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Parikh vectors
6DZR_1 2OZU_1 1NTR_1 Letter Amino acid
12 5 15 A Alanine
9 14 6 R Arginine
4 18 8 I Isoleucine
18 33 14 L Leucine
10 23 4 K Lycine
9 13 6 E Glutamic acid
3 10 3 H Histidine
18 10 5 T Threonine
9 9 2 N Asparagine
4 12 1 C Cysteine
7 17 6 Q Glutamine
2 6 5 M Methionine
8 12 3 F Phenylalanine
11 17 6 P Proline
35 19 7 S Serine
5 4 2 W Tryptophan
20 16 10 V Valine
5 14 11 D Aspartic acid
19 13 7 G Glycine
12 19 3 Y Tyrosine 

6DZR_1|Chain A[auth H]|h38c2 heavy chain|Homo sapiens (9606)
>2OZU_1|Chain A|Histone acetyltransferase MYST3|Homo sapiens (9606)
>1NTR_1|Chain A|NTRC RECEIVER DOMAIN|Salmonella typhimurium (90371)
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 \(w=f(c)\)
6DZR , Knot 98 220 0.80 40 142 211 
EVQLVESGGGLVQPGGSLRLSCAASGFTFSNYWMSWVRQSPEKGLEWVSEIRLRSDNYATHYAESVKGRFTISRDNSKNTLYLQMNSLRAEDTGIYYCRTYFYSFSYWGQGTLVTVSSASTKGPSVFPLAPSSKATSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKRVEPKS
2OZU , Knot 128 284 0.84 40 192 276 
GVTGPPDPQVRCPSVIEFGKYEIHTWYSSPYPQEYSRLPKLYLCEFCLKYMKSRTILQQHMKKCGWFHPPANEIYRKNNISVFEVDGNVSTIYCQNLCLLAKLFLDHKTLYYDVEPFLFYVLTQNDVKGCHLVGYFSKEKHCQQKYNVSCIMILPQYQRKGYGRFLIDFSYLLSKREGQAGSPEKPLSDLGRLSYMAYWKSVILECLYHQNDKQISIKKLSKLTGICPQDITSTLHHLRMLDFRSDQFVIIRREKLIQDHMAKLQLNLRPVDVDPECLRWTPVI
1NTR , Knot 63 124 0.81 40 97 120 
MQRGIVWVVDDDSSIRWVLERALAGAGLTCTTFENGNEVLAALASKTPDVLLSDIRMPGMDGLALLKQIKQRHPMLPVIIMTAHSDLDAAVSAYQQGAFDYLPKPFDIDEAVALVERAISHYQE

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 \(c\).

\(|P_{f(6DZR_1)}(2) \setminus P_{f(2OZU_1)}(2)|=67\), \(|P_{f(2OZU_1)}(2) \setminus P_{f(6DZR_1)}(2)|=117\). 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 1:0101100111110111010100110110100011011000100110110010100000100010010101010000000010101001010001100000010010011010110100100011011111100010011011110110001101101010011100110011111000110010011011000110000100100010000100010100
Pair \(Z_2\) Length of longest common subsequence
6DZR_1,2OZU_1 184 4
6DZR_1,1NTR_1 167 3
2OZU_1,1NTR_1 183 3

Newick tree

 
[
	2OZU_1:94.34,
	[
		6DZR_1:83.5,1NTR_1:83.5
	]:10.84
]

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 \((0.85)(0.8)(\frac{504 }{\log_{20} 504}-\frac{220}{\log_{20}220})=81.9\)
Status Protein1 Protein2 d d1/2
Query variables 6DZR_1 2OZU_1 107 91.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]