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Parikh vectors
1ICP_1 8XZD_1 4HBC_1 Letter Amino acid
16 16 27 S Serine
4 2 6 W Tryptophan
30 15 21 G Glycine
28 9 6 I Isoleucine
24 18 15 L Leucine
27 6 5 E Glutamic acid
10 9 1 H Histidine
26 16 10 A Alanine
24 12 6 R Arginine
11 6 6 Q Glutamine
20 13 31 T Threonine
7 11 7 C Cysteine
19 13 9 K Lycine
21 14 16 P Proline
15 17 7 F Phenylalanine
17 15 7 Y Tyrosine
26 23 23 V Valine
18 22 6 N Asparagine
24 9 5 D Aspartic acid
9 1 1 M Methionine 

1ICP_1|Chains A, B|12-OXOPHYTODIENOATE REDUCTASE 1|Solanum lycopersicum (4081)
>8XZD_1|Chain A[auth B]|Spike protein S1|Severe acute respiratory syndrome coronavirus 2 (2697049)
>4HBC_1|Chain A[auth H]|Antigen Binding Fragment, Immunoglobulin IgG - Heavy Chain|Oryctolagus cuniculus (9986)
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 \(w=f(c)\)
1ICP , Knot 160 376 0.84 40 213 361 
MENKVVEEKQVDKIPLMSPCKMGKFELCHRVVLAPLTRQRSYGYIPQPHAILHYSQRSTNGGLLIGEATVISETGIGYKDVPGIWTKEQVEAWKPIVDAVHAKGGIFFCQIWHVGRVSNKDFQPNGEDPISCTDRGLTPQIMSNGIDIAHFTRPRRLTTDEIPQIVNEFRVAARNAIEAGFDGVEIHGAHGYLIDQFMKDQVNDRSDKYGGSLENRCRFALEIVEAVANEIGSDRVGIRISPFAHYNEAGDTNPTALGLYMVESLNKYDLAYCHVVEPRMKTAWEKIECTESLVPMRKAYKGTFIVAGGYDREDGNRALIEDRADLVAYGRLFISNPDLPKRFELNAPLNKYNRDTFYTSDPIVGYTDYPFLETMT
8XZD , Knot 109 247 0.81 40 159 236 
MHSSALLCCLVLLTGVRARVQPTESIVRFPNITNLCPFDEVFNATTFASVYAWNRKRISNCVADYSVLYNFAPFFAFKCYGVSPTKLNDLCFTNVYADSFVIRGNEVSQIAPGQTGNIADYNYKLPDDFTGCVIAWNSNKLDSKVGGNYNYRYRLFRKSNLKPFERDISTEIYQAGNKPCNGVAGVNCYFPLQSYGFRPTYGVGHQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFHHHHHH
4HBC , Knot 98 215 0.81 40 132 202 
QSVEESGGRLVTPGTPLTLACTVSGFSLNTYSMFWVRQAPGKGLQWIGIISNFGVIYYATWAKGRFTISKTSTTVDLKITSPTTEDTATYFCVRKYGSEWGGDLWGPGTLVTVSSGQPKAPSVFPLAPCCGDTPSSTVTLGCLVKGYLPEPVTVTWNSGTLTNGVRTFPSVRQSSGLYSLSSVVSVTSSSQPVTCNVAHPATNTKVDKTVAPSTC

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 \(c\).

\(|P_{f(1ICP_1)}(2) \setminus P_{f(8XZD_1)}(2)|=123\), \(|P_{f(8XZD_1)}(2) \setminus P_{f(1ICP_1)}(2)|=69\). 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 1:1000110000100111101001101010001111110000001011010111000000001111110101100011100011111000010110111011010111110011011010000101010011000001101011001101101001001000011011001011100110111011010110101100110001000000011010000011101101110011000111010111000011000101111011001000011000110101001100100000111100100101111110000010011100010111010111001011001010111000000010000111100001110010
Pair \(Z_2\) Length of longest common subsequence
1ICP_1,8XZD_1 192 3
1ICP_1,4HBC_1 195 3
8XZD_1,4HBC_1 149 3

Newick tree

 
[
	1ICP_1:10.10,
	[
		8XZD_1:74.5,4HBC_1:74.5
	]:28.60
]

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 \((0.85)(0.8)(\frac{623 }{\log_{20} 623}-\frac{247}{\log_{20}247})=105.\)
Status Protein1 Protein2 d d1/2
Query variables 1ICP_1 8XZD_1 137 112
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]