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Parikh vectors
7ORR_1 3IKY_1 3VAZ_1 Letter Amino acid
7 24 26 D Aspartic acid
3 6 11 H Histidine
4 6 8 M Methionine
6 8 8 P Proline
1 3 2 W Tryptophan
1 11 14 R Arginine
6 23 15 N Asparagine
10 15 34 A Alanine
5 10 10 F Phenylalanine
13 21 29 G Glycine
6 30 26 L Leucine
13 21 26 T Threonine
5 12 8 Y Tyrosine
8 25 36 V Valine
13 2 2 C Cysteine
4 12 12 Q Glutamine
8 22 21 K Lycine
6 25 19 S Serine
2 18 23 E Glutamic acid
4 26 14 I Isoleucine 

7ORR_1|Chain A|Non-structural protein 10|Severe acute respiratory syndrome coronavirus 2 (2697049)
>3IKY_1|Chains A, B, C, D, E, F, G, H, I, J, K, L|Plasmid segregation protein parM|Escherichia coli (562)
>3VAZ_1|Chains A, B, C[auth O], D[auth P], E[auth Q], F[auth R]|Glyceraldehyde-3-phosphate dehydrogenase 1|Staphylococcus aureus (282458)
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 \(w=f(c)\)
7ORR , Knot 63 125 0.81 40 104 122 
TMGNSTVLSFCAFAVDAAKAYKDYLASGGQPITNCVKMLCTHTGTGQAITVTPEANMDQESFGGASCCLYCRCHIDHPNPKGFCDLKGKYVQIPTTCANDPVGFTLKNTVCTVCGMWKGYGCSCD
3IKY , Knot 140 320 0.84 40 188 307 
MLVFIDDGSTNIKLQWQESDGTIKQHISPNSFKREWAVSFGDKKVFNYTLNGEQYSFDPISPDAVVTTNIAWQYSDVNVVAVHHALLTSGLPVSEVDIVCTLPLTEYYDRNNQPNTENIERKKANFRKKITLNGGDTFTIKDVKVMPESIPAGYEVLQELDELDSLLIIDLGGTTLDISQVMGKLSGISKIYGDSSLGVSLVTSAVKDALSLARTKGSSYLADDIIIHRKDNNYLKQRINDENKISIVTEAMNEALRKLEQRVLNTLNEFSGYTHVMVIGGGAELICDAVKKHTQIRDERFFKTNNSQYDLVNGMYLIGN
3VAZ , Knot 143 344 0.81 40 192 321 
HHHHHHGSMAVKVAINGFGRIGRLAFRRIQEVEGLEVVAVNDLTDDDMLAHLLKYDTMQGRFTGEVEVVDGGFRVNGKEVKSFSEPDASKLPWKDLNIDVVLECTGFYTDKDKAQAHIEAGAKKVLISAPATGDLKTIVFNTNHQELDGSETVVSGASCTTNSLAPVAKVLNDDFGLVEGLMTTIHAYTGDQNTQDAPHRKGDKRRARAAAENIIPNSTGAAKAIGKVIPEIDGKLDGGAQRVPVATGSLTELTVVLEKQDVTVEQVNEAMKNASNESFGYTEDEIVSSDVVGMTYGSLFDATQTRVMSVGDRQLVKVAAWYDNEMSYTAQLVRTLAYLAELSK

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 \(c\).

\(|P_{f(7ORR_1)}(2) \setminus P_{f(3IKY_1)}(2)|=49\), \(|P_{f(3IKY_1)}(2) \setminus P_{f(7ORR_1)}(2)|=133\). 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 1:01100011010111101101000011011011000101100001010110101010100001111000100000100101011001010010110001001111010001001011101010000
Pair \(Z_2\) Length of longest common subsequence
7ORR_1,3IKY_1 182 3
7ORR_1,3VAZ_1 178 4
3IKY_1,3VAZ_1 136 4

Newick tree

 
[
	7ORR_1:96.22,
	[
		3VAZ_1:68,3IKY_1:68
	]:28.22
]

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 \((0.85)(0.8)(\frac{445 }{\log_{20} 445}-\frac{125}{\log_{20}125})=95.9\)
Status Protein1 Protein2 d d1/2
Query variables 7ORR_1 3IKY_1 124 85.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]