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Parikh vectors
7CFB_1 2TCT_1 1ENF_1 Letter Amino acid
17 7 15 N Asparagine
4 7 3 H Histidine
8 7 7 F Phenylalanine
17 12 10 T Threonine
23 13 23 D Aspartic acid
14 7 2 P Proline
12 16 17 E Glutamic acid
4 3 1 M Methionine
1 2 1 W Tryptophan
13 9 7 V Valine
23 8 21 I Isoleucine
20 33 18 L Leucine
15 6 25 K Lycine
17 23 9 A Alanine
13 16 6 R Arginine
4 0 2 C Cysteine
6 11 6 Q Glutamine
10 12 11 G Glycine
14 10 14 S Serine
7 5 14 Y Tyrosine 

7CFB_1|Chains A, B|FI20010p1|Drosophila melanogaster (7227)
>2TCT_1|Chain A|TETRACYCLINE REPRESSOR|Escherichia coli (562)
>1ENF_1|Chain A|ENTEROTOXIN H|Staphylococcus aureus (1280)
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 \(w=f(c)\)
7CFB , Knot 109 242 0.82 40 166 233 
SASIEKVNKLPKSPRNRFLLPPKGGTETTRRDIYNQILKDMAAFPENTIVTAVLASVDVTDNCAYVAKWDESSDRIKKVLQRQLPLQELDQLPDYGDIFAVLDSINNIITRITINSSSAGGGYDAYLIDFGEHIHFDGNETIFKLPDDIKRLPAQAIRCDLINCDIANMHCFVNTYIKIRVHENNNSTLVAEPVIDRLSRPTKTNTTKYPAGITEDDMAMLNEIDESTSDPLKAVLGFRPKD
2TCT , Knot 95 207 0.81 38 139 195 
ARLNRESVIDAALELLNETGIDGLTTRKLAQKLGIEQPTLYWHVKNKRALLDALAVEILARHHDYSLPAAGESWQSFLRNNAMSFRRALLRYRDGAKVHLGTRPDEKQYDTVETQLRFMTENGFSLRDGLYAISAVSHFTLGAVLEQQEHTAALTDRPAAPDENLPPLLREALQIMDSDDGEQAFLHGLESLIRGFEVQLTALLQIV
1ENF , Knot 91 212 0.76 40 129 200 
DLHDKSELTDLALANAYGQYNHPFIKENIKSDEISGEKDLIFRNQGDSGNDLRVKFATADLAQKFKNKNVDIYGASFYYKCEKISENISECLYGGTTLNSEKLAQERVIGANVWVDGIQKETELIRTNKKNVTLQELDIKIRKILSDKYKIYYKDSEISKGLIEFDMKTPRDYSFDIYDLKGENDYEIDKIYEDNKTLKSDDISHIDVNLYT

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 \(c\).

\(|P_{f(7CFB_1)}(2) \setminus P_{f(2TCT_1)}(2)|=89\), \(|P_{f(2TCT_1)}(2) \setminus P_{f(7CFB_1)}(2)|=62\). 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 1:01010010011001000111110110000000100011001111100011011110101000010110100000010011000111001001100101111100100110010100001111001011011001010100011011001001110110001100011010011000101010000000111011100100100000000111100001111001000000110111110100
Pair \(Z_2\) Length of longest common subsequence
7CFB_1,2TCT_1 151 3
7CFB_1,1ENF_1 143 5
2TCT_1,1ENF_1 156 4

Newick tree

 
[
	2TCT_1:78.43,
	[
		7CFB_1:71.5,1ENF_1:71.5
	]:6.93
]

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 \((0.85)(0.8)(\frac{449 }{\log_{20} 449}-\frac{207}{\log_{20}207})=70.6\)
Status Protein1 Protein2 d d1/2
Query variables 7CFB_1 2TCT_1 91 83
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]