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Parikh vectors
6IFH_1 2NXR_1 7ETQ_1 Letter Amino acid
3 10 0 N Asparagine
8 24 0 K Lycine
1 18 0 S Serine
7 17 0 V Valine
7 7 0 R Arginine
12 19 0 D Aspartic acid
0 1 0 C Cysteine
3 11 0 Q Glutamine
1 12 0 H Histidine
10 9 0 I Isoleucine
4 13 0 F Phenylalanine
0 7 0 W Tryptophan
8 13 0 A Alanine
9 13 0 E Glutamic acid
16 26 2 L Leucine
8 22 0 G Glycine
7 2 1 M Methionine
5 17 1 P Proline
6 12 0 T Threonine
4 7 0 Y Tyrosine 

6IFH_1|Chain A|Sporulation initiation phosphotransferase F|Paenisporosarcina sp. TG-14 (1231057)
>2NXR_1|Chain A|carbonic anhydrase 2|Homo sapiens (9606)
>7ETQ_1|Chain A|Pro-Met-Leu-Leu|synthetic construct (32630)
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 \(w=f(c)\)
6IFH , Knot 59 119 0.79 36 94 115 
MKQLLIVDDQQGIRLLLNEVFKREGYTTFLAANGIEALDIAERVKPDGVLLDMKIPGMDGIEILKRIKTRTPDVPVLMMTAYGELDLIKEAMDLGASHYFTKPFDIYELRDAVNEMLRD
2NXR , Knot 112 260 0.79 40 176 248 
MSHHWGFGKHNGPEHWHKDFPIAKGERQSPVDIDTHTAKYDPSLKPLSVSYDQATSLRILNNGHAFNVEFDDSQDKAVLKGGPLDGTYRLIQFHFHWGSLDGQGSEHTVDKKKYAAELHLVHWNTKYGDFGKAVQQPDGLAVLGIFLKVGSAKPGLQKVVDVLDSIKTKGKSADFTNFDPRGLLPESLDYWTYPGSLTTPPLLECVTWIVLKEPISVSSEQVLKFRKLNFNGEGEPEELMVDNWRPAQPLKNRQIKASFK
7ETQ , Knot 4 4 0.46 6 3 2 
PMLL

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 \(c\).

\(|P_{f(6IFH_1)}(2) \setminus P_{f(2NXR_1)}(2)|=44\), \(|P_{f(2NXR_1)}(2) \setminus P_{f(6IFH_1)}(2)|=126\). 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 1:10011110000110111001100010001111011011011001010111101011110110110010000101111110101010110011011100010011010010011001100
Pair \(Z_2\) Length of longest common subsequence
6IFH_1,2NXR_1 170 3
6IFH_1,7ETQ_1 93 2
2NXR_1,7ETQ_1 177 2

Newick tree

 
[
	2NXR_1:96.52,
	[
		6IFH_1:46.5,7ETQ_1:46.5
	]:50.02
]

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 \((0.85)(0.8)(\frac{379 }{\log_{20} 379}-\frac{119}{\log_{20}119})=79.3\)
Status Protein1 Protein2 d d1/2
Query variables 6IFH_1 2NXR_1 102 73
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]