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Parikh vectors
5TJC_1 9FSW_1 7YCK_1 Letter Amino acid
10 9 9 R Arginine
9 14 6 E Glutamic acid
1 6 0 M Methionine
14 6 11 P Proline
17 12 9 D Aspartic acid
12 22 7 I Isoleucine
23 17 13 L Leucine
6 9 10 K Lycine
16 11 16 S Serine
1 0 2 W Tryptophan
10 6 15 Y Tyrosine
13 19 12 A Alanine
4 1 8 C Cysteine
10 12 6 Q Glutamine
13 14 15 G Glycine
16 9 7 H Histidine
11 5 14 F Phenylalanine
12 7 16 V Valine
11 9 17 N Asparagine
14 11 11 T Threonine 

5TJC_1|Chain A|Mucolipin-1|Homo sapiens (9606)
>9FSW_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N|ATP-dependent Clp protease proteolytic subunit|Staphylococcus epidermidis (1282)
>7YCK_1|Chains A, D[auth B]|Spike protein S1|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 \(w=f(c)\)
5TJC , Knot 100 223 0.80 40 153 207 
GSGLSNQLAVTFREENTIAFRHLFLLGYSDGADDTFAAYTREQLYQAIFHAVDQYLALPDVSLGRYAYVRGGGDPWTNGSGLALCQRYYHRGHVDPANDTFDIDPMVVTDCIQVDPPERPPPPPSDDLTLLESSSSYKNLTLKFHKLVNVTIHFRLKTINLQSLINNEIPDCYTFSVLITFDNKAHSGRIPISLETQAHIQECKHPSVFQHGDNSLEHHHHHH
9FSW , Knot 93 199 0.82 38 143 192 
MNLIPTVIETTNRGERAYDIYSRLLKDRIIMLGSQIDDNVANSIVSQLLFLQAQDSEKDIYLYINSPGGSVTAGFAIYDTIQHIKPDVQTICIGMAASMGSFLLAAGAKGKRFALPNAEVMIHQPLGGAQGQATEIEIAANHILKTREKLNRILSERTGQSIEKIQQDTDRDNFLTAAEAKEYGLIDEVMEPEHHHHHH
7YCK , Knot 93 204 0.80 38 142 194 
TNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSHHHHHH

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 \(c\).

\(|P_{f(5TJC_1)}(2) \setminus P_{f(9FSW_1)}(2)|=89\), \(|P_{f(9FSW_1)}(2) \setminus P_{f(5TJC_1)}(2)|=79\). 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 1:1011000111010000011100111110001100011100000100111011000111101011001010111011001011110000000101011000101011110001010110011111000101100000000101010011010101010010100110001100001011101000100101110100010100000101100100010000000
Pair \(Z_2\) Length of longest common subsequence
5TJC_1,9FSW_1 168 7
5TJC_1,7YCK_1 181 6
9FSW_1,7YCK_1 155 6

Newick tree

 
[
	5TJC_1:90.34,
	[
		9FSW_1:77.5,7YCK_1:77.5
	]:12.84
]

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 \((0.85)(0.8)(\frac{422 }{\log_{20} 422}-\frac{199}{\log_{20}199})=65.6\)
Status Protein1 Protein2 d d1/2
Query variables 5TJC_1 9FSW_1 82 79.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]