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Parikh vectors
7YXG_1 1CGM_1 8SUV_1 Letter Amino acid
6 0 1 W Tryptophan
16 0 13 R Arginine
11 0 6 N Asparagine
11 0 4 F Phenylalanine
6 0 3 M Methionine
22 2 18 A Alanine
13 0 10 Q Glutamine
21 0 12 E Glutamic acid
19 0 7 Y Tyrosine
27 0 4 V Valine
16 1 8 G Glycine
9 0 2 H Histidine
25 0 8 S Serine
30 0 14 L Leucine
15 0 9 K Lycine
21 0 4 P Proline
11 0 2 T Threonine
24 0 5 D Aspartic acid
6 0 4 C Cysteine
13 0 5 I Isoleucine 

7YXG_1|Chains A, B|GH14974p|Drosophila melanogaster (7227)
>1CGM_1|Chain A[auth I]|RNA (5'-R(P*GP*AP*A)-3')|
>8SUV_1|Chains A, B, C, D|E3 ubiquitin-protein ligase CHIP|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 \(w=f(c)\)
7YXG , Knot 141 322 0.84 40 205 308 
GSHMASMSEVERALDVLLQEAEELCIGSSVVELDRIPTALEFCREFYSKNQPVVIRKALNWPAIGKWTPKYLIEALGDRSVDVAITPNGYADGLATQNGQEYFVLPLETKMKLSEVVRRLDDPTGAVHYIQKQNSNLSVDLPELAADLRVSDLDFAQQSFNKPPDAVNFWLGDERAVTSMHKDPYENVYCVISGHKDFVLIPPHQLSCVPRGIYPTGVYKTSDSGQFYIEPLRDEEGSDQFTEWVSVDPLSPDLAKYPEYARAKPLKVRVHAGDILYLPNYWFHHVSQSHKCIAVNFWYDLDYDSRYCYYRMLEQMTSARSG
1CGM , Knot 3 3 0.36 4 2 1 
GAA
8SUV , Knot 72 139 0.85 40 110 134 
GAMGSEKSPSAQELKEQGNRLFVGRKYPEAAACYGRAITRNPLVAVYYTNRALCYLKMQQHEQALADCRRALELDGQSVKAHFFLGQCQLEMESYDEAIANLQRAYSLAKEQRLNFGDDIPSALRIAKKKRWNSIEERR

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 \(c\).

\(|P_{f(7YXG_1)}(2) \setminus P_{f(1CGM_1)}(2)|=203\), \(|P_{f(1CGM_1)}(2) \setminus P_{f(7YXG_1)}(2)|=0\). 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 1:1001101001001101110010010110011010011011010001000001111001101111101010011011100010111010101011100010001111100010100110010010111001000000101011011101010010110001001101101111000110010001000100110100011111100100110110101100000010101011000010001001101011010110010010101101010110110110011001000000111011001000000000011001001001
Pair \(Z_2\) Length of longest common subsequence
7YXG_1,1CGM_1 203 2
7YXG_1,8SUV_1 187 4
1CGM_1,8SUV_1 108 2

Newick tree

 
[
	7YXG_1:10.27,
	[
		8SUV_1:54,1CGM_1:54
	]:54.27
]

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 \((0.85)(0.8)(\frac{325 }{\log_{20} 325}-\frac{3}{\log_{20}3})=108.\)
Status Protein1 Protein2 d d1/2
Query variables 7YXG_1 1CGM_1 140 70.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]