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Parikh vectors
5HDO_1 6RWE_1 4IBV_1 Letter Amino acid
3 0 6 I Isoleucine
1 0 6 M Methionine
8 22 14 T Threonine
12 17 7 A Alanine
8 0 18 R Arginine
1 0 7 H Histidine
9 0 14 L Leucine
2 0 1 W Tryptophan
6 0 8 Y Tyrosine
2 0 14 P Proline
9 0 15 V Valine
5 0 8 D Aspartic acid
4 24 11 C Cysteine
8 0 7 Q Glutamine
6 0 11 E Glutamic acid
16 7 14 G Glycine
4 0 7 K Lycine
4 0 9 N Asparagine
3 0 5 F Phenylalanine
17 0 18 S Serine 

5HDO_1|Chains A, B, C, D|Anti-HCV NS3/4A serine protease immoglobulin heavy chain|Camelus dromedarius (9838)
>6RWE_1|Chain A[auth T]|Template strand|synthetic construct (32630)
>4IBV_1|Chain A|Cellular tumor antigen p53|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 \(w=f(c)\)
5HDO , Knot 60 128 0.75 40 95 121 
QVQLQESGGGLVQAGGSLRLSCAASGFTLDSYAIGWFRQAPGKEREGVSCISASGGSTNYADSVKGRFTISRDNAKNTVYLQMNSLKSEDTAVYYCAADHPGLCTSESGRRRYLEVWGQGTQVTVSSA
6RWE , Knot 24 70 0.48 8 15 37 
GTCTTCAACTGCTTTCGCATGAAGTACCTCCCAACTACTTTTCCTCACACTTGTACTCCATGACTAAACC
4IBV , Knot 95 200 0.84 40 145 195 
SSSVPSQKTYQGSYGFRLGFLHSGTAKSVTCTYSPALNKMFCQLAKTCPVQLWVDSTPPPGTRVRAMAIYKQSQHMTEVVRRCPHHERCSDSDGLAPPQHLIRVEGNLRVEYLDDRNTFRHSVVVPYEPPEVGSDCTTIHYNYMCNRSCMGGMNRRPILTIITLEDSSGNLLGRNSFEVCVCACPGRDRRTEEENLRKKG

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 \(c\).

\(|P_{f(5HDO_1)}(2) \setminus P_{f(6RWE_1)}(2)|=89\), \(|P_{f(6RWE_1)}(2) \setminus P_{f(5HDO_1)}(2)|=9\). 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 1:01010001111101110101001101101000111110011100001100101011000010010101010000100010101001000001100011001110000010000101110100101001
Pair \(Z_2\) Length of longest common subsequence
5HDO_1,6RWE_1 98 3
5HDO_1,4IBV_1 152 3
6RWE_1,4IBV_1 146 3

Newick tree

 
[
	4IBV_1:81.25,
	[
		5HDO_1:49,6RWE_1:49
	]:32.25
]

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 \((0.85)(0.8)(\frac{198 }{\log_{20} 198}-\frac{70}{\log_{20}70})=42.7\)
Status Protein1 Protein2 d d1/2
Query variables 5HDO_1 6RWE_1 57 38
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]