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Parikh vectors
7WKO_1 2WQF_1 5RTG_1 Letter Amino acid
8 10 3 Q Glutamine
19 13 13 G Glycine
10 1 6 H Histidine
6 3 2 M Methionine
13 9 6 T Threonine
7 12 9 D Aspartic acid
13 19 19 L Leucine
6 13 22 V Valine
20 10 16 N Asparagine
4 8 2 R Arginine
6 0 3 C Cysteine
14 18 6 E Glutamic acid
14 12 13 K Lycine
12 10 11 S Serine
12 3 7 Y Tyrosine
6 24 15 A Alanine
10 12 5 F Phenylalanine
6 7 5 P Proline
2 6 0 W Tryptophan
12 12 6 I Isoleucine 

7WKO_1|Chain A|Csy1|Vibrio phage ICP1_2011_A (1296592)
>2WQF_1|Chain A|COPPER INDUCED NITROREDUCTASE D|LACTOCOCCUS LACTIS (1358)
>5RTG_1|Chains A, B|Non-structural protein 3|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
7WKO , Knot 92 200 0.81 40 138 192 
MGSSHHHHHHSSGRENLYFQGMIKEMIEDFISKGGLIFTHSGRYTNTNNSCFIFNKNDIGVDTKVDMYTPKSAGIKNEEGENLWQVLNKANMFYRIYSGELGEELQYLLKSCCTAKEDVTTLPQIYFKNGEGYDILVPIGNAHNLISGTEYLWEHKYYNTFTQKLGGSNPQNCTHACNKMRGGFKQFNCTPPQVEDNYNA
2WQF , Knot 96 202 0.84 38 146 194 
MSFIKSLENRRTIYALGRNVQDEEKVIETIKEAVRFSPTAFNSQTGRLLILTGDAQDKLWDEIVAPELKAAMEAQGVPESAWDNTRAKLDGFKAAFGTILFFEDQAVVKNLQEQFALYADNFPVWSEQGSGIISVNVWTALAELGLGANLQHYNPLIDEAVAKEWNLPESWKLRGQLVFGSIEAPAGEKTFMDDADRFIVAK
5RTG , Knot 80 169 0.81 38 119 162 
SMVNSFSGYLKLTDNVYIKNADIVEEAKKVKPTVVVNAANVYLKHGGGVAGALNKATNNAMQVESDDYIATNGPLKVGGSCVLSGHNLAKHCLHVVGPNVNKGEDIQLLKSAYENFNQHEVLLAPLLSAGIFGADPIHSLRVCVDTVRTNVYLAVFDKNLYDKLVSSFL

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 \(c\).

\(|P_{f(7WKO_1)}(2) \setminus P_{f(2WQF_1)}(2)|=86\), \(|P_{f(2WQF_1)}(2) \setminus P_{f(7WKO_1)}(2)|=94\). 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 1:11000000000010001010111001100110011111000100000000011100001110001010010011100001001101100101100100101100100110000010001001101010010100111111010011010001100000001000111001000001000101110010001101000001
Pair \(Z_2\) Length of longest common subsequence
7WKO_1,2WQF_1 180 3
7WKO_1,5RTG_1 159 4
2WQF_1,5RTG_1 149 3

Newick tree

 
[
	7WKO_1:88.11,
	[
		5RTG_1:74.5,2WQF_1:74.5
	]:13.61
]

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 \((0.85)(0.8)(\frac{402 }{\log_{20} 402}-\frac{200}{\log_{20}200})=59.6\)
Status Protein1 Protein2 d d1/2
Query variables 7WKO_1 2WQF_1 76 75
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]