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Parikh vectors
7GJV_1 7CZD_1 8QGM_1 Letter Amino acid
12 2 1 C Cysteine
9 4 19 E Glutamic acid
29 9 22 L Leucine
10 2 8 M Methionine
3 3 2 W Tryptophan
14 7 6 Q Glutamine
7 0 17 H Histidine
17 3 15 F Phenylalanine
17 7 15 A Alanine
11 6 17 K Lycine
13 3 10 P Proline
16 18 20 S Serine
27 7 19 V Valine
11 5 13 R Arginine
21 4 7 N Asparagine
17 6 18 D Aspartic acid
26 13 20 G Glycine
11 2 19 I Isoleucine
24 7 12 T Threonine
11 8 12 Y Tyrosine 

7GJV_1|Chains A, B|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>7CZD_1|Chains A, C|anti-PD-L1 VHH|Lama glama (9844)
>8QGM_1|Chain A|NAD kinase 1|Listeria monocytogenes EGD-e (169963)
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 \(w=f(c)\)
7GJV , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
7CZD , Knot 55 116 0.75 38 87 112 
EVQLQESGGGLVQPGGSLRLSCAASGFTFSSYWMYWLRQAPGKGLEWVSSINSDSSSTYYRDSVKGRFTISRDNAKNTLYLQMNSLKSEDTAVYYCAKDPGGYAKGQGTQVTVSSD
8QGM , Knot 123 272 0.84 40 185 261 
MKYMITSKGDEKSDLLRLNMIAGFGEYDMEYDDVEPEIVISIGGDGTFLSAFHQYEERLDEIAFIGIHTGHLGFYADWRPAEADKLVKLLAKGEYQKVSYPLLKTTVKYGIGKKEATYLALNESTVKSSGGPFVVDVVINDIHFERFRGDGLCMSTPSGTTAYNKSLGGALMHPSIEAMQLTEMASINNRVYRTIGSPLVFPKHHVVSLQPVNDKDFQISVDHLSILHRDVQEIRYEVSAKKIHFARFRSFPFWRRVHDSFIEDLEHHHHHH

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 \(c\).

\(|P_{f(7GJV_1)}(2) \setminus P_{f(7CZD_1)}(2)|=145\), \(|P_{f(7CZD_1)}(2) \setminus P_{f(7GJV_1)}(2)|=36\). 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 1:011001111010101011010010001011110011001001100000110100001110000001110110101011100100011010100101001000110101100101110001010110001101010101011010010111010000101001001011011011001010101111000010111000010101111101111010011100100010010111100000110000101111101001111101010100110011010011101110001011011000011010
Pair \(Z_2\) Length of longest common subsequence
7GJV_1,7CZD_1 181 3
7GJV_1,8QGM_1 171 4
7CZD_1,8QGM_1 174 3

Newick tree

 
[
	7CZD_1:89.82,
	[
		7GJV_1:85.5,8QGM_1:85.5
	]:4.32
]

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 \((0.85)(0.8)(\frac{422 }{\log_{20} 422}-\frac{116}{\log_{20}116})=92.4\)
Status Protein1 Protein2 d d1/2
Query variables 7GJV_1 7CZD_1 119 80.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]