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Parikh vectors
3FTD_1 6JPT_1 5KTD_1 Letter Amino acid
12 5 3 P Proline
10 4 9 D Aspartic acid
12 4 12 I Isoleucine
13 4 12 F Phenylalanine
30 13 13 L Leucine
4 3 3 M Methionine
14 2 16 N Asparagine
7 6 5 Q Glutamine
2 2 11 H Histidine
7 0 12 Y Tyrosine
30 23 7 V Valine
14 6 9 G Glycine
11 10 13 S Serine
8 8 8 T Threonine
24 7 17 E Glutamic acid
30 9 17 K Lycine
1 1 3 W Tryptophan
8 9 9 A Alanine
10 3 7 R Arginine
2 3 2 C Cysteine 

3FTD_1|Chain A|Dimethyladenosine transferase|Aquifex aeolicus (224324)
>6JPT_1|Chain A|Proteasome assembly chaperone 3|Homo sapiens (9606)
>5KTD_1|Chain A|FdhC|Acinetobacter nosocomialis (106654)
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 \(w=f(c)\)
3FTD , Knot 107 249 0.79 40 148 236 
SMVRLKKSFGQHLLVSEGVLKKIAEELNIEEGNTVVEVGGGTGNLTKVLLQHPLKKLYVIELDREMVENLKSIGDERLEVINEDASKFPFCSLGKELKVVGNLPYNVASLIIENTVYNKDCVPLAVFMVQKEVAEKLQGKKDTGWLSVFVRTFYDVNYVMTVPPRFFVPPPKVQSAVIKLVKNEKFPVKDLKNYKKFLTKIFQNRRKVLRKKIPEELLKEAGINPDARVEQLSLEDFFKLYRLIEDSGE
6JPT , Knot 63 122 0.82 38 94 118 
MEDTPLVISKQKTEVVCGVPTQVVCTAFSSHILVVVTQFGKMGTLVSLEPSSVASDVSKPVLTTKVLLGQDEPLIHVFAKNLVAFVSQEAGNRAVLLAVAVKDKSMEGLKALREVIRVCQVW
5KTD , Knot 87 188 0.80 40 138 181 
MVNFNLKANTTYLRLVEENDAEFICTLRNNDKLNTYISKSTGDIKSQAEWIRNYKNRENNGEEYYFIIFRSDDQSPIGTVRLYDFHENPKSFCWGSWILNEHKTKYAAVESALLVYEAGFSTLGFEQSHFEVMKGNDKVHSFHLKMGAQKISEDDENIYYIFPKSKYKENKIQYARFLGKLEHHHHHH

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 \(c\).

\(|P_{f(3FTD_1)}(2) \setminus P_{f(6JPT_1)}(2)|=98\), \(|P_{f(6JPT_1)}(2) \setminus P_{f(3FTD_1)}(2)|=44\). 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 1:011010001100111001110011001010010011011110101001110011001011010001100100110001011000100111001100101110110011011100010000011111111000110010100001110111001001001101110111111010011101100001110010000011001100000110001100110011101010100101001101001100010
Pair \(Z_2\) Length of longest common subsequence
3FTD_1,6JPT_1 142 5
3FTD_1,5KTD_1 148 3
6JPT_1,5KTD_1 152 3

Newick tree

 
[
	5KTD_1:76.29,
	[
		3FTD_1:71,6JPT_1:71
	]:5.29
]

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 \((0.85)(0.8)(\frac{371 }{\log_{20} 371}-\frac{122}{\log_{20}122})=76.0\)
Status Protein1 Protein2 d d1/2
Query variables 3FTD_1 6JPT_1 91 68
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]