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Parikh vectors
8WPT_1 6YLT_1 7SDG_1 Letter Amino acid
16 15 0 D Aspartic acid
0 4 6 C Cysteine
6 5 0 H Histidine
17 15 0 K Lycine
2 6 0 P Proline
9 11 0 S Serine
1 8 0 W Tryptophan
6 12 0 R Arginine
5 11 6 G Glycine
11 11 0 I Isoleucine
16 17 0 L Leucine
3 11 4 T Threonine
12 10 5 A Alanine
15 10 0 E Glutamic acid
11 6 0 Y Tyrosine
15 11 0 V Valine
10 11 0 N Asparagine
5 6 0 Q Glutamine
5 3 0 M Methionine
6 8 0 F Phenylalanine 

8WPT_1|Chain A|Truncated ferritin|Ureaplasma diversum (42094)
>6YLT_1|Chains A, B, C, D|Eukaryotic translation initiation factor 4E|Mus musculus (10090)
>7SDG_1|Chain A|DNA (5'-D(*GP*AP*GP*CP*AP*GP*CP*CP*TP*GP*TP*CP*TP*GP*GP*AP*CP*AP*TP*CP*A)-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 \(w=f(c)\)
8WPT , Knot 80 171 0.80 38 121 164 
MLYRERNNIMQKSNKINDALNQHYKLNVELGLVYAHYAHVADDEFDMPYLGKFIQHLSEDKLGVHKEYISDYFKRNGMKLKTDVSVAVKSIPSDAKALIQEVYARENEVRDHVKAIAKLALAEDDYESFYFIQWYVRDGLKDLTEVDDVVKLFNSSNDKLIIEETIKEMVE
6YLT , Knot 95 191 0.87 40 153 187 
MVANPEHYIKHPLQNRWALWFFKNDKSKTWQANLRLISKFDTVEDFWALYNHIQLSSNLMPGCDYSLFKDGIEPMWEDEKNKRGGRWLITLNKQQRRSDLDRFWLETLLCLIGESFDDYSDDVCGAVVNVRAKGDKIAIWTTECENRDAVTHIGRVYKERLGLPPKIVIGYQSHADTATKSGSTTKNRFVV
7SDG , Knot 10 21 0.48 8 12 17 
GAGCAGCCTGTCTGGACATCA

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 \(c\).

\(|P_{f(8WPT_1)}(2) \setminus P_{f(6YLT_1)}(2)|=63\), \(|P_{f(6YLT_1)}(2) \setminus P_{f(8WPT_1)}(2)|=95\). 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 1:110000001100000100110000010101111010010110001011011011001000011100001000100011010001011100110010111001010000100010111011110000001011010100110010010011011000000111000100110
Pair \(Z_2\) Length of longest common subsequence
8WPT_1,6YLT_1 158 3
8WPT_1,7SDG_1 133 1
6YLT_1,7SDG_1 157 2

Newick tree

 
[
	6YLT_1:82.43,
	[
		8WPT_1:66.5,7SDG_1:66.5
	]:15.93
]

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 \((0.85)(0.8)(\frac{362 }{\log_{20} 362}-\frac{171}{\log_{20}171})=57.4\)
Status Protein1 Protein2 d d1/2
Query variables 8WPT_1 6YLT_1 75 69.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]