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Parikh vectors
6BGW_1 1LHE_1 7NYV_1 Letter Amino acid
19 1 13 A Alanine
16 3 16 R Arginine
11 0 12 M Methionine
27 1 14 P Proline
20 3 10 S Serine
9 0 4 W Tryptophan
12 1 10 Y Tyrosine
11 3 13 D Aspartic acid
13 1 11 I Isoleucine
21 5 14 L Leucine
15 0 11 N Asparagine
10 0 1 H Histidine
23 2 6 F Phenylalanine
7 1 5 C Cysteine
10 0 11 Q Glutamine
35 6 14 E Glutamic acid
21 4 15 G Glycine
11 3 9 K Lycine
11 2 9 T Threonine
28 0 22 V Valine 

6BGW_1|Chain A|Lysine-specific demethylase 5A, linked KDM5A JMJ domain|Homo sapiens (9606)
>1LHE_1|Chain A[auth L]|ALPHA-THROMBIN|Homo sapiens (9606)
>7NYV_1|Chain A[auth B]|NADH-quinone oxidoreductase subunit B|Escherichia coli B (37762)
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 \(w=f(c)\)
6BGW , Knot 144 330 0.84 40 208 319 
HNMAGVGPGGYAAEFVPPPECPVFEPSWEEFTDPLSFIGRIRPLAEKTGICKIRPPKDWQPPFACEVKSFRFTPRVQRLNELEAMTRVRPREAFGFEQAVREYTLQSFGEMADNFKSDYFNMPVHMVPTELVEKEFWRLVSSIEEDVIVEYGADISSKDFGSGFPVKDGRRKILPEEEEYALSGWNLNNMPVLEQSVLAHINVDISGMKVPWLYVGMCFSSFCWHIEDHWSYSINYLHWGEPKTWYGVPSHAAEQLEEVMRELAPELFESQPDLLHQLVTIMNPNVLMEHGVPVYRTNQCAGEFVVTFPRAYHSGFNQGYNFAEAVNFCT
1LHE , Knot 24 36 0.79 28 34 34 
TFGSGEADCGLRPLFEKKSLEDKTERELLESYIDGR
7NYV , Knot 100 220 0.81 40 165 217 
MDYTLTRIDPNGENDRYPLQKQEIVTDPLEQEVNKNVFMGKLNDMVNWGRKNSIWPYNFGLSCCYVEMVTSFTAVHDVARFGAEVLRASPRQADLMVVAGTCFTKMAPVIQRLYDQMLEPKWVISMGACANSGGMYDIYSVVQGVDKFIPVDVYIPGCPPRPEAYMQALMLLQESIGKERRPLSWVVGDQGVYRANMQSERERKRGERIAVTNLRTPDEI

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 \(c\).

\(|P_{f(6BGW_1)}(2) \setminus P_{f(1LHE_1)}(2)|=184\), \(|P_{f(1LHE_1)}(2) \setminus P_{f(6BGW_1)}(2)|=10\). 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 1:001111111101101111100111010100100110111010111000110010110010111100100101010100100101100101001111001100001001101100100001011101110011000110110010001110011010000110111100100011100000110110100111100011101010101101111011101001010100010001001011010010111001100100110011101100010110011011010111001111000000110111011010001100100110110100
Pair \(Z_2\) Length of longest common subsequence
6BGW_1,1LHE_1 194 4
6BGW_1,7NYV_1 177 4
1LHE_1,7NYV_1 163 3

Newick tree

 
[
	6BGW_1:96.33,
	[
		7NYV_1:81.5,1LHE_1:81.5
	]:14.83
]

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 \((0.85)(0.8)(\frac{366 }{\log_{20} 366}-\frac{36}{\log_{20}36})=105.\)
Status Protein1 Protein2 d d1/2
Query variables 6BGW_1 1LHE_1 133 73
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]