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Parikh vectors
8CUT_1 2KQA_1 8BAE_1 Letter Amino acid
6 1 0 H Histidine
4 8 0 I Isoleucine
4 13 0 V Valine
4 11 0 N Asparagine
2 2 0 M Methionine
0 4 0 F Phenylalanine
0 6 2 T Threonine
2 2 0 W Tryptophan
7 12 0 S Serine
5 4 0 Y Tyrosine
5 4 0 R Arginine
8 18 2 G Glycine
30 6 0 L Leucine
15 3 0 K Lycine
4 8 0 P Proline
25 8 1 A Alanine
9 8 0 D Aspartic acid
0 4 2 C Cysteine
2 2 0 Q Glutamine
16 5 0 E Glutamic acid 

8CUT_1|Chain A|I432-1(Imd) Chain A|synthetic construct (32630)
>2KQA_1|Chain A|Cerato-platanin|Ceratocystis platani (88771)
>8BAE_1|Chains A, B|DNA (5'-D(*GP*CP*AP*TP*GP*CP*T)-3')|synthetic construct (32630)
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 \(w=f(c)\)
8CUT , Knot 50 148 0.56 34 63 102 
MRGHHHHHHGSSALAYVMLGLLLSLLNRLSLAAEAYKKAIELDPNDALAWLLLGSVLEKLKRLDEAAEAYKKAIELKPNDASAWKELGKVLEKLGRLDEAAKAYAEAIKLDPSDAEAAKELGKVLEKLGQLELAERAYQLAIELDPND
2KQA , Knot 66 129 0.82 40 103 125 
EEGVSLEKRVSISYDPIYAADLSMGSVACSNGDHGLMAQYPTLGEVPGFPNVGGIPDIAGWDSPSCGTCWKVTIPNGNSIFIRGVDSGRGGFNVNPTAFTKLVGSTEAGRVDNVNYVQVDLSNCINGAN
8BAE , Knot 5 7 0.46 8 5 5 
GCATGCT

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 \(c\).

\(|P_{f(8CUT_1)}(2) \setminus P_{f(2KQA_1)}(2)|=41\), \(|P_{f(2KQA_1)}(2) \setminus P_{f(8CUT_1)}(2)|=81\). 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 1:1010000001001110111111101100101110100011010100111111110110010010011010001101010010110011011001101001101010110101001011001101100110101100100111010100
Pair \(Z_2\) Length of longest common subsequence
8CUT_1,2KQA_1 122 3
8CUT_1,8BAE_1 68 1
2KQA_1,8BAE_1 108 1

Newick tree

 
[
	2KQA_1:63.55,
	[
		8CUT_1:34,8BAE_1:34
	]:29.55
]

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 \((0.85)(0.8)(\frac{277 }{\log_{20} 277}-\frac{129}{\log_{20}129})=46.2\)
Status Protein1 Protein2 d d1/2
Query variables 8CUT_1 2KQA_1 53 47
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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