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Parikh vectors
4NFE_1 6KSN_1 2ZFZ_1 Letter Amino acid
6 3 2 N Asparagine
9 6 6 D Aspartic acid
9 9 2 Q Glutamine
9 2 0 W Tryptophan
4 5 1 F Phenylalanine
18 2 4 P Proline
6 10 1 Y Tyrosine
19 8 6 V Valine
10 3 0 C Cysteine
21 15 9 G Glycine
12 3 1 H Histidine
6 3 3 I Isoleucine
8 5 6 R Arginine
12 5 0 K Lycine
12 9 7 T Threonine
18 19 3 S Serine
14 12 12 A Alanine
14 5 3 E Glutamic acid
26 7 11 L Leucine
4 4 2 M Methionine 

4NFE_1|Chain A|Kallikrein-2|Homo sapiens (9606)
>6KSN_1|Chains A, B|ICab3|Camelus dromedarius (9838)
>2ZFZ_1|Chains A, B, C, D, E, F|Arginine repressor|Mycobacterium tuberculosis (83332)
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 \(w=f(c)\)
4NFE , Knot 107 237 0.82 40 162 227 
IVGGWECEKHSQPWQVAVYSHGWAHCGGVLVHPQWVLTAAHCLKKNSQVWLGRHNLFEPEDTGQRVPVSHSFPHPLYNMSLLKHQSLRPDEDSSHDLMLLRLSEPAKITDVVKVLGLPTQEPALGTTCYASGWGSIEPEEFLRPRSLQCVSLHLLSNDMCARAYSEKVTEFMLCAGLWTGGKDTCGGDSGGPLVCNGVLQGITSWGPEPCALPEKPAVYTKVVHYRKWIKDTIAANP
6KSN , Knot 65 135 0.78 40 103 127 
MDASQVQLEESGGGSVQAGGSLRLSCAASGYMYSTYSTYCMGWFRQAPGKEREGVAFIKRGDHSTYYTDSVKGRFTISQDSAKNTVSLQMNNLKPEDTAIYYCAADFAHSFLLSVHSGAGQYSYWGQGTQVTVSS
2ZFZ , Knot 41 79 0.75 34 62 77 
GGTDRMARLLGELLVSTDDSGNLAVLRTPPGAAHYLASAIDRAALPQVVGTIAGDDTILVVAREPTTGAQLAGMFENLR

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 \(c\).

\(|P_{f(4NFE_1)}(2) \setminus P_{f(6KSN_1)}(2)|=111\), \(|P_{f(6KSN_1)}(2) \setminus P_{f(4NFE_1)}(2)|=52\). 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 1:111110000000110111000111001111101011101100100000111100011010001001110001101100101100001010000000111101001101001101111100011110000101110101001101001001010110001010100001001110111101100001100111110011101100111010111001110001100001100011101
Pair \(Z_2\) Length of longest common subsequence
4NFE_1,6KSN_1 163 4
4NFE_1,2ZFZ_1 150 3
6KSN_1,2ZFZ_1 113 2

Newick tree

 
[
	4NFE_1:84.34,
	[
		2ZFZ_1:56.5,6KSN_1:56.5
	]:27.84
]

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 \((0.85)(0.8)(\frac{372 }{\log_{20} 372}-\frac{135}{\log_{20}135})=71.9\)
Status Protein1 Protein2 d d1/2
Query variables 4NFE_1 6KSN_1 90 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]