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Parikh vectors
8DZA_1 3WYM_1 2DCG_1 Letter Amino acid
16 21 0 A Alanine
7 13 0 H Histidine
29 36 0 L Leucine
13 14 0 P Proline
25 22 0 T Threonine
3 7 0 W Tryptophan
11 12 0 Y Tyrosine
11 14 0 R Arginine
9 24 0 E Glutamic acid
21 14 0 N Asparagine
12 11 3 C Cysteine
27 16 0 V Valine
16 22 0 S Serine
17 15 0 D Aspartic acid
14 17 0 Q Glutamine
26 15 3 G Glycine
11 20 0 I Isoleucine
11 18 0 K Lycine
10 12 0 M Methionine
17 15 0 F Phenylalanine 

8DZA_1|Chains A, B|3C-like proteinase nsp5|Severe acute respiratory syndrome coronavirus 2 (2697049)
>3WYM_1|Chains A, B|cAMP and cAMP-inhibited cGMP 3',5'-cyclic phosphodiesterase 10A|Homo sapiens (9606)
>2DCG_1|Chains A, B|DNA (5'-D(*CP*GP*CP*GP*CP*G)-3')|
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 \(w=f(c)\)
8DZA , Knot 134 306 0.83 40 196 288 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQTAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
3WYM , Knot 150 338 0.86 40 219 329 
TSEEWQGLMQFTLPVRLCKEIELFHFDIGPFENMWPGIFVYMVHRSCGTSCFELEKLCRFIMSVKKNYRRVPYHNWKHAVTVAHCMYAILQNNHTLFTDLERKGLLIACLCHDLDHRGFSNSYLQKFDHPLAALYSTSTMEQHHFSQTVSILQLEGHNIFSTLSSSEYEQVLEIIRKAIIATDLALYFGNRKQLEEMYQTGSLNLNNQSHRDRVIGLMMTACDLCSVTKLWPVTKLTANDIYAEFWAEGDEMKKLGIQPIPMMDRDKKDEVPQGQLGFYNAVAIPCYTTLTQILPPTEPLLKACRDNLSQWEKVIRGEETATWISSPSVAQKAAASED
2DCG , Knot 3 6 0.29 4 2 2 
CGCGCG

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 \(c\).

\(|P_{f(8DZA_1)}(2) \setminus P_{f(3WYM_1)}(2)|=83\), \(|P_{f(3WYM_1)}(2) \setminus P_{f(8DZA_1)}(2)|=106\). 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 1:011001111010101011010010001011110011001001100000110100001110000001110110101011100100011010100101001000110101100101110001010110001101010101011010010111010000101001001011011011001010101111000010011000010101111101111010011100100010010111100000110000101111101001111101010100110011010011101110001011011000011010
Pair \(Z_2\) Length of longest common subsequence
8DZA_1,3WYM_1 189 4
8DZA_1,2DCG_1 194 2
3WYM_1,2DCG_1 219 2

Newick tree

 
[
	2DCG_1:10.25,
	[
		8DZA_1:94.5,3WYM_1:94.5
	]:11.75
]

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 \((0.85)(0.8)(\frac{644 }{\log_{20} 644}-\frac{306}{\log_{20}306})=93.9\)
Status Protein1 Protein2 d d1/2
Query variables 8DZA_1 3WYM_1 124 115.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]