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Parikh vectors
4YHI_1 5CYO_1 6IEA_1 Letter Amino acid
4 18 7 R Arginine
13 19 24 L Leucine
31 14 24 S Serine
21 19 20 V Valine
12 10 15 P Proline
5 4 18 C Cysteine
8 10 15 Q Glutamine
3 9 12 H Histidine
2 27 8 I Isoleucine
15 23 34 K Lycine
4 6 6 M Methionine
6 13 11 F Phenylalanine
4 2 1 W Tryptophan
13 7 13 Y Tyrosine
13 7 21 A Alanine
7 15 11 N Asparagine
7 15 20 D Aspartic acid
8 24 17 E Glutamic acid
21 14 24 G Glycine
25 18 15 T Threonine 

4YHI_1|Chains A, C[auth H]|aDabi-Fab2a heavy chain|Homo sapiens (9606)
>5CYO_1|Chains A, B|Septin-9|Homo sapiens (9606)
>6IEA_1|Chain A|NSmGnGc|Rift valley fever virus (11588)
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 \(w=f(c)\)
4YHI , Knot 94 222 0.76 40 141 205 
QVQLVQSGAEVKKPGASVKVSCKASGYTFTDYYMHWVRQAPGQGLEWMGETNPRNGGTTYNEKFKGKATMTRDTSTSTAYMELSSLRSEDTAVYYCTIGTSGYDYFDYWGQGTLVTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVEPKSC
5CYO , Knot 118 274 0.80 40 179 262 
QGFEFNIMVVGQSGLGKSTLINTLFKSKISRKSVQPTSEERIPKTIEIKSITHDIEEKGVRMKLTVIDTPGFGDHINNENCWQPIMKFINDQYEKYLQEEVNINRKKRIPDTRVHCCLYFIPATGHSLRPLDIEFMKRLSKVVNIVPVIAKADTLTLEERVHFKQRITADLLSNGIDVYPQKEFDEDSEDRLVNEKFREMIPFAVVGSDHEYQVNGKRILGRKTKWGTIEVENTTHCEFAYLRDLLIRTHMQNIKDITSSIHFEAYRVKRLNEG
6IEA , Knot 141 316 0.85 40 203 303 
EDPHLRNRPGKGHNYIDGMTQEDATCKPVTYAGACSSFDVLLEKGKFPLFQSYAHHRTLLEAVHDTIIAKADPPSCDLQSAHGNPCMKEKLVMKTHCPNDYQSAHYLNNDGKMASVKCPPKYELTEDCNFCRQMTGASLKKGSYPLQDLFCQSSEDDGSKLKTKMKGVCEVGVQALKKCDGQLSTAHEVVPFAVFKNSKKVYLDKLDLKTEENLLPDSFVCFEHKGQYKGTIDSGQTKRELKSFDISQCPKIGGHGSKKCTGDAAFCSAYECTAQYANAYCSHANGSGIVQIQVSGVWKKPLCVGYERVVVKRELS

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 \(c\).

\(|P_{f(4YHI_1)}(2) \setminus P_{f(5CYO_1)}(2)|=72\), \(|P_{f(5CYO_1)}(2) \setminus P_{f(4YHI_1)}(2)|=110\). 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 1:010110011010011101010001010010000101100111011011100010011000000101010100000000101010010000011000011001000100110101101001000110111111000000110111101100011011010100111001100111110001100100110110001100001001000100001000101000
Pair \(Z_2\) Length of longest common subsequence
4YHI_1,5CYO_1 182 4
4YHI_1,6IEA_1 176 4
5CYO_1,6IEA_1 178 5

Newick tree

 
[
	5CYO_1:90.66,
	[
		4YHI_1:88,6IEA_1:88
	]:2.66
]

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 \((0.85)(0.8)(\frac{496 }{\log_{20} 496}-\frac{222}{\log_{20}222})=79.0\)
Status Protein1 Protein2 d d1/2
Query variables 4YHI_1 5CYO_1 104 92.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]