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Parikh vectors
5YBP_1 7LRS_1 6BVC_1 Letter Amino acid
17 8 10 I Isoleucine
13 17 4 N Asparagine
15 9 13 D Aspartic acid
14 0 4 M Methionine
18 14 6 F Phenylalanine
3 15 9 Y Tyrosine
8 8 1 C Cysteine
17 1 4 H Histidine
22 6 8 E Glutamic acid
23 15 14 G Glycine
22 11 7 P Proline
25 15 12 S Serine
13 11 9 T Threonine
4 2 0 W Tryptophan
22 12 20 A Alanine
13 6 9 Q Glutamine
8 8 7 K Lycine
19 16 11 V Valine
21 9 11 R Arginine
17 13 18 L Leucine 

5YBP_1|Chains A, B|PrhA|Penicillium brasilianum (104259)
>7LRS_1|Chain A[auth C]|Spike glycoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
>6BVC_1|Chain A|Aminoglycoside-(3)-N-acetyltransferase|Serratia marcescens (615)
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 \(w=f(c)\)
5YBP , Knot 142 314 0.86 40 202 303 
MGSSHHHHHHSSGLVPRGSHMPPRLQRFPATASADEIFAAFQEDGCVVIEGFISPEQVARFSQEVDPAMEKIPVEVTNNGNSNDRTKRFSKCVIASPTFRNEIIESDLMHELCDRVFSKPGEGMGYHFNDNMVIEVQPGAPAQRLHRDQELYPWWNSMGPAGPECLINFFCAVTPFTEENGATRLVPGSHLWPEFTQINERDCPQFGKIETVPAIMQPGDCYLMSGKVIHGAGHNATTTDRRRALALSIIRRELRPMQAFSLSVPMKLAREMSERSQTMFGFRSSVQHCDVDMVHFWGNDGKDIAHHLGLISSA
7LRS , Knot 92 196 0.82 38 139 189 
ITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGP
6BVC , Knot 83 177 0.81 38 122 168 
MLRSSNDVTQQGSRPKTKLGGSSMGIIRTCRLGPDQVKSMRAALDLFGREFGDVATYSQHQPDSDYLGNLLRSKTFIALAAFDQEAVVGALAAYVLPKFEQPRSEIYIYDLAVSGEHRRQGIATALINLLKHEANALGAYVIYVQADYGDDPAVALYTKLGIREEVMHFDIDPSTAT

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 \(c\).

\(|P_{f(5YBP_1)}(2) \setminus P_{f(7LRS_1)}(2)|=118\), \(|P_{f(7LRS_1)}(2) \setminus P_{f(5YBP_1)}(2)|=55\). 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 1:11000000000011110100111010011101010011111000101110111010011010001011100111010001000000001000111010100011000110010001100110111001000111010111110010000010111001111110011011011011000011001111001110100100000101101001111101100011010110111001000000011110110001011011010111011001000000111100010000101101110010011001111001
Pair \(Z_2\) Length of longest common subsequence
5YBP_1,7LRS_1 173 4
5YBP_1,6BVC_1 178 3
7LRS_1,6BVC_1 159 3

Newick tree

 
[
	5YBP_1:90.34,
	[
		7LRS_1:79.5,6BVC_1:79.5
	]:10.84
]

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 \((0.85)(0.8)(\frac{510 }{\log_{20} 510}-\frac{196}{\log_{20}196})=90.9\)
Status Protein1 Protein2 d d1/2
Query variables 5YBP_1 7LRS_1 117 94
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]