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Parikh vectors
2WKU_1 5UOQ_1 2IFA_1 Letter Amino acid
64 20 27 A Alanine
5 3 0 C Cysteine
14 20 15 Q Glutamine
24 18 10 I Isoleucine
27 27 11 V Valine
20 29 12 S Serine
3 14 6 Y Tyrosine
20 15 17 E Glutamic acid
7 12 8 H Histidine
18 28 12 K Lycine
16 3 4 M Methionine
18 31 6 T Threonine
10 10 13 F Phenylalanine
14 33 8 P Proline
5 7 4 W Tryptophan
19 20 6 R Arginine
13 20 10 N Asparagine
20 19 9 D Aspartic acid
49 21 10 G Glycine
26 45 20 L Leucine 

2WKU_1|Chains A, B, C, D|ACETYL-COA ACETYLTRANSFERASE|ZOOGLOEA RAMIGERA (350)
>5UOQ_1|Chains A, B|INTEGRASE|Human spumaretrovirus (11963)
>2IFA_1|Chains A, B, C, D, E, F|Hypothetical protein SMU.260|Streptococcus mutans (210007)
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 \(w=f(c)\)
2WKU , Knot 156 392 0.79 40 197 361 
STPSIVIASAARTAVGSFNGAFANTPAHELGATVISAVLERAGVAAGEVNEVILGQVLPAGEGQNPARQAAMKAGVPQEATAWGMNQLCGSGLRAVALGMQQIATGDASIIVAGGMESMSMAPHCAHLRGGVKMGDFKMIDTMIKDGLTDAFYGYHMGTTAENVAKQWQLSRDEQDAFAVASQNKAEAAQKDGRFKDEIVPFIVKGRKGDITVDADEYIRHGATLDSMAKLRPAFDKEGTVTAGNASGLNDGAAAALLMSEAEASRRGIQPLGRIVSWATVGVDPKVMGTGPIPASRKALERAGWKIGDLDLVEAHEAFAAQACAVNKDLGWDPSIVNVNGGAIAIGHPIGASGARILNTLLFEMKRRGARKGLATLCIGGGMGVAMCIESL
5UOQ , Knot 168 395 0.84 40 221 376 
GPGCNTKKPNLDAELDQLLQGHYIKGYPKQYTYFLEDGKVKVSRPEGVKIIPPQSDRQKIVLQAHNLAHTGREATLLKIANLYWWPNMRKDVVKQLGRCQQCLITNASNKASGPILRPDRPQKPFDKFFIDYIGPLPPSQGYLYVLVVVDGMTGFTWLYPTKAPSTSATVKSLNVLTSIAIPKVIHSDQGAAFTSSTFAEWAKERGIHLEFSTPYHPQSSGKVERKNSDIKRLLTKLLVGRPTKWYDLLPVVQLALNNTYSPVLKYTPHQLLFGIDSNTPFANQDTLDLTREEELSLLQEIRTSLYHPSTPPASSRSWSPVVGQLVQERVARPASLRPRWHKPSTVLKVLNPRTVVILDHLGNNRTVSIDNLKPTSHQNGTTNDTATMDHLEKNE
2IFA , Knot 97 208 0.83 38 146 201 
MSNFLDLQKQRRSIYALGKTVDLSKAELVALIQNAIKQAPSAFNSQTSRALVLFGQDSQDFWNKIAYSELEKVTPAEAFAGTKAKLESFAAGVGTILLFEDQAVVRNLEENFPLYAENFQPWSEQAHGIALYAIWLALAEQNIGMSVQHYNPLVDAQVAEKYDLPTNWKMRAQIPFGSIEAPAGEKEFMADQERFKVFGDLEHHHHHH

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 \(c\).

\(|P_{f(2WKU_1)}(2) \setminus P_{f(5UOQ_1)}(2)|=71\), \(|P_{f(5UOQ_1)}(2) \setminus P_{f(2WKU_1)}(2)|=95\). 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 1:00101111011001110101111001100111011011100111111010011110111110100110011101111001011110010101101111110011010101111111001011100101011101101011001100110011010011001001100101000000111110000101100010100011111101001010101000100110100110101110001010110101100111111110010100011011101101101110101110111110001100111011010110100111101011000111010110101111111011110110110011101000110011101011111111101001
Pair \(Z_2\) Length of longest common subsequence
2WKU_1,5UOQ_1 166 3
2WKU_1,2IFA_1 159 4
5UOQ_1,2IFA_1 187 3

Newick tree

 
[
	5UOQ_1:91.18,
	[
		2WKU_1:79.5,2IFA_1:79.5
	]:11.68
]

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 \((0.85)(0.8)(\frac{787 }{\log_{20} 787}-\frac{392}{\log_{20}392})=106.\)
Status Protein1 Protein2 d d1/2
Query variables 2WKU_1 5UOQ_1 139 135
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]