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Parikh vectors
4NGC_1 7PGO_1 7FDS_1 Letter Amino acid
10 15 2 Q Glutamine
6 17 18 G Glycine
8 13 7 H Histidine
20 12 14 T Threonine
2 10 0 W Tryptophan
10 17 9 N Asparagine
19 17 6 I Isoleucine
14 12 1 F Phenylalanine
16 18 14 A Alanine
18 16 4 E Glutamic acid
41 18 5 L Leucine
19 18 7 K Lycine
4 8 3 M Methionine
26 6 5 P Proline
14 16 14 V Valine
17 14 6 D Aspartic acid
6 0 2 C Cysteine
20 15 9 S Serine
16 7 2 Y Tyrosine
16 11 0 R Arginine 

4NGC_1|Chain A|Endoribonuclease Dicer|Homo sapiens (9606)
>7PGO_1|Chains A[auth AAA], B[auth BBB], C[auth CCC], D[auth DDD]|Beta-lactamase|Klebsiella pneumoniae (573)
>7FDS_1|Chains A, B|Lipoprotein LpqH|Mycobacterium tuberculosis H37Rv (83332)
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 \(w=f(c)\)
4NGC , Knot 133 302 0.83 40 184 287 
SDQPCYLYVIGMVLTTPLPDELNFRRRKLYPPEDTTRCFGILTAKPIPQIPHFPVYTRSGEVTISIELAASGFMLSLQMLELITRLHQYIFSHILRLEKPALEFKPTDADSAYCVLPLNVVNDSSTLDIDFKFMEDIEKSEARIGIPSTKYTKETPFVFKLEDYQDAVIIPRYRNFDQPHRFYVADVYTDLTPLSKFPSPEYETFAEYYKTKYNLDLTNLNQPLLDVDHTSSRLNLLTPRHLNQKGKALPLSSAEKRKAKWESLQNKQILVPELCAIHPIPASLWRKAVCLPSILYRLHCLL
7PGO , Knot 118 260 0.84 38 175 253 
MHHHHHHSAGENLYFQGKEWQENKSWNAHFTEHKSQGVVVLWNENKQQGFTNNLKRANQAFLPASTFKIPNSLIALDLGVVKDEHQVFKWDGQTRDIATWNRDHNLITAMKYSVVPVYQEFARQIGEARMSKMLHAFDYGNEDISGNVDSFWLDGGIRISATEQISFLRKLYHNKLHVSERSQRIVKQAMLTEANGDYIIRAKTGYSTRIEPKIGWWVGWVELDDNVWFFAMNMDMPTSDGLGLAQAITKEVLKQEKIIP
7FDS , Knot 61 128 0.77 36 88 120 
MDSGPKVVIDGKDQNVTGSVVCTTAAGNVNIAIGGAATGIAAVLTDGNPPEVKSVGLGNVNGVTLGYTSGTGQGNASATKDGSHYKITGTATGVDMANPMSPVNKSFEIEVTCSTKLAAALEHHHHHH

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 \(c\).

\(|P_{f(4NGC_1)}(2) \setminus P_{f(7PGO_1)}(2)|=102\), \(|P_{f(7PGO_1)}(2) \setminus P_{f(4NGC_1)}(2)|=93\). 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 1:00010010111111001110010100001011000000111101011101101110000101010101110111101011011001000110011010011101010010010011110110000010101011001000010111100000000111101000001111100001001001011010001011001101000011000000001010010011101000000101101001000101111001000010100100001111010110111101100110110110010011
Pair \(Z_2\) Length of longest common subsequence
4NGC_1,7PGO_1 195 4
4NGC_1,7FDS_1 182 3
7PGO_1,7FDS_1 155 6

Newick tree

 
[
	4NGC_1:99.27,
	[
		7FDS_1:77.5,7PGO_1:77.5
	]:21.77
]

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 \((0.85)(0.8)(\frac{562 }{\log_{20} 562}-\frac{260}{\log_{20}260})=85.5\)
Status Protein1 Protein2 d d1/2
Query variables 4NGC_1 7PGO_1 111 104
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]