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Parikh vectors
6JFF_1 2OLP_1 4KUA_1 Letter Amino acid
16 4 12 R Arginine
6 6 5 H Histidine
19 16 16 L Leucine
5 8 4 T Threonine
7 10 23 A Alanine
12 6 6 I Isoleucine
7 9 7 F Phenylalanine
2 2 3 C Cysteine
8 6 10 Q Glutamine
15 4 8 E Glutamic acid
16 11 14 G Glycine
13 4 9 P Proline
8 10 4 S Serine
3 4 7 Y Tyrosine
12 8 9 V Valine
1 9 5 N Asparagine
11 12 8 D Aspartic acid
2 11 4 K Lycine
4 9 6 M Methionine
1 2 2 W Tryptophan 

6JFF_1|Chains A, B|Peptide deformylase|Pseudomonas aeruginosa (287)
>2OLP_1|Chains A, B|Hemoglobin II|Lucina pectinata (244486)
>4KUA_1|Chain A|GNAT superfamily acetyltransferase PA4794|Pseudomonas aeruginosa (208964)
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 \(w=f(c)\)
6JFF , Knot 79 168 0.80 40 120 164 
IREILKMGDERLLRIAQPVPSELLGSEELQRLIDDMFETMHHVGGVGLAAPQIGVDLQLVIFGFERSERYPDAPAVPPTILLNPRITPLDDEMEEGWEGCLSVPGLRGAVSRHRRIRYQGLDPQGQPIDRSVEGFHARVVQHECDHLIGRLYPSRITDFSKFGFTEVL
2OLP , Knot 74 152 0.81 42 116 149 
XTTLTNPQKAAIRSSWSKFMDNGVSNGQGFYMDLFKAHPETLTPFKSLFGGLTLAQLQDNPKMKAQSLVFCNGMSSFVDHLDDNDMLVVLIQKMAKLHNNRGIRASDLRTAYDILIHYMEDHNHMVGGAKDAWEVFVGFICKTLGDYMKELS
4KUA , Knot 79 162 0.82 40 117 156 
GHMQLSHRPAETGDLETVAGFPQDRDELFYCYPKAIWPFSVAQLAAAIAERRGSTVAVHDGQVLGFANFYQWQHGDFCALGNMMVAPAARGLGVARYLIGVMENLAREQYKARLMKISCFNANAAGLLLYTQLGYQPRAIAERHDPDGRRVALIQMDKPLEP

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 \(c\).

\(|P_{f(6JFF_1)}(2) \setminus P_{f(2OLP_1)}(2)|=74\), \(|P_{f(2OLP_1)}(2) \setminus P_{f(6JFF_1)}(2)|=70\). 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 1:100110110001101101110011100010011001100100111111111011101011111100000010111111011101010110001001101010111101110000010001101010110001011010110000001110101001001001110011
Pair \(Z_2\) Length of longest common subsequence
6JFF_1,2OLP_1 144 3
6JFF_1,4KUA_1 137 3
2OLP_1,4KUA_1 167 3

Newick tree

 
[
	2OLP_1:80.87,
	[
		6JFF_1:68.5,4KUA_1:68.5
	]:12.37
]

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 \((0.85)(0.8)(\frac{320 }{\log_{20} 320}-\frac{152}{\log_{20}152})=51.3\)
Status Protein1 Protein2 d d1/2
Query variables 6JFF_1 2OLP_1 65 61.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]