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Parikh vectors
6TXV_1 2KSW_1 3HRO_1 Letter Amino acid
7 5 3 G Glycine
4 4 2 H Histidine
5 2 5 I Isoleucine
7 5 2 L Leucine
1 1 3 M Methionine
11 2 0 T Threonine
5 2 1 Y Tyrosine
10 2 5 S Serine
11 3 1 A Alanine
3 4 0 N Asparagine
5 2 2 D Aspartic acid
0 1 1 Q Glutamine
10 6 5 E Glutamic acid
5 1 1 F Phenylalanine
7 7 0 P Proline
2 0 0 W Tryptophan
12 6 7 V Valine
4 1 4 R Arginine
1 6 0 C Cysteine
6 6 2 K Lycine 

6TXV_1|Chains A, B|Transthyretin|Homo sapiens (9606)
>2KSW_1|Chain A|Oryctin|Oryctes rhinoceros (72550)
>3HRO_1|Chain A|Transient receptor potential (TRP) channel subfamily P member 2 (TRPP2), also called Polycystin-2 or polycystic kidney disease 2(PKD2)|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 \(w=f(c)\)
6TXV , Knot 61 116 0.83 38 93 114 
CPLMVKVLDAVRGSPTINVAVHVFRKAADDTWEPFASGKTSESGELHGLTTEEEFVEGIYKVEIDTKSYWKALGISPFHEHAEVVFTANDSGPRRYTIAALLSPYSYSTTAVVTNP
2KSW , Knot 37 66 0.78 38 58 64 
VPVGSDCEPKLCTMDLVPHCFLNPEKGIVVVHGGCALSKYKCQNPNHEKLGYTHECEEAIKNAPRP
3HRO , Knot 25 44 0.71 30 38 42 
GSHMGVSYEEFQVLVRRVDRMEHSIGSIVSKIDAVIVKLEIMER

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 \(c\).

\(|P_{f(6TXV_1)}(2) \setminus P_{f(2KSW_1)}(2)|=78\), \(|P_{f(2KSW_1)}(2) \setminus P_{f(6TXV_1)}(2)|=43\). 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 1:01111011011010101011101100110001011101000001010110000011011001010000010111101100010111010001100001111101000000111001
Pair \(Z_2\) Length of longest common subsequence
6TXV_1,2KSW_1 121 2
6TXV_1,3HRO_1 105 3
2KSW_1,3HRO_1 84 2

Newick tree

 
[
	6TXV_1:60.74,
	[
		3HRO_1:42,2KSW_1:42
	]:18.74
]

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 \((0.85)(0.8)(\frac{182 }{\log_{20} 182}-\frac{66}{\log_{20}66})=39.1\)
Status Protein1 Protein2 d d1/2
Query variables 6TXV_1 2KSW_1 51 40
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]