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Parikh vectors
8AWL_1 9LAE_1 7RNS_1 Letter Amino acid
14 13 6 T Threonine
6 2 2 W Tryptophan
24 20 6 V Valine
7 7 4 Q Glutamine
1 0 4 M Methionine
5 9 4 I Isoleucine
10 13 3 P Proline
33 17 9 S Serine
8 21 9 N Asparagine
4 9 0 C Cysteine
13 12 4 A Alanine
7 9 10 D Aspartic acid
21 15 9 G Glycine
7 1 3 H Histidine
16 14 12 L Leucine
12 12 9 K Lycine
8 16 4 F Phenylalanine
10 15 7 Y Tyrosine
7 11 6 R Arginine
6 7 6 E Glutamic acid 

8AWL_1|Chain A[auth H]|Heavy chain Fab268|Homo sapiens (9606)
>9LAE_1|Chain A[auth G]|Spike protein S1|Severe acute respiratory syndrome coronavirus 2 (2697049)
>7RNS_1|Chain A|Isoform 2 of Phosphatidylinositol 3-kinase regulatory subunit alpha|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 \(w=f(c)\)
8AWL , Knot 100 219 0.82 40 145 208 
QVHLVESGGGVVQPGKSLRLSCAASGFIFNHFGIHWVRQSPGKGLEWVAVIWYDGSKKYFADSVKGRFSISRDNSQNTVYLQMNSLRTEDTAVYYCARERWSGHSYLDYWGHGALVTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVE
9LAE , Knot 103 223 0.83 38 153 214 
RVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNF
7RNS , Knot 62 117 0.84 38 96 115 
GSMGMNNNMSLQDAEWYWGDISREEVNEKLRDTADGTFLVRDASTKMHGDYTLTLRKGGNNKLIKIFHRDGKYGFSDPLTFSSVVELINHYRNESLAQYNPKLDVKLLYPVSKYQQD

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 \(c\).

\(|P_{f(8AWL_1)}(2) \setminus P_{f(9LAE_1)}(2)|=75\), \(|P_{f(9LAE_1)}(2) \setminus P_{f(8AWL_1)}(2)|=83\). 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 1:010110011111011001010011011110011101100011011011111100100001100101010100000000101010010000011000100010100010011011110100100011011111100000011011110110001101101010011100110011111000110010011011000110000100100010000100010
Pair \(Z_2\) Length of longest common subsequence
8AWL_1,9LAE_1 158 3
8AWL_1,7RNS_1 143 4
9LAE_1,7RNS_1 163 3

Newick tree

 
[
	9LAE_1:82.97,
	[
		8AWL_1:71.5,7RNS_1:71.5
	]:11.47
]

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 \((0.85)(0.8)(\frac{442 }{\log_{20} 442}-\frac{219}{\log_{20}219})=65.0\)
Status Protein1 Protein2 d d1/2
Query variables 8AWL_1 9LAE_1 83 81.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]