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Parikh vectors
4TPN_1 4OUE_1 7RSV_1 Letter Amino acid
12 19 18 H Histidine
17 17 22 F Phenylalanine
9 23 24 Y Tyrosine
31 27 38 V Valine
51 41 33 A Alanine
29 22 26 R Arginine
19 34 40 E Glutamic acid
6 8 16 M Methionine
18 21 40 S Serine
24 30 42 D Aspartic acid
3 9 7 C Cysteine
31 21 31 P Proline
25 29 29 T Threonine
9 33 46 K Lycine
6 15 4 W Tryptophan
16 16 28 N Asparagine
18 11 36 Q Glutamine
21 35 26 G Glycine
14 26 29 I Isoleucine
47 32 77 L Leucine

4TPN_1|Chain A|Putative P450-like protein|Streptomyces scabies (680198)
>4OUE_1|Chains A, B|Putative lipoprotein|Bacteroides thetaiotaomicron (226186)
>7RSV_1|Chains A, B|Phosphatidylinositol 3-kinase catalytic subunit type 3|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 \(w=f(c)\)
4TPN , Knot 169 406 0.83 40 221 385
MTVPSPLADPSIVPDPYPVYADLAQRRPVHWVERLNAWAVLTYADCAAGLKDPRLTADRGTEVLAAKFPGQPLPPDNIFHRWTKNVVMYTDPPLHDALRRSVRAGFTRAAHQHYDQVLQKVAHDLVASIPAGATEIDAVPALAAELPVRSAVHAFGVPEEDLGFLIPRVNTIMTYHSGPKDQPVTQEIILEKLTDLHTYASELLQGMRGKVLPDTVIARLAAAQDGLTETTPEQTVHQLALVFIALFAPTTPGSLSSGTLAFARNPRQVERFLADQACVDNTANEVLRYNASNQFTWRVAAKDVEMGGVRIEAGQTLALFLGSANRDANMFERPNDFDLDRPNSARHLSFGQGVHACLAAQLISLQLKWFYVALLNRFPGIRTAGEPIWNENLEFRSLRSLPLSLR
4OUE , Knot 195 469 0.85 40 255 444
MSLAPCGLVPSARQLEWYNREMIAFFHFGINTFEEYVNEGDGKASTAIFNPTALDCRQWMQTLKAAGIPAAILTAKHADGFCLWPSKYTDYSVKNAAWKNGKGDVVREFVDACEEYGLKAGIYLGPHDRHEHLSPLYTTERYKEYYAHQLGELMSDYGKIWETWWDGAGADELTTPVYRHWYKIVREKQPDCVIFGTKNSYPFADVRWMGNEAGEAGDPCWATTDSVAIRDEAQYYKGLNEGMLDGDAYIPAETDVSIRPSWFYHAEEDSRVKSVRELWDIYCTSVGRNSVLLLNFPPDRRGLIHSTDSLHAALLKQGIDETFSTNLLRGAKVKATNVRGAKYSPEKMLDNEKNTYFAGKDGEVKADIIFTLPKTIEFDCLMIEEVIELGHRTTKWSVEYTVDGKNWITIPEATDKQAIGHKWIVRLAPVKAKQVRLRIQDGKACPAIHTFGVYKQSPVFKEGHHHHHH
7RSV , Knot 245 612 0.85 40 271 564
HHHHHHGENLYFQGSDHDLKPNAATRDQLNIIVSYPPTKQLTYEEQDLVWKFRYYLTNQEKALTKFLKCVNWDLPQEAKQALELLGKWKPMDVEDSLELLSSHYTNPTVRRYAVARLRQADDEDLLMYLLQLVQALKYENFDDIKNGLEPTKKDSQSSVSENVSNSGINSAEIDSSQIITSPLPSVSSPPPASKTKEVPDGENLEQDLCTFLISRACKNSTLANYLYWYVIVECEDQDTQQRDPKTHEMYLNVMRRFSQALLKGDKSVRVMRSLLAAQQTFVDRLVHLMKAVQRESGNRKKKNERLQALLGDNEKMNLSDVELIPLPLEPQVKIRGIIPETATLFKSALMPAQLFFKTEDGGKYPVIFKHGDDLRQDQLILQIISLMDKLLRKENLDLKLTPYKVLATSTKHGFMQFIQSVPVAEVLDTEGSIQNFFRKYAPSENGPNGISAEVMDTYVKSCAGYCVITYILGVGDRHLDNLLLTKTGKLFHIDFGYILGRDPKPLPPPMKLNKEMVEGMGGTQSEQYQEFRKQCYTAFLHLRRYSNLILNLFSLMVDANIPDIALEPDKTVKKVQDKFRLDLSDEEAVHYMQSLIDESVHALFAAVVEQIH

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 \(c\).

\(|P_{f(4TPN_1)}(2) \setminus P_{f(4OUE_1)}(2)|=60\), \(|P_{f(4OUE_1)}(2) \setminus P_{f(4TPN_1)}(2)|=94\). 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 1:1011011101011101011010110001101100101111100100111100101010010011110111011110011001000111000111001100010111001100000011001100111011111001011111110111001101111100011111101001100001100011000111001001000100110110101110011101111001100001000100111111111110011010010111100100100111001010001001100010001010111001011110101100111111010001011001001010010010010110110101110110101011011110011110011011100010100100111010
Pair \(Z_2\) Length of longest common subsequence
4TPN_1,4OUE_1 154 3
4TPN_1,7RSV_1 152 4
4OUE_1,7RSV_1 150 6

Newick tree

 
[
	4TPN_1:76.99,
	[
		7RSV_1:75,4OUE_1:75
	]:1.99
]

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 \((0.85)(0.8)(\frac{875 }{\log_{20} 875}-\frac{406}{\log_{20}406})=125.\)
Status Protein1 Protein2 d d1/2
Query variables 4TPN_1 4OUE_1 161 148
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]