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Parikh vectors
5PFV_1 5EPR_1 8RHM_1 Letter Amino acid
12 8 7 D Aspartic acid
2 1 0 C Cysteine
2 7 0 Q Glutamine
5 8 5 R Arginine
8 1 3 H Histidine
13 14 8 L Leucine
6 5 0 M Methionine
6 5 5 P Proline
6 6 0 N Asparagine
9 10 5 E Glutamic acid
6 4 7 G Glycine
4 5 5 I Isoleucine
14 8 2 K Lycine
11 4 1 S Serine
2 0 0 W Tryptophan
8 5 4 V Valine
4 7 8 A Alanine
8 8 5 F Phenylalanine
8 5 4 T Threonine
4 5 2 Y Tyrosine 

5PFV_1|Chain A|Bromodomain adjacent to zinc finger domain protein 2B|Homo sapiens (9606)
>5EPR_1|Chain A|Peregrin|Homo sapiens (9606)
>8RHM_1|Chain A|Non-ribosomal peptide synthetase, putative|Burkholderia thailandensis E264 (271848)
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 \(w=f(c)\)
5PFV , Knot 66 138 0.78 40 109 129 
MHHHHHHSSGVDLGTENLYFQSMSVKKPKRDDSKDLALCSMILTEMETHEDAWPFLLPVNLKLVPGYKKVIKKPMDFSTIREKLSSGQYPNLETFALDVRLVFDNCETFNEDDSDIGRAGHNMRKYFEKKWTDTFKVS
5EPR , Knot 62 116 0.84 38 95 112 
SMEMQLTPFLILLRKTLEQLQEKDTGNIFSEPVPLSEVPDYLDHIKKPMDFFTMKQNLEAYRYLNFDDFEEDFNLIVSNCLKYNAKDTIFYRAAVRLREQGGAVLRQARRQAEKMG
8RHM , Knot 38 72 0.75 32 65 70 
GPGSRTPVELRLTEIFRDVLGHDAFGVLDDFFELGGDXFKAIRIAAKYGPPLEVTDIYDHPTIEALAAHLAR

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 \(c\).

\(|P_{f(5PFV_1)}(2) \setminus P_{f(5EPR_1)}(2)|=70\), \(|P_{f(5EPR_1)}(2) \setminus P_{f(5PFV_1)}(2)|=56\). 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 1:100000000110110001010010100100000001110011100100000111111110101111000110011010010001001001010011101011100000100000011011001000100010001010
Pair \(Z_2\) Length of longest common subsequence
5PFV_1,5EPR_1 126 7
5PFV_1,8RHM_1 126 3
5EPR_1,8RHM_1 114 3

Newick tree

 
[
	5PFV_1:64.87,
	[
		5EPR_1:57,8RHM_1:57
	]:7.87
]

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 \((0.85)(0.8)(\frac{254 }{\log_{20} 254}-\frac{116}{\log_{20}116})=43.7\)
Status Protein1 Protein2 d d1/2
Query variables 5PFV_1 5EPR_1 51 47
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]