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Parikh vectors
9LSL_1 4WOR_1 4LVZ_1 Letter Amino acid
10 9 0 V Valine
16 5 0 R Arginine
17 6 0 N Asparagine
17 8 0 D Aspartic acid
27 14 23 A Alanine
22 6 0 Q Glutamine
9 4 0 M Methionine
16 3 0 F Phenylalanine
9 6 0 P Proline
16 5 0 S Serine
12 4 0 H Histidine
23 5 0 I Isoleucine
21 23 0 K Lycine
43 11 0 L Leucine
16 10 0 T Threonine
4 1 0 W Tryptophan
7 7 0 Y Tyrosine
9 0 17 C Cysteine
24 12 0 E Glutamic acid
8 10 29 G Glycine 

9LSL_1|Chain A|cGMP-specific 3',5'-cyclic phosphodiesterase|Homo sapiens (9606)
>4WOR_1|Chain A|Thermonuclease|Staphylococcus aureus (1280)
>4LVZ_1|Chain A|THF riboswitch|null
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 \(w=f(c)\)
9LSL , Knot 141 326 0.83 40 202 306 
EETRELQSLAAAVVPSAQTLKITDFSFSDFELSDLETALCTIRMFTDLNLVQNFQMKHEVLCRWILSVKKNYRKNVAYHNWRHAFNTAQCMFAALKAGKIQNKLTDLEILALLIAALSHDLDHRGVNNSYIQRSEHPLAQLYCHSIMEHHHFDQCLMILNSPGNQILSGLSIEEYKTTLKIIKQAILATDLALYIKRRGEFFELIRKNQFNLEDPHQKELFLAMLMTACDLSAITKPWPIQQRIAELVATEFFDQGDRERKELNIEPTDLMNREKKNKIPSMQVGFIDAICLQLYEALTHVSEDCFPLLDGCRKNRQKWQALAEQQ
4WOR , Knot 71 149 0.79 38 110 141 
ATSTKKLHKEPATLIKAIDGDTVKLMYKGQPMTFRLLLVDTPETKHPKKGVEKYGPEASAFTKKMVENAKKIEVEFDKGQRTDKYGRGLAYIYADGKMVNEALVRQGLAKVAYVYKPNNTHEQHLRKSEAQAKKEKLNIWSEDNADSGQ
4LVZ , Knot 25 89 0.42 8 16 46 
GGAGAGUAGAUGAUUCGCGUUAAGUGUGUGUGAAUGGGAUGUCGUCACACAACGAAGCGAGAGCGCGGUGAAUCAUUGCAUCCGCUCCA

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 \(c\).

\(|P_{f(9LSL_1)}(2) \setminus P_{f(4WOR_1)}(2)|=141\), \(|P_{f(4WOR_1)}(2) \setminus P_{f(9LSL_1)}(2)|=49\). 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 1:00000100111111101001010010100101001001100101100101100101000110011101000000011000100110010011111011010001001011111111100010001100001000001110100001100001000111100110011011010000001011001111001110100010110110000101001000011111110100101100111100011011100110010000001010100110000000110101111011010100110010000111101000000010111000
Pair \(Z_2\) Length of longest common subsequence
9LSL_1,4WOR_1 190 3
9LSL_1,4LVZ_1 210 2
4WOR_1,4LVZ_1 126 1

Newick tree

 
[
	9LSL_1:10.74,
	[
		4WOR_1:63,4LVZ_1:63
	]:46.74
]

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 \((0.85)(0.8)(\frac{475 }{\log_{20} 475}-\frac{149}{\log_{20}149})=96.3\)
Status Protein1 Protein2 d d1/2
Query variables 9LSL_1 4WOR_1 127 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]