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Parikh vectors
2YER_1 2CLV_1 6XRQ_1 Letter Amino acid
7 3 0 M Methionine
9 7 0 F Phenylalanine
8 13 0 S Serine
16 23 8 G Glycine
14 8 0 N Asparagine
7 8 0 H Histidine
20 16 0 V Valine
17 19 1 A Alanine
6 5 4 C Cysteine
7 13 0 Q Glutamine
23 25 0 E Glutamic acid
28 26 0 L Leucine
22 11 0 K Lycine
8 19 0 T Threonine
10 16 0 Y Tyrosine
18 14 0 D Aspartic acid
17 7 0 I Isoleucine
17 16 0 P Proline
6 9 0 W Tryptophan
16 21 0 R Arginine 

2YER_1|Chain A|SERINE/THREONINE-PROTEIN KINASE CHK1|HOMO SAPIENS (9606)
>2CLV_1|Chains A, D[auth H]|H-2 CLASS I HISTOCOMPATIBILITY ANTIGEN, K-B ALPHA CHAIN|MUS MUSCULUS (10090)
>6XRQ_1|Chains A, B|RNA (5' GP*GP*CP*UP*CP*GP*GP*CP*GP*GP*CP*GP*GP*A-3')|Pseudorabies virus Ea (101947)
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 \(w=f(c)\)
2YER , Knot 123 276 0.83 40 173 266 
MAVPFVEDWDLVQTLGEGAYGEVQLAVNRVTEEAVAVKIVDMKRAVDCPENIKKEICINKMLNHENVVKFYGHRREGNIQYLFLEYCSGGELFDRIEPDIGMPEPDAQRFFHQLMAGVVYLHGIGITHRDIKPENLLLDERDNLKISDFGLATVFRYNNRERLLNKMCGTLPYVAPELLKRREFHAEPVDVWSCGIVLTAMLAGELPWDQPSDSCQEYSDWKEKKTYLNPWKKIDSAPLALLHKILVENPSARITIPDIKKDRWYNKPLKKGAKRP
2CLV , Knot 125 279 0.84 40 177 271 
GPHSLRYFVTAVSRPGLGEPRFISVGYVDNTEFVRFDSDAENPRYEPRARWMEQEGPEYWERETQKAKGNEQSFRVDLRTLLGYYNQSKGGSHTIQVISGCEVGSDGRLLRGYQQYAYDGCDYIALNEDLKTWTAADMAALITKHKWEQAGEAERLRAYLEGTCVEWLRRYLKNGNATLLRTDSPKAHVTHHSRPEDKVTLRCWALGFYPADITLTWQLNGEELIQDMELVETRPAGDGTFQKWASVVVPLGKEQYYTCHVYHQGLPEPLTLRWEPPPS
6XRQ , Knot 6 14 0.37 8 6 7 
GGCUCGGCGGCGGA

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 \(c\).

\(|P_{f(2YER_1)}(2) \setminus P_{f(2CLV_1)}(2)|=90\), \(|P_{f(2CLV_1)}(2) \setminus P_{f(2YER_1)}(2)|=94\). 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 1:111111001011001101101010111001000111101101001100100100010100110000110101000010100111000011011001010111101010011001111110101111000010100111000001010011110110000000110010101101110110000101011011001111011111011100100000000010000001011001001111110011100101010110100001000110011001
Pair \(Z_2\) Length of longest common subsequence
2YER_1,2CLV_1 184 3
2YER_1,6XRQ_1 173 2
2CLV_1,6XRQ_1 179 2

Newick tree

 
[
	2CLV_1:92.13,
	[
		2YER_1:86.5,6XRQ_1:86.5
	]:5.63
]

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 \((0.85)(0.8)(\frac{555 }{\log_{20} 555}-\frac{276}{\log_{20}276})=78.8\)
Status Protein1 Protein2 d d1/2
Query variables 2YER_1 2CLV_1 103 102.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]