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Parikh vectors
5OBU_1 5UMR_1 1GNY_1 Letter Amino acid
40 3 20 A Alanine
39 11 14 G Glycine
7 4 1 H Histidine
7 4 1 Y Tyrosine
26 7 3 R Arginine
33 5 6 N Asparagine
47 4 10 I Isoleucine
43 10 6 K Lycine
11 3 2 M Methionine
34 5 16 T Threonine
1 1 3 W Tryptophan
39 5 13 V Valine
9 6 5 F Phenylalanine
23 0 2 P Proline
32 5 11 S Serine
28 5 14 D Aspartic acid
2 0 2 C Cysteine
18 3 6 Q Glutamine
44 10 9 E Glutamic acid
46 11 9 L Leucine 

5OBU_1|Chain A|Chaperone protein DnaK|Mycoplasma genitalium G37 (243273)
>5UMR_1|Chain A|FACT complex subunit SSRP1|Homo sapiens (9606)
>1GNY_1|Chain A|XYLANASE 10C|PSEUDOMONAS CELLULOSA (155077)
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 \(w=f(c)\)
5OBU , Knot 208 529 0.82 40 220 488 
MSADNGLIIGIDLGTTNSCVSVMEGGRPVVLENPEGKRTTPSIVSYKNNEIIVGDAAKRQMVTNPNTIVSIKRLMGTSNKVKVQNADGTTKELSPEQVSAQILSYLKDFAEKKIGKKISRAVITVPAYFNDAERNATKTAGKIAGLNVERIINEPTAAALAYGIDKASREMKVLVYDLGGGTFDVSLLDIAEGTFEVLATAGDNRLGGDDWDNKIIEYISAYIAKEHQGLNLSKDKMAMQRLKEAAERAKIELSAQLETIISLPFLTVTQKGPVNVELKLTRAKFEELTKPLLERTRNPISDVIKEAKIKPEEINEILLVGGSTRMPAVQKLVESMVPGKKPNRSINPDEVVAIGAAIQGGVLRGDVKDVLLLDVTPLTLSIETLGGVATPLIKRNTTIPVSKSQIFSTAQDNQESVDVVVCQGERPMSRDNKSLGRFNLGGIQPAPKGKPQIEITFSLDANGILNVKAKDLTTQKENSITISDNGNLSEEEIQKMIRDAEANKERDNIIRERIELRNEGELEHHHHHH
5UMR , Knot 56 102 0.84 36 83 100 
GHMAETLEFNDVYQEVKGSMNDGRLRLSRQGIIFKNSKTGKVDNIQAGELTEGIWRRVALGHGLKLLTKNGHVYKYDGFRESEFEKLSDFFKTHYRLELMEK
1GNY , Knot 75 153 0.82 40 113 149 
GNVVIEVDMANGWRGNASGSTSHSGITYSADGVTFAALGDGVGAVFDIARPTTLEDAVIAMVVNVSAEFKASEANLQIFAQLKEDWSKGEWDCLAGSSELTADTDLTLTCTIDEDDDKFNQTARDVQVGIQAKGTPAGTITIKSVTITLAQEA

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 \(c\).

\(|P_{f(5OBU_1)}(2) \setminus P_{f(5UMR_1)}(2)|=159\), \(|P_{f(5UMR_1)}(2) \setminus P_{f(5OBU_1)}(2)|=22\). 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 1:1010011111101100000101101101111001010000101100000011110110001100100110100111000010100101000010100101011001001100011001001110111010010001000110111101001100101111101100100010111001111010101101101010111011000111001000110010101100001101000011100100110010101010100110111101000111010101001010010011100000110011001010100100111111000111100110011110010001010011111111011110101001111010110101001111101110000011100001100100000010111001001100000011010111101110101010101010101110101001000000010100010100001001100101000000110001010001010000000
Pair \(Z_2\) Length of longest common subsequence
5OBU_1,5UMR_1 181 3
5OBU_1,1GNY_1 157 3
5UMR_1,1GNY_1 138 3

Newick tree

 
[
	5OBU_1:89.33,
	[
		1GNY_1:69,5UMR_1:69
	]:20.33
]

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 \((0.85)(0.8)(\frac{631 }{\log_{20} 631}-\frac{102}{\log_{20}102})=154.\)
Status Protein1 Protein2 d d1/2
Query variables 5OBU_1 5UMR_1 188 111.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]