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Parikh vectors
6ZAD_1 1FFU_1 7YKM_1 Letter Amino acid
31 5 5 M Methionine
61 5 7 S Serine
54 8 13 R Arginine
41 8 5 Q Glutamine
75 13 5 E Glutamic acid
34 7 2 I Isoleucine
42 5 4 P Proline
27 4 1 Y Tyrosine
39 3 2 D Aspartic acid
34 8 1 N Asparagine
30 6 5 H Histidine
65 9 3 K Lycine
16 0 1 W Tryptophan
55 12 7 V Valine
63 16 9 A Alanine
50 15 12 G Glycine
122 14 14 L Leucine
42 4 3 F Phenylalanine
36 12 6 T Threonine
23 9 0 C Cysteine 

6ZAD_1|Chain A|Phosphatidylinositol 4,5-bisphosphate 3-kinase catalytic subunit delta isoform|Mus musculus (10090)
>1FFU_1|Chains A, D|CUTS, IRON-SULFUR PROTEIN OF CARBON MONOXIDE DEHYDROGENASE|Hydrogenophaga pseudoflava (47421)
>7YKM_1|Chain A|DciA DUF721 domain|Deinococcus radiodurans (1299)
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 \(w=f(c)\)
6ZAD , Knot 354 940 0.86 40 322 842 
GGDRVKKLINSQISLLIGKGLHEFDSLRDPEVNDFRTKMRQFCEEAAAHRQQLGWVEWLQYSFPLQLEPSARGWRAGLLRVSNRALLVNVKFEGSEESFTFQVSTKDMPLALMACALRKKATVFRQPLVEQPEEYALQVNGRHEYLYGNYPLCHFQYICSCLHSGLTPHLTMVHSSSILAMRDEQSNPAPQVQKPRAKPPPIPAKKPSSVSLWSLEQPFSIELIEGRKVNADERMKLVVQAGLFHGNEMLCKTVSSSEVNVCSEPVWKQRLEFDISVCDLPRMARLCFALYAVVEKAKKARSTKKKSKKADCPIAWANLMLFDYKDQLKTGERCLYMWPSVPDEKGELLNPAGTVRGNPNTESAAALVIYLPEVAPHPVYFPALEKILELGRHGERGRITEEEQLQLREILERRGSGELYEHEKDLVWKMRHEVQEHFPEALARLLLVTKWNKHEDVAQMLYLLCSWPELPVLSALELLDFSFPDCYVGSFAIKSLRKLTDDELFQYLLQLVQVLKYESYLDCELTKFLLGRALANRKIGHFLFWHLRSEMHVPSVALRFGLIMEAYCRGSTHHMKVLMKQGEALSKLKALNDFVKVSSQKTTKPQTKEMMHMCMRQETYMEALSHLQSPLDPSTLLEEVCVEQCTFMDSKMKPLWIMYSSEEAGSAGNVGIIFKNGDDLRQDMLTLQMIQLMDVLWKQEGLDLRMTPYGCLPTGDRTGLIEVVLHSDTIANIQLNKSNMAATAAFNKDALLNWLKSKNPGEALDRAIEEFTLSCAGYCVATYVLGIGDRHSDNIMIRESGQLFHIDFGHFLGNFKTKFGINRERVPFILTYDFVHVIQQGKTNNSEKFERFRGYCERAYTILRRHGLLFLHLFALMRAAGLPELSCSKDIQYLKDSLALGKTEEEALKHFRVKFNEALRESWKTKVNWLAHNVSKDNRQ
1FFU , Knot 78 163 0.81 38 123 157 
MAKKIITVNVNGKAQEKAVEPRTLLIHFLREELNLTGAHIGCETSHCGACTVDIDGRSVKSCTHLAVQCDGSEVLTVEGLANKGVLHAVQEGFYKEHGLQCGFCTPGMLMRAYRFLQENPNPTEAEIRMGMTGNLCRCTGYQNIVKAVQYAARKLQEPSTAAA
7YKM , Knot 52 105 0.76 38 81 102 
MTRSRRSGPLDMSTLMGATLGKGKLGYGVQRARALLLWPQAVGPEIARMTRPRSVQGGTLFVEVRDSAAAHHLTMQRHHFLKRLNELLGAGQEVSELRFSVGHIR

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 \(c\).

\(|P_{f(6ZAD_1)}(2) \setminus P_{f(1FFU_1)}(2)|=218\), \(|P_{f(1FFU_1)}(2) \setminus P_{f(6ZAD_1)}(2)|=19\). 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 1:1100100110001011110110010010010100100010010001110000111101100011101010101101111010001111010101000010101000011111110110001011001110010001101010000101001100100100010011010101100001111000000111010010101111110010010110100110101101001010001011101111010011000100001010001110001010101001101101011101110010010000000001001111101111000001001000101110110001011011101010100001111110110111011011110011011001001010000010100110001010100000011101000100011011101111001000001101101100110111101101101011000110111001001000011001101101100000100010011110111000110111101000101101110111110100010000101110010110010110011010000000100001101010000010110010011010011001010000110001011111000001101101111100100100011010110110111000110101010101101000111011100001101010000111011100011101100001101100110010100110011001111100000011100010110101101110100011100001111100011011001000000010010100001001100011111011111011111010000010010001111000001100101010011000100010111001000000
Pair \(Z_2\) Length of longest common subsequence
6ZAD_1,1FFU_1 237 4
6ZAD_1,7YKM_1 261 4
1FFU_1,7YKM_1 130 3

Newick tree

 
[
	6ZAD_1:13.94,
	[
		1FFU_1:65,7YKM_1:65
	]:73.94
]

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 \((0.85)(0.8)(\frac{1103 }{\log_{20} 1103}-\frac{163}{\log_{20}163})=255.\)
Status Protein1 Protein2 d d1/2
Query variables 6ZAD_1 1FFU_1 327 189.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]