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Parikh vectors
6WZP_1 6OIS_1 6CWA_1 Letter Amino acid
44 6 27 A Alanine
29 10 16 R Arginine
11 2 13 N Asparagine
21 9 20 T Threonine
3 4 2 W Tryptophan
9 5 2 Y Tyrosine
29 6 27 V Valine
26 14 17 D Aspartic acid
41 17 35 L Leucine
5 8 9 M Methionine
31 12 12 P Proline
14 10 18 I Isoleucine
6 0 11 C Cysteine
11 8 16 Q Glutamine
23 10 22 E Glutamic acid
31 9 32 G Glycine
8 13 3 H Histidine
13 4 18 K Lycine
19 5 8 F Phenylalanine
19 23 19 S Serine 

6WZP_1|Chain A|Cytochrome P450|Rhodopseudomonas palustris (strain HaA2) (316058)
>6OIS_1|Chains A, B|Protein RDM1|Arabidopsis thaliana (3702)
>6CWA_1|Chains A, B|D-3-phosphoglycerate dehydrogenase|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 \(w=f(c)\)
6WZP , Knot 166 393 0.84 40 206 372 
TIPHLAIDPFSLDFFDDPYPDQQTLRDAGPVVYLDKWNVYGVARYAEVHAVLNDPTTFCSSRGVGLSDFKKEKPWRPPSLILEADPPAHTRPRAVLSKVLSPATMKTIRDGFAAAADAKVDELLQRGCIDAIADLAEAYPLSVFPDAMGLKQEGREHLLPYAGLVFNAFGPPNELRQTAIERSAPHQAYVNEQCQRPNLAPGGFGACIHAFTDTGEITPDEAPLLVRSLLSAGLDATVNGIGAAVYCLARFPGELQRLRSDPTLARNAFEEAVRFESPVQTFFRTTTREVELGGAVIGEGEKVLMFLGSANRDPRRWSDPDLYDITRKTSGHVGFGSGVHMCVGQLVARLEGEVMLSALARKVAAIDIDGPVKRRFNNTLRGLESLPVKLTPA
6OIS , Knot 80 175 0.78 38 124 167 
MGSSHHHHHHSQDPSSMTMELRPSGDSGSSDVDAEISDGFSPLDTSHRDVADEGSLLRRAEMYQDYMKQVPIPTNRGSLIPFTSWVGLSISMKQLYGQPLHYLTNVLLQRWDQSRFGTDSEEQRLDSIIHPTKAEATIWLVEEIHRLTPSHLHMALLWRSDPMYHSFIDPIFPEK
6CWA , Knot 140 327 0.82 40 193 311 
SGVDLGTENLYFQSMANLRKVLISDSLDPCCRKILQDGGLQVVEKQNLSKEELIAELQDCEGLIVRSATKVTADVINAAEKLQVVGRAGTGVDNVDLEAATRKGILVMNTPNGNSLSAAELTCGMIMCLARQIPQATASMKDGKWERKKFMGTELNGKTLGILGLGRIGREVATRMQSFGMKTIGYDPIISPEVSASFGVQQLPLEEIWPLCDFITVHTPLLPSTTGLLNDNTFAQCKKGVRVVNCARGGIVDEGALLRALQSGQCAGAALDVFTEEPPRDRALVDHENVISCPHLGASTKEAQSRCGEEIAVQFVDMVKGKSLTGV

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 \(c\).

\(|P_{f(6WZP_1)}(2) \setminus P_{f(6OIS_1)}(2)|=128\), \(|P_{f(6OIS_1)}(2) \setminus P_{f(6WZP_1)}(2)|=46\). 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 1:011011101101011001010000100111110100101011100101011100100100001111001000011011011101011100010111001101101001001111110101001100101011101101011011101111000100011101111101111100100011000110010100000010111111110101100010101001111100110111010101111110011011101001000101100110011010011001100000010111111101001111110100010010010100100000101111011010110111010101110111001111010111000100010110011101011
Pair \(Z_2\) Length of longest common subsequence
6WZP_1,6OIS_1 174 4
6WZP_1,6CWA_1 161 4
6OIS_1,6CWA_1 183 3

Newick tree

 
[
	6OIS_1:92.01,
	[
		6WZP_1:80.5,6CWA_1:80.5
	]:11.51
]

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 \((0.85)(0.8)(\frac{568 }{\log_{20} 568}-\frac{175}{\log_{20}175})=113.\)
Status Protein1 Protein2 d d1/2
Query variables 6WZP_1 6OIS_1 141 101
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]