17 14 2 A Alanine
17 18 2 N Asparagine
2 5 3 M Methionine
3 23 3 F Phenylalanine
19 14 4 T Threonine
27 18 5 V Valine
12 20 3 R Arginine 

1EAU_1|Chain A|PORCINE PANCREATIC ELASTASE|Sus scrofa (9823)
>7FTL_1|Chain A|Cyclic GMP-AMP synthase|Homo sapiens (9606)
>6UYT_1|Chain A|Small ubiquitin-related modifier 1|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 \(w=f(c)\)
1EAU , Knot 108 240 0.82 40 162 230 
VVGGTEAQRNSWPSQISLQYRSGSSWAHTCGGTLIRQNWVMTAAHCVDRELTFRVVVGEHNLNQNNGTEQYVGVQKIVVHPYWNTDDVAAGYDIALLRLAQSVTLNSYVQLGVLPRAGTILANNSPCYITGWGLTRTNGQLAQTLQQAYLPTVDYAICSSSSYWGSTVKNSMVCAGGDGVRSGCQGDSGGPLHCLVNGQYAVHGVTSFVSRLGCNVTRKPTVFTRVSAYISWINNVIASN
7FTL , Knot 149 362 0.80 40 204 345 
GASKLRAVLEKLKLSRDDISTAAGMVKGVVDHLLLRLKCDSAFRGVGLLNTGSYYEHVKISAPNEFDVMFKLEVPRIQLEEYSNTRAYYFVKFKRNPKENPLSQFLEGEILSASKMLSKFRKIIKEEINDIKDTDVIMKRKRGGSPAVTLLISEKISVDITLALESKSSWPASTQEGLRIQNWLSAKVRKQLRLKPFYLVPKHAKEGNGFQEETWRLSFSHIEKEILNNHGKSKTCCENKEEKCCRKDCLKLMKYLLEQLKERFKDKKHLDKFSSYHVKTAFFHVCTQNPQDSQWDRKDLGLCFDNCVTYFLQCLRTEKLENYFIPEFNLFSSNLIDKRSKEFLTKQIEYERNNEFPVFDEF
6UYT , Knot 45 83 0.79 36 71 80 
GSKEGEYIKLKVIGQDSSEIHFKVKMTTHLKKLKESYAQRQGVPMNSLRFLFEGQRIADNHTPKELGMEEEDVIEVYQEQTGG

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 \(c\).

\(|P_{f(1EAU_1)}(2) \setminus P_{f(7FTL_1)}(2)|=76\), \(|P_{f(7FTL_1)}(2) \setminus P_{f(1EAU_1)}(2)|=118\). 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 1:111100100001100101000010011000110110001110110010001010111100010000100001110011101010000111100111101100101000101111101101110001001011110000101100100101101001100000011001000110111011001001001111001101001101100110011001000101100101010110011100
Pair \(Z_2\) Length of longest common subsequence
1EAU_1,7FTL_1 194 4
1EAU_1,6UYT_1 177 3
7FTL_1,6UYT_1 189 3

Newick tree

 
[
	7FTL_1:98.05,
	[
		1EAU_1:88.5,6UYT_1:88.5
	]:9.55
]

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 \((0.85)(0.8)(\frac{602 }{\log_{20} 602}-\frac{240}{\log_{20}240})=102.\)
Status Protein1 Protein2 d d1/2
Query variables 1EAU_1 7FTL_1 133 109.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]