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Parikh vectors
4NLZ_1 3OWZ_1 5IQQ_1 Letter Amino acid
12 0 4 N Asparagine
34 0 10 K Lycine
14 0 7 F Phenylalanine
14 0 5 P Proline
20 0 4 S Serine
18 0 3 R Arginine
21 0 3 D Aspartic acid
3 20 0 C Cysteine
27 0 6 E Glutamic acid
26 0 8 L Leucine
1 0 0 W Tryptophan
17 27 9 A Alanine
9 0 3 H Histidine
6 0 2 M Methionine
13 0 3 Q Glutamine
22 28 7 G Glycine
23 0 5 I Isoleucine
19 0 3 T Threonine
12 0 2 Y Tyrosine
18 0 7 V Valine 

4NLZ_1|Chain A|DNA polymerase beta|Homo sapiens (9606)
>3OWZ_1|Chain A|Domain II of glycine riboswitch|null
>5IQQ_1|Chains A, B, C, D, E|RNA-binding protein 7|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 \(w=f(c)\)
4NLZ , Knot 143 329 0.84 40 197 316 
PQETLNGGITDMLTELANFEKNVSQAIHKYNAYRKAASVIAKYPHKIKSGAEAKKLPGVGTKIAEKIDEFLATGKLRKLEKIRQDDTSSSINFLTRVSGIGPSAARKFVDEGIKTLEDLRKNEDKLNHHQRIGLKYFGDFEKRIPREEMLQMQDIVLNEVKKVDSEYIATVCGSFRRGAESSGDMDVLLTHPSFTSESTKQPKLLHQVVEQLQKVHFITDTLSKGETKFMGVCQLPSKNDEKEYPHRRIDIRLIPKDQYYCGVLYFTGSDIFNKNMRAHALEKGFTINEYTIRPLGVTGVAGEPLPVDSEKDIFDYIQWKYREPKDRSE
3OWZ , Knot 27 88 0.45 8 16 44 
GGCUCUGGAGAGAACCGUUUAAUCGGUCGCCGAAGGAGCAAGCUCUGCGGAAACGCAGAGUGAAACUCUCAGGCAAAAGGACAGAGUC
5IQQ , Knot 46 91 0.76 36 75 88 
MGAAAAEADRTLFVGNLETKVTEELLFELFHQAGPVIKVKIPKDKDGKPKQFAFVNFKHEVSVPYAMNLLNGIKLYGRPIKIQFRSGSSHA

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 \(c\).

\(|P_{f(4NLZ_1)}(2) \setminus P_{f(3OWZ_1)}(2)|=192\), \(|P_{f(3OWZ_1)}(2) \setminus P_{f(4NLZ_1)}(2)|=11\). 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 1:10001011100110011010001001100001000110111001001001101001111100110010011101010010010000000010110010111101100110011001001000000100000111001101000110001101001110010010000110101010011000101011100101000000010110011001001011000100100011110011000000001000101011100000011101010011000101011001101000010111101111011110000011001010000100000
Pair \(Z_2\) Length of longest common subsequence
4NLZ_1,3OWZ_1 203 2
4NLZ_1,5IQQ_1 170 4
3OWZ_1,5IQQ_1 85 4

Newick tree

 
[
	4NLZ_1:10.27,
	[
		5IQQ_1:42.5,3OWZ_1:42.5
	]:62.77
]

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 \((0.85)(0.8)(\frac{417 }{\log_{20} 417}-\frac{88}{\log_{20}88})=100.\)
Status Protein1 Protein2 d d1/2
Query variables 4NLZ_1 3OWZ_1 141 83.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]