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Parikh vectors
5XOR_1 9QUB_1 7ENM_1 Letter Amino acid
13 12 16 K Lycine
3 6 0 C Cysteine
8 10 4 Q Glutamine
5 11 6 I Isoleucine
1 2 3 M Methionine
2 4 0 W Tryptophan
6 8 1 A Alanine
13 9 10 E Glutamic acid
13 13 5 G Glycine
13 14 5 L Leucine
8 8 3 P Proline
3 8 7 Y Tyrosine
10 8 2 R Arginine
5 14 7 D Aspartic acid
10 4 2 H Histidine
8 22 1 T Threonine
9 10 9 V Valine
9 11 8 N Asparagine
8 8 6 F Phenylalanine
11 32 6 S Serine 

5XOR_1|Chains A, B, C, D, E|Rep protein|Porcine circovirus 2 (85708)
>9QUB_1|Chains A[auth C], B[auth E]|Fab-light chain|Mus musculus (10090)
>7ENM_1|Chain A|AcrIIA14 protein|Staphylococcus simulans (1286)
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 \(w=f(c)\)
5XOR , Knot 77 158 0.82 40 123 150 
MPSKKNGRSGPQPHKRWVFTLNNPSEDERKKIRDLPISLFDYFIVGEEGNEEGRTPHLQGFANFVKKQTFNKVKWYLGARCHIEKAKGTDQQNKEYCSKEGNLLIECGAPRSQGQRSDLSTAVSTLLESGSLVTVAEQHPVTFVRNFRGLLEHHHHHH
9QUB , Knot 98 214 0.82 40 148 205 
DIVMTQTTSSLSASLGDRVTISCRASQDISNYLNWFQQKPDGTVKLLICYTSRLHSGVPSRFSGSGSGTDYSLTISNLEQEDIATYFCQQDSKHPWTFGGGTKLEIKRADAAPTVSIFPPSSEQLTSGGASVVCFLNNFYPKDINVKWKIDGSERQNGVLNSWTDQDSKDSTYSMSSTLTLTKDEYERHNSYTCEATHKTSTSPIVKSFNRNEC
7ENM , Knot 50 101 0.76 36 78 99 
SMKSVKYISNMSKQEKGYRVYVNVVNEDTDKGFLFPSVPKEVIENDKIDELFNFEHHKPYVQKAKSRYDKNGIGYKIVQLDEGFQKFIELNKEKMKENLDY

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 \(c\).

\(|P_{f(5XOR_1)}(2) \setminus P_{f(9QUB_1)}(2)|=71\), \(|P_{f(9QUB_1)}(2) \setminus P_{f(5XOR_1)}(2)|=96\). 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 1:11000010011010001110100100000001001110110011110010001001010111011000010010101110001001010000000000001011100111000100001001100110010110110001101100101110000000
Pair \(Z_2\) Length of longest common subsequence
5XOR_1,9QUB_1 167 3
5XOR_1,7ENM_1 137 3
9QUB_1,7ENM_1 154 3

Newick tree

 
[
	9QUB_1:83.88,
	[
		5XOR_1:68.5,7ENM_1:68.5
	]:15.38
]

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 \((0.85)(0.8)(\frac{372 }{\log_{20} 372}-\frac{158}{\log_{20}158})=64.4\)
Status Protein1 Protein2 d d1/2
Query variables 5XOR_1 9QUB_1 81 70
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]