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Parikh vectors
5AGQ_1 7EOV_1 1ZOQ_1 Letter Amino acid
8 12 14 P Proline
8 24 12 S Serine
1 14 1 N Asparagine
12 27 13 E Glutamic acid
5 25 20 L Leucine
3 6 4 M Methionine
3 10 4 Y Tyrosine
8 15 20 V Valine
15 15 13 R Arginine
6 12 7 Q Glutamine
9 16 24 G Glycine
5 20 7 F Phenylalanine
4 12 4 H Histidine
6 25 3 I Isoleucine
5 22 4 K Lycine
4 9 9 W Tryptophan
4 11 9 A Alanine
2 10 8 D Aspartic acid
1 4 5 C Cysteine
4 13 10 T Threonine 

5AGQ_1|Chain A|BROMODOMAIN ADJACENT TO ZINC FINGER DOMAIN PROTEIN 2A|HOMO SAPIENS (9606)
>7EOV_1|Chain A|cytosolic sulfotransferase SULT2A8|Mus musculus (10090)
>1ZOQ_1|Chains A, C[auth B]|Interferon regulatory factor 3|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 \(w=f(c)\)
5AGQ , Knot 57 113 0.79 40 89 108 
GAMERRRIATPEEVRLPLQHGWRREVRIKKGSHRWQGETWYYGPCGKRMKQFPEVIKYLSRNVVHSVRREHFSFSPRMPVGDFFEERDTPEGLQWVQLSAEEIPSRIQAITGS
7EOV , Knot 135 302 0.85 40 193 290 
MGSSHHHHHHSSGLVPRGSHMTDEFLWIEGIPFPTVYYSQEIIREVRDRFVVRDEDTIIVTYPKSGTHWLNEIVCLILTKGDPTWVQSTIANERTPWIEFENNYRILNSKEGPRLMASLLPIQLFPKSFFSSKAKVIYLIRNPRDVLVSGYHYFNALKQGKEQVPWKIYFENFLQGKSYFGSWFEHACGWISLRKRENILVLSYEQLKKDTRNTIKKICEFLGENLESGELELVLKNISFQIMKERMISQSCLSNIEKHEFIMRKGITGDWKNHFTVAQAEAFDKAFQEKAADFPQELFSWE
1ZOQ , Knot 90 191 0.82 40 137 186 
LVPGEEWEFEVTAFYRGRQVFQQTISCPEGLRLVGSEVGDRTLPGWPVTLPDPGMSLTDRGVMSYVRHVLSCLGGGLALWRAGQWLWAQRLGHCHTYWAVSEELLPNSGHGPDGEVPKDKEGGVFDLGPFIVDLITFTEGSGRSPRYALWFCVGESWPQDQPWTKRLVMVKVVPTCLRALVEMARVGGASS

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 \(c\).

\(|P_{f(5AGQ_1)}(2) \setminus P_{f(7EOV_1)}(2)|=32\), \(|P_{f(7EOV_1)}(2) \setminus P_{f(5AGQ_1)}(2)|=136\). 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 1:11100001101001011100110001010010001010010011010010011011001000110010000101010111101100000101101101010011001011010
Pair \(Z_2\) Length of longest common subsequence
5AGQ_1,7EOV_1 168 4
5AGQ_1,1ZOQ_1 174 4
7EOV_1,1ZOQ_1 186 3

Newick tree

 
[
	1ZOQ_1:91.97,
	[
		5AGQ_1:84,7EOV_1:84
	]:7.97
]

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 \((0.85)(0.8)(\frac{415 }{\log_{20} 415}-\frac{113}{\log_{20}113})=91.5\)
Status Protein1 Protein2 d d1/2
Query variables 5AGQ_1 7EOV_1 118 80
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]