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Parikh vectors
7GHT_1 3GSX_1 1BBN_1 Letter Amino acid
14 17 7 Q Glutamine
26 20 3 G Glycine
17 18 6 D Aspartic acid
12 4 6 C Cysteine
7 13 5 H Histidine
11 23 9 R Arginine
9 21 12 E Glutamic acid
11 10 12 K Lycine
10 5 1 M Methionine
17 8 6 F Phenylalanine
24 23 15 T Threonine
11 14 2 Y Tyrosine
27 17 3 V Valine
21 2 4 N Asparagine
29 17 16 L Leucine
13 11 1 P Proline
16 14 8 S Serine
3 10 1 W Tryptophan
17 23 10 A Alanine
11 4 6 I Isoleucine 

7GHT_1|Chains A, B|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>3GSX_1|Chain A|HLA class I histocompatibility antigen, A-2 alpha chain|Homo sapiens (9606)
>1BBN_1|Chain A|INTERLEUKIN-4|Homo sapiens (9606)
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 \(w=f(c)\)
7GHT , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
3GSX , Knot 121 274 0.82 40 183 262 
GSHSMRYFFTSVSRPGRGEPRFIAVGYVDDTQFVRFDSDAASQRMEPRAPWIEQEGPEYWDGETRKVKAHSQTHRVDLGTLRGYYNQSEAGSHTVQRMYGCDVGSDWRFLRGYHQYAYDGKDYIALKEDLRSWTAADMAAQTTKHKWEAAHVAEQLRAYLEGTCVEWLRRYLENGKETLQRTDAPKTHMTHHAVSDHEATLRCWALSFYPAEITLTWQRDGEDQTQDTELVETRPAGDGTFQKWVAVVVPSGQEQRYTCHVQHEGLPKPLTLRW
1BBN , Knot 65 133 0.79 40 101 128 
EAEAHKCDITLQEIIKTLNSLTEQKTLCTELTVTDIFAASKDTTEKETFCRAATVLRQFYSHHEKDTRCLGATAQQFHRHKQLIRFLKRLDRNLWGLAGLNSCPVKEADQSTLENFLERLKTIMREKYSKCSS

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 \(c\).

\(|P_{f(7GHT_1)}(2) \setminus P_{f(3GSX_1)}(2)|=99\), \(|P_{f(3GSX_1)}(2) \setminus P_{f(7GHT_1)}(2)|=86\). 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
7GHT_1,3GSX_1 185 3
7GHT_1,1BBN_1 195 3
3GSX_1,1BBN_1 178 3

Newick tree

 
[
	7GHT_1:96.96,
	[
		3GSX_1:89,1BBN_1:89
	]:7.96
]

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 \((0.85)(0.8)(\frac{580 }{\log_{20} 580}-\frac{274}{\log_{20}274})=86.2\)
Status Protein1 Protein2 d d1/2
Query variables 7GHT_1 3GSX_1 113 107
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]