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Parikh vectors
6BJM_1 1MOE_1 6NBR_1 Letter Amino acid
17 11 29 E Glutamic acid
9 11 16 I Isoleucine
28 16 39 L Leucine
13 14 13 Y Tyrosine
19 7 11 R Arginine
4 4 8 C Cysteine
15 28 21 G Glycine
16 20 21 T Threonine
30 16 24 V Valine
16 18 19 A Alanine
5 6 15 N Asparagine
13 10 26 K Lycine
10 3 6 M Methionine
14 12 15 D Aspartic acid
14 15 5 Q Glutamine
9 2 7 H Histidine
18 8 9 F Phenylalanine
16 12 14 P Proline
12 23 23 S Serine
6 4 5 W Tryptophan 

6BJM_1|Chain A|ABO blood group (Transferase A, alpha 1-3-N-acetylgalactosaminyltransferase transferase B, alpha 1-3-galactosyltransferase)|Homo sapiens (9606)
>1MOE_1|Chains A, B|anti-CEA mAb T84.66|Mus musculus (10090)
>6NBR_1|Chains A, B, C, D|Kavalactone reductase 1|Piper methysticum (130404)
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 \(w=f(c)\)
6BJM , Knot 127 284 0.84 40 194 277 
FMVSLPRMVYPQPKVLTPCRKDVLVVTPWLAPIVWEGTFNIDILNEQFRLQNTTIGLTVFAIKKYVAFLKLFLETAEKHFMVGHRVHYYVFTDQPAAVPRVTLGTGRQLSVLEVGAYKRWQDVSMRKMEMISDFCERRFLSEVDYLVCVDVDMEFRDHVGVEILTPLFGTLHPSFYGSSREAFTYERRPQSQAYIPKDEGDFYYMGAFFGGSVQEVQRLTRACHQAMMVDQANGIEAVWHDESHLNKYLLRHKPTKVLSPEYLWDQQLLGWPAVLRKLRFTAVP
1MOE , Knot 111 240 0.84 40 158 232 
DIVLTQSPASLAVSLGQRATMSCRAGESVDIFGVGFLHWYQQKPGQPPKLLIYRASNLESGIPVRFSGTGSRTDFTLIIDPVEADDVATYYCQQTNEDPYTFGGGTKLEIKGGGSGGGGEVQLQQSGAELVEPGASVKLSCTASGFNIKDTYMHWVKQRPEQGLEWIGRIDPANGNSKYVPKFQGKATITADTSSNTAYLQLTSLTSEDTAVYYCAPFGYYVSDYAMAYWGQGTSVTVSS
6NBR , Knot 145 326 0.85 40 201 313 
METERKSRICVTGAGGFVASWVVKLFLSKGYLVHGTVRDLGEEKTAHLRKLEGAYHNLQLFKADLLDYESLLGAITGCDGVLHVATPVPSSKTAYSGTELVKTAVNGTLNVLRACTEAKVKKVIYVSSTAAVLVNPNLPKDKIPDEDCWTDEEYCRTTPFFLNWYCIAKTAAEKNALEYGDKEGINVISICPSYIFGPMLQPTINSSNLELLRLMKGDDESIENKFLLMVDVRDVAEAILLLYEKQETSGRYISSPHGMRQSNLVEKLESLQPGYNYHKNFVDIKPSWTMISSEKLKKLGWKPRPLEDTISETVLCFEEHGLLENE

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 \(c\).

\(|P_{f(6BJM_1)}(2) \setminus P_{f(1MOE_1)}(2)|=103\), \(|P_{f(1MOE_1)}(2) \setminus P_{f(6BJM_1)}(2)|=67\). 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 1:11101101101010110100001111011111111010101011000101000011101111000111101110010001111001000110001111101011010010110111000100101001011001000011001001101010101000111011011110101010100001100000100010110001010011111110100100100100011110010110111000001000110001001101001100011111111001010111
Pair \(Z_2\) Length of longest common subsequence
6BJM_1,1MOE_1 170 3
6BJM_1,6NBR_1 185 4
1MOE_1,6NBR_1 171 4

Newick tree

 
[
	6NBR_1:90.38,
	[
		6BJM_1:85,1MOE_1:85
	]:5.38
]

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 \((0.85)(0.8)(\frac{524 }{\log_{20} 524}-\frac{240}{\log_{20}240})=81.2\)
Status Protein1 Protein2 d d1/2
Query variables 6BJM_1 1MOE_1 105 95
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]