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Parikh vectors
2KJQ_1 9MEP_1 3HUS_1 Letter Amino acid
10 1 1 H Histidine
4 0 6 I Isoleucine
8 0 0 F Phenylalanine
4 0 0 P Proline
6 0 6 R Arginine
6 0 6 D Aspartic acid
8 0 1 Y Tyrosine
5 0 1 N Asparagine
7 0 7 K Lycine
7 0 3 S Serine
4 0 0 T Threonine
2 1 0 W Tryptophan
1 0 2 C Cysteine
7 0 8 Q Glutamine
11 0 1 G Glycine
17 3 7 L Leucine
4 0 1 M Methionine
9 0 7 V Valine
16 3 4 A Alanine
13 1 5 E Glutamic acid 

2KJQ_1|Chain A|DnaA-related protein|Neisseria meningitidis serogroup B (491)
>9MEP_1|Chains A, B|Co-MAHF-9 A8W|synthetic construct (32630)
>3HUS_1|Chains A, D|Fibrinogen alpha chain|Homo sapiens (9606)
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 \(w=f(c)\)
2KJQ , Knot 71 149 0.79 40 117 140 
MGHHHHHHSHMDYPSFDKFLGTENAELVYVLRHKHGQFIYVWGEEGAGKSHLLQAWVAQALEAGKNAAYIDAASMPLTDAAFEAEYLAVDQVEKLGNEEQALLFSIFNRFRNSGKGFLLLGSEYTPQQLVIREDLRTRMAYCLVYEVKP
9MEP , Knot 8 11 0.58 12 9 9 
XLAEALHWALX
3HUS , Knot 35 66 0.74 32 54 63 
VIEKVQHIQLLQKNVRAQLVDMKRLEVDIDIKIRSCRGSCSRALAREVDLKDYEDQQKQLEQVIAK

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 \(c\).

\(|P_{f(2KJQ_1)}(2) \setminus P_{f(9MEP_1)}(2)|=113\), \(|P_{f(9MEP_1)}(2) \setminus P_{f(2KJQ_1)}(2)|=5\). 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 1:11000000001001010011100010110110000101101110011100011011110110110011010110111001110100111001001100001111011001000101111110000100111000100011001100101
Pair \(Z_2\) Length of longest common subsequence
2KJQ_1,9MEP_1 118 2
2KJQ_1,3HUS_1 121 3
9MEP_1,3HUS_1 59 2

Newick tree

 
[
	2KJQ_1:66.86,
	[
		9MEP_1:29.5,3HUS_1:29.5
	]:37.36
]

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 \((0.85)(0.8)(\frac{160 }{\log_{20} 160}-\frac{11}{\log_{20}11})=54.8\)
Status Protein1 Protein2 d d1/2
Query variables 2KJQ_1 9MEP_1 69 36.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]