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Parikh vectors
7HXX_1 4RQW_1 4YQV_1 Letter Amino acid
10 7 14 A Alanine
9 10 9 D Aspartic acid
5 11 12 I Isoleucine
12 15 27 L Leucine
2 3 7 M Methionine
6 12 9 T Threonine
3 5 5 W Tryptophan
14 13 10 V Valine
3 9 13 F Phenylalanine
14 20 18 S Serine
8 4 9 Y Tyrosine
9 6 9 R Arginine
5 15 11 N Asparagine
5 12 6 Q Glutamine
7 17 24 E Glutamic acid
14 21 15 G Glycine
6 3 2 H Histidine
2 8 23 K Lycine
4 2 16 P Proline
6 2 5 C Cysteine 

7HXX_1|Chains A, B[auth C]|Protease 2A|Coxsackievirus A16 (31704)
>4RQW_1|Chains A, B|Transcription factor MYC3|Arabidopsis thaliana (3702)
>4YQV_1|Chains A, B, C|Glutathione S-transferase omega-1|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 \(w=f(c)\)
7HXX , Knot 70 144 0.80 40 112 139 
SGAIYVGNYRVVNRHLATHNDWANLVWEDSSRDLLVSSTTAQGCDTIARCDCQTGVYYCSSRRKHYPVSFSKPSLIFVEASEYYPARYQSHLMLAVGHSEPGDCGGILRCQHGVVGIVSTGGNGLVGFADVRDLLWLDEEAMEQ
4RQW , Knot 91 195 0.82 40 143 189 
QPQFNEDTLQQRLQALIESAGENWTYAIFWQISHDFDSSTGDNTVILGWGDGYYKGEEDKEKKKNNTNTAEQEHRKRVIRELNSLISGGIGVSDESNDEEVTDTEWFFLVSMTQSFVNGVGLPGESFLNSRVIWLSGSGALTGSGCERAGQGQIYGLKTMVCIATQNGVVELGSSEVISQSSDLMHKVNNLFNFN
4YQV , Knot 111 244 0.83 40 162 238 
SNAMSGESARSLGKGSAPPGPVPEGSIRIYSMRFCPFAERTRLVLKAKGIRHEVININLKNKPEWFFKKNPFGLVPVLENSQGQLIYESAITCEYLDEAYPGKKLLPDDPYEKACQKMILELFSKVPSLVGSFIRSQNKEDYAGLKEEFRKEFTKLEEVLTNKKTTFFGGNSISMIDYLIWPWFERLEAMKLNECVDHTPKLKLWMAAMKEDPTVSALLTSEKDWQGFLELYLQNSPEACDYGL

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 \(c\).

\(|P_{f(7HXX_1)}(2) \setminus P_{f(4RQW_1)}(2)|=63\), \(|P_{f(4RQW_1)}(2) \setminus P_{f(7HXX_1)}(2)|=94\). 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 1:011101100011000110000110111000000111000010100011000000110000000000110100101111010000110000011111100011001111000011111100110111111010011110001100
Pair \(Z_2\) Length of longest common subsequence
7HXX_1,4RQW_1 157 3
7HXX_1,4YQV_1 190 3
4RQW_1,4YQV_1 169 4

Newick tree

 
[
	4YQV_1:93.39,
	[
		7HXX_1:78.5,4RQW_1:78.5
	]:14.89
]

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 \((0.85)(0.8)(\frac{339 }{\log_{20} 339}-\frac{144}{\log_{20}144})=59.5\)
Status Protein1 Protein2 d d1/2
Query variables 7HXX_1 4RQW_1 77 66
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]