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Parikh vectors
5XKI_1 6DSX_1 5SBM_1 Letter Amino acid
30 0 7 L Leucine
12 0 10 V Valine
4 3 6 C Cysteine
15 0 5 H Histidine
20 0 5 K Lycine
19 0 3 M Methionine
7 0 7 P Proline
19 2 15 T Threonine
13 3 10 A Alanine
17 0 10 D Aspartic acid
16 0 4 Q Glutamine
10 0 8 E Glutamic acid
11 3 9 G Glycine
18 0 10 I Isoleucine
15 0 6 F Phenylalanine
4 0 0 W Tryptophan
11 0 8 R Arginine
11 0 11 N Asparagine
18 0 8 Y Tyrosine
23 0 10 S Serine 

5XKI_1|Chains A, B|FAD-linked sulfhydryl oxidase|Autographa californica nuclear polyhedrosis virus (46015)
>6DSX_1|Chain A[auth P]|DNA (5'-D(*GP*CP*GP*AP*TP*CP*AP*CP*GP*TP*A)-3')|synthetic construct (32630)
>5SBM_1|Chain A|CD44 antigen|Mus musculus (10090)
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 \(w=f(c)\)
5XKI , Knot 136 293 0.88 40 198 279 
MGSSHHHHHHSSGLVPRGSHMASMTGGQQMGRGSMIPLTPLFSRYKDSYLLYSFRLIDLLRASKSTHLTKLLSSQATYLYHFACLMKYKDIQKYEVQQLIEWAINASPDMDLQQFRIEFMDKTTELNLRSCQPKSFTYTFTTIWDTMHFLSLIIDDMVYTRDKSSLDFVMQQLKTMKVLFYNVFFILQCAMCRDHYMNVKGFIIYHIELIEIALDKEKYGTDITFVDSYQQETAGADVAVVSNNMLMKNLMAYVSMTFHNHINDYKWIQRNKKPPAHYERMTWGEYKKLLNLQ
6DSX , Knot 7 11 0.50 8 9 9 
GCGATCACGTA
5SBM , Knot 76 152 0.83 38 122 147 
MNQIDLNVTCRYAGVFHVEKNGRYSISRTEAADLCQAFNSTLPTMDQMKLALSKGFETCRYGFIEGNVVIPRIHPNAICAANHTGVYILVTSNTSHYDTYCFNASAPPEEDCTSVTDLPNSFDGPVTITIVNRDGTRYSKKGEYRTHQEDID

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 \(c\).

\(|P_{f(5XKI_1)}(2) \setminus P_{f(6DSX_1)}(2)|=192\), \(|P_{f(6DSX_1)}(2) \setminus P_{f(5XKI_1)}(2)|=3\). 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 1:11000000000011110100110101100110101111011100000001100101101101000001001100010010011011000010000100110111010101010010101100000101000010010001001100101101110011000000010111001001011100111110011000001010111100101101110000010010110000000111011110001110011101010100010000110000011100001011000011010
Pair \(Z_2\) Length of longest common subsequence
5XKI_1,6DSX_1 195 2
5XKI_1,5SBM_1 188 3
6DSX_1,5SBM_1 125 2

Newick tree

 
[
	5XKI_1:10.52,
	[
		5SBM_1:62.5,6DSX_1:62.5
	]:42.02
]

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 \((0.85)(0.8)(\frac{304 }{\log_{20} 304}-\frac{11}{\log_{20}11})=98.9\)
Status Protein1 Protein2 d d1/2
Query variables 5XKI_1 6DSX_1 130 67
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]