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Parikh vectors
7VFF_1 1CEC_1 1ZYH_1 Letter Amino acid
8 9 0 H Histidine
25 22 0 F Phenylalanine
52 15 0 S Serine
39 10 2 T Threonine
36 25 0 D Aspartic acid
24 33 0 E Glutamic acid
27 16 4 G Glycine
8 8 0 M Methionine
32 21 0 Y Tyrosine
4 5 3 C Cysteine
13 8 0 Q Glutamine
31 28 0 L Leucine
31 29 0 K Lycine
26 11 0 P Proline
49 15 0 V Valine
17 16 3 A Alanine
38 22 0 N Asparagine
51 26 0 I Isoleucine
2 8 0 W Tryptophan
18 16 0 R Arginine 

7VFF_1|Chains A, B, C|Scaffold protein D13|Vaccinia virus (strain Western Reserve) (10254)
>1CEC_1|Chain A|ENDOGLUCANASE CELC|Clostridium thermocellum (1515)
>1ZYH_1|Chain A|5'-D(*CP*AP*AP*CP*CP*AP*GP*GP*GP*TP*TP*G)-3'|null
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 \(w=f(c)\)
7VFF , Knot 214 531 0.84 40 245 496 
RSNVFAVDSQIPTLYMPQYISLSGVMTNDGPDNQAIASFEIRDQYITALNHLVLSLELPEVKGMGRFGYVPYVGYKCINHVSISSCNGVIWEIEGEELYNNCINNTIALKHSGYSSELNDISIGLTPNDTIKEPSTVYVYIKTPFDVEDTFSSLKLSDSKITVTVTFNPVSDIVIRDSSFDFETFNKEFVYVPELSFIGYMVKNVQIKPSFIEKPRRVIGQINQPTATVTEVHAATSLSVYTKPYYGNTDNKFISYPGYSQDEKDYIDAYVSRLLDDLVIVSDGPPTGYPESAEIVEVPEDGIVSIQDADVYVKIDNVPDNMSVYLHTNLLMFGTRKNSFIYNISKKFSAITGTYSDATKRTIFAHISHSINIIDTSIPVSLWTSQRNVYNGDNRSAESKAKDLFINDPFIKGIDFKNKTDIISRLEVRFGNDVLYSENGPISRIYNELLTKSNNGTRTLTFNFTPKIFFRPTTITANVSRGKDKLSVRVVYSTMDVNHPIYYVQKQLVVVCNDLYKVSYDQGVSITKIMG
1CEC , Knot 152 343 0.86 40 216 336 
MVSFKAGINLGGWISQYQVFSKEHFDTFITEKDIETIAEAGFDHVRLPFDYPIIESDDNVGEYKEDGLSYIDRCLEWCKKYNLGLVLDMHHAPGYRFQDFKTSTLFEDPNQQKRFVDIWRFLAKRYINEREHIAFELLNEVVEPDSTRWNKLMLECIKAIREIDSTMWLYIGGNNYNSPDELKNLADIDDDYIVYNFHFYNPFFFTHQKAHWSESAMAYNRTVKYPGQYEGIEEFVKNNPKYSFMMELNNLKLNKELLRKDLKPAIEFREKKKCKLYCGEFGVIAIADLESRIKWHEDYISLLEEYDIGGAVWNYKKMDFEIYNEDRKPVSQELVNILARRKT
1ZYH , Knot 6 12 0.41 8 9 10 
CAACCAGGGTTG

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 \(c\).

\(|P_{f(7VFF_1)}(2) \setminus P_{f(1CEC_1)}(2)|=96\), \(|P_{f(1CEC_1)}(2) \setminus P_{f(7VFF_1)}(2)|=67\). 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 1:000111100011010110010101110001100011101010000101100111010110101110110110110001001010000111101010010000100011100010000100101110100010010010101001101000100101000010101010110011100001010010001101101011101100101010110010011101001010100101100101000100100000110011000000001010100110011110011101010010110110011101001010101001100101010001111100000110010001011010000100001110100010110001110110000010010000100010011100111011010000011001010110011000011100100011000001000101010101110100101010010001010110001010011001000111100010010000110100111
Pair \(Z_2\) Length of longest common subsequence
7VFF_1,1CEC_1 163 4
7VFF_1,1ZYH_1 246 2
1CEC_1,1ZYH_1 221 2

Newick tree

 
[
	1ZYH_1:12.53,
	[
		7VFF_1:81.5,1CEC_1:81.5
	]:45.03
]

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 \((0.85)(0.8)(\frac{874 }{\log_{20} 874}-\frac{343}{\log_{20}343})=143.\)
Status Protein1 Protein2 d d1/2
Query variables 7VFF_1 1CEC_1 180 149.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]