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Parikh vectors
4FZN_1 2JQV_1 8BYX_1 Letter Amino acid
12 1 0 Q Glutamine
18 5 0 I Isoleucine
19 7 0 P Proline
4 4 0 M Methionine
11 5 0 F Phenylalanine
23 14 0 S Serine
23 8 2 A Alanine
13 7 0 R Arginine
14 12 0 D Aspartic acid
10 15 0 E Glutamic acid
28 11 4 G Glycine
9 7 0 Y Tyrosine
19 10 0 N Asparagine
10 4 0 H Histidine
26 9 0 L Leucine
18 7 10 T Threonine
2 1 2 C Cysteine
5 11 0 K Lycine
3 4 0 W Tryptophan
16 23 0 V Valine 

4FZN_1|Chain A|Bacteriocin|Pseudomonas syringae pv. tomato (223283)
>2JQV_1|Chain A|AIG2 protein-like|Arabidopsis thaliana (3702)
>8BYX_1|Chains A[auth C], D, G[auth H]|DNA|Homo sapiens (9606)
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 \(w=f(c)\)
4FZN , Knot 126 283 0.83 40 174 275 
PIELPPTYITPYPEISAGGNGTYRGQDLSSGQSFPRGMQNPVATVLLLQGDLYCSPNCLATFQDQARRDSFGIQSKVALKTFAAADQREAEGRDLRTAYNEIATDIGRSQQINENIIKYPPGNHVLSGGLMTPFHALAHGMFGLGAPLTFPIQNVGLNVDIRGIPDVMNVIQSARPVGTSSLDVNFAYDVGKDSNASWLTLGNITLRLVGTIDKNASGAWTFSGEIRAFNAVYDANPSNHRGWLGENLTSLLSAVPFTSYSIEIPGSLPVTVSGNLEHHHHHH
2JQV , Knot 81 165 0.83 40 126 158 
STSSDPQSHNVFVYGSILEPAVAAVILDRTADTVPAVLHGYHRYKLKGLPYPCIVSSDSGKVNGKVITGVSDAELNNFDVIEGNDYERVTVEVVRMDNSEKVKVETYVWVNKDDPRMYGEWDFEEWRVVHAEKFVETFRKMLEWNKNPNGKSMEEAVGSLLSSGD
8BYX , Knot 8 18 0.42 8 8 12 
GTTGTATTTTATTGGTCC

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 \(c\).

\(|P_{f(4FZN_1)}(2) \setminus P_{f(2JQV_1)}(2)|=115\), \(|P_{f(2JQV_1)}(2) \setminus P_{f(4FZN_1)}(2)|=67\). 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 1:1101110010101010111010001001001001101100111011110101000100110100010000111000111001111000010100100100011001100001000110011100110111101101110111111111011100111010101110110110010111000101011001100001011011010101110100010111010101011011001010000111100100110111100001011101110101010000000
Pair \(Z_2\) Length of longest common subsequence
4FZN_1,2JQV_1 182 4
4FZN_1,8BYX_1 174 2
2JQV_1,8BYX_1 130 2

Newick tree

 
[
	4FZN_1:95.69,
	[
		8BYX_1:65,2JQV_1:65
	]:30.69
]

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 \((0.85)(0.8)(\frac{448 }{\log_{20} 448}-\frac{165}{\log_{20}165})=83.6\)
Status Protein1 Protein2 d d1/2
Query variables 4FZN_1 2JQV_1 111 86
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]