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Parikh vectors
8CYV_1 7SVB_1 6HAG_1 Letter Amino acid
0 0 0 W Tryptophan
4 0 0 Y Tyrosine
6 0 0 Q Glutamine
4 0 0 L Leucine
0 0 0 R Arginine
3 0 0 N Asparagine
6 0 0 D Aspartic acid
5 0 0 P Proline
4 0 0 S Serine
19 0 0 V Valine
0 4 9 C Cysteine
15 0 0 K Lycine
4 0 0 M Methionine
1 0 0 H Histidine
2 0 0 I Isoleucine
2 0 0 F Phenylalanine
10 2 0 T Threonine
19 2 11 A Alanine
18 0 0 E Glutamic acid
18 3 12 G Glycine 

8CYV_1|Chains A, B, C, D, E, F, G[auth I], H[auth J], I[auth K], J[auth L], K[auth M], L[auth N]|Alpha-synuclein|Homo sapiens (9606)
>7SVB_1|Chain A[auth C]|DNA (5'-D(P*TP*CP*GP*AP*CP*GP*GP*AP*TP*CP*C)-3')|synthetic construct (32630)
>6HAG_1|Chain A|SAM Riboswitch|Proteobacteria (1224)
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 \(w=f(c)\)
8CYV , Knot 59 140 0.69 34 86 121 
MDVFMKGLSKAKEGVVAAAEKTKQGVAEAAGKTKEGVLYVGSKTKEGVVHGVATVAEKTKEQVTNVGGAVVTGVTAVAQKTVEGAGSIAAATGFVKKDQLGKNEEGAPQEGILEDMPVDPDNEAYEMPSEEGYQDYEPEA
7SVB , Knot 7 11 0.50 8 7 9 
TCGACGGATCC
6HAG , Knot 18 43 0.52 8 16 33 
GUCACAACGGCUUCCUGACGUGGCAGAUUGAAUUAUUGGAGCA

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 \(c\).

\(|P_{f(8CYV_1)}(2) \setminus P_{f(7SVB_1)}(2)|=83\), \(|P_{f(7SVB_1)}(2) \setminus P_{f(8CYV_1)}(2)|=4\). 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 1:10111011001001111110000011101110000111011000001110111011000000100111111011011100010111011110111000011000011100111001110100010011000100000101
Pair \(Z_2\) Length of longest common subsequence
8CYV_1,7SVB_1 87 3
8CYV_1,6HAG_1 94 3
7SVB_1,6HAG_1 13 4

Newick tree

 
[
	8CYV_1:52.15,
	[
		7SVB_1:6.5,6HAG_1:6.5
	]:45.65
]

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 \((0.85)(0.8)(\frac{151 }{\log_{20} 151}-\frac{11}{\log_{20}11})=51.9\)
Status Protein1 Protein2 d d1/2
Query variables 8CYV_1 7SVB_1 58 31
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]