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Parikh vectors
5TBC_1 3NZH_1 3ALO_1 Letter Amino acid
21 11 24 D Aspartic acid
36 14 25 K Lycine
19 20 11 T Threonine
14 10 18 P Proline
21 27 28 S Serine
23 6 22 I Isoleucine
8 1 11 M Methionine
12 12 14 Y Tyrosine
18 13 14 A Alanine
19 6 16 R Arginine
12 7 9 N Asparagine
3 5 8 C Cysteine
13 14 11 Q Glutamine
27 9 21 E Glutamic acid
23 13 17 G Glycine
15 2 11 H Histidine
26 14 29 L Leucine
14 10 12 F Phenylalanine
1 2 4 W Tryptophan
18 18 22 V Valine 

5TBC_1|Chain A|DNA polymerase beta|Homo sapiens (9606)
>3NZH_1|Chain A[auth L]|5F6 LIGHT CHAIN|Homo sapiens (9606)
>3ALO_1|Chain A|Dual specificity mitogen-activated protein kinase kinase 4|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 \(w=f(c)\)
5TBC , Knot 148 343 0.84 40 201 326 
MGMSKRKAPQETLNGGITDMLTELANFEKNVSQAIHKYNAYRKAASVIAKYPHKIKSGAEAKKLPGVGTKIAEKIDEFLATGKLRKLEKIRQDDTSSSINFLTRVSGIGPSAARKFVDEGIKTLEDLRKNEDKLNHHQRIGLKYFGDFEKRIPREEMLQMQDIVLNEVKKVDSEYIATVCGSFRRGAESSGDMDVLLTHPSFTSESTKQPKLLHQVVEQLQKVHFITDTLSKGETKFMGVCQLPSKNDEKEYPHRRIDIRLIPKDQYYCGVLYFTGSDIFNKNMRAHALEKGFTINEYTIRPLGVTGVAGEPLPVDSEKDIFDYIQWKYREPKDRSEHHHHHH
3NZH , Knot 101 214 0.84 40 156 210 
SIVMTQTPKFLLVSAGDRVTITCKASQSVSNDVAWYQQKPGQSPKLLIYYASNRYTGVPDRFTGSGYGTDFTFTISTVQAEDLAVYFCQQDYSSPYTFGGGTKLEIKRTVAAPSVFIFPPSDEQLKSGTASVVCLLNNFYPREAKVQWKVDNALQSGNSQESVTEQDSKDSTYSLSSTLTLSKADYEKHKVYACEVTHQGLSSPVTKSFNRGEC
3ALO , Knot 148 327 0.87 40 206 316 
MSIESSGKLKISPEQHWDFTAEDLKDLGEIGRGAYGSVNKMVHKPSGQIMAVKRIRSTVDEKEQKQLLMDLDVVMRSSDCPYIVQFYGALFREGDCWICMELMSTSFDKFYKYVYSVLDDVIPEEILGKITLATVKALNHLKENLKIIHRDIKPSNILLDRSGNIKLCDFGISGQLVDSIAKTRDAGCRPYMAPERIDPSASRQGYDVRSDVWSLGITLYELATGRFPYPKWNSVFDQLTQVVKGDPPQLSNSEEREFSPSFINFVNLCLTKDESKRPKYKELLKHPFILMYEERAVEVACYVCKILDQMPATPSSPMYVDHHHHHH

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 \(c\).

\(|P_{f(5TBC_1)}(2) \setminus P_{f(3NZH_1)}(2)|=100\), \(|P_{f(3NZH_1)}(2) \setminus P_{f(5TBC_1)}(2)|=55\). 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 1:1110000110001011100110011010001001100001000110111001001001101001111100110010011101010010010000000010110010111101100110011001001000000100000111001101000110001101001110010010000110101010011000101011100101000000010110011001001011000100100011110011000000001000101011100000011101010011000101011001101000010111101111011110000011001010000100000000000
Pair \(Z_2\) Length of longest common subsequence
5TBC_1,3NZH_1 155 4
5TBC_1,3ALO_1 169 6
3NZH_1,3ALO_1 172 4

Newick tree

 
[
	3ALO_1:87.68,
	[
		5TBC_1:77.5,3NZH_1:77.5
	]:10.18
]

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 \((0.85)(0.8)(\frac{557 }{\log_{20} 557}-\frac{214}{\log_{20}214})=98.2\)
Status Protein1 Protein2 d d1/2
Query variables 5TBC_1 3NZH_1 122 99
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]