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Parikh vectors
3ZPF_1 7AHW_1 6LEB_1 Letter Amino acid
7 8 20 Q Glutamine
16 3 15 I Isoleucine
10 1 2 M Methionine
16 8 27 S Serine
1 0 2 W Tryptophan
13 2 34 N Asparagine
3 12 27 D Aspartic acid
18 12 19 G Glycine
13 23 12 L Leucine
9 3 4 R Arginine
2 2 0 C Cysteine
6 17 9 E Glutamic acid
8 19 3 H Histidine
9 6 14 F Phenylalanine
12 9 5 P Proline
13 5 39 T Threonine
3 1 21 Y Tyrosine
6 27 13 A Alanine
17 7 22 V Valine
8 14 27 K Lycine 

3ZPF_1|Chain A|FIBER|AVIRULENT TURKEY HEMORRHAGIC ENTERITIS VIRUS (318490)
>7AHW_1|Chain A[auth AAA]|Uncharacterized protein|Pseudomonas aeruginosa PAO1 (208964)
>6LEB_1|Chains A, B|Ser-Asp rich fibrinogen-binding, bone sialoprotein-binding protein|Staphylococcus aureus (1280)
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 \(w=f(c)\)
3ZPF , Knot 87 190 0.80 40 131 182 
MGSSHHHHHHSSGLVPRGSHMASMTGGQQMGRGSEFASIGPPTTMVTGTVSPGRATNGQFVTKTAKVLRYKFVRWDALLIIQFIDNIGVMENPTFYRNKSIELRSADFLSPMLNNTYIVPLNGGVRVESPTIPVQLEVILENNSSFIQVGFVRLTVKNGNPHMIIQCNPVPGNIKMIKIKSVMLFTCLIG
7AHW , Knot 74 179 0.71 38 107 157 
HDDHDHDHAHGSLGKHEHGVAQLNVALDGKTLELELDSPAMNLVGFEHAASTDADKAAVAKARAQLEKPLELFALPVTAGCSVASQELRSPLFGDKAPAHAHKEKAGHEHEHEHEHEHGHADIHAHYQLSCEKPELLKLLTLAEFFKRFPATQKIQVQLIGPDGQKGADLAPASAELKL
6LEB , Knot 133 315 0.81 38 167 294 
QGTNVNDKVHFTNIDIAIDKGHVNKTTGNTEFWATSSDVLKLKANYTIDDSVKEGDTFTFKYGQYFRPGSVRLPSQTQNLYNAQGNIIAKGIYDSKTNTTTYTFTNYVDQYTNVSGSFEQVAFAKRENATTDKTAYKMEVTLGNDTYSKDVIVDYGNQKGQQLISSTNYINNEDLSRNMTVYVNQHKKTYTKETFVTNLTGYKFNPDAKNFKIYEVTDQNQFVDSFTPDTSKLKDVTGQFDVIYSNDNKTATVDLLNGQSSSDKQYIIQQVAYPDNSSTDNGKIDYTLETQNGKSSWSNSYSNVNGSSTANGDQK

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 \(c\).

\(|P_{f(3ZPF_1)}(2) \setminus P_{f(7AHW_1)}(2)|=91\), \(|P_{f(7AHW_1)}(2) \setminus P_{f(3ZPF_1)}(2)|=67\). 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 1:1100000000001111010011010110011010011011110011010101101001011000101100011010111110110011110010100000101001011011100001111011101001011101011100000110111101010010101110001111010110100111100111
Pair \(Z_2\) Length of longest common subsequence
3ZPF_1,7AHW_1 158 4
3ZPF_1,6LEB_1 162 3
7AHW_1,6LEB_1 172 3

Newick tree

 
[
	6LEB_1:84.99,
	[
		3ZPF_1:79,7AHW_1:79
	]:5.99
]

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 \((0.85)(0.8)(\frac{369 }{\log_{20} 369}-\frac{179}{\log_{20}179})=56.8\)
Status Protein1 Protein2 d d1/2
Query variables 3ZPF_1 7AHW_1 73 68
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]