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Parikh vectors
6WTC_1 1QPL_1 4ETL_1 Letter Amino acid
6 5 10 Q Glutamine
15 7 35 L Leucine
11 5 10 S Serine
1 1 7 W Tryptophan
5 6 30 D Aspartic acid
1 3 7 H Histidine
2 5 12 I Isoleucine
4 7 14 T Threonine
2 6 16 R Arginine
4 1 11 N Asparagine
5 7 13 E Glutamic acid
0 7 20 P Proline
1 5 16 F Phenylalanine
0 3 12 Y Tyrosine
9 9 18 V Valine
6 5 30 A Alanine
3 1 3 C Cysteine
1 13 21 G Glycine
6 8 11 K Lycine
4 3 6 M Methionine 

6WTC_1|Chains A, C|Non-structural protein 7|Severe acute respiratory syndrome coronavirus 2 (2697049)
>1QPL_1|Chains A, B[auth C]|PROTEIN (FK506-BINDING PROTEIN)|Homo sapiens (9606)
>4ETL_1|Chain A|Phenylalanine-4-hydroxylase|Chromobacterium violaceum (243365)
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 \(w=f(c)\)
6WTC , Knot 44 86 0.76 36 69 79 
SNASKMSDVKCTSVVLLSVLQQLRVESSSKLWAQCVQLHNDILLAKDTTEAFEKMVSLLSVLLSMQGAVDINKLCEEMLDNRATLQ
1QPL , Knot 57 107 0.83 40 89 103 
GVQVETISPGDGRTFPKRGQTCVVHYTGMLEDGKKFDSSRDRNKPFKFMLGKQEVIRGWEEGVAQMSVGQRAKLTISPDYAYGATGHPGIIPPHATLVFDVELLKLE
4ETL , Knot 134 302 0.84 40 188 288 
GLPGSMNDRADFVVPDITTRKNVGLSHDANDFTLPQPLDRYSAEDHATWATLYQRQCKLLPGRACDEFLEGLERLEVDADRVPDFNKLNEKLMAATGWKIVAVPGLIPDDVFFEHLANRRFPVTWWLREPHQLDYLQEPDVFHDLFGHVPLLINPVFADYLEAYGKGGVKAKALGALPMLARLYWYTVEFGLINTPAGMRIYGAGILSSKSESIYCLDSASPNRVGFDLMRIMNTRYRIDTFQKTYFVIDSFKQLFDATAPDAAPLYLQLADAQPWGAGDIAPDDLVLNAGDHQGWADTEDV

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 \(c\).

\(|P_{f(6WTC_1)}(2) \setminus P_{f(1QPL_1)}(2)|=50\), \(|P_{f(1QPL_1)}(2) \setminus P_{f(6WTC_1)}(2)|=70\). 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 1:00100100100001111011001010000011100101000111100000110011011011101011101001000110001010
Pair \(Z_2\) Length of longest common subsequence
6WTC_1,1QPL_1 120 3
6WTC_1,4ETL_1 169 3
1QPL_1,4ETL_1 173 3

Newick tree

 
[
	4ETL_1:92.45,
	[
		6WTC_1:60,1QPL_1:60
	]:32.45
]

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 \((0.85)(0.8)(\frac{193 }{\log_{20} 193}-\frac{86}{\log_{20}86})=35.3\)
Status Protein1 Protein2 d d1/2
Query variables 6WTC_1 1QPL_1 46 40
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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