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Parikh vectors
3OQQ_1 5NTI_1 7SPO_1 Letter Amino acid
18 17 9 R Arginine
25 6 19 N Asparagine
30 5 9 D Aspartic acid
34 24 7 E Glutamic acid
12 11 8 I Isoleucine
15 13 14 F Phenylalanine
24 21 16 S Serine
2 7 8 C Cysteine
36 11 16 G Glycine
27 13 11 K Lycine
8 2 2 W Tryptophan
4 13 7 H Histidine
39 34 13 L Leucine
9 6 0 M Methionine
37 9 13 T Threonine
42 16 16 V Valine
28 17 12 A Alanine
14 15 6 Q Glutamine
13 8 12 P Proline
18 9 15 Y Tyrosine 

3OQQ_1|Chain A|Putative lipoprotein|Bacteroides ovatus (411476)
>5NTI_1|Chains A, B, C, D|Nuclear receptor ROR-gamma|Homo sapiens (9606)
>7SPO_1|Chains A, B|Spike protein S1|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
3OQQ , Knot 180 435 0.83 40 227 411 
GNELEKGNDGSGTVDPVNASTLVNVYSDKSGSEASLLVGDVLVKDSRTLTLNVPAACEKVYMKYNTVSGTEATKEFALSPVSRGVDQSTGFNFETNRLASVTLALPEDAVQPTNETDQGYLFYHNTGVVMFEDGWPIQLDSWYDEDFNDVVFEYDLKVTECHSQQMMETVGGKEELLLTLDVRAVGGIYPTVLGVVLDGLKSEYVDRITASLILKGGQGTMTDLAKEELSTKNIVKVENKNWNWSNDTRKEPRFAILTVDKAQAEGTVITLDGLTSLMDNNQDMFQVTQGKVREGLPMLRAEVRLIGKEGLTGAERDAQLAAFRELILDTNRQNFFIKVNGGKEIHMRGYAPTSAYKAEYEALVAGDTTLDANVYYSNTKGSTWGVKLPVGTRHAYERVPFREAYPDFTKWVDSKGVSNQKWYENFVDEKTIRYW
5NTI , Knot 119 257 0.85 40 169 249 
GPYASLTEIEHLVQSVCKSYRETCQLRLEDLLRQRSNIFSREEVTGYQRKSMWEMWERCAHHLTEAIQYVVEFAKRLSGFMELCQNDQIVLLKAGAMEVVLVRMCRAYNADNRTVFFEGKYGGMELFRALGCSELISSIFDFSHSLSALHFSEDEIALYTALVLINAHRPGLQEKRKVEQLQYNLELAFHHHLSKTHRQSILAKLPPKGKLRSLCSQHVERLQIFQHLHPIVVQAAFPPLYKELFSTETESPVGLSK
7SPO , Knot 98 213 0.82 38 147 203 
ETGPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSTNKHHHHHH

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 \(c\).

\(|P_{f(3OQQ_1)}(2) \setminus P_{f(5NTI_1)}(2)|=124\), \(|P_{f(5NTI_1)}(2) \setminus P_{f(3OQQ_1)}(2)|=66\). 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 1:100100100101010110100110100000100101111011100000101011110001010000101001000111011001100001101000011010111100110100000010110000111110011110100100001001110001010000000110011100011101010111110101111110110000100101011101101010011000100001101000010100000001011110100101010110101100110000011010010100111110101011100110110001011110011100000011101011001010101100100100011111000101010000001001110111100010001110010101001100011000010001100001001
Pair \(Z_2\) Length of longest common subsequence
3OQQ_1,5NTI_1 190 3
3OQQ_1,7SPO_1 184 4
5NTI_1,7SPO_1 160 3

Newick tree

 
[
	3OQQ_1:97.60,
	[
		7SPO_1:80,5NTI_1:80
	]:17.60
]

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 \((0.85)(0.8)(\frac{692 }{\log_{20} 692}-\frac{257}{\log_{20}257})=121.\)
Status Protein1 Protein2 d d1/2
Query variables 3OQQ_1 5NTI_1 153 123
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]