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Parikh vectors
5XWZ_1 5GYY_1 1QFW_1 Letter Amino acid
13 27 3 R Arginine
15 24 2 D Aspartic acid
14 17 1 I Isoleucine
10 14 6 K Lycine
20 39 8 S Serine
5 12 0 W Tryptophan
21 25 6 V Valine
23 18 5 A Alanine
7 8 5 Q Glutamine
16 17 4 E Glutamic acid
20 27 4 G Glycine
12 3 3 H Histidine
9 10 3 M Methionine
10 15 4 Y Tyrosine
9 29 4 N Asparagine
14 39 4 L Leucine
9 20 4 F Phenylalanine
21 18 7 P Proline
20 31 9 T Threonine
3 12 10 C Cysteine 

5XWZ_1|Chains A, B, C, D|Unplaced genomic scaffold supercont1.36, whole genome shotgun sequence|Cladophialophora bantiana CBS 173.52 (1442370)
>5GYY_1|Chains A, B|S-receptor kinase SRK9|Brassica rapa subsp. oleifera (3711)
>1QFW_1|Chain A|GONADOTROPIN ALPHA SUBUNIT|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 \(w=f(c)\)
5XWZ , Knot 122 271 0.84 40 175 260 
HHHHHHMAPERLRSTILTKDGINWYYEQEGSGPDVVLIPDGLGDCQMFDKPMSIIGSSGFKVTTFDMPGMSRSSSAPPETYQDVTGQKLANYIVTVMDQLGIKTASVWGCSSGASTVLALCSGFPERVRNGMPHEVPTANPENLQNIHDADPATISRDMAAVSRAMSANEEAWDALGPEVHERLRDNYVRWAYGYPRTIPGSAATKTEDLHKVPIDWTVGAAGPTQVFFENVVIATRESIPIKTLPGFHFPYVSHPEAFAKYVVETTRKYL
5GYY , Knot 166 405 0.82 40 224 381 
AAAAALSTLSSTESLTISSNRTLVSPGNIFELGFFRTNSRWYLGMWYKKLSGRTYVWVANRDNPLSNSIGTLKISNMNLVLLDHSNKSVWSTNLTRENVRSPVVAELLANGNFVVRDPSGFLWQSFDYPTDTLLPEMKLGYDLKTGLNRFLVSWRSSDDPSSGDFSYKLDIQRGLPEFYTFKDNTLVHRTGPWNGIRFSGIPEEQQLSYMVYNFTENSEEVAYTFLVTNNSIYSRLTINFSGFFERLTWTPSLVIWNPIWSSPASFQCDPYMICGPGSYCDVNTLPLCNCIQGFKPLNVQEWDMRDHTRGCIRRTRLSCRGDGFTRMKNMKLPETTMATVDRSIGVKECEKKCLSDCNCTAFANADIRDGGTGCVIWTGRLDDMRNYAVSGQDLYVRLAAADVVE
1QFW , Knot 49 92 0.80 38 81 89 
APDTQDCPECTLQENPFFSQPGAPILQCMGCCFSRAYPTPLRSKKTMLVQKNVTSESTCCVAKSYNRVTVMGGFKVENHTACHCSTCYYHKS

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 \(c\).

\(|P_{f(5XWZ_1)}(2) \setminus P_{f(5GYY_1)}(2)|=70\), \(|P_{f(5GYY_1)}(2) \setminus P_{f(5XWZ_1)}(2)|=119\). 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 1:0000001110010001100011010000010110111110111000110011011100110100101111000001110000010100110011011001110010111000110011110011100100111001101010010010010110100011110011010001101111010001000010110101001110110000010011101011111100111001111000011100111101101001011100110000001
Pair \(Z_2\) Length of longest common subsequence
5XWZ_1,5GYY_1 189 3
5XWZ_1,1QFW_1 172 4
5GYY_1,1QFW_1 211 3

Newick tree

 
[
	5GYY_1:10.44,
	[
		5XWZ_1:86,1QFW_1:86
	]:18.44
]

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 \((0.85)(0.8)(\frac{676 }{\log_{20} 676}-\frac{271}{\log_{20}271})=112.\)
Status Protein1 Protein2 d d1/2
Query variables 5XWZ_1 5GYY_1 144 118.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]