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Parikh vectors
8ELN_1 7RAW_1 6WLJ_1 Letter Amino acid
11 27 0 T Threonine
29 29 37 A Alanine
12 19 0 D Aspartic acid
24 17 40 G Glycine
9 8 0 I Isoleucine
19 12 0 P Proline
8 13 0 N Asparagine
14 12 0 S Serine
5 4 0 W Tryptophan
13 15 0 Y Tyrosine
2 6 26 C Cysteine
12 6 0 Q Glutamine
23 15 0 E Glutamic acid
28 16 0 L Leucine
11 16 0 K Lycine
17 3 0 R Arginine
18 10 0 H Histidine
9 3 0 M Methionine
18 7 0 F Phenylalanine
19 13 0 V Valine 

8ELN_1|Chains A, B, E, F, I, J|CFTR inhibitory factor|Pseudomonas aeruginosa PA14 (652611)
>7RAW_1|Chain A|Dockerin domain-containing protein|Ruminococcus bromii L2-63 (657321)
>6WLJ_1|Chain A|RNA (130-MER)|synthetic construct (32630)
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 \(w=f(c)\)
8ELN , Knot 136 301 0.86 40 202 292 
AEEFPVPNGFESAYREVDGVKLHYVKGGQGPLVMLVHGFGQTWYEWHQLMPELAKRFTVIAPDLPGLGQSEPPKTGYSGEQVAVYLHKLARQFSPDRPFDLVAHDIGIWNTYPMVVKNQADIARLVYMEAPIPDARIYRFPAFTAQGESLVWHFSFFAADDRLAETLIAGKERFFLEHFIKSHASNTEVFSERLLDLYARSYAKPHSLNASFEYYRALNESVRQNAELAKTRLQMPTMTLAGGGHGGMGTFQLEQMKAYAEDVEGHVLPGCGHWLPEECAAPMNRLVIDFLSRGRHHHHHH
7RAW , Knot 113 251 0.83 40 163 238 
HHHHHHENLYFQGEETDTKIYFDASNLPAEWGTTKTVYCHLYAVAGDDLPETSWQGKAEKCKKDTATGLYYFDTAKLKSADGTNHGGLKDNADYAVIFSTIDTKSQSHQTCNVTLGKPCLGDTIYLTGGTVENTEDSSKRDFAATWKNNSDNYGPKAAITSLGHVTEGRFPIYLSRAEMVAQAIFNWAVKNPKNYTPETVADICAQVEAEPMDVYNAYAEMYATELADPAAYPDCAPLTTVATLLGVDPSG
6WLJ , Knot 35 130 0.43 8 16 56 
GGCGAUAUGGCAUGGAAUCAGCUCAAGGAACUGUGAACGUAUAUCGGGCAACGACUAGGAAACUAGUCGUUGGGAAGAAACUGCCGAUAUACGGGAGUUCCUUGAGCGGGAGAUUCCAUGCCUAAGUCGC

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 \(c\).

\(|P_{f(8ELN_1)}(2) \setminus P_{f(7RAW_1)}(2)|=104\), \(|P_{f(7RAW_1)}(2) \setminus P_{f(8ELN_1)}(2)|=65\). 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 1:1001111011001000101101001011011111110111001001001110110010111101111100011001001001110100110010100110111001111000111100010110110101111010100111101010011101011110001100111100011100110001000011000110101000101001010100001100010001011000101101011111011110101001010100101011110101110001111001110110010000000
Pair \(Z_2\) Length of longest common subsequence
8ELN_1,7RAW_1 169 6
8ELN_1,6WLJ_1 206 3
7RAW_1,6WLJ_1 171 2

Newick tree

 
[
	6WLJ_1:97.80,
	[
		8ELN_1:84.5,7RAW_1:84.5
	]:13.30
]

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 \((0.85)(0.8)(\frac{552 }{\log_{20} 552}-\frac{251}{\log_{20}251})=85.5\)
Status Protein1 Protein2 d d1/2
Query variables 8ELN_1 7RAW_1 108 97
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]