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Parikh vectors
5EHY_1 4DXI_1 4XUA_1 Letter Amino acid
30 10 4 I Isoleucine
11 10 5 M Methionine
6 13 7 F Phenylalanine
10 10 4 A Alanine
4 3 2 C Cysteine
20 5 1 Q Glutamine
17 16 8 E Glutamic acid
15 20 4 G Glycine
12 15 7 T Threonine
16 13 3 Y Tyrosine
16 8 5 N Asparagine
20 15 11 D Aspartic acid
24 15 11 L Leucine
7 8 5 R Arginine
15 12 2 H Histidine
4 2 2 W Tryptophan
29 20 14 K Lycine
14 12 6 P Proline
26 10 9 S Serine
17 14 7 V Valine 

5EHY_1|Chain A|Dual specificity protein kinase TTK|Homo sapiens (9606)
>4DXI_1|Chains A, B, C, D|GREEN FLUORESCENT PROTEIN|synthetic construct (32630)
>4XUA_1|Chain A|Bromodomain adjacent to zinc finger domain protein 2B|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 \(w=f(c)\)
5EHY , Knot 138 313 0.84 40 194 300 
MHHHHHHSSGVDLGTENLYFQSMSVKGRIYSILKQIGSGGSSKVFQVLNEKKQIYAIKYVNLEEADNQTLDSYRNEIAYLNKLQQHSDKIIRLYDYEITDQYIYMVMECGNIDLNSWLKKKKSIDPWERKSYWKNMLEAVHTIHQHGIVHSDLKPANFLIVDGMLKLIDFGIANQMQPDTTSVVKDSQVGTVNYMPPEAIKDMSSSRENGKSKSKISPKSDVWSLGCILYYMTYGKTPFQQIINQISKLHAIIDPNHEIEFPDIPEKDLQDVLKCCLKRDPKQRISIPELLAHPYVQIQTHPVNQMAKGTTEE
4DXI , Knot 106 231 0.83 40 171 220 
MSVIKSDMKIKLRMEGTVNGHKFVIEGEGEGKPYEGTQTMNLKVKEGAPLPFAYDILTTAFQYGNRVFTKYPKDIPDYFKQSFPEGYSWERSMTFEDGGICTATSDITLEGDCFFYEIRFDGVNFPPNGPVMQKKTLKWEPSTEKMYVRDGVLMGDVNMALLLEGGGHYRCDFKTTYKAKKGVQLPDYHFVDHRIEILSHDKDYNNVKLYEHAVARSSLLPMTAAHHHHHH
4XUA , Knot 59 117 0.80 40 98 112 
SMSVKKPKRDDSKDLALCSMILTEMETHEDAWPFLLPVNLKLVPGYKKVIKKPMDFSTIREKLSSGQYPNLETFALDVRLVFDNCETFNEDDSDIGRAGHNMRKYFEKKWTDTFKVS

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 \(c\).

\(|P_{f(5EHY_1)}(2) \setminus P_{f(4DXI_1)}(2)|=100\), \(|P_{f(4DXI_1)}(2) \setminus P_{f(5EHY_1)}(2)|=77\). 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 1:1000000001101100010100101010100110011011000110110000010110010100100001000000110100100000011010000100001011100101010011000001011000001001101100100011100010110111101110110111100101000011000011010011101100100000010000010100011011011001001001100110010010111010001011011000100110001000100010110111010101000110011010000
Pair \(Z_2\) Length of longest common subsequence
5EHY_1,4DXI_1 177 6
5EHY_1,4XUA_1 182 5
4DXI_1,4XUA_1 161 3

Newick tree

 
[
	5EHY_1:92.63,
	[
		4DXI_1:80.5,4XUA_1:80.5
	]:12.13
]

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 \((0.85)(0.8)(\frac{544 }{\log_{20} 544}-\frac{231}{\log_{20}231})=89.4\)
Status Protein1 Protein2 d d1/2
Query variables 5EHY_1 4DXI_1 116 99.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]