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Parikh vectors
7RZC_1 6CIK_1 8IAO_1 Letter Amino acid
13 27 6 D Aspartic acid
18 22 0 Q Glutamine
26 61 26 L Leucine
2 6 5 W Tryptophan
7 46 1 R Arginine
16 23 5 N Asparagine
24 43 1 K Lycine
9 22 0 H Histidine
11 29 14 I Isoleucine
19 34 26 G Glycine
12 25 11 F Phenylalanine
12 26 3 P Proline
16 44 8 S Serine
33 27 6 T Threonine
23 20 9 Y Tyrosine
11 15 4 C Cysteine
16 57 8 E Glutamic acid
20 37 20 V Valine
22 42 8 A Alanine
8 19 11 M Methionine 

7RZC_1|Chains A, B, C|Non-structural protein 3|Severe acute respiratory syndrome coronavirus 2 (2697049)
>6CIK_1|Chains A, C|V(D)J recombination-activating protein 1|Mus musculus (10090)
>8IAO_10|Chain J|NADH-ubiquinone oxidoreductase chain 6|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 \(w=f(c)\)
7RZC , Knot 142 318 0.85 40 203 304 
SNAEVRTIKVFTTVDNINLHTQVVDMSMTYGQQFGPTYLDGADVTKIKPHNSHEGKTFYVLPNDDTLRVEAFEYYHTTDPSFLGRYMSALNHTKKWKYPQVNGLTSIKWADNNCYLATALLTLQQIELKFNPPALQDAYYRARAGEAANFCALILAYCNKTVGELGDVRETMSYLFQHANLDSCKRVLNVVCKTCGQQQTTLKGVEAVMYMGTLSYEQFKKGVQIPCTCGKQATKYLVQQESPFVMMSAPPAQYELKHGTFTCASEYTGNYQCGHYKHITSKETLYCIDGALLTKSSEYKGPITDVFYKENSYTTTIK
6CIK , Knot 247 625 0.84 40 276 584 
VHINKGGRPRQHLLSLTRRAQKHRLRELKIQVKEFADKEEGGDVKAVCLTLFLLALRARNEHRQADELEAIMQGRGSGLQPAVCLAIRVNTFLSCSQYHKMYRTVKAITGRQIFQPLHALRNAEKVLLPGYHPFEWQPPLKNVSSRTDVGIIDGLSGLASSVDEYPVDTIAKRFRYDSALVSALMDMEEDILEGMRSQDLDDYLNGPFTVVVKESCDGMGDVSEKHGSGPAVPEKAVRFSFTVMRITIEHGSQNVKVFEEPKPNSELCCKPLCLMLADESDHETLTAILSPLIAEREAMKSSELTLEMGGIPRTFKFIFRGTGYDEKLVREVEGLEASGSVYICTLCDTTRLEASQNLVFHSITRSHAENLQRYEVWRSNPYHESVEELRDRVKGVSAKPFIETVPSIDALHCDIGNAAEFYKIFQLEIGEVYKHPNASKEERKRWQATLDKHLRKRMNLKPIMRMNGNFARKLMTQETVDAVCELIPSEERHEALRELMDLYLKMKPVWRSSCPAKECPESLCQYSFNSQRFAELLSTKFKYRYEGKITNYFHKTLAHVPEIIERDGSIGAWASEGNQSGNKLFRRFRKMNARQSKCYEMEDVLKHHWLYTSKYLQKFMNAHNA
8IAO , Knot 76 172 0.75 36 107 156 
MNNYIFVLSSLFLVGCLGLALKPSPIYGGLGLIVSGFVGCLMVLGFGGSFLGLMVFLIYLGGMLVVFGYTTAMATEEYPETWGSNWLILGFLVLGVIMEVFLICVLNYYDEVGVINLDGLGDWLMYEVDDVGVMLEGGIGVAAMYSCATWMMVVAGWSLFAGIFIIIEITRD

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 \(c\).

\(|P_{f(7RZC_1)}(2) \setminus P_{f(6CIK_1)}(2)|=53\), \(|P_{f(6CIK_1)}(2) \setminus P_{f(7RZC_1)}(2)|=126\). 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 1:001010010110010010100011010100100111001011010010100000100101110000101011000000010111001011000001001010110010110000011011101001010101111001000101101101011111000001101101000100110010100000110110000100000101101110110100001001101100010010001100001111101111000100101001000010000100001000001001011110000000111001100000000010
Pair \(Z_2\) Length of longest common subsequence
7RZC_1,6CIK_1 179 4
7RZC_1,8IAO_1 194 4
6CIK_1,8IAO_1 221 3

Newick tree

 
[
	8IAO_1:10.36,
	[
		7RZC_1:89.5,6CIK_1:89.5
	]:18.86
]

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 \((0.85)(0.8)(\frac{943 }{\log_{20} 943}-\frac{318}{\log_{20}318})=168.\)
Status Protein1 Protein2 d d1/2
Query variables 7RZC_1 6CIK_1 216 160.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]