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Parikh vectors
9ERW_1 9FCM_1 7RGY_1 Letter Amino acid
3 3 3 M Methionine
3 4 8 F Phenylalanine
2 4 1 W Tryptophan
2 3 14 N Asparagine
4 2 1 C Cysteine
5 5 8 K Lycine
11 15 6 S Serine
9 10 5 T Threonine
8 11 13 V Valine
4 9 4 Q Glutamine
16 15 8 G Glycine
9 6 13 L Leucine
5 8 9 R Arginine
5 4 9 P Proline
12 13 3 Y Tyrosine
2 6 4 H Histidine
3 3 10 I Isoleucine
9 15 6 A Alanine
11 9 7 D Aspartic acid
5 4 6 E Glutamic acid 

9ERW_1|Chain A[auth E]|Chains: E|Vicugna pacos (30538)
>9FCM_1|Chains A, B, C|Single-domain antibody R3DC23|Lama glama (9844)
>7RGY_1|Chain A|Galectin-3|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 \(w=f(c)\)
9ERW , Knot 60 128 0.75 40 99 125 
EVQLEESGGGLVQAGGSLTLSCAASGFTFDDYAMGWYRQAPGKERVGVSCISRTDGYTYYLDSVKGRFTISTDHAKHTVYLQMNNLKPDDTGLYYCAADADPEYGSRCPDPYYGMDYWGKGILVTVSS
9FCM , Knot 68 149 0.76 40 111 142 
QVQLQESGGGLVQAGDSLTLSCAVSGRIFSTYTMGWFRQAPGKEREFVAAVRWGAGTIYYADSMKGRFTISRDSAKNTVDLQMNSTKPEDTAVYYCGAAYVSKANYGSLWYQDSRRYDYWGQGTQVTVSSAAAYPYDVPDYGSHHHHHH
7RGY , Knot 68 138 0.81 40 112 135 
MLIVPYNLPLPGGVVPRMLITILGTVKPNANRIALDFQRGNDVAFHFNPRFNENNRRVIVCNTKLDNNWGREERQSVFPFESGKPFKIQVLVEPDHFKVAVNDAHLLQYNHRVKKLNEISKLGISGDIDLTSASYTMI

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 \(c\).

\(|P_{f(9ERW_1)}(2) \setminus P_{f(9FCM_1)}(2)|=40\), \(|P_{f(9FCM_1)}(2) \setminus P_{f(9ERW_1)}(2)|=52\). 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 1:01010001111101110101001101101000111100011100011100100001000010010101010000100010101001010001100011010100100010100110011011110100
Pair \(Z_2\) Length of longest common subsequence
9ERW_1,9FCM_1 92 10
9ERW_1,7RGY_1 145 3
9FCM_1,7RGY_1 149 3

Newick tree

 
[
	7RGY_1:80.61,
	[
		9ERW_1:46,9FCM_1:46
	]:34.61
]

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 \((0.85)(0.8)(\frac{277 }{\log_{20} 277}-\frac{128}{\log_{20}128})=46.5\)
Status Protein1 Protein2 d d1/2
Query variables 9ERW_1 9FCM_1 43 40
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]