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Parikh vectors
4DMW_1 8ICV_1 6BZS_1 Letter Amino acid
32 0 10 D Aspartic acid
16 1 23 G Glycine
12 0 7 H Histidine
48 0 12 I Isoleucine
0 1 6 C Cysteine
22 0 17 Q Glutamine
49 0 6 K Lycine
10 0 2 M Methionine
5 0 4 W Tryptophan
28 0 4 Y Tyrosine
18 0 8 R Arginine
50 0 6 N Asparagine
60 0 31 L Leucine
27 2 8 T Threonine
19 0 22 V Valine
29 4 26 A Alanine
44 0 13 E Glutamic acid
25 0 5 F Phenylalanine
12 0 13 P Proline
50 0 15 S Serine 

4DMW_1|Chain A|Toxin A|Clostridium difficile (1496)
>8ICV_1|Chain A[auth T]|DNA (5'-D(*CP*AP*TP*TP*AP*GP*AP*A)-3')|
>6BZS_1|Chain A|Multidrug resistance-associated protein 6|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 \(w=f(c)\)
4DMW , Knot 220 556 0.83 38 240 506 
MAHHHHHHDDDDKGSMSLISKEELIKLAYSIRPRENEYKTILTNLDEYNKLTTNNNENKYLQLKKLNESIDVFMNKYKTSSRNRALSNLKKDILKEVILIKNSNTSPVEKNLHFVWIGGEVSDIALEYIKQWADINAEYNIKLWYDSEAFLVNTLKKAIVESSTTEALQLLEEEIQNPQFDNMKFYKKRMEFIYDRQKRFINYYKSQINKPTVPTIDDIIKSHLVSEYNRDETVLESYRTNSLRKINSNHGIDIRANSLFTEQELLNIYSQELLNRGNLAAASDIVRLLALKNFGGVYLDVDMLPGIHSDLFKTISRPSSIGLDRWEMIKLEAIMKYKKYINNYTSENFDKLDQQLKDNFKLIIESKSEKSEIFSKLENLNVSDLEIKIAFALGSVINQALISKQGSYLTNLVIEQVKNRYQFLNQHLNPAIESDNNFTDTTKIFHDSLFNSATAENSMFLTKIAPYLQVGFMPEARSTISLSGPGAYASAYYDFINLQENTIEKTLKASDLIEFKFPENNLSQLTEQEINSLWSFDQASAKYQFEKYVRDYTGGS
8ICV , Knot 6 8 0.52 8 7 6 
CATTAGAA
6BZS , Knot 109 238 0.83 40 156 229 
SAAGKDCITIHSATFAWSQESPPCLHRINLTVPQGCLLAVVGPVGAGKSSLLSALLGELSKVEGFVSIEGAVAYVPQEAWVQNTSVVENVCFGQELDPPWLERVLEACALQPDVDSFPEGIHTSIGEQGMNLSGGQKQRLSLARAVYRKAAVYLLDDPLAALDAHVGQHVFNQVIGPGGLLQGTTRILVTHALHILPQADWIIVLANGAIAEMGSYQELLQRKGALVCLLDQARQPGD

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 \(c\).

\(|P_{f(4DMW_1)}(2) \setminus P_{f(8ICV_1)}(2)|=235\), \(|P_{f(8ICV_1)}(2) \setminus P_{f(4DMW_1)}(2)|=2\). 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 1:1100000000000101011000011011001010000000110010000010000000001010010001011100000000001100100011001111000000110001011111101001110010011010100010110000111100100111000000110110001001010010100001011000000110000001001011010011000110000000011000000010010000110101001100001101000011001011110011011110011110101011111000110010010011100101101011100000100000001001000100010111000000001100100101001010111111011001110001001001110010000011000101110000010000011000110010100011100111010111110100010101111010100011010000100010100110101100010010000100110100101000100010000110
Pair \(Z_2\) Length of longest common subsequence
4DMW_1,8ICV_1 237 2
4DMW_1,6BZS_1 180 4
8ICV_1,6BZS_1 151 2

Newick tree

 
[
	4DMW_1:11.40,
	[
		6BZS_1:75.5,8ICV_1:75.5
	]:37.90
]

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 \((0.85)(0.8)(\frac{564 }{\log_{20} 564}-\frac{8}{\log_{20}8})=173.\)
Status Protein1 Protein2 d d1/2
Query variables 4DMW_1 8ICV_1 216 109.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]