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Parikh vectors
6DXM_1 8CND_1 1DWC_1 Letter Amino acid
0 35 3 S Serine
1 32 2 T Threonine
0 31 1 Y Tyrosine
0 35 3 R Arginine
0 27 0 H Histidine
0 49 3 K Lycine
0 34 2 F Phenylalanine
0 22 1 A Alanine
0 21 0 N Asparagine
0 45 3 D Aspartic acid
0 49 5 L Leucine
0 40 1 P Proline
1 26 1 C Cysteine
0 29 0 Q Glutamine
7 32 4 G Glycine
0 28 1 I Isoleucine
0 44 6 E Glutamic acid
0 14 0 M Methionine
0 11 0 W Tryptophan
0 36 0 V Valine 

6DXM_1|Chain A|DNA (5'-D(*TP*GP*GP*GP*CP*GP*GP*GP*G)-3')|Homo sapiens (9606)
>8CND_1|Chain A|histone acetyltransferase|Mus musculus (10090)
>1DWC_1|Chain A[auth L]|ALPHA-THROMBIN (SMALL SUBUNIT)|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 \(w=f(c)\)
6DXM , Knot 4 9 0.32 6 4 5 
TGGGCGGGG
8CND , Knot 259 640 0.87 40 305 604 
HHHHHHDYDIPTTENLYFQGAMGSSQPRKKIFKPEELRQALMPTLEALYRQDPESLPFRQPVDPQLLGIPDYFDIVKNPMDLSTIKRKLDTGQYQEPWQYVDDVWLMFNNAWLYNRKTSRVYKFCSKLAEVFEQEIDPVMQSLGYCCGRKYEFSPQTLCCYGKQLCTIPRDAAYYSYQNRYHFCEKCFTEIQGENVTLGDDPSQPQTTISKDQFEKKKNDTLDPEPFVDCKECGRKMHQICVLHYDIIWPSGFVCDNCLKKTGRPRKENKFSAKRLQTTRLGNHLEDRVNKFLRRQNHPEAGEVFVRVVASSDKTVEVKPGMKSRFVDSGEMSESFPYRTKALFAFEEIDGVDVCFFGMHVQEYGSDCPPPNTRRVYISYLDSIHFFRPRCLRTAVYHEILIGYLEYVKKLGYVTGHIWACPPSEGDDNIFHCHPPDQKIPKPKRLQEWYKKMLDKAFAERIINDYKDIFKQANEDRLTSAKELPYFEGDFWPNVLEESIKESGGSGSQKLYATMEKHKEVFFVIHLHAGPVISTQPPIVDPDPLLSCDLMDGRDAFLTLARDKHWEFSSLRRSKWSTLCMLVELHTQGQDRFVYTCNECKHHVETRWHCTVCEDYDLCINCYNTKSHTHKMVKWGLGLD
1DWC , Knot 24 36 0.79 28 34 34 
TFGSGEADCGLRPLFEKKSLEDKTERELLESYIDGR

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 \(c\).

\(|P_{f(6DXM_1)}(2) \setminus P_{f(8CND_1)}(2)|=1\), \(|P_{f(8CND_1)}(2) \setminus P_{f(6DXM_1)}(2)|=302\). 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 1:011101111
Pair \(Z_2\) Length of longest common subsequence
6DXM_1,8CND_1 303 2
6DXM_1,1DWC_1 36 2
8CND_1,1DWC_1 277 4

Newick tree

 
[
	8CND_1:16.27,
	[
		6DXM_1:18,1DWC_1:18
	]:14.27
]

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 \((0.85)(0.8)(\frac{649 }{\log_{20} 649}-\frac{9}{\log_{20}9})=195.\)
Status Protein1 Protein2 d d1/2
Query variables 6DXM_1 8CND_1 257 129.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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