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Parikh vectors
9GVM_1 6YPT_1 7HDI_1 Letter Amino acid
14 6 9 D Aspartic acid
16 8 13 G Glycine
20 3 13 K Lycine
13 3 7 Y Tyrosine
8 7 2 R Arginine
8 1 3 C Cysteine
18 9 6 E Glutamic acid
10 17 6 T Threonine
11 6 3 Q Glutamine
9 13 6 H Histidine
10 6 6 I Isoleucine
35 24 19 L Leucine
3 1 2 M Methionine
12 5 5 F Phenylalanine
13 16 5 P Proline
23 16 11 S Serine
3 1 0 W Tryptophan
22 7 15 A Alanine
14 7 16 N Asparagine
17 4 22 V Valine 

9GVM_1|Chains A, B|Nicotinamide N-methyltransferase|Homo sapiens (9606)
>6YPT_1|Chains A, C|RNA replicase polyprotein|Turnip yellow mosaic virus (12154)
>7HDI_1|Chains A, B|Non-structural protein 3|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 \(w=f(c)\)
9GVM , Knot 121 279 0.81 40 180 262 
HNHNHNHNHNHNAAAENLYFQSGFTSKDTYLSHFNPRDYLEKYYKFGSRHSAESQILKHLLKNLFKIFCLDGVKGDLLIDIGSGPTIYQLLSACESFKEIVVTDYSDQNLQELEKWLKAAPAAFDWSPVVTYVCDLEGNRVKGPEKEEKLRQAVKQVLKCDVTQSQPLGAVPLPPADCVLSTLCLDAACPDLPTYCRALRNLGSLLKPGGFLVIMDALKSSYYMIGEQKFSSLPLGREAVEAAVKEAGYTIEWFEVISQSYSSTMANNEGLFSLVARKL
6YPT , Knot 76 160 0.80 40 113 153 
MHHHHHHGSSQLLPAPLTNDPTAIGPVLPFEELHPRRYPENTATFLTRLRSLPSNHLPQPTLNCLLSAVSDQTKVSEEHLWESLQTILPDSQLSNEETNTLGLSTEHLTALAHLYNFQATVYSDRGPILFGPSDTIKRIDITHTTGPPSHFSPGKRLLGS
7HDI , Knot 80 169 0.81 38 119 162 
SMVNSFSGYLKLTDNVYIKNADIVEEAKKVKPTVVVNAANVYLKHGGGVAGALNKATNNAMQVESDDYIATNGPLKVGGSCVLSGHNLAKHCLHVVGPNVNKGEDIQLLKSAYENFNQHEVLLAPLLSAGIFGADPIHSLRVCVDTVRTNVYLAVFDKNLYDKLVSSFL

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 \(c\).

\(|P_{f(9GVM_1)}(2) \setminus P_{f(6YPT_1)}(2)|=122\), \(|P_{f(6YPT_1)}(2) \setminus P_{f(9GVM_1)}(2)|=55\). 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 1:000000000000111001010011000000100101000100000110000100011001100110110101101011101101101001101000100111000000010010011011111101011100100101001011000001001100110001000011111111110011001010110101100001100110110111111110110000011100010011110011011100110010110110000000110001110111001
Pair \(Z_2\) Length of longest common subsequence
9GVM_1,6YPT_1 177 4
9GVM_1,7HDI_1 163 4
6YPT_1,7HDI_1 150 4

Newick tree

 
[
	9GVM_1:88.17,
	[
		7HDI_1:75,6YPT_1:75
	]:13.17
]

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 \((0.85)(0.8)(\frac{439 }{\log_{20} 439}-\frac{160}{\log_{20}160})=82.7\)
Status Protein1 Protein2 d d1/2
Query variables 9GVM_1 6YPT_1 107 82.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]