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Parikh vectors
1GVO_1 4TVE_1 7UDF_1 Letter Amino acid
15 19 13 N Asparagine
18 14 27 D Aspartic acid
26 21 24 E Glutamic acid
3 4 6 M Methionine
13 8 9 Y Tyrosine
21 10 30 V Valine
46 16 45 A Alanine
10 17 18 F Phenylalanine
25 10 29 R Arginine
1 8 6 C Cysteine
23 23 25 S Serine
15 5 11 Q Glutamine
34 17 31 G Glycine
9 13 8 H Histidine
23 16 16 I Isoleucine
30 26 41 L Leucine
12 21 13 K Lycine
20 15 33 P Proline
17 11 22 T Threonine
3 4 3 W Tryptophan 

1GVO_1|Chain A|PENTAERYTHRITOL TETRANITRATE REDUCTASE|ENTEROBACTER CLOACAE (550)
>4TVE_1|Chain A|Naumovozyma dairenensis Eps1p|Naumovozyma dairenensis (1071378)
>7UDF_1|Chain A|Cytochrome P450|Rhodopseudomonas palustris HaA2 (316058)
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 \(w=f(c)\)
1GVO , Knot 156 364 0.84 40 204 345 
SAEKLFTPLKVGAVTAPNRVFMAPLTRLRSIEPGDIPTPLMGEYYRQRASAGLIISEATQISAQAKGYAGAPGLHSPEQIAAWKKITAGVHAEDGRIAVQLWHTGRISHSSIQPGGQAPVSASALNANTRTSLRDENGNAIRVDTTTPRALELDEIPGIVNDFRQAVANAREAGFDLVELHSAHGYLLHQFLSPSSNQRTDQYGGSVENRARLVLEVVDAVCNEWSADRIGIRVSPIGTFQNVDNGPNEEADALYLIEELAKRGIAYLHMSETDLAGGKPYSEAFRQKVRERFHGVIIGAGAYTAEKAEDLIGKGLIDAVAFGRDYIANPDLVARLQKKAELNPQRPESFYGGGAEGYTDYPSL
4TVE , Knot 119 278 0.80 40 178 260 
HHHHHHSSGLVPRGSPEGFPKPLTGSTFDNEMKNGLHIVEFFSPYCHHCKSLAPIWEKTWESFHEEGSKLNITLSQVNCVEDGDLCSKENIEYFPYIKLYGPSGFIKNYDGARKEEAFIKFARKEALDPLNVDISHVESQSILLSKLEFAKYLAGKGKDPILISFWPTNEMKNSDDRIAFENCADCTTFQRAWKMLSKNLLADGVLTGHMNCEENPLICNELGFGELSKIKNHRSDRVPRVALVLPNRATNNLFIFKGDIASPLSQYQDFATRTYANS
7UDF , Knot 172 410 0.84 40 213 387 
MISNSSAESISAPPNDSTIPHLAIDPFSLDFFDDPYPDQQTLRDAGPVVYLDKWNVYGVARYAEVHAVLNDPTTFCSSRGVGLSDFKKEKPWRPPSLILEADPPAHTRPRAVLSKVLSPATMKTIRDGFAAAADAKVDELLQRGCIDAIADLAEAYPLSVFPDAMGLKQEGREHLLPYAGLVFNAFGPPNELRQTAIERSAPHQAYVNEQCQRPNLAPGGFGACIHAFTDTGEITPDEAPLLVRSLLSAGLDTTVNGIGAAVYCLARFPGELQRLRSDPTLARNAFEEAVRFESPVQTVFRTTTREVELGGAVIGEGEKVLMFLGSANRDPRRWSDPDLYDITRKTSGHVGFGSGVHMCVGQLVARLEGEVMLSALARKVAAIDIDGPVKRRFNNTLRGLESLPVKLTPA

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 \(c\).

\(|P_{f(1GVO_1)}(2) \setminus P_{f(4TVE_1)}(2)|=100\), \(|P_{f(4TVE_1)}(2) \setminus P_{f(1GVO_1)}(2)|=74\). 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 1:0100110110111101100111111001001011011011110000001011111001001010101011111100100111100101110100101110110010100001011101110101101000001000010110100001011010011111001001110100111011010010101100110100000000011010001011101101100010100111010111010010011000101101100110011101010000111101000110001000101111111100100100111011101111100011010111010001010100100101111010000101
Pair \(Z_2\) Length of longest common subsequence
1GVO_1,4TVE_1 174 3
1GVO_1,7UDF_1 133 5
4TVE_1,7UDF_1 179 3

Newick tree

 
[
	4TVE_1:94.40,
	[
		1GVO_1:66.5,7UDF_1:66.5
	]:27.90
]

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 \((0.85)(0.8)(\frac{642 }{\log_{20} 642}-\frac{278}{\log_{20}278})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 1GVO_1 4TVE_1 130 112
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]