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Parikh vectors
7ZEI_1 6DCF_1 8WLT_1 Letter Amino acid
6 2 6 M Methionine
14 6 15 T Threonine
16 2 2 W Tryptophan
21 2 7 Y Tyrosine
19 7 22 A Alanine
27 10 7 D Aspartic acid
17 3 12 I Isoleucine
7 1 14 Q Glutamine
22 9 24 G Glycine
16 2 11 F Phenylalanine
19 6 6 K Lycine
13 4 20 S Serine
16 7 18 V Valine
16 14 10 R Arginine
4 1 1 C Cysteine
15 2 2 H Histidine
18 7 14 P Proline
11 3 19 N Asparagine
22 13 7 E Glutamic acid
19 13 15 L Leucine 

7ZEI_1|Chains A, B, C, D, E, F|Ch_Gaf159A|Caldicellulosiruptor hydrothermalis (413888)
>6DCF_1|Chain A[auth J]|RNA polymerase-binding protein RbpA|Mycobacterium smegmatis (strain ATCC 700084 / mc(2)155) (246196)
>8WLT_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z|Flagellar L-ring protein|Salmonella enterica subsp. enterica serovar Typhimurium str. LT2 (99287)
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 \(w=f(c)\)
7ZEI , Knot 140 318 0.84 40 208 303 
VPRPPAPLFRDPIYDGAADPTIIYNHLEKSWWILYTNRRANQKLPGKAFMHGTDIGIAESKDGGRTWFYRGTIELQYGRGRNTFWAPEVIFYEGEYHMYVSFVPGVPQDWNAERYILYYKSKNLWDWEFVCKLELSSNKVIDACVFQMPDGTFRMWYKDEADHSYIYAAESNNLKDWKILGPALTDRPQEGPNVFWWKSKYWMITDPWCGLGVYSSEDATAWHRHENILDRPGKREDDGQIGHHADVLVIDDETAYIFYFTHPEGMEGTEEFWKDSKYWRTSLQVAKLEYVDGKVVCDRDKEFDFYLPDLFAHHHHHH
6DCF , Knot 58 114 0.80 40 88 110 
MADRVLRGSRLGAVSYETDRNHDLAPRQVARYRTDNGEEFDVPFADDAEIPGTWLCRNGLEGTLIEGDVPEPKKVKPPRTHWDMLLERRSVEELEELLKERLDLIKAKRRGTGS
8WLT , Knot 108 232 0.84 40 158 221 
MQKYALHAYPVMALMVATLTGCAWIPAKPLVQGATTAQPIPGPVPVANGSIFQSAQPINYGYQPLFEDRRPRNIGDTLTIVLQENVSASKSSSANASRDGKTSFGFDTVPRYLQGLFGNSRADMEASGGNSFNGKGGANASNTFSGTLTVTVDQVLANGNLHVVGEKQIAINQGTEFIRFSGVVNPRTISGSNSVPSTQVADARIEYVGNGYINEAQNMGWLQRFFLNLSPM

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 \(c\).

\(|P_{f(7ZEI_1)}(2) \setminus P_{f(6DCF_1)}(2)|=156\), \(|P_{f(6DCF_1)}(2) \setminus P_{f(7ZEI_1)}(2)|=36\). 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 1:110111111001100111010110001000111100000100011101110100111100001100110010101001010001111011100100010101111110010100011000000110101100101000011010110110101011000010000101100001001011111100010011011110000111001101111000001011000001100110000010110010111100001011010010110100011000001000101101001010110000001010110111000000
Pair \(Z_2\) Length of longest common subsequence
7ZEI_1,6DCF_1 192 3
7ZEI_1,8WLT_1 202 3
6DCF_1,8WLT_1 174 3

Newick tree

 
[
	7ZEI_1:10.08,
	[
		6DCF_1:87,8WLT_1:87
	]:15.08
]

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 \((0.85)(0.8)(\frac{432 }{\log_{20} 432}-\frac{114}{\log_{20}114})=95.9\)
Status Protein1 Protein2 d d1/2
Query variables 7ZEI_1 6DCF_1 123 82
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]