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Parikh vectors
4NPH_1 2IGU_1 5DKD_1 Letter Amino acid
9 0 6 Q Glutamine
27 0 10 E Glutamic acid
8 0 15 K Lycine
7 0 3 M Methionine
15 1 12 S Serine
8 0 5 Y Tyrosine
23 1 8 D Aspartic acid
39 0 13 L Leucine
1 1 0 W Tryptophan
31 0 8 V Valine
7 4 1 C Cysteine
26 1 2 G Glycine
19 1 6 P Proline
21 0 3 T Threonine
32 1 2 A Alanine
32 2 7 R Arginine
4 0 6 N Asparagine
11 0 1 H Histidine
20 0 9 I Isoleucine
11 0 4 F Phenylalanine 

4NPH_1|Chain A|Probable secretion system apparatus ATP synthase SsaN|Salmonella enterica subsp. enterica serovar Typhimurium (99287)
>2IGU_1|Chain A|Alpha-conotoxin ImI|null
>5DKD_1|Chains A, B|Transcription activator BRG1|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 \(w=f(c)\)
4NPH , Knot 145 351 0.80 40 192 322 
MQVPVGEALLGRVIDGFGRPLDGRELPDVCWKDYDAMPPPAMVRQPITQPLMTGIRAIDSVATCGEGQRVGIFSAPGVGKSTLLAMLCNAPDADSNVLVLIGERGREVREFIDFTLSEETRKRCVIVVATSDRPALERVRALFVATTIAEFFRDNGKRVVLLADSLTRYARAAREIALAAGETAVSGEYPPGVFSALPRLLERTGMGEKGSITAFYTVLVEGDDMNEPLADEVRSLLDGHIVLSRRLAERGHYPAIDVLATLSRVFPVVTSHEHRQLAAILRRCLALYQEVELLIRIGEYQRGVDTDTDKAIDTYPDICTFLRQSKDEVCGPELLIEKLHQILTEHHHHHH
2IGU , Knot 9 12 0.62 16 10 10 
GCCSDPRCAWRC
5DKD , Knot 59 121 0.78 38 89 118 
SMLSPNPPNLTKKMKKIVDAVIKYKDSSSGRQLSEVFIQLPSRKELPEYYELIRKPVDFKKIKERIRNHKYRSLNDLEKDVMLLCQNAQTFNLEGSLIYEDSIVLQSVFTSVRQKIEKEDD

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 \(c\).

\(|P_{f(4NPH_1)}(2) \setminus P_{f(2IGU_1)}(2)|=189\), \(|P_{f(2IGU_1)}(2) \setminus P_{f(4NPH_1)}(2)|=7\). 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 1:101111011110110111011010011010100001111111100110011101101100110010100111101111100011111001101000111111001001001101010000000011111000011100101111100110110001001111100100010110011111100110100111110111011000111001010110011101001001110010011010111000110010011101110100111110000000111110001110001011101100001100000011000101001100000010110111001001100000000
Pair \(Z_2\) Length of longest common subsequence
4NPH_1,2IGU_1 196 2
4NPH_1,5DKD_1 179 3
2IGU_1,5DKD_1 99 1

Newick tree

 
[
	4NPH_1:10.52,
	[
		5DKD_1:49.5,2IGU_1:49.5
	]:55.02
]

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 \((0.85)(0.8)(\frac{363 }{\log_{20} 363}-\frac{12}{\log_{20}12})=115.\)
Status Protein1 Protein2 d d1/2
Query variables 4NPH_1 2IGU_1 140 72.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]