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Parikh vectors
2ZBM_1 7UJI_1 2JTA_1 Letter Amino acid
18 32 1 S Serine
15 42 0 A Alanine
15 21 1 R Arginine
19 23 0 N Asparagine
23 26 2 D Aspartic acid
15 13 0 Q Glutamine
38 46 2 L Leucine
10 10 0 M Methionine
14 21 1 Y Tyrosine
21 29 0 V Valine
19 35 0 K Lycine
11 20 0 F Phenylalanine
7 24 0 P Proline
18 27 1 E Glutamic acid
12 19 0 H Histidine
22 22 1 T Threonine
2 8 0 C Cysteine
29 47 1 G Glycine
22 22 0 I Isoleucine
6 4 0 W Tryptophan 

2ZBM_1|Chain A|Protein-tyrosine-phosphatase|Shewanella sp. (50422)
>7UJI_1|Chains A, B|Serine hydroxymethyltransferase|Glycine max (3847)
>2JTA_1|Chain A|10-mer ubiquitin peptide|null
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 \(w=f(c)\)
2ZBM , Knot 148 336 0.85 40 204 324 
MGNTATEFDGPYVITPISGQSTAYWICDNRLKTTSIEKLQVNRPEHCGDLPETKLSSEIKQIMPDTYLGIKKVVALSDVHGQYDVLLTLLKKQKIIDSDGNWAFGEGHMVMTGDMFDRGHQVNEVLWFMYQLDQQARDAGGMVHLLMGNHEQMVLGGDLRYVHQRYDIATTLINRPYNKLYGADTEIGQWLRSKNTIIKINDVLYMHGGISSEWISRELTLDKANALYRANVDASKKSLKADDLLNFLFFGNGPTWYRGYFSETFTEAELDTILQHFNVNHIVVGHTSQERVLGLFHNKVIAVDSSIKVGKSGELLLLENNRLIRGLYDGTRETLQ
7UJI , Knot 197 491 0.82 40 245 454 
MGSSHHHHHHSSGLVPRGSHMDPVSVWGNTPLATVDPEIHDLIEKEKRRQCRGIELIASENFTSFAVIEALGSALTNKYSEGMPGNRYYGGNEYIDQIENLCRSRALQAFHLDAQSWGVNVQPYSGSPANFAAYTAVLNPHDRIMGLDLRSGGHLTHGYYTSGGKKISATSIYFESLPYKVNSTTGYIDYDRLEEKALDFRPKLIICGGSAYPRDWDYKRFREVADKCGALLLCDMAHTSGLVAAQEVNSPFEYCDIVTTTTHKSLRGPRAGMIFYRKGPKPPKKGQPENAVYDFEDKINFAVFPSLQGGPHNHQIGALAVALKQAASPGFKAYAKQVKANAVALGKYLMGKGYSLVTGGTENHLVLWDLRPLGLTGNKVEKLCDLCNITVNKNAVFGDSSALAPGGVRIGAPAMTSRGLVEKDFEQIGEFLHRAVTLTLEIQKEHGKLLKDFNKGLVNNKAIEDLKADVEKFSALFDMPGFLVSEMKYKD
2JTA , Knot 8 10 0.61 16 9 8 
LEDGRTLSDY

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 \(c\).

\(|P_{f(2ZBM_1)}(2) \setminus P_{f(7UJI_1)}(2)|=62\), \(|P_{f(7UJI_1)}(2) \setminus P_{f(2ZBM_1)}(2)|=103\). 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 1:110010010110110110100010110000100001001010010001011000100010011100011100111100101000111011000011000101111010111010110010010011111001000100111110111100001111101001000001100110010001011000110110000011010011010111000110001010010110010101000010100110111110110100101000100101001100101001111000000111110001111000101100101111000011011001000010
Pair \(Z_2\) Length of longest common subsequence
2ZBM_1,7UJI_1 165 4
2ZBM_1,2JTA_1 203 3
7UJI_1,2JTA_1 246 2

Newick tree

 
[
	2JTA_1:12.18,
	[
		2ZBM_1:82.5,7UJI_1:82.5
	]:38.68
]

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 \((0.85)(0.8)(\frac{827 }{\log_{20} 827}-\frac{336}{\log_{20}336})=133.\)
Status Protein1 Protein2 d d1/2
Query variables 2ZBM_1 7UJI_1 167 141
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]