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Parikh vectors
8SIQ_1 6EFC_1 6BZE_1 Letter Amino acid
17 28 4 N Asparagine
8 0 2 C Cysteine
6 14 14 E Glutamic acid
16 11 2 G Glycine
11 12 1 P Proline
2 2 0 W Tryptophan
12 21 4 A Alanine
7 10 8 I Isoleucine
13 10 16 L Leucine
16 20 5 S Serine
15 12 2 Y Tyrosine
9 9 7 D Aspartic acid
7 0 3 H Histidine
14 3 2 F Phenylalanine
16 26 4 V Valine
9 17 10 R Arginine
6 9 3 Q Glutamine
10 9 13 K Lycine
0 1 0 M Methionine
11 20 6 T Threonine 

8SIQ_1|Chain A|Spike protein S1|Severe acute respiratory syndrome coronavirus 2 (2697049)
>6EFC_1|Chain A|Streptococcal hemagglutinin|Streptococcus gordonii str. Challis (29390)
>6BZE_1|Chains A, B, C, D, E, F, G, H|B-cell lymphoma/leukemia 10|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 \(w=f(c)\)
8SIQ , Knot 94 205 0.81 38 143 195 
TNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSGHHHHHH
6EFC , Knot 101 234 0.78 36 141 219 
LNTNQSVSARNQNARVRTRRAVAANDTEAPQVKSGDYVVYRGESFEYYAEITDNSGQVNRVVIRNVEGGANSTYLSPNWVKYSTENLGRPGNATVQNPLRTRIFGEVPLNEIVNEKSYYTRYIVAWDPSGNATQMVDNANRNGLERFVLTVKSQNEKYDPAESSVTYVNNLSNLSTSEREAVAAAVRAANPNIPPTAKITVSQNGTVTITYPDKSTDTIPANRVVKDLQISKSN
6BZE , Knot 52 106 0.76 36 83 104 
EEDLTEVKKDALENLRVYLCEKIIAERHFDHLRAKKILSREDTEEISCRTSSRKRAGKLLDYLQENPKGLDTLVESIRREKTQNFLIQKITDEVLKLRNIKLEHLK

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 \(c\).

\(|P_{f(8SIQ_1)}(2) \setminus P_{f(6EFC_1)}(2)|=75\), \(|P_{f(6EFC_1)}(2) \setminus P_{f(8SIQ_1)}(2)|=73\). 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 1:0010111011010011010110000100011000110001010010001101001001010010100111010010011110010110000011001010111100001000111000010011000010110001000100110010011011000111000110100111001001111010110111010110001000000
Pair \(Z_2\) Length of longest common subsequence
8SIQ_1,6EFC_1 148 4
8SIQ_1,6BZE_1 166 3
6EFC_1,6BZE_1 140 3

Newick tree

 
[
	8SIQ_1:81.30,
	[
		6EFC_1:70,6BZE_1:70
	]:11.30
]

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 \((0.85)(0.8)(\frac{439 }{\log_{20} 439}-\frac{205}{\log_{20}205})=68.5\)
Status Protein1 Protein2 d d1/2
Query variables 8SIQ_1 6EFC_1 86 80
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]