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Parikh vectors
2EOO_1 3SRY_1 1WVB_1 Letter Amino acid
0 1 2 W Tryptophan
4 15 8 H Histidine
1 12 23 I Isoleucine
2 10 23 P Proline
0 14 22 T Threonine
0 23 19 D Aspartic acid
2 2 3 C Cysteine
4 16 18 E Glutamic acid
10 11 20 S Serine
4 7 13 R Arginine
9 27 36 G Glycine
0 6 4 M Methionine
2 13 9 F Phenylalanine
3 21 24 K Lycine
1 13 9 Y Tyrosine
0 18 25 V Valine
0 10 16 A Alanine
2 14 9 N Asparagine
0 7 6 Q Glutamine
2 20 33 L Leucine 

2EOO_1|Chain A|Zinc finger protein 95 homolog|Homo sapiens (9606)
>3SRY_1|Chain A|Green fluorescent protein|Aequorea victoria (6100)
>1WVB_1|Chains A, B|Arginase 1|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 \(w=f(c)\)
2EOO , Knot 25 46 0.69 26 34 39 
GSSGSSGSGERPYGCNECGKNFGRHSHLIEHLKRHFREKSSGPSSG
3SRY , Knot 117 260 0.83 40 166 241 
MVSKGEELFTGVVPILVELDGDVNGHKFSVSGEGEGDATYGKLTLKFICTTGKLPVPWPTLVTTFGYGVQCFARYPDHMRQHDFFKSAMPEGYVQERTIFFKDDGNYKTRAEVKFEGDTLVNRIELKGIDFKEDGNILGHKLEYNYNSHNVYIMADKQKNGIKVNFKIRHNIEDGSVQLADHYAQNTPIGDGPVLLPDNHYLSYQSALSKDPNEKRDHMVLLEFVTAAGITLGMDELYKGGSNDYKDDDDKGGSHHHHHH
1WVB , Knot 142 322 0.85 40 195 312 
MSAKSRTIGIIGAPFSKGQPRGGVEEGPTVLRKAGLLEKLKEQECDVKDYGDLPFADIPNDSPFQIVKNPRSVGKASEQLAGKVAEVKKNGRISLVLGGDHSLAIGSISGHARVHPDLGVIWVDAHTDINTPLTTTSGNLHGQPVSFLLKELKGKIPDVPGFSWVTPCISAKDIVYIGLRDVDPGEHYILKTLGIKYFSMTEVDRLGIGKVMEETLSYLLGRKKRPIHLSFDVDGLDPSFTPATGTPVVGGLTYRQGLYITEEIYKTGLLSGLDIMEVNPSLGKTPEEVTRTVNTAVAITLACFGLAREGNHKPIDYLNPPK

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 \(c\).

\(|P_{f(2EOO_1)}(2) \setminus P_{f(3SRY_1)}(2)|=16\), \(|P_{f(3SRY_1)}(2) \setminus P_{f(2EOO_1)}(2)|=148\). 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 1:1001001010010100001001100001100100010000011001
Pair \(Z_2\) Length of longest common subsequence
2EOO_1,3SRY_1 164 3
2EOO_1,1WVB_1 189 2
3SRY_1,1WVB_1 157 4

Newick tree

 
[
	2EOO_1:91.55,
	[
		3SRY_1:78.5,1WVB_1:78.5
	]:13.05
]

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 \((0.85)(0.8)(\frac{306 }{\log_{20} 306}-\frac{46}{\log_{20}46})=84.4\)
Status Protein1 Protein2 d d1/2
Query variables 2EOO_1 3SRY_1 109 62.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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