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Parikh vectors
9CYL_1 7GHP_1 3SEA_1 Letter Amino acid
9 11 13 K Lycine
12 24 9 T Threonine
8 11 7 Y Tyrosine
16 17 8 D Aspartic acid
15 9 13 E Glutamic acid
5 7 3 H Histidine
11 11 17 I Isoleucine
2 10 3 M Methionine
2 12 0 C Cysteine
7 14 9 Q Glutamine
16 29 13 L Leucine
15 13 3 P Proline
13 16 15 S Serine
16 27 15 V Valine
3 11 5 R Arginine
9 21 6 N Asparagine
12 17 7 F Phenylalanine
4 3 1 W Tryptophan
8 17 10 A Alanine
12 26 10 G Glycine 

9CYL_1|Chain A|H-2 class II histocompatibility antigen, A-B alpha chain|Mus musculus (10090)
>7GHP_1|Chains A, B|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>3SEA_1|Chains A, B|GTP-binding protein Rheb|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 \(w=f(c)\)
9CYL , Knot 96 195 0.86 40 148 191 
EDDIEADHVGTYGISVYQSPGDIGQYTFEFDGDELFYVDLDKKETVWMLPEFGQLASFDPQGGLQNIAVVKHNLGVLTKRSNSTPATNEAPQATVFPKSPVLLGQPNTLICFVDNIFPPVINITWLRNSKSVADGVYETSFFVNRDYSFHKLSYLTFIPSDDDIYDCKVEHWGLEEPVLKHWEPEIPAPMSELTE
7GHP , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
3SEA , Knot 79 167 0.80 38 126 162 
QSKSRKIAILGYRSVGKSSLTIQFVEGQFVDSADPTIENTFTKLITVNGQEYHLQLVDTAGQDEYSIFPQTYSIDINGYILVYSVTSIKSFEVIKVIHGKLLDMVGKVQIPIMLVGNKKDLHMERVISYEEGKALAESWNAAFLESSAKENQTAVDVFRRIILEAEK

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 \(c\).

\(|P_{f(9CYL_1)}(2) \setminus P_{f(7GHP_1)}(2)|=66\), \(|P_{f(7GHP_1)}(2) \setminus P_{f(9CYL_1)}(2)|=114\). 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 1:000101001100110100011011000101010011010100000111110110110101011100111100011110000000110001101011100111110100110110011111101011000001101100001110000010010010111000010000100111001110010101111100100
Pair \(Z_2\) Length of longest common subsequence
9CYL_1,7GHP_1 180 3
9CYL_1,3SEA_1 162 3
7GHP_1,3SEA_1 182 4

Newick tree

 
[
	7GHP_1:93.45,
	[
		9CYL_1:81,3SEA_1:81
	]:12.45
]

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 \((0.85)(0.8)(\frac{501 }{\log_{20} 501}-\frac{195}{\log_{20}195})=88.8\)
Status Protein1 Protein2 d d1/2
Query variables 9CYL_1 7GHP_1 109 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]