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Parikh vectors
7DMA_1 7WSQ_1 5LZU_1 Letter Amino acid
10 35 15 L Leucine
4 23 17 K Lycine
4 36 9 S Serine
2 27 10 Y Tyrosine
7 30 12 V Valine
5 51 14 A Alanine
10 30 33 R Arginine
3 13 9 Q Glutamine
3 14 11 H Histidine
4 36 9 P Proline
6 36 4 N Asparagine
6 22 6 E Glutamic acid
7 32 8 I Isoleucine
8 11 6 F Phenylalanine
0 8 5 W Tryptophan
2 33 5 D Aspartic acid
0 6 2 C Cysteine
8 47 18 G Glycine
8 22 3 M Methionine
6 32 8 T Threonine 

7DMA_1|Chain A|Flagellar motor switch protein FliM|Vibrio alginolyticus (663)
>7WSQ_1|Chains A, D|Fructose dehydrogenase large subunit|Gluconobacter japonicus (376620)
>5LZU_13|Chain M[auth N]|Ribosomal protein L15|Oryctolagus cuniculus (9986)
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 \(w=f(c)\)
7DMA , Knot 58 103 0.87 36 87 101 
GSHMQDRIVRGPMPTLELINERFARHMRISLFNMLRKTAEVSINGVQMMKFGEYQNTLYVPTSLNMVRFRPLKGTALITMEARLVFILVENFFGGDGRFHAKI
7WSQ , Knot 220 544 0.85 40 257 511 
MSNETLSADVVIIGAGICGSLLAHKLVRNGLSVLLLDAGPRRDRSQIVENWRNMPPDNKSQYDYATPYPSVPWAPHTNYFPDNNYLIVKGPDRTAYKQGIIKGVGGTTWHWAASSWRYLPNDFKLHSTYGVGRDYAMSYDELEPYYYEAECEMGVMGPNGEEITPSAPRQNPWPMTSMPYGYGDRTFTEIVSKLGFSNTPVPQARNSRPYDGRPQCCGNNNCMPICPIGAMYNGVYAAIKAEKLGAKIIPNAVVYAMETDAKNRITAISFYDPDKQSHRVVAKTFVIAANGIETPKLLLLAANDRNPHGIANSSDLVGRNMMDHPGIGMSFQSAEPIWAGGGSVQMSSITNFRDGDFRSEYAATQIGYNNTAQNSRAGMKALSMGLVGKKLDEEIRRRTAHGVDIYANHEVLPDPNNRLVLSKDYKDALGIPHPEVTYDVGEYVRKSAAISRQRLMDIAKAMGGTEIEMTPYFTPNNHITGGTIMGHDPRDSVVDKWLRTHDHSNLFLATGATMAASGTVNSTLTMAALSLRAADAILNDLKQG
5LZU , Knot 96 204 0.83 40 140 193 
MGAYKYIQELWRKKQSDVMRFLLRVRCWQYRQLSALHRAPRPTRPDKARRLGYKAKQGYVIYRIRVRRGGRKRPVPKGATYGKPVHHGVNQLKFARSLQSVAEERAGRHCGALRVLNSYWVGEDSTYKFFEVILIDPFHKAIRRNPDTQWITKPVHKHREMRGLTSAGRKSRGLGKGHKFHHTIGGSRRAAWRRRNTLQLHRYR

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 \(c\).

\(|P_{f(7DMA_1)}(2) \setminus P_{f(7WSQ_1)}(2)|=24\), \(|P_{f(7WSQ_1)}(2) \setminus P_{f(7DMA_1)}(2)|=194\). 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 1:1001000110111101011000110010101101100010101011011011000001011001011010110101110101011111100111101010101
Pair \(Z_2\) Length of longest common subsequence
7DMA_1,7WSQ_1 218 3
7DMA_1,5LZU_1 149 3
7WSQ_1,5LZU_1 199 3

Newick tree

 
[
	7WSQ_1:11.56,
	[
		7DMA_1:74.5,5LZU_1:74.5
	]:38.06
]

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 \((0.85)(0.8)(\frac{647 }{\log_{20} 647}-\frac{103}{\log_{20}103})=158.\)
Status Protein1 Protein2 d d1/2
Query variables 7DMA_1 7WSQ_1 204 121
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]