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Parikh vectors
4JFY_1 5QPL_1 3GPI_1 Letter Amino acid
11 25 16 E Glutamic acid
6 14 15 I Isoleucine
9 18 5 F Phenylalanine
29 14 18 S Serine
7 15 22 R Arginine
12 24 13 D Aspartic acid
12 16 14 Q Glutamine
13 13 17 P Proline
19 21 13 T Threonine
7 17 14 Y Tyrosine
15 35 16 V Valine
12 36 32 A Alanine
8 8 6 N Asparagine
5 8 2 C Cysteine
19 30 34 L Leucine
2 15 5 M Methionine
2 6 4 W Tryptophan
13 18 22 G Glycine
2 6 13 H Histidine
11 25 5 K Lycine 

4JFY_1|Chains A, C[auth L]|Fab light chain|Homo sapiens (9606)
>5QPL_1|Chain A|Farnesyl diphosphate synthase|Trypanosoma cruzi (5693)
>3GPI_1|Chain A|NAD-dependent epimerase/dehydratase|Methylobacillus flagellatus KT (265072)
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 \(w=f(c)\)
4JFY , Knot 97 214 0.81 40 147 201 
DIVLTQSPATLSLSPGERATLSCMTSTDIDDDMNWYQQKPGQAPRLLISEGNTLRPGVPARFSGSGSGTDFTLTISSLEPEDFAVYYCLQSFNVPLTFGQGTKVEIKRTVAAPSVFIFPPSDSQLKSGTASVVCLLNNFYPREAKVQWKVDNALQSGNSQESVTEQDSKDSTYSLSSTLTLSKADYEKHKVYACEVTHQGLSSPVTKSFNRGEC
5QPL , Knot 157 364 0.84 40 211 347 
GPMASMERFLSVYDEVQAFLLDQLQSKYEIDPNRARYLRIMMDTTCLGGKYFRGMTVVNVAEGFLAVTQHDEATKERILHDACVGGWMIEFLQAHYLVEDDIMDGSVMRRGKPCWYRFPGVTTQCAINDGIILKSWTQIMAWHYFADRPFLKDLLCLFQKVDYATAVGQMYDVTSMCDSNKLDPEVAQPMTTDFAEFTPAIYKRIVKYKTTFYTYLLPLVMGLLVSEAAASVEMNLVERVAHLIGEYFQVQDDVMDCFTPPEQLGKVGTDIEDAKCSWLAVTFLGKANAAQVAEFKANYGEKDPAKVAVVKRLYSKANLQADFAAYEAEVVREVESLIEQLKVKSPTFAESVAVVWEKTHKRKK
3GPI , Knot 124 286 0.81 40 172 268 
MSLSKILIAGCGDLGLELARRLTAQGHEVTGLRRSAQPMPAGVQTLIADVTRPDTLASIVHLRPEILVYCVAASEYSDEHYRLSYVEGLRNTLSALEGAPLQHVFFVSSTGVYGQEVEEWLDEDTPPIAKDFSGKRMLEAEALLAAYSSTILRFSGIYGPGRLRMIRQAQTPEQWPARNAWTNRIHRDDGAAFIAYLIQQRSHAVPERLYIVTDNQPLPVHDLLRWLADRQGIAYPAGATPPVQGNKKLSNARLLASGYQLIYPDYVSGYGALLAAMREGHHHHHH

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 \(c\).

\(|P_{f(4JFY_1)}(2) \setminus P_{f(5QPL_1)}(2)|=53\), \(|P_{f(5QPL_1)}(2) \setminus P_{f(4JFY_1)}(2)|=117\). 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 1:0111000110101011001010010000100010100001101101110010010111110101010100101010010100111000100101110110100101000111101111110000100101011011001010010101010011001000001000000000001000101001000000101001000110011000100100
Pair \(Z_2\) Length of longest common subsequence
4JFY_1,5QPL_1 170 3
4JFY_1,3GPI_1 165 4
5QPL_1,3GPI_1 189 4

Newick tree

 
[
	5QPL_1:92.20,
	[
		4JFY_1:82.5,3GPI_1:82.5
	]:9.70
]

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 \((0.85)(0.8)(\frac{578 }{\log_{20} 578}-\frac{214}{\log_{20}214})=103.\)
Status Protein1 Protein2 d d1/2
Query variables 4JFY_1 5QPL_1 133 104
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]