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Parikh vectors
9UDA_1 7GAM_1 5ZSW_1 Letter Amino acid
16 7 6 Q Glutamine
9 3 3 H Histidine
29 9 7 S Serine
32 3 8 A Alanine
20 9 3 R Arginine
24 5 4 D Aspartic acid
19 8 9 I Isoleucine
23 6 4 P Proline
47 11 5 V Valine
29 12 2 E Glutamic acid
38 4 5 G Glycine
44 10 12 L Leucine
28 9 4 K Lycine
13 4 5 N Asparagine
5 0 0 C Cysteine
12 4 2 M Methionine
16 7 3 F Phenylalanine
28 6 6 T Threonine
3 0 0 W Tryptophan
11 4 1 Y Tyrosine 

9UDA_1|Chain A|Na(+)-translocating NADH-quinone reductase subunit A|Vibrio cholerae O395 (345073)
>7GAM_1|Chain A|Microtubule-associated proteins 1A/1B light chain 3B|Homo sapiens (9606)
>5ZSW_1|Chain A|RNA-binding protein 10|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 \(w=f(c)\)
9UDA , Knot 178 446 0.81 40 222 419 
MITIKKGLDLPIAGTPSQVISDGKAIKKVALLGEEYVGMRPTMHVRVGDEVKKAQILFEDKKNPGVKFTSPVSGKVVEINRGAKRVLQSVVIEVAGDDQVTFDKFEANQLASLNRDAIKTQLVESGLWTAFRTRPFSKVPAIDSTSEAIFVTAMDTNPLAAEPTVVINEQSEAFVAGLDVLSALTTGKVYVCKKGTSLPRSQQPNVEEHVFDGPHPAGLAGTHMHFLYPVSADHVAWSINYQDVIAVGQLFLTGELYTQRVVSLAGPVVNKPRLVRTVMGASLEQLVDSEIMPGEVRIISGSVLSGTKATGPHAYLGRYHLQVSVLREGRDKELFGWAMPGKNKFSVTRSFLGHLFKGQVYNMTTTTNGSDRSMVPIGNYEKVMPLDMEPTLLLRDLCAGDSDSAVRLGALELDEEDLALCTFVCPGKYEYGQLLRECLDKIEKEG
7GAM , Knot 59 121 0.78 36 90 118 
SMPSEKTFKQRRTFEQRVEDVRLIREQHPTKIPVIIERYKGEKQLPVLDKTKFLVPDHVNMSELIKIIRRRLQLNANQAFFLLVNGHSMVSVSTPISEVYESEKDEDGFLYMVYASQETFG
5ZSW , Knot 47 89 0.79 36 71 87 
GHMDTIILRNLNPHSTMDSILGALAPYAVLSSSNVRVIKDKQTQLNRGFAFIQLSTIVEAAQLLQILQALHPPLTIDGKTINVEFAKGS

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 \(c\).

\(|P_{f(9UDA_1)}(2) \setminus P_{f(7GAM_1)}(2)|=152\), \(|P_{f(7GAM_1)}(2) \setminus P_{f(9UDA_1)}(2)|=20\). 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 1:11010011011111010011001011001111100011101010101100100101110000011101001101011010011001100111011100010100101001101000110001100111011000110011110000011110110001111010111000001111110110110010101000100110000101000110110111111001011011010011101000011111011101010000110111111001011001111010011000111101011010110100101101011000101011001000011111111000101000111011010100100000100001111100001111010101110010110000110111101000011100110110000101100010010001
Pair \(Z_2\) Length of longest common subsequence
9UDA_1,7GAM_1 172 3
9UDA_1,5ZSW_1 191 4
7GAM_1,5ZSW_1 111 3

Newick tree

 
[
	9UDA_1:99.92,
	[
		7GAM_1:55.5,5ZSW_1:55.5
	]:44.42
]

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 \((0.85)(0.8)(\frac{567 }{\log_{20} 567}-\frac{121}{\log_{20}121})=130.\)
Status Protein1 Protein2 d d1/2
Query variables 9UDA_1 7GAM_1 163 102.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]