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Parikh vectors
6WJB_1 2OEE_1 3LXC_1 Letter Amino acid
13 17 17 E Glutamic acid
8 7 17 K Lycine
25 8 16 V Valine
40 9 29 A Alanine
35 12 40 L Leucine
23 5 24 S Serine
15 4 14 T Threonine
0 0 16 W Tryptophan
8 6 20 N Asparagine
21 5 29 D Aspartic acid
2 0 12 C Cysteine
32 5 31 G Glycine
6 1 13 H Histidine
3 7 15 M Methionine
9 4 15 Y Tyrosine
20 6 19 R Arginine
10 11 22 Q Glutamine
14 5 21 I Isoleucine
11 4 15 F Phenylalanine
15 1 19 P Proline 

6WJB_1|Chains A, B|NAD-dependent epimerase/dehydratase family protein|Pseudomonas fluorescens (strain ATCC BAA-477 / NRRL B-23932 / Pf-5) (220664)
>2OEE_1|Chains A, B|UPF0342 protein yheA|Bacillus subtilis (1423)
>3LXC_1|Chains A, B|Alpha-galactosidase A|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 \(w=f(c)\)
6WJB , Knot 129 310 0.79 38 174 290 
MSAERILVTGGAGFIGSHLVDALLAKGYAVRVLDDLSTGKVGNLPMGDAGLELLVGDAADAALLADAVQGCDAVVHLAAVASVQASVEDPVATHQSNFIATLRLCEAMTAAGIRRVVFASSAAVYGNNGEGTPIAEDTPKSPLTPYAADKLASEYYLDFYRRQHGLEPVILRFFNIFGPRQDPSSPYSGVISIFSERAKAGRPITLFGDGGQTRDFVYVADLVKILVQGLESPAPAADATNVGLGGVTTLNDLIGALQQISGKPLQVSHGATRSGDIRHSKADNRRLRERFDLGTPSSLAEGLERLYRSL
2OEE , Knot 56 117 0.76 36 87 115 
MAVNFYDVAYDLENALRGSEEFTRLKNLYDEVNADESAKRMFENFRDVQLRLQQKQMAGEEITQEEVTQAQKTVALVQQHEKISQLMEAEQRMSMLIGELNKIIMKPLEELYGSVEG
3LXC , Knot 171 404 0.84 40 233 381 
LDNGLARTPTMGWLHWERFMCNLDCQEEPDSCISEKLFMEMAELMVSEGWKDAGYEYLCIDDCWMAPQRDSEGRLQADPQRFPHGIRQLANYVHSKGLKLGIYADVGNKTCAGFPGSFGYYDIDAQTFADWGVDLLKFDGCYCDSLENLADGYKHMSLALNRTGRSIVYSCSWPAYMWPFQKPNYTEIRQYCNHWRNFADIDDSWKSIKSILDWTSFNQERIVDVAGPGGWNDPDMLVIGNFGLSWNQQVTQMALWAIMAAPLFMSNDLRHISPQAKALLQDKDVIAINQDPLGKQGYQLRQGDNFEVWERPLSGLAWAVAMINRQEIGGPRSYTIAVASLGKGVACNPACFITQLLPVKRKLGFYEWTSRLRSHINPTGTVLLQLENTMQMSLKDLLHHHHHH

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 \(c\).

\(|P_{f(6WJB_1)}(2) \setminus P_{f(2OEE_1)}(2)|=130\), \(|P_{f(2OEE_1)}(2) \setminus P_{f(6WJB_1)}(2)|=43\). 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 1:1010011101111111001101111010110110010010110111101110111101101111101101001110111110101010011100000111010100110111100111100111010010101110001001101011001100001010000011011110110111100010010011101100010110110111011000011011011011101100111110100111111001001111100101011010011000101000010000100010110100110110010001
Pair \(Z_2\) Length of longest common subsequence
6WJB_1,2OEE_1 173 3
6WJB_1,3LXC_1 167 4
2OEE_1,3LXC_1 204 3

Newick tree

 
[
	2OEE_1:97.98,
	[
		6WJB_1:83.5,3LXC_1:83.5
	]:14.48
]

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 \((0.85)(0.8)(\frac{427 }{\log_{20} 427}-\frac{117}{\log_{20}117})=93.5\)
Status Protein1 Protein2 d d1/2
Query variables 6WJB_1 2OEE_1 118 81
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]