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Parikh vectors
7FGK_1 6ODF_1 1OOC_1 Letter Amino acid
23 36 31 T Threonine
6 20 11 E Glutamic acid
2 14 9 H Histidine
12 29 9 P Proline
34 36 35 S Serine
5 16 2 C Cysteine
15 22 16 L Leucine
11 25 19 K Lycine
1 4 4 M Methionine
5 6 4 W Tryptophan
7 19 29 D Aspartic acid
18 30 36 G Glycine
6 26 32 I Isoleucine
5 19 14 F Phenylalanine
11 20 14 Y Tyrosine
21 38 23 V Valine
16 41 28 A Alanine
5 11 8 R Arginine
6 16 26 N Asparagine
10 13 11 Q Glutamine 

7FGK_1|Chain A[auth H]|Fab Heavy Chain|Mus musculus (10090)
>6ODF_1|Chains A, C, E, G|E1|Eastern equine encephalitis virus (11021)
>1OOC_1|Chains A, B|Pectate lyase A|Erwinia chrysanthemi (556)
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 \(w=f(c)\)
7FGK , Knot 98 219 0.80 40 140 201 
QVQLQQSGAALVRPGTSVKVSCRASEYAFTNYVIEWVKQRPGQGLEWIGVINPGSGGTNYNEKFKGKATLIADKSSSTAYMQLSSLTSDDSAVYFCARSTYYSGALDYWGQGTSVTVSSAKTTAPSVYPLAPVCGDTTGSSVTLGCLVKGYFPEPVTLTWNSGSLSSGVHTFPAVLQSDLYTLSSSVTVTSSTWPSQSITCNVAHPASSTKVDKKIEPR
6ODF , Knot 186 441 0.85 40 229 415 
YEHTAVMPNKVGIPYKALVERPGYAPVHLQIQLVNTRIIPSTNLEYITCKYKTKVPSPVVKCCGATQCTSKPHPDYQCQVFTGVYPFMWGGAYCFCDTENTQMSEAYVERSEECSIDHAKAYKVHTGTVQAMVNITYGSVSWRSADVYVNGETPAKIGDAKLIIGPLSSAWSPFDNKVVVYGHEVYNYDFPEYGTGKAGSFGDLQSRTSTSNDLYANTNLKLQRPQAGIVHTPFTQAPSGFERWKRDKGAPLNDVAPFGCSIALEPLRAENCAVGSIPISIDIPDAAFTRISETPTVSDLECKITECTYASDFGGIATVAYKSSKAGNCPIHSPSGVAVIKENDVTLAESGSFTFHFSTANIHPAFKLQVCTSAVTCKGDCKPPKDHIVDYPAQHTESFTSAISATAWSWLKVLVGGTSAFIVLGLIATAVVALVLFFHRH
1OOC , Knot 149 361 0.81 40 193 336 
AELVSDKALESAPTVGWASQNGFTTGGAAATSDNIYIVTNISEFTSALSAGAEAKIIQIKGTIDISGGTPYTDFADQKARSQINIPANTTVIGLGTDAKFINGSLIIDGTDGTNNVIIRNVYIQTPIDVEPHYEKGDGWNAEWDAMNITNGAHHVWIDHVTISDGNFTDDMYTTKDGETYVQHDGALDIKRGSDYVTISNSLIDQHDKTMLIGHSDSNGSQDKGKLHVTLFNNVFNRVTERAPRVRYGSIHSFNNVFKGDAKDPVYRYQYSFGIGTSGSVLSEGNSFTIANLSASKACKVVKKFNGSIFSDNGSVLNGSAVDLSGCGFSAYTSKIPYIYDVQPMTTELAQSITDNAGSGKL

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 \(c\).

\(|P_{f(7FGK_1)}(2) \setminus P_{f(6ODF_1)}(2)|=41\), \(|P_{f(6ODF_1)}(2) \setminus P_{f(7FGK_1)}(2)|=130\). 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 1:010100011111011001010001000110001101100011011011111011011000000101010111000000101010010000011010100000011100110100101001000110101111101000100101101101011011010100101001100111110001001000101000011000100011011000010001010
Pair \(Z_2\) Length of longest common subsequence
7FGK_1,6ODF_1 171 3
7FGK_1,1OOC_1 161 4
6ODF_1,1OOC_1 168 4

Newick tree

 
[
	6ODF_1:86.12,
	[
		7FGK_1:80.5,1OOC_1:80.5
	]:5.62
]

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 \((0.85)(0.8)(\frac{660 }{\log_{20} 660}-\frac{219}{\log_{20}219})=124.\)
Status Protein1 Protein2 d d1/2
Query variables 7FGK_1 6ODF_1 160 116
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]