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Parikh vectors
1LTQ_1 8CQU_1 2IEQ_1 Letter Amino acid
19 14 8 I Isoleucine
13 6 0 P Proline
14 15 9 A Alanine
9 5 10 N Asparagine
22 11 4 D Aspartic acid
4 2 0 C Cysteine
4 5 3 H Histidine
21 16 4 E Glutamic acid
29 13 4 K Lycine
14 0 2 Y Tyrosine
19 7 3 R Arginine
24 9 8 G Glycine
17 4 10 T Threonine
8 4 0 W Tryptophan
28 12 7 V Valine
8 9 10 Q Glutamine
14 16 13 L Leucine
12 8 0 M Methionine
9 8 3 F Phenylalanine
13 16 11 S Serine 

1LTQ_1|Chain A|POLYNUCLEOTIDE KINASE|Enterobacteria phage T4 (10665)
>8CQU_1|Chains A, B|Putative NADH dehydrogenase/NAD(P)H nitroreductase|Bacteroides thetaiotaomicron (818)
>2IEQ_1|Chains A, B, C|Spike glycoprotein|Human coronavirus (277944)
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 \(w=f(c)\)
1LTQ , Knot 133 301 0.84 40 199 293 
MKKIILTIGCPGSGKSTWAREFIAKNPGFYNINRDDYRQSIMAHEERDEYKYTKKKEGIVTGMQFDTAKSILYGGDSVKGVIISDTNLNPERRLAWETFAKEYGWKVEHKVFDVPWTELVKRNSKRGTKAVPIDVLRSMYKSMREYLGLPVYNGTPGKPKAVIFDVDGTLAKMNGRGPYDLEKCDTDVINPMVVELSKMYALMGYQIVVVSGRESGTKEDPTKYYRMTRKWVEDIAGVPLVMQCQREQGDTRKDDVVKEEIFWKHIAPHFDVKLAIDDRTQVVEMWRRIGVECWQVASGDF
8CQU , Knot 85 180 0.81 38 133 174 
GPMENFSELIKNRRSMRKFTDEELTQDEVVALMKAALMSPSSKRSNSWQFVVVDDKEKLKELSHCKEQASSFIADAALAIVVMADPLASDVWIEDASIASIMIQLQAEDLGLGSCWVQVRERFTATGMPSDEFVHGILDIPLQLQILSVIAIGHKGMERKPFNEEHLQWEKIHINKFGGK
2IEQ , Knot 53 109 0.76 32 83 105 
KAINNIVASFSSVNDAITQTAEAIHTVTIALNKIQDVVNQQGSALNHLTSQLRHNFQSGGRGSGRGGNLTYLNLSSELKQLEAKTASLFQTTVELQGLIDQINSTYVDL

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 \(c\).

\(|P_{f(1LTQ_1)}(2) \setminus P_{f(8CQU_1)}(2)|=121\), \(|P_{f(8CQU_1)}(2) \setminus P_{f(1LTQ_1)}(2)|=55\). 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 1:1001110110110100011001110011100100000000111000000000000001110110100100110110010111100001010001110011000110100011011100110000001001111011001000100011111001011010111101010110101011001000000110111101001011110011110100010000100000100011001111111100000010000001100011100111010101110000011011001110010110101
Pair \(Z_2\) Length of longest common subsequence
1LTQ_1,8CQU_1 176 3
1LTQ_1,2IEQ_1 200 3
8CQU_1,2IEQ_1 136 3

Newick tree

 
[
	1LTQ_1:10.42,
	[
		8CQU_1:68,2IEQ_1:68
	]:33.42
]

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 \((0.85)(0.8)(\frac{481 }{\log_{20} 481}-\frac{180}{\log_{20}180})=88.0\)
Status Protein1 Protein2 d d1/2
Query variables 1LTQ_1 8CQU_1 113 88
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]