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Parikh vectors
3TCQ_1 4MEA_1 7BWJ_1 Letter Amino acid
7 18 7 E Glutamic acid
8 13 7 H Histidine
24 23 9 I Isoleucine
35 25 13 L Leucine
11 9 0 M Methionine
21 27 12 A Alanine
10 6 11 R Arginine
2 0 8 C Cysteine
22 16 18 V Valine
11 15 18 N Asparagine
9 17 15 F Phenylalanine
8 19 15 Y Tyrosine
15 9 7 Q Glutamine
36 19 13 P Proline
2 4 2 W Tryptophan
23 23 16 S Serine
23 13 12 T Threonine
19 17 9 D Aspartic acid
20 30 15 G Glycine
20 28 10 K Lycine 

3TCQ_1|Chain A|Matrix protein VP40|Sudan ebolavirus (128948)
>4MEA_1|Chains A, B|Predicted protein|Acinetobacter sp. RUH2624 (575564)
>7BWJ_1|Chain A[auth E]|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 \(w=f(c)\)
3TCQ , Knot 137 326 0.81 40 197 309 
MRRVTVPTAPPAYADIGYPMSMLPIKSSRAVSGIQQKQEVLPGMDTPSNSMRPVADDNIDHTSHTPNGVASAFILEATVNVISGPKVLMKQIPIWLPLGIADQKTYSFDSTTAAIMLASYTITHFGKANNPLVRVNRLGQGIPDHPLRLLRMGNQAFLQEFVLPPVQLPQYFTFDLTALKLVTQPLPAATWTDETPSNLSGALRPGLSFHPKLRPVLLPGKTGKKGHVSDLTAPDKIQTIVNLMQDFKIVPIDPAKSIIGIEVPELLVHKLTGKKMSQKNGQPIIPVLLPKYIGLDPISPGDLTMVITPDYDDCHSPASCSYLSEK
4MEA , Knot 144 331 0.84 38 200 312 
EYDPNLKSIDTPPAVSQQMFNKVKSNGLGQYAYAKGLSSKFIESEGVKLHYVEGGSKGTPIVFIHGFGSTWKMWEPVMLSYMKDHKVIAIDLPGLGQSGPILNDDYSAENTSKILIGAIKKIAGKGPIYYVSHDLGNTASYPLVANNQGYIKKAVFMDSPIPDRAMFEYPGYTADGPGLGWHFGYFSFGDIAEKQIANDPNLFFSYFIKTYAGKKEIFTPELLAELIEPYSTRDKLKAAFGYYRSHADSIRQNEALLANGKKLTIPSMALTGQKGVNDVLVKEMRARFVADPAQYTAIILPDTGHWMVEENAEGVEKSLSNFLFKHHHHHH
7BWJ , Knot 100 217 0.82 38 149 206 
RVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKHHHHHH

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 \(c\).

\(|P_{f(3TCQ_1)}(2) \setminus P_{f(4MEA_1)}(2)|=73\), \(|P_{f(4MEA_1)}(2) \setminus P_{f(3TCQ_1)}(2)|=76\). 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 1:10010110111101011011011110000110110000011111001000101110001000000101110111101010110110111001111111111000000100001111110001001101001110100110111001101101100111001111110110010101011011001111101000010010111011101010101111110010010100101100100110110010111101100111101101110010100100001011111111001110110110101110100000001100001000
Pair \(Z_2\) Length of longest common subsequence
3TCQ_1,4MEA_1 149 4
3TCQ_1,7BWJ_1 186 3
4MEA_1,7BWJ_1 179 7

Newick tree

 
[
	7BWJ_1:96.20,
	[
		3TCQ_1:74.5,4MEA_1:74.5
	]:21.70
]

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 \((0.85)(0.8)(\frac{657 }{\log_{20} 657}-\frac{326}{\log_{20}326})=91.5\)
Status Protein1 Protein2 d d1/2
Query variables 3TCQ_1 4MEA_1 115 113
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]