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Parikh vectors
1PHW_1 7CXK_1 6OQT_1 Letter Amino acid
4 1 0 C Cysteine
10 9 7 M Methionine
4 8 1 Y Tyrosine
13 17 9 Q Glutamine
16 23 10 I Isoleucine
14 18 12 S Serine
8 13 4 T Threonine
0 0 1 W Tryptophan
26 17 29 A Alanine
10 7 11 R Arginine
25 11 8 G Glycine
22 24 8 K Lycine
16 15 6 F Phenylalanine
10 9 6 N Asparagine
19 20 9 D Aspartic acid
15 20 17 E Glutamic acid
6 7 2 H Histidine
23 39 18 L Leucine
15 11 3 P Proline
28 14 16 V Valine 

1PHW_1|Chain A|2-dehydro-3-deoxyphosphooctonate aldolase|Escherichia coli (562)
>7CXK_1|Chain A|Peroxisome proliferator-activated receptor gamma|Homo sapiens (9606)
>6OQT_1|Chain A[auth W]|ATP synthase subunit delta|Escherichia coli (562)
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 \(w=f(c)\)
1PHW , Knot 125 284 0.82 38 173 277 
MKQKVVSIGDINVANDLPFVLFGGMNVLESRDLAMRICEHYVTVTQKLGIPYVFKASFDKANRSSIHSYRGPGLEEGMKIFQELKQTFGVKIITDVHEPSQAQPVADVVDVIQLPAFLARQTDLVEAMAKTGAVINVKKPQFVSPGQMGNIVDKFKEGGNEKVILCDRGANFGYDNLVVDMLGFSIMKKVSGNSPVIFDVTHALQCRDPFGAASGGRRAQVAELARAGMAVGLAGLFIEAHPDPEHAKCDGPSALPLAKLEPFLKQMKAIDDLVKGFEELDTSK
7CXK , Knot 124 283 0.82 38 175 271 
AEISSDIDQLNPESADLRALAKHLYDSYIKSFPLTKAKARAILTGKTTDKSPFVIYDMNSLMMGEDKIKFKHITPLQEQSKEVAIRIFQGCQFHSVEAVQEITEYAKSIPGFVNLDLNDQVTLLKYGVHEIIYTMLASLMNKDGVLISEGQGFMTREFLKSLRKPFGDFMEPKFEFAVKFNALELDDSDLAIFIAVIILSGDRPGLLNVKPIEDIQDNLLQALELQLKLNHPESSQLFAKLLQKMTDLRQIVTEHVQLLQVIKKTETDMSLHPLLQEIYKDLY
6OQT , Knot 82 177 0.80 38 113 165 
MSEFITVARPYAKAAFDFAVEHQSVERWQDMLAFAAEVTKNEQMAELLSGALAPETLAESFIAVAGEQLDENGQNLIRVMAENGRLNALPDVLEQFIHLRAVSEATAEVDVISAAALSEQQLAKISAAMEKRLSRKVKLNAKIDKSVMAGVIIRAGDMVIDGSVRGRLERLADVLQS

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 \(c\).

\(|P_{f(1PHW_1)}(2) \setminus P_{f(7CXK_1)}(2)|=74\), \(|P_{f(7CXK_1)}(2) \setminus P_{f(1PHW_1)}(2)|=76\). 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 1:10001101101011001111111110110000111010000101000111101101010010000100001111001101100100011101100100100101110110110111111000011011100111101001011011011011001001100011100011011000111011110110010100111101001100001111101100101101101111111111110101010010001101111101011100101100110110010000
Pair \(Z_2\) Length of longest common subsequence
1PHW_1,7CXK_1 150 3
1PHW_1,6OQT_1 158 4
7CXK_1,6OQT_1 146 4

Newick tree

 
[
	1PHW_1:78.32,
	[
		7CXK_1:73,6OQT_1:73
	]:5.32
]

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 \((0.85)(0.8)(\frac{567 }{\log_{20} 567}-\frac{283}{\log_{20}283})=80.0\)
Status Protein1 Protein2 d d1/2
Query variables 1PHW_1 7CXK_1 101 101
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]