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Parikh vectors
7DVV_1 3PKC_1 8TIR_1 Letter Amino acid
10 25 8 A Alanine
6 5 0 Q Glutamine
18 18 0 L Leucine
19 8 0 K Lycine
4 18 0 P Proline
7 10 0 S Serine
8 28 5 T Threonine
0 5 0 W Tryptophan
8 18 0 D Aspartic acid
0 4 11 C Cysteine
13 17 0 E Glutamic acid
5 27 8 G Glycine
7 8 0 H Histidine
10 19 0 I Isoleucine
7 6 0 M Methionine
6 9 0 Y Tyrosine
9 28 0 V Valine
6 15 0 R Arginine
5 10 0 N Asparagine
5 7 0 F Phenylalanine 

7DVV_1|Chains A, B|HTH marR-type domain-containing protein|Streptococcus agalactiae serotype III (strain NEM316) (211110)
>3PKC_1|Chain A|Methionine aminopeptidase|Mycobacterium tuberculosis (1773)
>8TIR_1|Chain A|DNA (5'-D(A*CP*CP*CP*GP*GP*AP*CP*CP*TP*GP*TP*GP*AP*CP*AP*AP*AP*TP*TP*GP*CP*CP*CP*TP*CP*AP*GP*AP*CP*GP*G)-3')|Escherichia coli (562)
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 \(w=f(c)\)
7DVV , Knot 73 153 0.80 36 116 145 
MENPLQKARILVNQLEKYLDRYAKEYDVEHLAGPQGHLVMHLYKHPDKDMSIKDAEEILHISKSVASNLVKRMEKNGFIAIVPSKTDKRVKYLYLTHLGKQKATQFEIFLEKLHSTMLAGITKEEIRTTKKVIRTLAKNMAMEDFDSLEVLFQ
3PKC , Knot 127 285 0.84 40 184 273 
MPSRTALSPGVLSPTRPVPNWIARPEYVGKPAAQEGSEPWVQTPEVIEKMRVAGRIAAGALAEAGKAVAPGVTTDELDRIAHEYLVDNGAYPSTLGYKGFPKSCCTSLNEVICHGIPDSTVITDGDIVNIDVTAYIGGVHGDTNATFPAGDVADEHRLLVDRTREATMRAINTVKPGRALSVIGRVIESYANRFGYNVVRDFTGHGIGTTFHNGLVVLHYDQPAVETIMQPGMTFTIEPMINLGALDYEIWDDGWTVVTKDRKWTAQFEHTLLVTDTGVEILTCL
8TIR , Knot 13 32 0.46 8 15 24 
ACCCGGACCTGTGACAAATTGCCCTCAGACGG

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 \(c\).

\(|P_{f(7DVV_1)}(2) \setminus P_{f(3PKC_1)}(2)|=57\), \(|P_{f(3PKC_1)}(2) \setminus P_{f(7DVV_1)}(2)|=125\). 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 1:100110010111001000100010000100111101011101000100010100100110100011001100100011111110000001001010011000100101110010001111100001000001100110011100100101110
Pair \(Z_2\) Length of longest common subsequence
7DVV_1,3PKC_1 182 3
7DVV_1,8TIR_1 125 2
3PKC_1,8TIR_1 177 3

Newick tree

 
[
	3PKC_1:97.16,
	[
		7DVV_1:62.5,8TIR_1:62.5
	]:34.66
]

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 \((0.85)(0.8)(\frac{438 }{\log_{20} 438}-\frac{153}{\log_{20}153})=84.7\)
Status Protein1 Protein2 d d1/2
Query variables 7DVV_1 3PKC_1 110 84
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]