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Parikh vectors
6MZU_1 1UBT_1 3OBK_1 Letter Amino acid
12 7 19 R Arginine
17 15 27 E Glutamic acid
15 23 21 G Glycine
15 14 11 I Isoleucine
20 19 32 L Leucine
6 10 16 Y Tyrosine
33 31 36 A Alanine
6 16 9 N Asparagine
6 11 27 D Aspartic acid
13 7 9 Q Glutamine
9 10 27 S Serine
6 12 24 K Lycine
4 6 19 M Methionine
7 11 8 F Phenylalanine
1 3 2 W Tryptophan
0 11 5 C Cysteine
4 8 5 H Histidine
9 22 21 P Proline
11 15 12 T Threonine
18 16 26 V Valine 

6MZU_1|Chains A, B, C, D, E, F|Microcompartments protein|Haliangium ochraceum (strain DSM 14365 / JCM 11303 / SMP-2) (502025)
>1UBT_1|Chain A[auth S]|Periplasmic [NiFe] hydrogenase Small subunit|Desulfovibrio vulgaris str. 'Miyazaki F' (883)
>3OBK_1|Chains A, B, C, D, E, F, G, H|Delta-aminolevulinic acid dehydratase|Toxoplasma gondii ME49 (508771)
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 \(w=f(c)\)
6MZU , Knot 97 212 0.81 38 140 196 
MSITLRTYIFLDALQPQLATFIGKTARGFLPVPGQASLWVEIAPGIAINRVTDAALKATKVQPAVQVVERAYGLLEVHHFDQGEVLAAGSTILDKLEVREEGRLKPQVMTHQIIRAVEAYQTQIINRNSQGMMILPGESLFILETQPAGYAVLAANEAEKAANVHLVNVTPYGAFGRLYLAGSEAEIDAAAEAAEAAIRSVSGVAQESFRDR
1UBT , Knot 120 267 0.83 40 183 259 
LMGPRRPSVVYLHNAECTGCSESVLRAFEPYIDTLILDTLSLDYHETIMAAAGDAAEAALEQAVNSPHGFIAVVEGGIPTAANGIYGKVANHTMLDICSRILPKAQAVIAYGTCATFGGVQAAKPNPTGAKGVNDALKHLGVKAINIAGCPPNPYNLVGTIVYYLKNKAAPELDSLNRPTMFFGQTVHEQCPRLPHFDAGEFAPSFESEEARKGWCLYELGCKGPVTMNNCPKIKFNQTNWPVDAGHPCIGCSEPDFWDAMTPFYQN
3OBK , Knot 151 356 0.83 40 205 339 
MTPRGPLDNNNYGEVWLPIQARPRRNRKNRAVRQLVQENLVKPSSLIYPLFVHDEETSVPIPSMPGQSRLSMEDLLKEVGEARSYGIKAFMLFPKVDDELKSVMAEESYNPDGLLPRAIMALKEAFPDVLLLADVALDPYSSMGHDGVVDEQSGKIVNDLTVHQLCKQAITLARAGADMVCPSDMMDGRVSAIRESLDMEGCTDTSILAYSCKYASSFYGPFRDALDSHMVGGTDKKTYQMDPSNSREAEREAEADASEGADMLMVKPGLPYLDVLAKIREKSKLPMVAYHVSGEYAMLKAAAEKGYISEKDTVLEVLKSFRRAGADAVATYYAKEAAKWMVEDMKGTQKFTEPCY

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 \(c\).

\(|P_{f(6MZU_1)}(2) \setminus P_{f(1UBT_1)}(2)|=64\), \(|P_{f(1UBT_1)}(2) \setminus P_{f(6MZU_1)}(2)|=107\). 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 1:10101000111011010110111001011111110101110111111100100111010010111011001011101001001011111001100101000101010110001101101000011000001111111001111000111011111001001101011010101111010111001010111011011100101110001000
Pair \(Z_2\) Length of longest common subsequence
6MZU_1,1UBT_1 171 5
6MZU_1,3OBK_1 161 4
1UBT_1,3OBK_1 174 3

Newick tree

 
[
	1UBT_1:88.08,
	[
		6MZU_1:80.5,3OBK_1:80.5
	]:7.58
]

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 \((0.85)(0.8)(\frac{479 }{\log_{20} 479}-\frac{212}{\log_{20}212})=77.4\)
Status Protein1 Protein2 d d1/2
Query variables 6MZU_1 1UBT_1 100 87
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]