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Parikh vectors
7SOV_1 8ZIZ_1 6NEY_1 Letter Amino acid
6 15 5 F Phenylalanine
1 4 0 W Tryptophan
3 3 7 Y Tyrosine
8 7 12 R Arginine
1 21 6 N Asparagine
8 14 14 E Glutamic acid
7 8 1 H Histidine
5 21 5 P Proline
7 14 5 S Serine
7 13 3 I Isoleucine
10 28 14 L Leucine
3 22 5 T Threonine
6 15 9 V Valine
2 1 3 M Methionine
5 14 14 A Alanine
8 17 7 D Aspartic acid
0 13 3 C Cysteine
3 12 4 Q Glutamine
2 22 6 G Glycine
7 12 8 K Lycine 

7SOV_1|Chain A|Isoform 2 of La-related protein 1|Homo sapiens (9606)
>8ZIZ_1|Chain A|Enteropeptidase non-catalytic heavy chain|Homo sapiens (9606)
>6NEY_1|Chain A|Uncharacterized protein|Trypanosoma cruzi (5693)
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 \(w=f(c)\)
7SOV , Knot 49 99 0.75 38 83 93 
MGSSHHHHHHSQELLKDYIKRQIEYYFSVDNLERDFFLRRKMDADGFLPITLIASFHRVQALTTDISLIFAALKDSKVVEIVDEKVRRREEPEKWPLPP
8ZIZ , Knot 122 276 0.82 40 174 263 
EPTLVPTPPPELPTDCGGPFELWEPNTTFSSTNFPNSYPNLAFCVWILNAQKGKNIQLHFQEFDLENINDVVEIRDGEEADSLLLAVYTGPGPVKDVFSTTNRMTVLLITADVLARGGFKANFTTGYHLGIPEPCKADHFQCKNGECVPLVNLCDGHLHCEDGSDEADCVRFFNGTTNNNGLVRFRIQSIWHTACAENWTTQISNDVCQLLGLGSGNSSKPIFPTDGGPFVKLNTAPDGHLILTPSQQCLQDSLIRLQCNHKSCGKKLAAQDITPK
6NEY , Knot 66 131 0.81 38 106 129 
GMEERRQKFYPEEELVALVRSLDRPQDEGLFSMDVLVVYPHLEQEYTRVCPKRCDLATAAEKAANEAYSYDVNLTALREDIKLMVNNCYRFNGTKGPLANIAERFEAFAKEQIDAYVTKKAGGRRLSSLRL

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 \(c\).

\(|P_{f(7SOV_1)}(2) \setminus P_{f(8ZIZ_1)}(2)|=42\), \(|P_{f(8ZIZ_1)}(2) \setminus P_{f(7SOV_1)}(2)|=133\). 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 1:110000000000011000100010001010010001110001010111110111010010110001011111100001101100010000010011111
Pair \(Z_2\) Length of longest common subsequence
7SOV_1,8ZIZ_1 175 4
7SOV_1,6NEY_1 125 2
8ZIZ_1,6NEY_1 172 4

Newick tree

 
[
	8ZIZ_1:93.44,
	[
		7SOV_1:62.5,6NEY_1:62.5
	]:30.94
]

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 \((0.85)(0.8)(\frac{375 }{\log_{20} 375}-\frac{99}{\log_{20}99})=84.9\)
Status Protein1 Protein2 d d1/2
Query variables 7SOV_1 8ZIZ_1 106 72
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]