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Parikh vectors
8CFB_1 7PIN_1 3VZV_1 Letter Amino acid
30 7 4 D Aspartic acid
34 1 9 K Lycine
12 14 7 Y Tyrosine
17 12 4 R Arginine
18 6 4 Q Glutamine
41 30 5 G Glycine
31 28 4 I Isoleucine
11 25 3 F Phenylalanine
46 31 1 A Alanine
31 17 5 E Glutamic acid
15 11 3 M Methionine
16 14 3 P Proline
7 10 0 W Tryptophan
35 24 8 V Valine
8 5 1 C Cysteine
12 10 2 H Histidine
41 28 12 L Leucine
19 24 5 S Serine
27 16 5 T Threonine
21 23 2 N Asparagine 

8CFB_1|Chains A, B, C, D|Adenosylhomocysteinase|Pseudomonas aeruginosa PAO1 (208964)
>7PIN_1|Chains A, XB[auth A1], YA[auth a], Z[auth a1]|Photosystem II protein D1|Dunaliella salina (3046)
>3VZV_1|Chains A, B|E3 ubiquitin-protein ligase Mdm2|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 \(w=f(c)\)
8CFB , Knot 195 472 0.84 40 247 448 
SNAMSAVMTPAGFTDYKVADITLAAWGRRELIIAESEMPALMGLRRKYAGQQPLKGAKILGCIHMTIQTGVLIETLVALGAEVRWSSCNIFSTQDQAAAAIAAAGIPVFAWKGETEEEYEWCIEQTILKDGQPWDANMVLDDGGDLTEILHKKYPQMLERIHGITEETTTGVHRLLDMLKNGTLKVPAINVNDSVTKSKNDNKYGCRHSLNDAIKRGTDHLLSGKQALVIGYGDVGKGSSQSLRQEGMIVKVAEVDPICAMQACMDGFEVVSPYKNGINDGTEASIDAALLGKIDLIVTTTGNVNVCDANMLKALKKRAVVCNIGHFDNEIDTAFMRKNWAWEEVKPQVHKIHRTGKDGFDAHNDDYLILLAEGRLVNLGNATGHPSRIMDGSFANQVLAQIHLFEQKYADLPAAEKAKRLSVEVLPKKLDEEVALEMVKGFGGVVTQLTPKQAEYIGVSVEGPFKPDTYRY
7PIN , Knot 144 336 0.83 40 192 318 
ENTSLWARFCEWITSTENRLYIGWFGVIMIPTLLTAISVYIIAFIAAPPVDIDGIREPVSGSLLYGNNIITGAVVPTSNAIGLHFYPIWEAASLDEWLYNGGPYQLVVCHFFLGVCCYMGREWELSYRLGMRPWIAVAYSAPVAAATAVFIIYPIGQGSFSDGMPLGISGTFNFMIVFQAEHNILMHPFHMFGVAGVFGGSLFSAMHGSLVTSSLIRETTENESANAGYKFGQEEETYNIVAAHGYFGRLIFQYASFNNSRSLHFFLAVWPVVCIWLTALGISTMAFNLNGFNFNQSVVDSNGRVLNTWADIINRANLGMEVMHERNAHNFPLDLA
3VZV , Knot 47 87 0.80 38 74 83 
GSETLVRPKPELLKLLKSVGAQKDTYTMKEVLFYLGQYIMTKRLYDEKQQHIVYCSNDLLGDLFGVPSFSVKEHRKIYTMIYRNLVV

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 \(c\).

\(|P_{f(8CFB_1)}(2) \setminus P_{f(7PIN_1)}(2)|=118\), \(|P_{f(7PIN_1)}(2) \setminus P_{f(8CFB_1)}(2)|=63\). 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 1:0011011101111000011010111110001111000111111100001100110110111010101001111001111110101000011000001111111111111110100000001010001100101101011100110100110000101100101100000011001101100101011110100010000000001000010011001000110100111110101101000010001111011010110110101011011010001100100101011111010111000101010010110110001110011010001001110001110010101001000100110100000111110101101101010100110101100111010110000101111001001010111001000111011011111100101001001110101110100000
Pair \(Z_2\) Length of longest common subsequence
8CFB_1,7PIN_1 181 3
8CFB_1,3VZV_1 209 4
7PIN_1,3VZV_1 188 3

Newick tree

 
[
	3VZV_1:10.17,
	[
		8CFB_1:90.5,7PIN_1:90.5
	]:11.67
]

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 \((0.85)(0.8)(\frac{808 }{\log_{20} 808}-\frac{336}{\log_{20}336})=128.\)
Status Protein1 Protein2 d d1/2
Query variables 8CFB_1 7PIN_1 168 142
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]