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Parikh vectors
7FWX_1 5NPV_1 1DEI_1 Letter Amino acid
11 20 0 D Aspartic acid
9 22 2 E Glutamic acid
8 14 2 S Serine
2 10 2 Y Tyrosine
4 4 4 C Cysteine
12 11 1 G Glycine
5 10 0 M Methionine
2 7 0 W Tryptophan
15 11 1 V Valine
6 12 0 R Arginine
4 7 2 N Asparagine
1 12 0 H Histidine
8 18 2 I Isoleucine
14 20 0 K Lycine
5 15 0 F Phenylalanine
13 14 1 T Threonine
5 13 0 A Alanine
3 14 2 Q Glutamine
7 29 2 L Leucine
1 19 0 P Proline 

7FWX_1|Chain A|Fatty acid-binding protein, adipocyte|Homo sapiens (9606)
>5NPV_1|Chains A, C|Autophagy protein 5|Homo sapiens (9606)
>1DEI_1|Chains A, C|INSULIN|Sus scrofa (9823)
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 \(w=f(c)\)
7FWX , Knot 69 135 0.83 40 105 130 
GSHMCDAFVGTWKLVSSENFDDYMKELGVGFATRKMGGMAKPNCIISVNGDVITIKTESTLKNTEISFILGQEFDEVTADDRKVKSTITLDGGVLVQVQKWDGKSTTIKRKREDDKLVVECVMKGVTCTRVYERA
5NPV , Knot 127 282 0.84 40 194 275 
GAHMSGRMTDDKDVLRDVWFGRIPTCFTLYQDEITEREAEPYYLLLPRVSYLTLVTDKVKKHFQKVMRQEDISEIWFEYEGTPLKWHYPIGLLFDLLASSSALPWNITVHFKSFPEKDLLHCPSKDAIEAHFMSCMKEADALKHKSQVINEMQKKDHKQLWMGLQNDRFDQFWAINRKLMEYPAEENGFRYIPFRIYQTTTERPFIQKLFRPVAADGQLHTLGDLLKEVCPSAIDPEDGEKKNQVMIHGIEPMLETPLQWLSEHLSYPDNFLHISIIPQPTD
1DEI , Knot 15 21 0.72 22 20 19 
GIVEQCCTSICSLYQLENYCN

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 \(c\).

\(|P_{f(7FWX_1)}(2) \setminus P_{f(5NPV_1)}(2)|=49\), \(|P_{f(5NPV_1)}(2) \setminus P_{f(7FWX_1)}(2)|=138\). 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 1:100100111101011000010001001111110001111101001101010110100000100001011110010010100001000101011111010010100001000000001110011011000010001
Pair \(Z_2\) Length of longest common subsequence
7FWX_1,5NPV_1 187 3
7FWX_1,1DEI_1 119 2
5NPV_1,1DEI_1 200 3

Newick tree

 
[
	5NPV_1:10.37,
	[
		7FWX_1:59.5,1DEI_1:59.5
	]:46.87
]

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 \((0.85)(0.8)(\frac{417 }{\log_{20} 417}-\frac{135}{\log_{20}135})=84.7\)
Status Protein1 Protein2 d d1/2
Query variables 7FWX_1 5NPV_1 111 81
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]