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Parikh vectors
3NEF_1 3JCR_1 7LZK_1 Letter Amino acid
19 4 6 R Arginine
18 5 6 E Glutamic acid
16 8 13 L Leucine
17 6 8 V Valine
14 5 6 N Asparagine
12 3 11 D Aspartic acid
3 1 1 C Cysteine
16 1 7 T Threonine
4 0 4 Y Tyrosine
7 3 12 A Alanine
10 6 2 I Isoleucine
5 6 12 K Lycine
3 6 6 M Methionine
18 4 12 S Serine
2 0 1 W Tryptophan
9 3 7 Q Glutamine
8 7 9 G Glycine
7 2 2 H Histidine
8 3 10 F Phenylalanine
6 3 2 P Proline 

3NEF_1|Chains A, B|Abscisic acid receptor PYL1|Arabidopsis thaliana (3702)
>3JCR_14|Chains FA[auth U], N[auth u]|SmG|Homo sapiens (9606)
>7LZK_1|Chains A, B|Dehaloperoxidase B|Amphitrite ornata (129555)
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 \(w=f(c)\)
3NEF , Knot 97 202 0.85 40 146 194 
ISTLHHQTMPSDLTQDEFTQLSQSIAEFHTYQLGNGRCSSLLAQRIHAPPETVWSVVRRFDRPQIYKHFIKSCNVSEDFEMRVGCTRDVNVISGLPANTSRERLDLLDDDRRVTGFSITGGEHRLRNYKSVTTVHRFEKEEEEERIWTVVLESYVVDVPEGNSEEDTRLFADTVIRLNLQKLASITEAMNRNNNNNNSSQVR
3JCR , Knot 42 76 0.79 36 68 74 
MSKAHPPELKKFMDKKLSLKLNGGRHVQGILRGFDPFMNLVIDECVEMATSGQQNNIGMVVIRGNSIIMLEALERV
7LZK , Knot 68 137 0.81 40 105 134 
GFKQDIATLRGDLRTYAQDIFLAFLNKYPDEKRNFKNYVGKSDQELKSMAKFGDHTEKVFNLMMEVADRATDCVPLASDASTLVQMKQHSGLTTGNFEKLFVALVEYMRASGQSFDSQSWDRFGKNLVSALSSAGMK

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 \(c\).

\(|P_{f(3NEF_1)}(2) \setminus P_{f(3JCR_1)}(2)|=117\), \(|P_{f(3JCR_1)}(2) \setminus P_{f(3NEF_1)}(2)|=39\). 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 1:1001000011001000010010001101000011010000111001011100110110010010100011000010001010110000101101111000000101100000101101011000100000100100100000000110111000110110100000001110011010100110100110000000000010
Pair \(Z_2\) Length of longest common subsequence
3NEF_1,3JCR_1 156 3
3NEF_1,7LZK_1 165 3
3JCR_1,7LZK_1 127 3

Newick tree

 
[
	3NEF_1:85.14,
	[
		3JCR_1:63.5,7LZK_1:63.5
	]:21.64
]

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 \((0.85)(0.8)(\frac{278 }{\log_{20} 278}-\frac{76}{\log_{20}76})=64.8\)
Status Protein1 Protein2 d d1/2
Query variables 3NEF_1 3JCR_1 82 56
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]