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Parikh vectors
6XAL_1 5WMJ_1 4NKK_1 Letter Amino acid
35 0 4 E Glutamic acid
48 0 10 L Leucine
6 0 2 C Cysteine
3 0 5 N Asparagine
9 0 6 Q Glutamine
31 1 13 G Glycine
15 0 1 H Histidine
8 1 10 I Isoleucine
30 1 11 V Valine
36 0 4 R Arginine
21 0 3 D Aspartic acid
4 1 6 K Lycine
6 0 1 M Methionine
17 0 2 F Phenylalanine
23 0 8 T Threonine
49 0 3 A Alanine
24 1 0 S Serine
5 1 2 W Tryptophan
4 0 1 Y Tyrosine
27 0 7 P Proline 

6XAL_1|Chain A|NzeB|Streptomyces sp. NRRL F-5053 (1463854)
>5WMJ_1|Chains A, B|Superoxide dismutase [Cu-Zn]|Homo sapiens (9606)
>4NKK_1|Chain A|HIV-1 protease|Human immunodeficiency virus 1 (11676)
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 \(w=f(c)\)
6XAL , Knot 162 401 0.80 40 192 372 
VTTTATLTYPFHDWSQELSPRYAQLRASDAPVCPVVSEGTGDPLWLVTRYATAVKLLEDSRFSSEAAQASGAPRQEPVELRAPGTRGDAIAMLREAGLRSVLADGLGPRAVRRHQGWINDLAETLMSELASREGTFDLAADFVEPLSSALVSRTLLGELSADERDLLAHCADTGLRFCGVTHEEQVHAFTQMHEFFLEHARRLAGTPGEHLLKLIAEAPVDQGPLSDEALAEAGSLLVVAGFPTSSGFLCGALLTLLRHPDAVQELHAHPERVPSAVEELLRYTPLSTGSVKRMATEDLEIDGVRIKAGEVVMVSLEAVNHDPDAFEDPDVFRPGREGPMHFGFGRGRHFCPGNRLARCVIEATVRAVARRPGLRLAVAPEEISWHEGLFFRRPRAIPATW
5WMJ , Knot 6 6 0.59 12 5 4 
KVWGSI
4NKK , Knot 50 99 0.77 38 82 93 
PQITLWQRPVVTIKIGGQLKEALLNTGADDTVLEEVNLPGRWKPKLIGGIGGFVKVRQYDQVPIEICGHKVIGTVLVGPTPANVIGRNLMTQIGCTLNF

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 \(c\).

\(|P_{f(6XAL_1)}(2) \setminus P_{f(5WMJ_1)}(2)|=191\), \(|P_{f(5WMJ_1)}(2) \setminus P_{f(6XAL_1)}(2)|=4\). 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 1:10001010011001000101001010100111011100101011111000101101100001000110101110001101011100101111100111001110111101100001110011001100110001010111011011001110001110101000011100100110101100000101100100111001001110110011011101110011100011101101111111100011101111011001011001010100110110011000110010100110001010110101101111010110001011001011011001110111101001011001100110101011100111011111001010011110010111101
Pair \(Z_2\) Length of longest common subsequence
6XAL_1,5WMJ_1 195 2
6XAL_1,4NKK_1 182 3
5WMJ_1,4NKK_1 85 2

Newick tree

 
[
	6XAL_1:10.09,
	[
		4NKK_1:42.5,5WMJ_1:42.5
	]:63.59
]

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 \((0.85)(0.8)(\frac{407 }{\log_{20} 407}-\frac{6}{\log_{20}6})=131.\)
Status Protein1 Protein2 d d1/2
Query variables 6XAL_1 5WMJ_1 159 81
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]