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Parikh vectors
7DRT_1 6TXN_1 2AMN_1 Letter Amino acid
29 7 4 R Arginine
11 9 0 Q Glutamine
22 23 0 E Glutamic acid
13 4 0 H Histidine
20 15 2 L Leucine
25 0 0 C Cysteine
30 7 1 G Glycine
6 6 0 M Methionine
21 9 4 V Valine
14 8 0 D Aspartic acid
14 9 3 I Isoleucine
15 12 4 K Lycine
14 9 0 F Phenylalanine
16 2 1 P Proline
9 3 1 W Tryptophan
11 9 2 Y Tyrosine
28 13 2 A Alanine
10 6 1 N Asparagine
30 9 0 S Serine
14 4 1 T Threonine 

7DRT_1|Chain A|Protein Wnt-3a|Homo sapiens (9606)
>6TXN_1|Chains A, B, C, D, E, F, G, H|Ferritin|Thermotoga maritima (strain ATCC 43589 / MSB8 / DSM 3109 / JCM 10099) (243274)
>2AMN_1|Chain A|cathelicidin|null
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 \(w=f(c)\)
7DRT , Knot 155 352 0.86 40 216 338 
MAPLGYFLLLCSLKQALGSYPIWWSLAVGPQYSSLGSQPILCASIPGLVPKQLRFCRNYVEIMPSVAEGIKIGIQECQHQFRGRRWNCTTVHDSLAIFGPVLDKATRESAFVHAIASAGVAFAVTRSCAEGTAAICGCSSRHQGSPGKGWKWGGCSEDIEFGGMVSREFADARENRPDARSAMNRHNNEAGRQAIASHMHLKCKCHGLSGSCEVKTCWWSQPDFRAIGDFLKDKYDSASEMVVEKHRESRGWVETLRPRYTYFKVPTERDLVYYEASPNFCEPNPETGSFGTRDRTCNVSSHGIDGCDLLCCGRGHNARAERRREKCRCVFHWCCYVSCQECTRVYDVHTCK
6TXN , Knot 78 164 0.80 38 121 161 
MMVISEKVRKALNDQLNREIYSSYLYLSMATYFDAEGFKGFAHWMKKQAQEELTHAMKFYEYIYERGGRVELEAIEKPPSNWNGIKDAFEAALKHEEFVTQSIYNILELASEEKDHATVSFLKWFVDEQVEEEDQVREILDLLEKANGQMSVIFQLDRYLGQRE
2AMN , Knot 16 26 0.66 24 22 24 
RVKRVWPLVIRTVIAGYNLYRAIKKK

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 \(c\).

\(|P_{f(7DRT_1)}(2) \setminus P_{f(6TXN_1)}(2)|=146\), \(|P_{f(6TXN_1)}(2) \setminus P_{f(7DRT_1)}(2)|=51\). 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 1:1111101111001001110011110111110000110011101011111100101000010111011011011100000010100100001000111111110010000111011101111111000010101110100000010110110111000010111110001101000010100110000001100111001010000011010001000110010101110110000001001110000000111001010000101100001100010101001010010110000000100011010011001010010100000000011010001000000010010000
Pair \(Z_2\) Length of longest common subsequence
7DRT_1,6TXN_1 197 3
7DRT_1,2AMN_1 214 3
6TXN_1,2AMN_1 127 2

Newick tree

 
[
	7DRT_1:11.94,
	[
		6TXN_1:63.5,2AMN_1:63.5
	]:49.44
]

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 \((0.85)(0.8)(\frac{516 }{\log_{20} 516}-\frac{164}{\log_{20}164})=102.\)
Status Protein1 Protein2 d d1/2
Query variables 7DRT_1 6TXN_1 134 97
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]