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Parikh vectors
6XKR_1 8ZVG_1 8XAB_1 Letter Amino acid
9 9 3 N Asparagine
10 9 4 H Histidine
12 6 2 P Proline
6 12 5 F Phenylalanine
34 12 7 S Serine
16 25 6 A Alanine
5 14 1 R Arginine
18 12 3 G Glycine
3 17 4 I Isoleucine
14 15 5 K Lycine
3 5 3 M Methionine
11 9 6 Y Tyrosine
4 13 6 D Aspartic acid
8 9 1 Q Glutamine
7 26 11 E Glutamic acid
15 24 11 L Leucine
5 4 1 W Tryptophan
5 3 3 C Cysteine
23 12 6 T Threonine
23 14 8 V Valine 

6XKR_1|Chain A[auth H]|Sasanlimab Fab Heavy chain|Homo sapiens (9606)
>8ZVG_1|Chains A, B|AetD|Aetokthonos hydrillicola Thurmond2011 (2712845)
>8XAB_1|Chain A|Papain-like protease nsp3|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
6XKR , Knot 97 231 0.76 40 144 212 
QVQLVQSGAEVKKPGASVKVSCKASGYTFTSYWINWVRQAPGQGLEWMGNIYPGSSLTNYNEKFKNRVTMTRDTSTSTVYMELSSLRSEDTAVYYCARLSTGTFAYWGQGTLVTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVEPKSCAAAHHHHHHHH
8ZVG , Knot 109 250 0.80 40 165 235 
GAGAGAGAGAGMKAILQLILEKRQEFEKLPCFEFVRDETISPEERLILYPCIAAFALNFRDLNRYDYRDDNSSDYYQKIINIHTQEDAKHWEWFLNDLELLGFDKTMRFSEALRFVWSDDLLHTRRLCHNIAVLSHDLEPVMKMVVIEAMETAGLVIFHALAKPGESIAKATRRKYLYVADSHVEVETGHAVGTENIITILEQTQLSSEQEEKAKEIVNKVFQWSTNLIGEFERYVKAHRSEKAQPTAAY
8XAB , Knot 52 96 0.82 40 81 93 
MYKSVNITFELDERIDKVLNEKCSAYTVELGTEVNEFACVVADAVIKTLQPVSELLTPLGIDLDEWSMATYYLFDESGEFKLASHMYCSFYLEHHH

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 \(c\).

\(|P_{f(6XKR_1)}(2) \setminus P_{f(8ZVG_1)}(2)|=83\), \(|P_{f(8ZVG_1)}(2) \setminus P_{f(6XKR_1)}(2)|=104\). 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 1:010110011010011101010001010010001101100111011011101011001000000100010100000000101010010000011000101001011011010110100100011011111100000011011110110001101101010011100110011111000110010011011000110000100100010000100010100011100000000
Pair \(Z_2\) Length of longest common subsequence
6XKR_1,8ZVG_1 187 3
6XKR_1,8XAB_1 147 3
8ZVG_1,8XAB_1 156 3

Newick tree

 
[
	8ZVG_1:89.90,
	[
		6XKR_1:73.5,8XAB_1:73.5
	]:16.40
]

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 \((0.85)(0.8)(\frac{481 }{\log_{20} 481}-\frac{231}{\log_{20}231})=72.1\)
Status Protein1 Protein2 d d1/2
Query variables 6XKR_1 8ZVG_1 93 88.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]