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Parikh vectors
3IKC_1 5FHV_1 7NHZ_1 Letter Amino acid
12 15 8 V Valine
12 7 5 N Asparagine
15 14 5 L Leucine
15 25 5 K Lycine
9 13 7 P Proline
21 13 6 T Threonine
9 13 4 Y Tyrosine
11 20 4 D Aspartic acid
4 0 4 C Cysteine
10 24 6 E Glutamic acid
2 12 4 H Histidine
4 3 2 W Tryptophan
9 10 8 R Arginine
8 10 6 I Isoleucine
33 14 7 S Serine
11 12 17 A Alanine
10 10 3 Q Glutamine
13 30 14 G Glycine
3 14 4 M Methionine
7 10 1 F Phenylalanine 

3IKC_1|Chains A, C|Immunoglobulin light chain (IGG3)|Mus musculus (10090)
>5FHV_1|Chain A|mCherry-BME|Discosoma sp. (86600)
>7NHZ_1|Chain A|Uncharacterized protein Rv1813c|Mycobacterium tuberculosis (strain ATCC 25618 / H37Rv) (83332)
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 \(w=f(c)\)
3IKC , Knot 103 218 0.84 40 157 209 
DIVMTQSPSSLAVSAGEKVTMSCKSSQSLLNSRTRKNYLAWYQQKPGQSPKLLIYWASTRESGVPDRFTGSGSGTDFTLTISSVQAEDLAVYYCKQSNNLRTFGGGTKLEIKRADAAPTVSIFPPSSEQLTSGGASVVCFLNNFYPKDINVKWKIDGSERQNGVLNSWTDQDSKDSTYSMSSTLTLTKDEYERHNSYTCEATHKTSTSPIVKSFNRNE
5FHV , Knot 117 269 0.81 38 170 254 
MRGSHHHHHHGMASMTGGQQMGRDLYDDDDKDPMVSKGEEDNMAIIKEFMRFKVHMEGSVNGHEFEIEGEGEGRPYEGTQTAKLKVTKGGPLPFAWDILSPQFMYGSKAYVKHPADIPDYLKLSFPEGFKWERVMNFEDGGVVTVTQDSSLQDGEFIYKVKLRGTNFPSDGPVMQKKTMGWEASSERMYPEDGALKGEIKQRLKLKDGGHYDAEVKTTYKAKKPVQLPGAYNVNIKLDITSHNEDYTIVEQYERAEGRHSTGGMDELYK
7NHZ , Knot 61 120 0.81 40 98 116 
GPHMPTVDAHLANGSMSEVMMSEIAGLPIPPIIHYGAIAYAPSGASGKAWHQRTPARAEQVALEKCGDKTCKVVSRFTRCGAVAYNGSKYQGGTGLTRRAAEDDAVNRLEGGRIVNWACN

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 \(c\).

\(|P_{f(3IKC_1)}(2) \setminus P_{f(5FHV_1)}(2)|=80\), \(|P_{f(5FHV_1)}(2) \setminus P_{f(3IKC_1)}(2)|=93\). 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 1:01110001001110110010100000001100000000111000011001011101100000111001010101001010100101001110000000010011110010100101110101111000010011101101100101001010101010000011100100000000000100010100000000000000100000001110010000
Pair \(Z_2\) Length of longest common subsequence
3IKC_1,5FHV_1 173 3
3IKC_1,7NHZ_1 159 3
5FHV_1,7NHZ_1 174 3

Newick tree

 
[
	5FHV_1:89.03,
	[
		3IKC_1:79.5,7NHZ_1:79.5
	]:9.53
]

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 \((0.85)(0.8)(\frac{487 }{\log_{20} 487}-\frac{218}{\log_{20}218})=77.8\)
Status Protein1 Protein2 d d1/2
Query variables 3IKC_1 5FHV_1 99 91
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]