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Parikh vectors
2ASM_1 1BDW_1 4WBL_1 Letter Amino acid
21 4 14 V Valine
12 0 1 N Asparagine
19 0 23 K Lycine
28 0 16 E Glutamic acid
28 1 25 G Glycine
9 0 4 H Histidine
30 0 4 I Isoleucine
27 0 11 T Threonine
4 4 3 W Tryptophan
18 0 7 R Arginine
11 0 11 Q Glutamine
23 0 14 S Serine
22 0 9 D Aspartic acid
16 0 2 M Methionine
26 4 28 L Leucine
12 0 10 F Phenylalanine
19 0 11 P Proline
16 0 8 Y Tyrosine
29 2 17 A Alanine
5 0 3 C Cysteine 

2ASM_1|Chain A|Actin, alpha skeletal muscle|Oryctolagus cuniculus (9986)
>1BDW_1|Chains A, B|GRAMICIDIN A|BREVIBACILLUS BREVIS (1393)
>4WBL_1|Chain A|2',3'-cyclic-nucleotide 3'-phosphodiesterase|Mus musculus (10090)
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 \(w=f(c)\)
2ASM , Knot 159 375 0.83 40 219 360 
DEDETTALVCDNGSGLVKAGFAGDDAPRAVFPSIVGRPRHQGVMVGMGQKDSYVGDEAQSKRGILTLKYPIEHGIITNWDDMEKIWHHTFYNELRVAPEEHPTLLTEAPLNPKANREKMTQIMFETFNVPAMYVAIQAVLSLYASGRTTGIVLDSGDGVTHNVPIYEGYALPHAIMRLDLAGRDLTDYLMKILTERGYSFVTTAEREIVRDIKEKLCYVALDFENEMATAASSSSLEKSYELPDGQVITIGNERFRCPETLFQPSFIGMESAGIHETTYNSIMKCDIDIRKDLYANNVMSGGTTMYPGIADRMQKEITALAPSTMKIKIIAPPERKYSVWIGGSILASLSTFQQMWITKQEYDEAGPSIVHRKCF
1BDW , Knot 8 16 0.46 12 10 11 
VGALAVVVWLWLWLWX
4WBL , Knot 97 221 0.79 40 141 210 
GGLEKDFLPLYFGWFLTKKSSETLRKAGQVFLEELGNHKAFKKELRHFISGDEPKEKLELVSYFGKRPPGVLHCTTKACDYGKAAGAEEYAQQEVVKRSYGKAFKLSISALFVTPKTAGAQVVLTDQELQLWPSDLDKPSASEGLPPGSRAHVTLGCAADVQPVQTGLDLLDILQQVKGGSQGEAVGELPRGKLYSLGKGRWMLSLTKKMEVKAIFTGYYG

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 \(c\).

\(|P_{f(2ASM_1)}(2) \setminus P_{f(1BDW_1)}(2)|=214\), \(|P_{f(1BDW_1)}(2) \setminus P_{f(2ASM_1)}(2)|=5\). 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 1:000000111000101110111110011011110111010001111111000001100100001110100110011100100100110001000101110001011001110101000010011100101111011101110101010001111001011000111001011101110101110010001101100010011001000110010001001110100011011000010000011010110110001001001101011110011100000001100010100010100110110010111100100010111100101011111000001111101110100100111000000011101100001
Pair \(Z_2\) Length of longest common subsequence
2ASM_1,1BDW_1 219 3
2ASM_1,4WBL_1 186 4
1BDW_1,4WBL_1 139 2

Newick tree

 
[
	2ASM_1:11.22,
	[
		4WBL_1:69.5,1BDW_1:69.5
	]:40.72
]

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 \((0.85)(0.8)(\frac{391 }{\log_{20} 391}-\frac{16}{\log_{20}16})=121.\)
Status Protein1 Protein2 d d1/2
Query variables 2ASM_1 1BDW_1 156 80
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]