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Parikh vectors
8SZD_1 5YWX_1 4IHS_1 Letter Amino acid
5 5 8 H Histidine
4 6 0 W Tryptophan
10 15 2 D Aspartic acid
1 3 1 C Cysteine
4 9 3 Y Tyrosine
9 9 6 V Valine
15 12 8 E Glutamic acid
10 5 6 S Serine
7 9 2 N Asparagine
2 9 7 Q Glutamine
14 7 4 G Glycine
11 14 5 I Isoleucine
11 23 10 L Leucine
8 8 4 F Phenylalanine
17 13 6 A Alanine
11 10 6 R Arginine
8 10 4 P Proline
6 14 4 T Threonine
4 12 5 K Lycine
7 5 3 M Methionine 

8SZD_1|Chain A|Dihydrofolate reductase|Yersinia pestis (632)
>5YWX_1|Chains A, B, C, D|Hematopoietic prostaglandin D synthase|Homo sapiens (9606)
>4IHS_1|Chains A, B, C, D|HTH-type transcriptional regulator BenM|Acinetobacter sp. (62977)
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 \(w=f(c)\)
8SZD , Knot 79 164 0.82 40 121 160 
SGGGMIISLIAALAADRVIGMENAMPWHLPADLAWFKRNTLNKPVIMGRKTFESIGRPLPGRLNIVISSQPGTDERVTWAASIEEALAFAGNAEEVMVMGGGRVYKQFLDRANRMYLTHIDAEVGGDTHFPDYEPDEWESVFSEFHDADEANSHSYCFEILERR
5YWX , Knot 97 198 0.86 40 150 195 
PNYKLTYFNMRGRAEIIRYIFAYLDIQYEDHRIEQADWPEIKSTLPFGKIPILEVDGLTLHQSLAIARYLTKNTDLAGNTEMEQCHVDAIVDTLDDFMSCFPWAEKKQDVKEQMFNELLTYNAPHLMQDLDTYLGGREWLIGNSVTWADFYWEICSTTLLVFKPDLLDNHPRLVTLRKKVQAIPAVANWIKRRPQTKL
4IHS , Knot 50 94 0.80 38 76 89 
MELRHLRYFVAVVEEQSFTKAADKLCIAQPPLSRQIQNLEEELGIQLLERGSRPVKTTPEGHFFYQYAIKLLSNVDQMVSMTKRIASGHHHHHH

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 \(c\).

\(|P_{f(8SZD_1)}(2) \setminus P_{f(5YWX_1)}(2)|=64\), \(|P_{f(5YWX_1)}(2) \setminus P_{f(8SZD_1)}(2)|=93\). 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 1:01111110111111100111100111101110111100001001111100010011011110101110001100001011101001111110100111111101000110010010100101011100011000100100110010010010000001011000
Pair \(Z_2\) Length of longest common subsequence
8SZD_1,5YWX_1 157 4
8SZD_1,4IHS_1 161 3
5YWX_1,4IHS_1 164 2

Newick tree

 
[
	4IHS_1:82.15,
	[
		8SZD_1:78.5,5YWX_1:78.5
	]:3.65
]

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 \((0.85)(0.8)(\frac{362 }{\log_{20} 362}-\frac{164}{\log_{20}164})=59.6\)
Status Protein1 Protein2 d d1/2
Query variables 8SZD_1 5YWX_1 76 70
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]