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Parikh vectors
9CAX_1 1WTU_1 5NMN_1 Letter Amino acid
62 11 0 A Alanine
16 0 0 H Histidine
11 2 0 M Methionine
41 6 2 S Serine
33 8 1 T Threonine
8 0 0 C Cysteine
30 9 3 E Glutamic acid
53 6 2 G Glycine
77 8 4 L Leucine
32 13 6 K Lycine
34 4 4 F Phenylalanine
46 8 2 V Valine
23 2 5 R Arginine
22 6 1 Q Glutamine
19 3 1 N Asparagine
26 3 2 D Aspartic acid
45 5 3 I Isoleucine
34 4 1 P Proline
8 0 0 W Tryptophan
20 1 0 Y Tyrosine 

9CAX_1|Chain A|Soluble cytochrome b562,Solute carrier family 2, facilitated glucose transporter member 9|Homo sapiens (9606)
>1WTU_1|Chains A, B|TRANSCRIPTION FACTOR 1|Bacillus phage SPO1 (10685)
>5NMN_1|Chain A|Cathelicidin antimicrobial peptide|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 \(w=f(c)\)
9CAX , Knot 248 640 0.83 40 263 573 
MASDYKDDDDKGALEVLFQGPSSPMADLEDNWETLNDNLKVIEKADNAAQVKDALTKMRAAALDAQKATPPKLEDKSPDSPEMKDFRHGFDILVGQIDDALKLANEGKVKEAQAAAEQLKTTRNAYIQKYLSCSLLVASLAGAFGSSFLYGYNLSVVNAPTPYIKAFYNESWERRHGRPIDPDTLTLLWSVTVSIFAIGGLVGTLIVKMIGKVLGRKHTLLANNGFAISAALLMACSLQAGAFEMLIVGRFIMGIDGGVALSVLPMYLSEISPKEIRGSLGQVTAIFICIGVFTGQLLGLPELLGKESTWPYLFGVIVVPAVVQLLSLPFLPDSPRYLLLEKHNEARAVKAFQTFLGKADVSQEVEEVLAESRVQRSIRLVSVLELLRAPYVRWQVVTVIVTMACYQLCGLNAIWFYTNSIFGKAGIPPAKIPYVTLSTGGIETLAAVFSGLVIEHLGRRPLLIGGFGLMGLFFGTLTITLTLQDHAPWVPYLSIVGILAIIASFCSGPGGIPFILTGEFFQQSQRPAAFIIAGTVNWLSNFAVGLLFPFIQKSLDTYCFLVFATICITGAIYLYFVLPETKNRTYAEISQAFSKRNKAYPPEEKIDSAVTDGKINGRPGLVPRGSSAHHHHHHHHHHGA
1WTU , Knot 49 99 0.75 34 79 95 
MNKTELIKAIAQDTELTQVSVSKMLASFEKITTETVAKGDKVQLTGFLNIKPVARQARKGFNPQTQEALEIAPSVGVSVKPGESLKKAAEGLKYEDFAK
5NMN , Knot 21 37 0.68 28 33 35 
LLGDFFRKSKEKIGKEFKRIVQRIKDFLRNLVPRTES

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 \(c\).

\(|P_{f(9CAX_1)}(2) \setminus P_{f(1WTU_1)}(2)|=197\), \(|P_{f(1WTU_1)}(2) \setminus P_{f(9CAX_1)}(2)|=13\). 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 1:1100000000011101110110011101000100100010110010011010011001011110100101101000010010100100110111101001101100101001011100100000101000100011110111111001101001011011010101100001000010110100101110101011111111101110111011100001110011110111111001011110111110111110111110111101001010010101101011110111101011111011100001101111111111101101111100100111000001011011001110101000100111000100010110110110110101011011101100010110111100001110111111011010100111001111101111001100111111111111111010101010001111101011111111101001111111110101100000111111110101100111111111100010000111110101011101011110000000101001100000101100010011001010101111101001000000000011
Pair \(Z_2\) Length of longest common subsequence
9CAX_1,1WTU_1 210 3
9CAX_1,5NMN_1 238 4
1WTU_1,5NMN_1 90 3

Newick tree

 
[
	9CAX_1:12.94,
	[
		1WTU_1:45,5NMN_1:45
	]:81.94
]

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 \((0.85)(0.8)(\frac{739 }{\log_{20} 739}-\frac{99}{\log_{20}99})=184.\)
Status Protein1 Protein2 d d1/2
Query variables 9CAX_1 1WTU_1 228 130.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]