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Parikh vectors
7XQC_1 7LXQ_1 3BVM_1 Letter Amino acid
14 0 16 S Serine
53 0 6 A Alanine
29 0 13 E Glutamic acid
15 0 10 F Phenylalanine
27 0 9 I Isoleucine
36 0 30 K Lycine
34 0 21 D Aspartic acid
39 9 12 G Glycine
7 0 6 H Histidine
7 0 8 M Methionine
25 0 14 T Threonine
15 0 18 Y Tyrosine
36 0 16 V Valine
15 1 3 R Arginine
9 0 5 Q Glutamine
35 0 15 L Leucine
8 0 3 W Tryptophan
23 0 23 N Asparagine
0 0 2 C Cysteine
23 18 7 P Proline 

7XQC_1|Chains A, B, C, D|Fusion protein of Maltose-binding periplasmic protein and RNA-binding protein KhpA|Escherichia coli K-12 (83333)
>7LXQ_1|Chains A, B, C|Collagen mimetic peptide|synthetic construct (32630)
>3BVM_1|Chain A|Enterotoxin type C-3|Staphylococcus aureus (1280)
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 \(w=f(c)\)
7XQC , Knot 176 450 0.79 38 203 401 
KIEEGKLVIWINGDKGYNGLAEVGKKFEKDTGIKVTVEHPDKLEEKFPQVAATGDGPDIIFWAHDRFGGYAQSGLLAEITPDKAFQDKLYPFTWDAVRYNGKLIAYPIAVEALSLIYNKDLLPNPPKTWEEIPALDKELKAKGKSALMFNLQEPYFTWPLIAADGGYAFKYENGKYDIKDVGVDNAGAKAGLTFLVDLIKNKHMNADTDYSIAEAAFNKGETAMTINGPWAWSNIDTSKVNYGVTVLPTFKGQPSKPFVGVLSAGINAASPNKELAKEFLENYLLTDEGLEAVNKDKPLGAVALKSYEEELAKDPRIAATMENADKGEIMPNIPQMSAFWYAVRTAVINAASGRQTVDEALAAAQTNAAHMSAVVVDAVEHLVRGIVDNPDDVRVDLITSRRGRTVEVHVHPDDLGKVIGRGGRTATALRTLVAGIGGRGIRVDVVDTDQ
7LXQ , Knot 6 30 0.22 8 8 10 
PPGPPGPPGPPGPXGPRXPPGPPGPPGPPG
3BVM , Knot 107 237 0.82 40 159 227 
ESQPDPMPDDLHKSSEFTGTMGNMKYLYDDHYVSATKVKSVDKFLAHDLIYNISDKKLKNYDKVKTELLNEDLAKKYKDEVVDVYGSNYYVNCYFSSKDNKWWPGKTCMYGGITKHEGNHFDNGNLQNVLVRVYENKRNTISFEVQTDKKSVTAQELDIKARNFLINKKNLYEFNSSPYETGYIKFIENNGNTFWYDMMPAPGDKFDQSKYLMMYNDNKTVDSKSVKIEVHLTTKNG

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 \(c\).

\(|P_{f(7XQC_1)}(2) \setminus P_{f(7LXQ_1)}(2)|=200\), \(|P_{f(7LXQ_1)}(2) \setminus P_{f(7XQC_1)}(2)|=5\). 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 1:010010111110100100111011001000011010100100100011011101011011111000111010011110101001100010110101100010111011110110110000111011001001111000101010011110100101011111101101100001000100111001110111011101100001010000011011100100110101111100100001001101110101010011111101110110100011001100011000110110000111111100000011001011101001001011101101011101100111011010001001111100011010111101100110111001001010110000100101010100110111011001011001111111011010110000
Pair \(Z_2\) Length of longest common subsequence
7XQC_1,7LXQ_1 205 2
7XQC_1,3BVM_1 166 4
7LXQ_1,3BVM_1 165 2

Newick tree

 
[
	7XQC_1:96.58,
	[
		3BVM_1:82.5,7LXQ_1:82.5
	]:14.08
]

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 \((0.85)(0.8)(\frac{480 }{\log_{20} 480}-\frac{30}{\log_{20}30})=140.\)
Status Protein1 Protein2 d d1/2
Query variables 7XQC_1 7LXQ_1 173 89
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]