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Parikh vectors
7MXI_1 6BST_1 7CWY_1 Letter Amino acid
8 0 43 D Aspartic acid
5 3 0 C Cysteine
17 3 44 G Glycine
18 0 51 A Alanine
15 0 51 L Leucine
3 0 22 M Methionine
19 0 22 P Proline
21 0 35 S Serine
22 0 19 T Threonine
5 0 11 W Tryptophan
4 0 35 Y Tyrosine
15 0 51 E Glutamic acid
10 0 42 K Lycine
9 0 34 N Asparagine
11 0 14 Q Glutamine
14 0 24 H Histidine
6 0 41 I Isoleucine
9 0 19 F Phenylalanine
17 0 46 V Valine
19 0 16 R Arginine 

7MXI_1|Chains A, B|IgE Fc|Homo sapiens (9606)
>6BST_1|Chains A, B|DNA (5'-D(*CP*GP*CP*GP*CP*G)-3')|synthetic construct (32630)
>7CWY_1|Chains A, B, C|Decarboxylase|Enterococcus faecalis (1351)
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 \(w=f(c)\)
7MXI , Knot 107 247 0.79 40 163 236 
APMAEGGGQNHHHHHHHHGGENLYFQGGSCADSNPRGVSAYLSRPSPFDLFIRKSPTITCLVVDLAPSKGTVNLTWSRASGKPVNHSTRKEEKQRNGTLTVTSTLPVGTRDWIEGETYQCRVTHPHLPRALMRSTTKTSGPRAAPEVYAFATPEWPGSRDKRTLACLIQNFMPEDISVQWLHNEVQLPDARHSTTQPRKTKGSGFFVFSRLEVTRAEWEQKDEFICRAVHEAASPSQTVQRAVSVNP
6BST , Knot 3 6 0.29 4 2 2 
CGCGCG
7CWY , Knot 244 620 0.84 38 264 582 
MKNEKLAKGEMNLNALFIGDKAENGQLYKDLLIDLVDEHLGWRQNYMPQDMPVISSQERTSKSYEKTVNHMKDVLNEISSRMRTHSVPWHTAGRYWGHMNSETLMPSLLAYNFAMLWNGNNVAYESSPATSQMEEEVGHEFAHLMSYKNGWGHIVADGSLANLEGLWYARNIKSLPFAMKEVKPELVAGKSDWELLNMPTKEIMDLLESAEDEIDEIKAHSARSGKHLQAIGKWLVPQTKHYSWLKAADIIGIGLDQVIPVPVDHNYRMDINELEKIVRGLAEEQIPVLGVVGVVGSTEEGAVDSIDKIIALRDELMKDGIYYYVHVDAAYGGYGRAIFLDEDNNFIPYEDLQDVHEEYGVFKEKKEHISREVYDAYKAIELAESVTIDPHKMGYIPYSAGGIVIQDIRMRDVISYFATYVFEKGADIPALLGAYILEGSKAGATAASVWAAHHVLPLNVAGYGKLIGASIEGSHHFYNFLNDLTFKVGDKEIEVHTLTHPDFNMVDYVFKEKGNDDLVAMNKLNHDVYDYASYVKGNIYNNEFITSHTDFAIPDYGNSPLKFVNSLGFSDEEWNRAGKVTVLRAAVMTPYMNDKEEFDVYAPKIQAALQEKLEQIYDVK

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 \(c\).

\(|P_{f(7MXI_1)}(2) \setminus P_{f(6BST_1)}(2)|=163\), \(|P_{f(6BST_1)}(2) \setminus P_{f(7MXI_1)}(2)|=2\). 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 1:1111011100000000001100101011001000101101010010110111000101001110111001010101001010110000000000001010100011110001101000000100101101110000000110111010111010111000000110110011100101011000101101000000100001011111001010010100000110011001101000100110101
Pair \(Z_2\) Length of longest common subsequence
7MXI_1,6BST_1 165 1
7MXI_1,7CWY_1 195 3
6BST_1,7CWY_1 266 1

Newick tree

 
[
	7CWY_1:12.94,
	[
		7MXI_1:82.5,6BST_1:82.5
	]:43.44
]

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 \((0.85)(0.8)(\frac{253 }{\log_{20} 253}-\frac{6}{\log_{20}6})=86.3\)
Status Protein1 Protein2 d d1/2
Query variables 7MXI_1 6BST_1 106 54
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]