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Parikh vectors
3TAT_1 8TDY_1 7MOZ_1 Letter Amino acid
17 0 17 F Phenylalanine
18 0 16 P Proline
5 0 2 W Tryptophan
51 4 19 A Alanine
26 0 22 E Glutamic acid
6 0 14 H Histidine
43 0 29 L Leucine
13 0 24 K Lycine
11 0 16 M Methionine
21 0 17 S Serine
30 0 22 V Valine
23 0 17 R Arginine
19 0 22 D Aspartic acid
15 0 13 Q Glutamine
30 4 35 G Glycine
17 0 19 I Isoleucine
17 0 18 N Asparagine
5 3 9 C Cysteine
15 0 16 T Threonine
15 0 29 Y Tyrosine 

3TAT_1|Chains A, B, C, D, E, F|TYROSINE AMINOTRANSFERASE|Escherichia coli (562)
>8TDY_1|Chain A|RNA|synthetic construct (32630)
>7MOZ_1|Chains A, B, C|Histone deacetylase 2|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 \(w=f(c)\)
3TAT , Knot 167 397 0.84 40 223 370 
MFQKVDAYAGDPILTLMERFKEDPRSDKVNLSIGLYYNEDGIIPQLQAVAEAEARLNAQPHGASLYLPMEGLNCYRHAIAPLLFGADHPVLKQQRVATIQTLGGSGALKVGADFLKRYFPESGVWVSDPTWENHVAIFAGAGFEVSTYPWYDEATNGVRFNDLLATLKTLPARSIVLLHPCCHNPTGADLTNDQWDAVIEILKARELIPFLDIAYQGFGAGMEEDAYAIRAIASAGLPALVSNSFSKIFSLYGERVGGLSVMCEDAEAAGRVLGQLKATVRRNYSSPPNFGAQVVAAVLNDEALKASWLAEVEEMRTRILAMRQELVKVLSTEMPERNFDYLLNQRGMFSYTGLSAAQVDRLREEFGVYLIASGRMCVAGLNTANVQRVAKAFAAVM
8TDY , Knot 8 16 0.46 8 7 10 
AGAGGAGAUCUUCUCU
7MOZ , Knot 164 376 0.86 40 231 362 
MAYSQGGGKKKVCYYYDGDIGNYYYGQGHPMKPHRIRMTHNLLLNYGLYRKMEIYRPHKATAEEMTKYHSDEYIKFLRSIRPDNMSEYSKQMQRFNVGEDCPVFDGLFEFCQLSTGGSVAGAVKLNRQQTDMAVNWAGGLHHAKKSEASGFCYVNDIVLAILELLKYHQRVLYIDIDIHHGDGVEEAFYTTDRVMTVSFHKYGEYFPGTGDLRDIGAGKGKYYAVNFPMRDGIDDESYGQIFKPIISKVMEMYQPSAVVLQCGADSLSGDRLGCFNLTVKGHAKCVEVVKTFNLPLLMLGGGGYTIRNVARCWTYETAVALDCEIPNELPYNDYFEYFGPDFKLHISPSNMTNQNTPEYMEKIKQRLFENLRMLPH

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 \(c\).

\(|P_{f(3TAT_1)}(2) \setminus P_{f(8TDY_1)}(2)|=220\), \(|P_{f(8TDY_1)}(2) \setminus P_{f(3TAT_1)}(2)|=4\). 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 1:1100101011011101100100010000101011100000111101011101010101010110101110110000011111111100111000011010011101110111011000110011110010100011111111101000110001001101001110100111001111010000101101000010111011010011111011001111110001011011101111111000100110101001111011000101110111010101000000110111011111100011010111010010001111000110110001100010011000111000110110100100011101110101011110010100110111111
Pair \(Z_2\) Length of longest common subsequence
3TAT_1,8TDY_1 224 4
3TAT_1,7MOZ_1 158 3
8TDY_1,7MOZ_1 232 3

Newick tree

 
[
	8TDY_1:12.50,
	[
		3TAT_1:79,7MOZ_1:79
	]:44.50
]

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 \((0.85)(0.8)(\frac{413 }{\log_{20} 413}-\frac{16}{\log_{20}16})=127.\)
Status Protein1 Protein2 d d1/2
Query variables 3TAT_1 8TDY_1 164 84.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]