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Parikh vectors
6QVH_1 6COR_1 6OHK_1 Letter Amino acid
9 2 12 L Leucine
10 0 14 T Threonine
9 3 2 R Arginine
9 1 8 D Aspartic acid
4 1 3 Q Glutamine
1 0 10 N Asparagine
2 1 15 I Isoleucine
1 3 17 K Lycine
3 1 2 M Methionine
0 2 14 F Phenylalanine
3 1 4 S Serine
0 0 2 W Tryptophan
8 0 13 V Valine
26 1 6 A Alanine
18 0 1 C Cysteine
9 1 16 E Glutamic acid
7 0 20 G Glycine
3 0 2 H Histidine
2 0 3 P Proline
2 0 6 Y Tyrosine 

6QVH_1|Chain A|cytosolic copper storage protein|Streptomyces lividans 1326 (1200984)
>6COR_1|Chain A|Competence-stimulating peptide type 1|Streptococcus pneumoniae (1313)
>6OHK_1|Chain A|Flavodoxin|Fusobacterium nucleatum (851)
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 \(w=f(c)\)
6QVH , Knot 59 126 0.75 36 83 114 
TYPADLGGVDREAMARCIEECLRCAQACTACADACLSEPTVADLTKCIRTDMDCADVCTATAAVLSRHTGYDANVTRAVLQACATVCAACGDECARHAGMHEACRVCAEACRSCEQACQELLAGLG
6COR , Knot 14 17 0.77 22 16 15 
EMRLSKFFRDAILQRKK
6OHK , Knot 82 170 0.82 40 118 161 
GSFMKTIGIFYATLTGTTVGIVDEIEFFLKKDDFKTFNVKNGVKEIENFENLILVTPTYQVGEAHAAWMNNLKKLEEIDFTGKVVGLVGLGNQFAFGESFCGGIRYLYDIVVKKGGKVVGFTSTDGYHYEETSIIENGKFIGLALDEENQPNLTPKRIGDWITEIKKEFK

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 \(c\).

\(|P_{f(6QVH_1)}(2) \setminus P_{f(6COR_1)}(2)|=80\), \(|P_{f(6COR_1)}(2) \setminus P_{f(6QVH_1)}(2)|=13\). 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 1:001101111000111001000100101001010101001011010001000100101001011110000100101001110101010110100010011100100101010000001000111111
Pair \(Z_2\) Length of longest common subsequence
6QVH_1,6COR_1 93 2
6QVH_1,6OHK_1 149 3
6COR_1,6OHK_1 126 2

Newick tree

 
[
	6OHK_1:75.00,
	[
		6QVH_1:46.5,6COR_1:46.5
	]:28.50
]

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 \((0.85)(0.8)(\frac{143 }{\log_{20} 143}-\frac{17}{\log_{20}17})=46.4\)
Status Protein1 Protein2 d d1/2
Query variables 6QVH_1 6COR_1 54 30.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]