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Parikh vectors
8QPC_1 6POH_1 6XJZ_1 Letter Amino acid
3 12 0 L Leucine
3 9 0 T Threonine
6 17 7 A Alanine
5 12 0 D Aspartic acid
0 2 20 C Cysteine
0 14 0 Q Glutamine
1 5 0 I Isoleucine
14 17 0 K Lycine
2 6 0 M Methionine
2 11 0 F Phenylalanine
2 8 0 Y Tyrosine
4 3 0 R Arginine
1 7 0 N Asparagine
7 12 0 E Glutamic acid
1 2 0 W Tryptophan
5 13 21 G Glycine
0 3 0 H Histidine
1 7 0 P Proline
3 8 0 S Serine
6 21 0 V Valine 

8QPC_1|Chain A[auth AA]|DNA-binding protein 7b|Sulfolobus acidocaldarius (2285)
>6POH_1|Chains A, B|Thiol:disulfide interchange protein DsbA|Escherichia coli (strain K12) (83333)
>6XJZ_1|Chains A, B|Self-alkylating ribozyme (58-MER)|Aeropyrum pernix (56636)
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 \(w=f(c)\)
8QPC , Knot 36 66 0.76 34 55 63 
MVKVKFKYKGEEKEVDTSKIKKVWRAGKAVSFTYDDNGKTGRGAVSEKDAPKELLDMLARAEREKK
6POH , Knot 86 189 0.79 40 134 185 
AQYEDGKQYTTLEKPVAGAPQVLEFFSFFCPHCYQFEEVLHISDNVKKKLPEGVKMTKYHVNFMGGDLGKDLTQAWAVAMALGVEDKVTVPLFEGVQKTQTIRSASDIRDVFINAGIKGEEYDAAWNSFVVKSLVAQQEKAAADVQLRGVPAMFVNGKYQLNPQGMDTSNMDVFVQQYADTVKYLSEKK
6XJZ , Knot 19 58 0.44 8 15 34 
GGCCGCUCCAGAAGAGGGCCCCCUUGCCCGUUAUCGGGGGCUAGGCUCGAUGUCGGCC

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 \(c\).

\(|P_{f(8QPC_1)}(2) \setminus P_{f(6POH_1)}(2)|=28\), \(|P_{f(6POH_1)}(2) \setminus P_{f(8QPC_1)}(2)|=107\). 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 1:110101000100001000010011011011010000010010111000011001101110100000
Pair \(Z_2\) Length of longest common subsequence
8QPC_1,6POH_1 135 4
8QPC_1,6XJZ_1 66 2
6POH_1,6XJZ_1 141 3

Newick tree

 
[
	6POH_1:77.38,
	[
		8QPC_1:33,6XJZ_1:33
	]:44.38
]

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 \((0.85)(0.8)(\frac{255 }{\log_{20} 255}-\frac{66}{\log_{20}66})=61.6\)
Status Protein1 Protein2 d d1/2
Query variables 8QPC_1 6POH_1 76 51
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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