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Parikh vectors
1ZPX_1 5FUK_1 9EKY_1 Letter Amino acid
1 18 25 G Glycine
0 21 66 L Leucine
0 9 38 K Lycine
2 19 38 S Serine
2 2 28 Y Tyrosine
0 16 26 T Threonine
6 2 19 C Cysteine
0 3 27 Q Glutamine
0 13 30 E Glutamic acid
0 6 9 H Histidine
0 4 12 M Methionine
0 9 41 F Phenylalanine
0 13 28 R Arginine
0 16 23 N Asparagine
0 18 45 I Isoleucine
2 11 31 V Valine
3 20 25 A Alanine
0 14 34 D Aspartic acid
5 17 14 P Proline
0 3 7 W Tryptophan 

1ZPX_1|Chain A|mini-collagen|null
>5FUK_1|Chains A, B|MROUPO|MARASMIUS ROTULA (182057)
>9EKY_1|Chains A, B, C, D|Mucolipin-2|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 \(w=f(c)\)
1ZPX , Knot 14 23 0.63 16 19 20 
XPCGSYCPSVCAPACAPVCCYPX
5FUK , Knot 106 234 0.82 40 154 227 
SAHPWKAPGPNDSRGPCPGLNTLANHGFLPRNGRNISVPMIVKAGFEGYNVQSDILILAGKIGMLTSREADTISLEDLKLHGTIEHDASLSREDVAIGDNLHFNEAIFTTLANSNPGADVYNISSAAQVQHDRLADSLARNPNVTNTDLTATIRSSESAFFLTVMSAGDPLRGEAPKKFVNVFFREERMPIKEGWKRSTTPITIPLLGPIIERITELSDWKPTGDNCGAIVLSP
9EKY , Knot 228 566 0.85 40 269 529 
MARQPYRFPQARIPERGSGVFRLTVRNAMAHRDSEMKEECLREDLKFYFMSPCEKYRARRQIPWKLGLQILKIVMVTTQLVRFGLSNQLVVAFKEDNTVAFKHLFLKGYSGTDEDDYSCSVYTQEDAYESIFFAINQYHQLKDITLGTLGYGENEDNRIGLKVCKQHYKKGTMFPSNETLNIDNDVELDCVQLDLQDLSKKPPDWKNSSFFRLEFYRLLQVEISFHLKGIDLQTIHSRELPDCYVFQNTIIFDNKAHSGKIKIYFDSDAKIEECKDLNIFGSTQKNAQYVLVFDAFVIVICLASLILCTRSIVLALRLRKRFLNFFLEKYKRPVCDTDQWEFINGWYVLVIISDLMTIIGSILKMEIKAKNLTNYDLCSIFLGTSTLLVWVGVIRYLGYFQAYNVLILTMQASLPKVLRFCACAGMIYLGYTFCGWIVLGPYHDKFENLNTVAECLFSLVNGDDMFATFAQIQQKSILVWLFSRLYLYSFISLFIYMILSLFIALITDSYDTIKKFQQNGFPETDLQEFLKECSSKEEYQKESSAFLSCICCRRRKRSDDHLIPIS

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 \(c\).

\(|P_{f(1ZPX_1)}(2) \setminus P_{f(5FUK_1)}(2)|=14\), \(|P_{f(5FUK_1)}(2) \setminus P_{f(1ZPX_1)}(2)|=149\). 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 1:01010001010111011100010
Pair \(Z_2\) Length of longest common subsequence
1ZPX_1,5FUK_1 163 2
1ZPX_1,9EKY_1 264 3
5FUK_1,9EKY_1 189 4

Newick tree

 
[
	9EKY_1:12.91,
	[
		1ZPX_1:81.5,5FUK_1:81.5
	]:42.41
]

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 \((0.85)(0.8)(\frac{257 }{\log_{20} 257}-\frac{23}{\log_{20}23})=79.4\)
Status Protein1 Protein2 d d1/2
Query variables 1ZPX_1 5FUK_1 102 56
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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