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Parikh vectors
5AYO_1 2ORL_1 2OKF_1 Letter Amino acid
22 3 5 R Arginine
11 4 8 D Aspartic acid
16 4 4 P Proline
11 5 4 Y Tyrosine
32 7 11 A Alanine
9 7 4 N Asparagine
16 7 9 E Glutamic acid
26 4 12 I Isoleucine
77 8 13 L Leucine
12 16 11 K Lycine
31 4 8 F Phenylalanine
40 4 7 S Serine
21 9 7 T Threonine
37 3 14 V Valine
1 2 0 C Cysteine
15 2 10 Q Glutamine
39 12 7 G Glycine
6 4 2 H Histidine
6 2 2 M Methionine
12 1 2 W Tryptophan 

5AYO_1|Chain A|Solute carrier family 39 (Iron-regulated transporter)|Bdellovibrio bacteriovorus (264462)
>2ORL_1|Chain A|Cytochrome c iso-1|Saccharomyces cerevisiae (4932)
>2OKF_1|Chains A, B|FdxN element excision controlling factor protein|Anabaena variabilis (264691)
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 \(w=f(c)\)
5AYO , Knot 177 440 0.81 40 205 410 
MKVQSLLRIETQLLLGRLLTRSGDQAWDFVVPFALLVIFPGKLQVAAFYYLIVKIGTFLLTPSSGKWIDTHPRIQVVKWGVWLQFFAILAGMVFFGMLDGLVRAGGRESWLLSVLFIALALSGVMASLGSQITDISVGNDLAPSLVAPEKLTHFNSWLRRIDLATEVGAPILAGALFAFHPEQLPLAGLFLIGLWNLVSFVPEYFLLRNVIQRSGLKIKVLTEAQSWKDTFHINLRGSFSDPIFWLILSYALLWLSVLSPHGVLLAAYLKDEMRLPETEIGLFRGLGAVFGLISTVSFPYLVRRLGLISSSRWHLGFQGVTLGIAVTAFAMGSTASVYVFLGCILLSRVGLYGFSNGEFELRQRLIPEGRRGELNSLSSLTTTSATLILFSAGSLLPQTEDFKYLVYVSLAAVLLANVVFIKWSSRQGVVTSGSENLYFQ
2ORL , Knot 59 108 0.85 40 92 105 
TEFKAGSAKKGATLFKTRCLQCHTVEKGGPHKVGPNLHGIFGRHSGQAEGYSYTDANIKKNVLWDENNMSEYLTNPKKYIPGTKMAFGGLKKEKDRNDLITYLKKATE
2OKF , Knot 73 140 0.86 38 113 136 
GMSARDVFHEVVKTALKKDGWQITDDPLTISVGGVNLSIDLAAQKLIAAERQGQKIAVEVKSFLKQSSAISEFHTALGQFINYRGALRKVEPDRVLYLAVPLTTYKTFFQLDFPKEIIIENQVKMLVYDVEQEVIFQWIN

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 \(c\).

\(|P_{f(5AYO_1)}(2) \setminus P_{f(2ORL_1)}(2)|=150\), \(|P_{f(2ORL_1)}(2) \setminus P_{f(5AYO_1)}(2)|=37\). 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 1:10100110100011110110001001101111111111111010111100111011011101001011000101011011111011111111111111011101110001110111111110111101100100101100111011110010010011001011001111111111111010011111111111101101110011100110001101011001001000101010101001111111001111101101011111101000101100011110111111111001011011001111000010111011011111011111001010111101110011101100101010001110100101001001000010111101101110000100110101111111011110100001110010001010
Pair \(Z_2\) Length of longest common subsequence
5AYO_1,2ORL_1 187 3
5AYO_1,2OKF_1 166 4
2ORL_1,2OKF_1 143 3

Newick tree

 
[
	5AYO_1:93.36,
	[
		2OKF_1:71.5,2ORL_1:71.5
	]:21.86
]

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 \((0.85)(0.8)(\frac{548 }{\log_{20} 548}-\frac{108}{\log_{20}108})=130.\)
Status Protein1 Protein2 d d1/2
Query variables 5AYO_1 2ORL_1 157 97.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]