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Parikh vectors
6YWO_1 6IXF_1 6DPQ_1 Letter Amino acid
15 6 16 N Asparagine
7 4 17 H Histidine
16 4 19 F Phenylalanine
18 12 15 T Threonine
7 17 18 Q Glutamine
30 26 26 E Glutamic acid
15 4 29 G Glycine
18 7 18 I Isoleucine
10 6 10 M Methionine
6 2 5 W Tryptophan
25 12 26 V Valine
21 29 28 A Alanine
43 23 53 L Leucine
22 25 33 K Lycine
15 3 23 P Proline
19 11 29 S Serine
28 18 17 R Arginine
29 13 23 D Aspartic acid
9 0 8 C Cysteine
10 6 12 Y Tyrosine 

6YWO_1|Chains A, B, C, D|CutA|Thermothielavioides terrestris NRRL 8126 (578455)
>6IXF_1|Chains A, B|SH3 domain-binding protein 5|Homo sapiens (9606)
>6DPQ_1|Chains A, B|Indoleamine 2,3-dioxygenase 1|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 \(w=f(c)\)
6YWO , Knot 157 363 0.85 40 211 346 
ETAIPFSRRRMPYSLGTDKLEKVDPDKIKSKLSEDVERKLETDMRELYDRLLPTEAIEVNRRELVSKLERLFNTEWPGHDIRVHLFGSSGNLLCSDDSDVDICITTPWRELESVCMIAELLDRHGMEKVVCVSSAKVPIVKIWDPELKLACDMNVNNTLALENTRMVRTYVSIDDRVRPLAMIIKYWTRRRVVNDAAFGGTLSSYTWICMIIAFLQLRDPPVLPALHQQHDLKLVKQDGALSDFADDIPKLRGFGAKNKDSLAVLLFQFFRFYAHEFDYDKYTLSIRMGTLLTKAEKNWQYLVNNALCVEEPFNDGRNLGNTADETSFRGLHMELRRAFDLIAEGKLEECCEQYVFPKEEERV
6IXF , Knot 99 228 0.78 38 137 213 
SHVDPRIQGELEKLNQSTDDINRRETELEDARQKFRSVLVEATVKLDELVKKIGKAVEDSKPYWEARRVARQAQLEAQKATQDFQRATEVLRAAKETISLAEQRLLEDDKRQFDSAWQEMLNHATQRVAEAEQTKTRSELVHKETAARYNAAMGRMRQLEKKLKRAINKSKPYFELKAKYYVQLEQLKKTVDDLQAKLTLAKGEYKMALKNLEMISDEIHEAAASSAM
6DPQ , Knot 182 425 0.86 40 233 394 
MSKEYHIDEEVGFALPNPQENLPDFYNDWMFIAKHLPDLIESGQLRERVEKLNMLSIDHLTDHKSQRLARLVLGCITMAYVWGKGHGDVRKVLPRNIAVPYCQLSKKLELPPILVYADCVLANWKKKDPNKPLTYENMDVLFSFRDGDCSKGFFLVSLLVEIAAASAIKVIPTVFKAMQMQERDTLLKALLEIASCLEKALQVFHQIHDHVNPKAFFSVLRIYLSGWKGNPQLSDGLVYEGFWEDPKEFAGGSAGQSSVFQCFDVLLGIQQTAGGGHAAQFLQDMRRYMPPAHRNFLCSLESNPSVREFVLSKGDAGLREAYDACVKALVSLRSYHLQIVTKYILIPASQQPKENKTSEDPSKLEAKGTGGTDLMNFLKTVRSTTEKSLLKEGKGELNSKLEGKPIPNPLLGLDSTRTGHHHHHH

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 \(c\).

\(|P_{f(6YWO_1)}(2) \setminus P_{f(6IXF_1)}(2)|=128\), \(|P_{f(6IXF_1)}(2) \setminus P_{f(6YWO_1)}(2)|=54\). 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 1:001111000011001100010010100100010001000100010010001110011010000110010011000111001010111001011000000101010011001001011101100011001101001011110110101011001010001110000110001010001011111100100001100111110100001101111110100111111100000101100011100110011010111100000111111011010100100000010101101100100010011001101001100100110010000101101010011011101010000000111000001
Pair \(Z_2\) Length of longest common subsequence
6YWO_1,6IXF_1 182 4
6YWO_1,6DPQ_1 162 4
6IXF_1,6DPQ_1 184 4

Newick tree

 
[
	6IXF_1:94.74,
	[
		6YWO_1:81,6DPQ_1:81
	]:13.74
]

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 \((0.85)(0.8)(\frac{591 }{\log_{20} 591}-\frac{228}{\log_{20}228})=103.\)
Status Protein1 Protein2 d d1/2
Query variables 6YWO_1 6IXF_1 132 104.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]