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Parikh vectors
7XBN_1 8AWG_1 7WBF_1 Letter Amino acid
30 12 6 V Valine
32 14 12 G Glycine
23 3 1 H Histidine
53 24 8 L Leucine
21 19 10 S Serine
49 24 12 A Alanine
2 2 8 C Cysteine
24 10 7 T Threonine
6 2 6 W Tryptophan
4 17 6 K Lycine
33 5 2 P Proline
8 10 3 Y Tyrosine
45 13 11 R Arginine
33 14 7 D Aspartic acid
29 29 2 E Glutamic acid
13 10 6 I Isoleucine
6 7 14 N Asparagine
8 7 3 Q Glutamine
13 9 2 M Methionine
11 5 3 F Phenylalanine 

7XBN_1|Chains A, B|Cytochrome P450 monooxygenase PikC|Streptomyces venezuelae (54571)
>8AWG_1|Chain A|14-3-3 protein sigma|Homo sapiens (9606)
>7WBF_1|Chain A|Lysozyme C|Gallus gallus (9031)
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 \(w=f(c)\)
7XBN , Knot 179 444 0.82 42 213 401 
MGSSHHHHHHSSGLVPRGSHMRRTQQGTTASPPVLDLGALGQDFAADPYPTYARLRAEGPAHRVRTPEGDEVWLVVGYDRARAVLADPRFSKDWRNSTTPLTEAEAALNHNMLESDPPRHTRLRKLVAREFTMRRVELLRPRVQEIVDGLVDAMLAAPDGRADLMESLAWPLPITVISELLGVPEPDRAAFRVWTDAFVFPDDPAQAQTAMAEMSGYLSRLIDSKRGQDGEDLLSALVRTSDEDGSRLTSEELLGMAXILLVAGHETTVNLIANGMYALLSHPDQLAALRADMTLLDGAVEEMLRYEGPVESATYRFPVEPVDLDGTVIPAGDTVLVVLADAHRTPERFPDPHRFDIRRDTAGHLAFGHGIHFCIGAPLARLEARIAVRALLERCPDLALDVSPGELVWYPNPMIRGLKALPIRWRRGREAGRRTGLEHHHHHH
8AWG , Knot 108 236 0.83 40 164 229 
GAMGSMERASLIQKAKLAEQAERYEDMAAFMKGAVEKGEELSCEERNLLSVAYKNVVGGQRAAWRVLSSIEQKSNEEGSEEKGPEVREYREKVETELQGVCDTVLGLLDSHLIKEAGDAESRVFYLKMKGDYYRYLAEVATGDDKKRIIDSARSAYQEAMDISKKEMPPTNPIRLGLALNFSVFHYEIANSPEEAISLAKTTFDEAMADLHTLSEDSYKDSTLIMQLLRDNLTLWT
7WBF , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL

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 \(c\).

\(|P_{f(7XBN_1)}(2) \setminus P_{f(8AWG_1)}(2)|=103\), \(|P_{f(8AWG_1)}(2) \setminus P_{f(7XBN_1)}(2)|=54\). 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 1:110000000000111101001000001001011110111110011101010010101011100100101001111110001011110101000100000110010111000110001100001001110010100101101010011011101111110101011001111111011001111101001110110011111001101001110101010011000010010011011100000010010000111110111111000010111011011100100111101010110111001100011100100011101101010111110011111101000100110100101000011011110110101111110101011101110001011101011011101011101101111010010011000110000000
Pair \(Z_2\) Length of longest common subsequence
7XBN_1,8AWG_1 157 4
7XBN_1,7WBF_1 197 4
8AWG_1,7WBF_1 176 3

Newick tree

 
[
	7WBF_1:97.86,
	[
		7XBN_1:78.5,8AWG_1:78.5
	]:19.36
]

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 \((0.85)(0.8)(\frac{680 }{\log_{20} 680}-\frac{236}{\log_{20}236})=124.\)
Status Protein1 Protein2 d d1/2
Query variables 7XBN_1 8AWG_1 153 117.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]