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Parikh vectors
4IPH_1 2KKE_1 6CCK_1 Letter Amino acid
6 3 19 A Alanine
11 4 8 I Isoleucine
5 2 9 M Methionine
0 0 1 W Tryptophan
2 2 2 Y Tyrosine
7 4 7 P Proline
9 3 9 S Serine
11 5 14 V Valine
7 6 8 R Arginine
9 2 6 N Asparagine
3 3 7 D Aspartic acid
2 1 9 H Histidine
14 5 15 L Leucine
7 4 10 E Glutamic acid
2 0 9 F Phenylalanine
2 0 0 C Cysteine
6 0 8 Q Glutamine
9 4 6 G Glycine
5 3 6 K Lycine
6 2 8 T Threonine 

4IPH_1|Chain A|Replication protein A 70 kDa DNA-binding subunit|Homo sapiens (9606)
>2KKE_1|Chains A, B|Uncharacterized protein|Methanothermobacter thermautotrophicus str. Delta H (187420)
>6CCK_1|Chains A, B|Phosphopantetheine adenylyltransferase|Escherichia coli (strain K12) (83333)
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 \(w=f(c)\)
4IPH , Knot 63 123 0.82 38 102 118 
GSHMVGQLSRGAIAAIMQKGDTNIKPILQVINIRPITTGNSPPRYRLLMSDGLNTLSSFMLATQLNPLVEEEQLSSNCVCQIHRFIVNTLKDGRRVVILMELEVLKSAEAVGVKIGNPVPYNE
2KKE , Knot 31 53 0.77 32 47 51 
MVGRRPGGGLKDTKPVVVRLYPDEIEALKSRVPANTSMSAYIRRIILNHLEDE
6CCK , Knot 79 161 0.83 38 124 156 
MQKRAIYPGTFDPITNGHIDIVTRATQMFDHVILAIAASPSKKPMFTLEERVALAQQATAHLGNVEVVGFSDLMANFARNQHATVLIRGLRAVADFEYEMQLAHMNRHLMPELESVFLMPSKEWSFISSSLVKEVARHQGDVTHFLPENVHQALMAKLAVD

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 \(c\).

\(|P_{f(4IPH_1)}(2) \setminus P_{f(2KKE_1)}(2)|=77\), \(|P_{f(2KKE_1)}(2) \setminus P_{f(4IPH_1)}(2)|=22\). 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 1:100111010011111110010001011101101011001001100011100110010011110010111000010000100100111001001001111101011001011110110111000
Pair \(Z_2\) Length of longest common subsequence
4IPH_1,2KKE_1 99 3
4IPH_1,6CCK_1 144 4
2KKE_1,6CCK_1 145 2

Newick tree

 
[
	6CCK_1:78.37,
	[
		4IPH_1:49.5,2KKE_1:49.5
	]:28.87
]

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 \((0.85)(0.8)(\frac{176 }{\log_{20} 176}-\frac{53}{\log_{20}53})=42.1\)
Status Protein1 Protein2 d d1/2
Query variables 4IPH_1 2KKE_1 52 36
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]