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Parikh vectors
8SID_1 1UTS_1 7GPG_1 Letter Amino acid
20 4 12 A Alanine
19 0 10 R Arginine
9 0 5 Q Glutamine
27 0 17 T Threonine
13 0 6 M Methionine
16 0 7 P Proline
7 0 0 W Tryptophan
22 0 7 Y Tyrosine
26 0 13 I Isoleucine
36 0 13 L Leucine
21 0 10 F Phenylalanine
19 0 10 N Asparagine
25 0 12 D Aspartic acid
11 0 6 E Glutamic acid
3 0 6 H Histidine
32 0 16 V Valine
3 9 3 C Cysteine
18 10 18 G Glycine
15 0 7 K Lycine
22 0 4 S Serine 

8SID_1|Chains A, C|Gamma-aminobutyric acid receptor subunit beta-2|Homo sapiens (9606)
>1UTS_1|Chain A[auth B]|RNA (5'-(*GP*GP*CP*AP*GP*AP*UP*CP*UP*GP*AP*GP *CP*CP*UP*GP*GP*GP*AP*GP*CP*UP*CP*UP*CP*UP*GP*CP*C) -3')|HUMAN IMMUNODEFICIENCY VIRUS 1 (11676)
>7GPG_1|Chains A, B|Protease 3C|Human Enterovirus D68 (42789)
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 \(w=f(c)\)
8SID , Knot 157 364 0.84 40 221 347 
QSVNDPSNMSLVKETVDRLLKGYDIRLRPDFGGPPVAVGMNIDIASIDMVSEVNMDYTLTMYFQQAWRDKRLSYNVIPLNLTLDNRVADQLWVPDTYFLNDKKSFVHGVTVKNRMIRLHPDGTVLYGLRITTTAACMMDLRRYPLDEQNCTLEIESYGYTTDDIEFYWRGDDNAVTGVTKIELPQFSIVDYKLITKKVVFSTGSYPRLSLSFKLKRNIGYFILQTYMPSILITILSWVSFWINYDASAARVALGITTVLTMTTINTHLRETLPKIPYVKAIDMYLMGCFVFVFMALLEYALVNYIFFSQPARAAAIDRWSRIFFPVVFSFFNIVYWLYYVNVDGSGATNFSLLKQAGDVEENPG
1UTS , Knot 12 29 0.46 8 10 19 
GGCAGAUCUGAGCCUGGGAGCUCUCUGCC
7GPG , Knot 86 182 0.82 38 139 179 
MGPGFDFAQAIMKKNTVIARTEKGEFTMLGVYDRVAVIPTHASVGEIIYINDVETRVLDACALRDLTDTNLEITIVKLDRNQKFRDIRHFLPRCEDDYNDAVLSVHTSKFPNMYIPVGQVTNYGFLNLGGTPTHRILMYNFPTRAGQCGGVVTTTGKVIGIHVGGNGAQGFAAMLLHSYFTD

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 \(c\).

\(|P_{f(8SID_1)}(2) \setminus P_{f(1UTS_1)}(2)|=217\), \(|P_{f(1UTS_1)}(2) \setminus P_{f(8SID_1)}(2)|=6\). 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 1:0010010010110001001101001010101111111111010110101100101000101010011000010001111010100011001111000110000011011010001101010101101101000110110100011000000101000100000101010100011011001011010110001100011100100101010101000110111000110111011011011100010110111110011010010001000110110101101011101111111110011100111001101111001001111111011011011001010101100101100110100011
Pair \(Z_2\) Length of longest common subsequence
8SID_1,1UTS_1 223 2
8SID_1,7GPG_1 172 3
1UTS_1,7GPG_1 141 2

Newick tree

 
[
	8SID_1:10.52,
	[
		7GPG_1:70.5,1UTS_1:70.5
	]:37.02
]

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 \((0.85)(0.8)(\frac{393 }{\log_{20} 393}-\frac{29}{\log_{20}29})=116.\)
Status Protein1 Protein2 d d1/2
Query variables 8SID_1 1UTS_1 154 81.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]