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Parikh vectors
6TXV_1 5GGV_1 4GUG_1 Letter Amino acid
11 13 33 A Alanine
4 6 12 R Arginine
10 34 15 S Serine
1 1 10 M Methionine
5 9 9 F Phenylalanine
5 11 5 Y Tyrosine
12 14 25 V Valine
5 10 18 D Aspartic acid
5 7 18 I Isoleucine
7 15 23 L Leucine
6 13 14 K Lycine
10 9 17 E Glutamic acid
7 12 18 G Glycine
4 2 12 H Histidine
7 12 7 P Proline
11 18 23 T Threonine
2 2 1 W Tryptophan
3 6 6 N Asparagine
1 5 0 C Cysteine
0 15 10 Q Glutamine 

6TXV_1|Chains A, B|Transthyretin|Homo sapiens (9606)
>5GGV_1|Chain A[auth L]|light chain|Homo sapiens (9606)
>4GUG_1|Chains A, B|3-dehydroquinate dehydratase|Salmonella enterica subsp. enterica serovar Typhimurium (99287)
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
5GGV , Knot 99 214 0.82 40 149 200 
DIQMTQSPSSLSASVGDRVTITCRASQSINSYLDWYQQKPGKAPKLLIYAASSLQSGVPSRFSGSGSGTDFTLTISSLQPEDFATYYCQQYYSTPFTFGPGTKVEIKRTVAAPSVFIFPPSDEQLKSGTASVVCLLNNFYPREAKVQWKVDNALQSGNSQESVTEQDSKDSTYSLSSTLTLSKADYEKHKVYACEVTHQGLSSPVTKSFNRGEC
4GUG , Knot 118 276 0.80 38 169 263 
MHHHHHHSSGVDLGTENLYFQSNAMKTVTVRDLVVGEGAPKIIVSLMGKTITDVKSEALAYREADFDILEWRVDHFANVTTAESVLEAAGAIREIITDKPLLFTFRSAKAGGEQALTTGQYIDLNRAAVDSGLVDMIDLELFTGDDEVKATVGYAHQHNVAVIMSNHDFHKTPAAEEIVQRLRKMQELGADIPKIAVMPQTKADVLTLLTATVEMQERYADRPIITMSMSKTGVISRLAGEVFGSAATFGAVKKASAPGQISVADLRTVLTILHQA

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 \(c\).

\(|P_{f(6TXV_1)}(2) \setminus P_{f(5GGV_1)}(2)|=50\), \(|P_{f(5GGV_1)}(2) \setminus P_{f(6TXV_1)}(2)|=106\). 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_1,5GGV_1 156 4
6TXV_1,4GUG_1 156 4
5GGV_1,4GUG_1 172 3

Newick tree

 
[
	4GUG_1:83.41,
	[
		6TXV_1:78,5GGV_1:78
	]:5.41
]

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 \((0.85)(0.8)(\frac{330 }{\log_{20} 330}-\frac{116}{\log_{20}116})=66.2\)
Status Protein1 Protein2 d d1/2
Query variables 6TXV_1 5GGV_1 87 65.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]