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Parikh vectors
6FXL_1 3IWC_1 6HOW_1 Letter Amino acid
13 2 13 H Histidine
6 5 24 L Leucine
6 3 7 F Phenylalanine
13 3 13 R Arginine
4 1 7 C Cysteine
1 3 10 Q Glutamine
14 7 15 E Glutamic acid
15 3 14 I Isoleucine
7 2 10 K Lycine
4 2 7 M Methionine
0 0 1 W Tryptophan
20 4 35 A Alanine
5 3 6 Y Tyrosine
6 2 10 D Aspartic acid
16 4 22 G Glycine
7 1 12 P Proline
12 5 25 S Serine
8 3 13 T Threonine
17 8 27 V Valine
5 1 17 N Asparagine 

6FXL_1|Chains A, B, C, D|Ribose 5-phosphate isomerase, putative|Trypanosoma cruzi (strain CL Brener) (353153)
>3IWC_1|Chains A[auth B], C[auth D]|S-adenosylmethionine decarboxylase|Thermotoga maritima (2336)
>6HOW_1|Chains A, B, C|Pteridine reductase|Trypanosoma brucei brucei (5702)
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 \(w=f(c)\)
6FXL , Knot 83 179 0.80 38 126 173 
MGSSHHHHHHSSGLVPRGSHMTRRVAIGTDHPAFAIHENLILYVKEAGDEFVPVYCGPKTAESVDYPDFASRVAEMVARKEVEFGVLACGSGIGMSIAANKVPGVRAALCYDHYTAAISRIHNDANIVCVGERTTGVEVIREIIITFLQTPFSGEERHARRIEKIRAIEASHAGNKGVK
3IWC , Knot 37 62 0.82 38 56 60 
MKSLGRHLVAEFYECDREVLDNVQLIEQEMKQAAYESGATIVTSTFHRFLPYGVSGVVVISE
6HOW , Knot 127 288 0.83 40 179 275 
MGSSHHHHHHSSGLVPRGSHMEAPAAVVTGAAKRIGRAIAVKLHQTGYRVVIHYHNSAEAAVSLADELNKERSNTAVVCQADLTNSNVLPASCEEIINSCFRAFGRCDVLVNNASAFYPTPLVQGDHEDNSNGKTVETQVAELIGTNAIAPFLLTMSFAQRQKGTNPNCTSSNLSIVNLCDAMVDQPCMAFSLYNMGKHALVGLTQSAALELAPYGIRVNGVAPGVSLLPVAMGEEEKDKWRRKVPLGRREASAEQIADAVIFLVSGSAQYITGSIIKVDGGLSLVHA

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 \(c\).

\(|P_{f(6FXL_1)}(2) \setminus P_{f(3IWC_1)}(2)|=106\), \(|P_{f(3IWC_1)}(2) \setminus P_{f(6FXL_1)}(2)|=36\). 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 1:11000000000011110100100011110001111100011101001100111100110010010010110011011100010111110101111011100111101110000001110010001011011000011011001110110011010000100100101101001100110
Pair \(Z_2\) Length of longest common subsequence
6FXL_1,3IWC_1 142 3
6FXL_1,6HOW_1 139 21
3IWC_1,6HOW_1 175 3

Newick tree

 
[
	3IWC_1:82.79,
	[
		6FXL_1:69.5,6HOW_1:69.5
	]:13.29
]

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 \((0.85)(0.8)(\frac{241 }{\log_{20} 241}-\frac{62}{\log_{20}62})=58.9\)
Status Protein1 Protein2 d d1/2
Query variables 6FXL_1 3IWC_1 75 50.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]