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Parikh vectors
2JCP_1 1SXP_1 9ITT_1 Letter Amino acid
8 0 18 Y Tyrosine
11 6 56 A Alanine
8 0 34 R Arginine
6 1 2 C Cysteine
5 0 3 H Histidine
6 0 11 F Phenylalanine
7 0 26 P Proline
0 0 1 W Tryptophan
10 0 16 N Asparagine
10 0 29 D Aspartic acid
10 0 41 I Isoleucine
5 0 19 K Lycine
3 0 8 M Methionine
11 0 23 S Serine
10 0 48 V Valine
5 0 31 Q Glutamine
8 0 33 E Glutamic acid
9 3 45 G Glycine
7 0 48 L Leucine
15 3 30 T Threonine 

2JCP_1|Chain A|CD44 ANTIGEN|MUS MUSCULUS (10090)
>1SXP_1|Chain A[auth C]|5'-D(*A*AP*TP*AP*CP*TP*AP*AP*GP*AP*TP*AP*G)-3'|
>9ITT_1|Chains A, B, C|ATP synthase subunit alpha|Chloroflexus aurantiacus J-10-fl (324602)
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 \(w=f(c)\)
2JCP , Knot 77 154 0.84 38 123 149 
MQQIDLNVTCRYAGVFHVEKNGRYSISRTEAADLCQAFNSTLPTMDQMKLALSKGFETCRYGFIEGNVVIPRIHPNAICAANHTGVYILVTSNTSHYDTYCFNASAPPEEDCTSVTDLPNSFDGPVTITIVNRDGTRYSKKGEYRTHQEDIDAS
1SXP , Knot 6 13 0.39 8 7 9 
GATACTAAGATAG
9ITT , Knot 208 522 0.83 40 224 481 
MTTITEELIARLKQGITSGVDLQPRQVNVGTVIAVGDGVARLSGLDQVVASEIVEFPPKAGRNESIYGIALNLEQDSVAAIILGDDETIEEGDMVTSTGRVISVPVGQGLLGRVVNPLGQPIDGKGPIVYEKTRPIERIAPGVITRKSVDTPVQTGIIAIDALIPIGRGQRELIIGDRQTGKTAVAIDTILNQKGQGMVCIYVAIGQRRAQVAQVVGTLERFGAMEYTIVVSATASESAALQYIAPYAGCAMGEEIMENGVMLNGQLVKDALIVYDDLSKHAVAYRQVSLLLRRPPGREAYPGDVFYLHSRLLERAARLNEEYGGGSLTALPVIETQANDVSAYIPTNVISITDGQIYLESDLFNAGQRPALNVGISVSRVGGAAQTRAMRAVAGKLKGELAQFRDLAAFAQFASDLDATTKAQIERGQRLQELLKQPQYQPLPVEDQVAVLYAATNNYLDDVPVPLITKWRDDFLAFLRTAHPEVRKLIYDNRLDRKFPTPEVKEALEAAIKEFKATSNYS

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 \(c\).

\(|P_{f(2JCP_1)}(2) \setminus P_{f(1SXP_1)}(2)|=120\), \(|P_{f(1SXP_1)}(2) \setminus P_{f(2JCP_1)}(2)|=4\). 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 1:1001010100001111010001000100001101001100011010010111001100000111010111101010110110001101110000000000010101110000001001100101110101100010000001000000001010
Pair \(Z_2\) Length of longest common subsequence
2JCP_1,1SXP_1 124 2
2JCP_1,9ITT_1 179 3
1SXP_1,9ITT_1 221 3

Newick tree

 
[
	9ITT_1:11.44,
	[
		2JCP_1:62,1SXP_1:62
	]:48.44
]

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 \((0.85)(0.8)(\frac{167 }{\log_{20} 167}-\frac{13}{\log_{20}13})=56.1\)
Status Protein1 Protein2 d d1/2
Query variables 2JCP_1 1SXP_1 74 39
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]