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Parikh vectors
8UYJ_1 1STD_1 7GXW_1 Letter Amino acid
0 6 3 H Histidine
0 8 9 I Isoleucine
0 14 4 K Lycine
0 10 7 T Threonine
0 7 0 W Tryptophan
0 11 9 R Arginine
0 1 7 N Asparagine
0 6 6 M Methionine
0 5 3 P Proline
0 7 3 Y Tyrosine
0 17 8 D Aspartic acid
32 1 5 C Cysteine
0 12 6 E Glutamic acid
43 13 5 G Glycine
0 11 15 L Leucine
0 11 10 V Valine
25 7 8 A Alanine
0 6 4 Q Glutamine
0 9 7 F Phenylalanine
0 10 9 S Serine 

8UYJ_1|Chain A|BtCoV-HKU5 5' proximal stem-loop 5, conformation 4|Pipistrellus bat coronavirus HKU5 (694008)
>1STD_1|Chain A|SCYTALONE DEHYDRATASE|Magnaporthe grisea (148305)
>7GXW_1|Chain A|B-cell lymphoma 6 protein|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 \(w=f(c)\)
8UYJ , Knot 37 135 0.44 8 16 49 
GGAGCAUCGUGUCUCAAGUGCUUCACGGUCACAAUAUACCGUUUCGUCGGGUGCGUGGCAAUUCGGUGCACAUCAUGUCUUUCGUGGCUGGUGUGGCUCCUCAAGGUGCGAGGGGCAAGUAUAGAGCAGAGCUCC
1STD , Knot 84 172 0.83 40 136 167 
MGSQVQKSDEITFSDYLGLMTCVYEWADSYDSKDWDRLRKVIAPTLRIDYRSFLDKLWEAMPAEEFVGMVSSKQVLGDPTLRTQHFIGGTRWEKVSEDEVIGYHQLRVPHQRYKDTTMKEVTMKGHAHSANLHWYKKIDGVWKFAGLKPDIRWGEFDFDRIFEDGRETFGDK
7GXW , Knot 65 128 0.82 38 98 125 
GPGADSCIQFTRHASDVLLNLNRLRSRDILTDVVIVVSREQFRAHKTVLMACSGLFYSIFTDQLKCNLSVINLDPEINPEGFCILLDFMYTSRLNLREGNIMAVMATAMYLQMEHVVDTCRKFIKASE

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 \(c\).

\(|P_{f(8UYJ_1)}(2) \setminus P_{f(1STD_1)}(2)|=14\), \(|P_{f(1STD_1)}(2) \setminus P_{f(8UYJ_1)}(2)|=134\). 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 1:111101001010000111010000101100101101010010000100111010101101100011010101001010000001011001101011000000111101011111101110101111011110000
Pair \(Z_2\) Length of longest common subsequence
8UYJ_1,1STD_1 148 2
8UYJ_1,7GXW_1 110 2
1STD_1,7GXW_1 170 3

Newick tree

 
[
	1STD_1:86.36,
	[
		8UYJ_1:55,7GXW_1:55
	]:31.36
]

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 \((0.85)(0.8)(\frac{307 }{\log_{20} 307}-\frac{135}{\log_{20}135})=53.1\)
Status Protein1 Protein2 d d1/2
Query variables 8UYJ_1 1STD_1 80 58
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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