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Parikh vectors
7ETA_1 7RGX_1 7CJY_1 Letter Amino acid
14 6 41 E Glutamic acid
19 10 24 I Isoleucine
29 13 48 L Leucine
16 6 26 S Serine
24 13 41 V Valine
16 7 41 D Aspartic acid
6 3 15 M Methionine
5 8 31 F Phenylalanine
9 3 24 Y Tyrosine
11 9 25 P Proline
28 6 30 A Alanine
8 9 29 R Arginine
11 14 12 N Asparagine
2 1 10 C Cysteine
17 4 17 Q Glutamine
22 8 31 G Glycine
2 4 20 H Histidine
15 8 42 K Lycine
9 5 25 T Threonine
3 1 10 W Tryptophan 

7ETA_1|Chains A, B, C|4-hydroxy-2-oxoheptanedioate aldolase|Acinetobacter baumannii (470)
>7RGX_1|Chain A|Galectin-3|Homo sapiens (9606)
>7CJY_1|Chains A, B|(-)-drimenol synthase|Persicaria hydropiper (46901)
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 \(w=f(c)\)
7ETA , Knot 119 266 0.83 40 162 249 
MVNTVNYFKQKLKTEQQIGMWVGLADGYCAEIAANVGYDWLLIDGEHAPNDVRSILAQLQSIAAYPSQAVVRPVSGDVPLIKQLLDIGAQTLLIPMVESAEQAELMVKATRYPPEGIRGVGAALARASRWNNISDYLQTADEQICLLVQVESKKGLDNLDEILNVDGVDGIFIGPADLSAALGYRGNPGHEFVQNIIVQTIQKIRAAGKAAGILSADEKLAKQYLELGTEFVAVGVDTSLLMKSMKQLLSKFKNVDGPVSTSPSVY
7RGX , Knot 68 138 0.81 40 112 135 
MLIVPYNLPLPGGVVPRMLITILGTVKPNANRIALDFQRGNDVAFHFNPRFNENNRRVIVCNTKLDNNWGREERQSVFPFESGKPFKIQVLVEPDHFKVAVNDAHLLQYNHRVKKLNEISKLGISGDIDLTSASYTMI
7CJY , Knot 223 542 0.86 40 272 512 
GIASFHPSPWGDYFLKYVPCDQVTQAKMEDEVKKVEEDVKKELRKLAKAVGKPLELLNFIDVVERLGVGYRLEQEIEDLVQAIFDNDKFGVDEFDLYHTSLWFRLLRQHGFHVSCDVFGKFKGRNGRFKDSLASDVKGILGLYEASHVRTHGDDTLDEALVFTTTHLKAVVTNQPNHPLVPQVTHALMQPYHKGMPRLESRHFIAFYEKDPYHDKTLLKFGKLDFNLVQALHKKELKDLSRWWKDLDMHAKMPFPSRDRVPEGYFWTLGPFYEPQFALCRKFFLQVFKVTSIVDDIYDAYGTIDELTAFTKAAERWDRSCLDELPEYMKVSYASLIDTFEEFERDLAPQGRSWSVKYAREEMIQMCRVYYQEAKWCHEKYSPTCDEYLEKASIVSFGYNLGTVVCFLGMGDVATKEAFEWARGNPKVVRAAGIIGRLMDDIGSHHFEQGRDHVPSAVECYIRQHGVDEVTAQRELGKRVESSWKDINEMMLKPYMMPKPLLTRILNECRIVDVIYKGEDSYTFSNTTMKKNISHILTDPIPI

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 \(c\).

\(|P_{f(7ETA_1)}(2) \setminus P_{f(7RGX_1)}(2)|=104\), \(|P_{f(7RGX_1)}(2) \setminus P_{f(7ETA_1)}(2)|=54\). 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 1:11001001000100000111111110100101110110011110100110010011101001110100111011010111100110111001111110010010111010001101101111111010010010001001000101110100001100100110101101111111010111100101100110011100100101110111110100011000101100111111000111001001100100101110001010
Pair \(Z_2\) Length of longest common subsequence
7ETA_1,7RGX_1 158 3
7ETA_1,7CJY_1 202 4
7RGX_1,7CJY_1 206 4

Newick tree

 
[
	7CJY_1:10.59,
	[
		7ETA_1:79,7RGX_1:79
	]:29.59
]

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 \((0.85)(0.8)(\frac{404 }{\log_{20} 404}-\frac{138}{\log_{20}138})=80.0\)
Status Protein1 Protein2 d d1/2
Query variables 7ETA_1 7RGX_1 99 75
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]