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Parikh vectors
5OCV_1 3LXR_1 5XCA_1 Letter Amino acid
3 5 4 Y Tyrosine
6 10 2 I Isoleucine
2 12 15 P Proline
7 8 9 T Threonine
7 15 9 D Aspartic acid
12 12 23 G Glycine
6 14 8 K Lycine
2 16 10 E Glutamic acid
1 2 15 H Histidine
2 5 1 M Methionine
10 7 8 S Serine
6 2 5 W Tryptophan
14 6 14 N Asparagine
8 5 12 C Cysteine
3 5 10 Q Glutamine
6 16 14 V Valine
3 7 6 F Phenylalanine
12 14 10 A Alanine
11 10 7 R Arginine
8 14 8 L Leucine 

5OCV_1|Chains A, B|Lysozyme C|Gallus gallus (9031)
>3LXR_1|Chain A|Transforming protein RhoA|Homo sapiens (9606)
>5XCA_1|Chain A|Endo-beta-1,4-glucanase|Ampullaria crossean (1245466)
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 \(w=f(c)\)
5OCV , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL
3LXR , Knot 88 185 0.82 40 141 180 
GPLGSAAIRKKLVIVGDGACGKTCLLIVFSKDQFPEVYVPTVFENYVADIEVDGKQVELALWDTAGQEDYDRLRPLSYPDTDVILMCFSIDSPDSLENIPEKWTPEVKHFCPNVPIILVGNKKDLRNDEHTRRELAKMKQEPVKPEEGRDMANRIGAFGYMECSAKTKDGVREVFEMATRAALQA
5XCA , Knot 90 190 0.82 40 139 183 
SLEKRAQLCQPDAHGVRRFNGRPCASTTRYVDGHKGACGCGQKGSDTPFPWNLQKHVTAPSERYFDDGGSNLWCGKNCGKCVRLTPTGGFVPGKGGAPPNHNPVVFMVTNACPINGNEEWCGISGKPGTNHVNSHGYEVHFALQDQVGQVEALHWDNPEVTWEEVPCPGDLQANYQQCECHNSDHHHHHH

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 \(c\).

\(|P_{f(5OCV_1)}(2) \setminus P_{f(3LXR_1)}(2)|=63\), \(|P_{f(3LXR_1)}(2) \setminus P_{f(5OCV_1)}(2)|=100\). 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 1:011100011111000110000100110110110100010001000000100001110100011000100110001001100111000101010010011001011011111000001001011101001
Pair \(Z_2\) Length of longest common subsequence
5OCV_1,3LXR_1 163 3
5OCV_1,5XCA_1 163 2
3LXR_1,5XCA_1 172 4

Newick tree

 
[
	5XCA_1:84.52,
	[
		5OCV_1:81.5,3LXR_1:81.5
	]:3.02
]

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 \((0.85)(0.8)(\frac{314 }{\log_{20} 314}-\frac{129}{\log_{20}129})=57.1\)
Status Protein1 Protein2 d d1/2
Query variables 5OCV_1 3LXR_1 74 62
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]