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Parikh vectors
7JJA_1 6BHD_1 4JVT_1 Letter Amino acid
17 23 5 K Lycine
8 7 5 N Asparagine
12 5 14 Q Glutamine
11 15 17 E Glutamic acid
6 14 14 I Isoleucine
13 8 6 F Phenylalanine
6 18 12 S Serine
2 7 2 W Tryptophan
14 14 16 D Aspartic acid
14 18 19 G Glycine
8 21 38 L Leucine
4 5 6 M Methionine
4 9 9 H Histidine
4 9 13 P Proline
17 12 22 T Threonine
10 15 19 V Valine
13 10 52 A Alanine
3 13 23 R Arginine
0 3 3 C Cysteine
15 13 2 Y Tyrosine 

7JJA_1|Chain A|Zinc-binding lipoprotein AdcA|Streptococcus pneumoniae (strain ATCC BAA-255 / R6) (171101)
>6BHD_1|Chain A|Histone-lysine N-methyltransferase SETDB1|Homo sapiens (9606)
>4JVT_1|Chain A|Enoyl-CoA hydratase|Thermobifida fusca (269800)
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 \(w=f(c)\)
7JJA , Knot 85 181 0.81 38 124 175 
DTKTVQNGYFEDAAVKDRTLSDYAGNWQSVYPFLEDGTFDQVFDYKAKLTGKMTQAEYKAYYTKGYQTDVTKINITDNTMEFVQGGQSKKYTYKYVGKKILTYKKGNRGVRFLFEATDADAGQFKYVQFSDHNIAPVKAEHFHIFFGGTSQETLFEEMDNWPTYYPDNLSGQEIAQEMLAH
6BHD , Knot 106 239 0.81 40 162 226 
MHHHHHHSSGRENLYFQGGELSKDGDLIVSMRILGKKRTKTWHKGTLIAIQTVGPGKKYKVKFDNKGKSLLSGNHIAYDYHPPADKLYVGSRVVAKYKDGNQVWLYAGIVAETPNVKNKLRFLIFFDDGYASYVTQSELYPICRPLKKTWEDIEDISCRDFIEEYVTAYPNRPMVLLKSGQLIKTEWEGTWWKSRVEEVDGSLVRILFLDDKRCEWIYRGSTRLEPMFSMKTSSASALE
4JVT , Knot 123 297 0.78 40 148 269 
MHHHHHHSSGVDLGTENLYFQSMAQTKAPTAEELAAAGLTLTIDGEVARITLSRPHRRNAMTGRMWTELARIGHTLPQAVRIVVITGEGPTFSSGIDLDMFQAGKVDGEPTPFTLLARDPNSTAALDQVIASYQEGFLWLRRADIVSIAAVRGHAIGAGFQLALSCDIRILSDTAQLCMKEPALGLVPDLTGTQPLVELVGVNRAIELCLTARTIDAAEAAQLRLAERVVADAELDAAVDALVAQLLAVPAAAARATKELLLQAGRNDLATQARVERTAQLARLAELAKASAAPRRP

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 \(c\).

\(|P_{f(7JJA_1)}(2) \setminus P_{f(6BHD_1)}(2)|=64\), \(|P_{f(6BHD_1)}(2) \setminus P_{f(7JJA_1)}(2)|=102\). 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 1:0000100101001110000100011010010111001010011000101010100100010000100001001010000101101100000000011001100001001101110100101101001010000111101001011111000001100100110001001010011001110
Pair \(Z_2\) Length of longest common subsequence
7JJA_1,6BHD_1 166 3
7JJA_1,4JVT_1 170 4
6BHD_1,4JVT_1 148 10

Newick tree

 
[
	7JJA_1:87.08,
	[
		6BHD_1:74,4JVT_1:74
	]:13.08
]

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 \((0.85)(0.8)(\frac{420 }{\log_{20} 420}-\frac{181}{\log_{20}181})=70.7\)
Status Protein1 Protein2 d d1/2
Query variables 7JJA_1 6BHD_1 91 78
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]