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Parikh vectors
5IER_1 5SLF_1 2RBU_1 Letter Amino acid
4 20 6 H Histidine
3 14 5 M Methionine
13 31 14 T Threonine
8 15 20 E Glutamic acid
2 23 1 C Cysteine
3 16 9 Q Glutamine
9 40 25 L Leucine
2 25 14 Y Tyrosine
9 43 14 V Valine
4 27 19 N Asparagine
12 29 26 G Glycine
8 25 10 I Isoleucine
7 30 18 F Phenylalanine
3 10 6 W Tryptophan
8 34 25 D Aspartic acid
6 22 10 R Arginine
4 30 23 K Lycine
5 26 15 P Proline
10 29 15 S Serine
12 34 17 A Alanine 

5IER_1|Chains A, B, C, D|OHP9|synthetic construct (32630)
>5SLF_1|Chain A[auth D]|Proofreading exoribonuclease nsp14|Severe acute respiratory syndrome coronavirus 2 (2697049)
>2RBU_1|Chain A[auth X]|Cytochrome C Peroxidase|Saccharomyces cerevisiae (307796)
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 \(w=f(c)\)
5IER , Knot 67 132 0.82 40 108 130 
TQSPALIASQSLWRCTQAHDREGWLALMADDVVIETPIGKSVTNPDGSGIKGKEAVGAFFDTHIAATRLTVTCEETFPSSSPDEIAHILVAHSEFDGGFTSEVRGVFTYRVNKAGLITNLRGYWNLDMMTFG
5SLF , Knot 217 523 0.86 40 267 499 
SMLFKDCSKVITGLHPTQAPTHLSVDTKFKTEGLCVDIPGIPKDMTYRRLISMMGFKMNYQVNGYPNMFITREEAIRHVRAWIGFDVEGCHATREAVGTNLPLQLGFSTGVNLVAVPTGYVDTPNNTDFSRVSAKPPPGDQFKHLIPLMYKGLPWNVVRIKIVQMLSDTLKNLSDRVVFVLWAHGFELTSMKYFVKIGPERTCCLCDRRATCFSTASDTYACWHHSIGFDYVYNPFMIDVQQWGFTGNLQSNHDLYCQVHGNAHVASCDAIMTRCLAVHECFVKRVDWTIEYPIIGDELKINAACRKVQHMVVKAALLADKFPVLHDIGNPKAIKCVPQADVEWKFYDAQPCSDKAYKIEELFYSYATHSDKFTDGVCLFWNCNVDRYPANSIVCRFDTRVLSNLNLPGCDGGSLYVNKHAFHTPAFDKSAFVNLKQLPFFYYSDSPCESHGKQVVSDIDYVPLKSATCITRCNLGGAVCRHHANEYRLYLDAYNMMISAGFSLWVYKQFDTYNLWNTFTRLQ
2RBU , Knot 133 292 0.86 40 193 286 
TLVHVASVEKGRSYEDFQKVYNAIALKLREDDEYDNYIGYGPVLVRLAWHISGTWDKHDNTGGSYGGTYRFKKEFNDPSNAGLQNGFKFLEPIHKEFPWISSGDLFSLGGVTAVQEMQGPKIPWRCGRVDTPEDTTPDNGRLPDADKDAGYVRTFFQRLNMNDREVVALMGAHALGKTHLKNSGYEGPGGAANNVFTNEFYLNLLNEDWKLEKNDANNEQWDSKSGYMMLPTDYSLIQDPKYLSIVKEYANDQDKFFKDFSKAFEKLLEDGITFPKDAPSPFIFKTLEEQGL

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 \(c\).

\(|P_{f(5IER_1)}(2) \setminus P_{f(5SLF_1)}(2)|=26\), \(|P_{f(5SLF_1)}(2) \setminus P_{f(5IER_1)}(2)|=185\). 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 1:000111110001100001000011111110011100111001001010110100111111000111001010000011000100110111100010111000101110001001111001010101011011
Pair \(Z_2\) Length of longest common subsequence
5IER_1,5SLF_1 211 4
5IER_1,2RBU_1 163 3
5SLF_1,2RBU_1 170 4

Newick tree

 
[
	5SLF_1:10.11,
	[
		5IER_1:81.5,2RBU_1:81.5
	]:18.61
]

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 \((0.85)(0.8)(\frac{655 }{\log_{20} 655}-\frac{132}{\log_{20}132})=150.\)
Status Protein1 Protein2 d d1/2
Query variables 5IER_1 5SLF_1 193 119
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]