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Parikh vectors
6YJZ_1 5CFQ_1 7CTQ_1 Letter Amino acid
17 10 49 R Arginine
19 6 31 Q Glutamine
11 9 9 I Isoleucine
14 4 6 M Methionine
20 7 62 A Alanine
19 14 24 D Aspartic acid
9 2 9 H Histidine
27 19 49 L Leucine
17 16 1 K Lycine
13 7 9 T Threonine
37 11 46 V Valine
9 5 5 N Asparagine
20 11 17 S Serine
21 18 25 E Glutamic acid
21 13 43 G Glycine
8 11 11 F Phenylalanine
14 9 17 P Proline
3 3 12 W Tryptophan
10 9 4 Y Tyrosine
5 3 3 C Cysteine 

6YJZ_1|Chains A, B, C, D|Pyridoxal Kinase|Mus musculus (10090)
>5CFQ_1|Chains A, B|Stimulator of Interferon Genes|Nematostella vectensis (45351)
>7CTQ_1|Chains A, B|Peptidyl tryptophan dihydroxylase|Pseudomonas putida (303)
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 \(w=f(c)\)
6YJZ , Knot 138 314 0.84 40 200 303 
GPMEGECRVLSIQSHVVRGYVGNRAAMFPLQVLGFEVDAVNSVQFSNHTGYAHWKGQVLKSQELHELYEGLKVNDVNKYDYVLTGYTRDKSFLAMVVDIVRELKQQNSRLVYVCDPVMGDKWNGEGSMYVPQDLLPVYRDKVVPVADIITPNQFEAELLSGRKIHSQEEAFEVMDMLHCMGPDTVVITSSDLPSSQGSDYLIALGSQRMRKPDGSTVTQRIRMEMRKVEAVFVGTGDLFAAMLLAWTHKHPDNLKVACEKTVSAMQHVLQRTIRCAKAEAGEGQKPSPAQLELRMVQSKRDIEDPEIVVQATVL
5CFQ , Knot 87 187 0.81 40 141 177 
GSNVADGLAWSYYFGYLKFVLPELEKQIEKTSKFRSKEKFVKKMFILIPSNCFWDDKIPGSDYDPQNRITFEGNTEPLEKTRGGVFLRHYKHSVYEIKDGENEPWFCIMEYATPLLTLYDMSVAQPGELSREERDAQVVVFLRKLQDILEGDRACQGKYELVTFSPDRDLADVMLRKLKDSELEIGG
7CTQ , Knot 166 432 0.77 40 175 389 
GHMAEPRIVVLGAGPAGAATAIGLRRLGYAVTVVSEWRRFAAVEGVSQRVLEGLRHVGLGGALRQAAMPATRQVHWNGQQLHLNQEFLLDRQRFDRALRDDLQRAGVSVVEGRVREVVRDVGHGIRLDDGQVLQADFLVEARGRQAPLAADRLRGPETVSLLNVWQAAPGAPASAVESLADGWAWMARLEDGRCYWQVTLDAAGLPGKAGLADYCAARRADSALVTELFDARALASAEVHARSSTAILAGECVGQDWIRVGDAAMAVDPLSGNGIFQSLSSALQAPVVINTLLRRPERAGLARQFHQQRIEQLFLRFARIGRDFYGQEQGRVGQPFWARRQGWPDMQALHVAADWSAVRVERRPVLRDGLVDEAEVVVTADQPLGVWHLQGVELAPAVRELQAGRPLEAVVSGLSGEQQRMVRRWLLEQGLV

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 \(c\).

\(|P_{f(6YJZ_1)}(2) \setminus P_{f(5CFQ_1)}(2)|=112\), \(|P_{f(5CFQ_1)}(2) \setminus P_{f(6YJZ_1)}(2)|=53\). 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 1:11101000110100011010110011111101111010110010100001010101011000010010011010010000011010000001111110110010000001101001111001010101011001111000011111011010010101101001000001101101100111001110000110001000111110001001010010001010100101111101011111111100001001011000010110011000100101011010010110101011000001001011101011
Pair \(Z_2\) Length of longest common subsequence
6YJZ_1,5CFQ_1 165 4
6YJZ_1,7CTQ_1 179 4
5CFQ_1,7CTQ_1 184 3

Newick tree

 
[
	7CTQ_1:93.34,
	[
		6YJZ_1:82.5,5CFQ_1:82.5
	]:10.84
]

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 \((0.85)(0.8)(\frac{501 }{\log_{20} 501}-\frac{187}{\log_{20}187})=91.3\)
Status Protein1 Protein2 d d1/2
Query variables 6YJZ_1 5CFQ_1 115 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]