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Parikh vectors
7UFO_1 6DIK_1 1AHH_1 Letter Amino acid
6 7 16 N Asparagine
9 9 2 Y Tyrosine
9 6 13 D Aspartic acid
3 1 8 M Methionine
12 6 9 P Proline
32 4 18 S Serine
15 6 34 A Alanine
5 14 4 C Cysteine
9 1 11 Q Glutamine
6 6 12 E Glutamic acid
4 2 4 H Histidine
6 2 11 F Phenylalanine
22 5 11 T Threonine
5 1 1 W Tryptophan
7 5 8 R Arginine
18 10 24 G Glycine
6 3 21 I Isoleucine
14 10 21 L Leucine
15 19 11 K Lycine
23 4 16 V Valine 

7UFO_1|Chain A[auth H]|P3-42 Fab Heavy chain|Homo sapiens (9606)
>6DIK_1|Chains A, B|Basic phospholipase A2 homolog bothropstoxin-1|Bothrops jararacussu (8726)
>1AHH_1|Chains A, B|7 ALPHA-HYDROXYSTEROID DEHYDROGENASE|Escherichia coli (562)
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 \(w=f(c)\)
7UFO , Knot 103 226 0.82 40 149 214 
QVHLVQSGAEVKKPGASVKVSCKASGYTFTSYAIHWVRQAPGQRLEWMGWIKGGNGNTRYSQKFQDRVTITRDTSASTAYMELSSLRSEDTAVYYCALLTVITPDDRFDIWGQGTMVTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVEPKSCDK
6DIK , Knot 58 121 0.76 40 89 117 
SLFELGKMILQETGKNPAKSYGAYGCNCGVLGRGKPKDATDRCCYVHKCCYKKLTGCNPKKDRYSYSWKDKTIVCGENNPCLKELCECDKAVAICLRENLGTYNKKYRYHLKPFCKKADPC
1AHH , Knot 108 255 0.78 40 154 237 
MFNSDNLRLDGKCAIITGAGAGIGKEIAITFATAGASVVVSDINADAANHVVDEIQQLGGQAFACRCDITSEQELSALADFAISKLGKVDILVNNAGGGGPKPFDMPMADFRRAYELNVFSFFHLSQLVAPEMEKNGGGVILTITSMAAENKNINMTSYASSKAAASHLVRNMAFDLGEKNIRVNGIAPGAILTDALKSVITPEIEQKMLQHTPIRRLGQPQDIANAALFLCSPAASWVSGQILTVSGGGVQELN

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 \(c\).

\(|P_{f(7UFO_1)}(2) \setminus P_{f(6DIK_1)}(2)|=112\), \(|P_{f(6DIK_1)}(2) \setminus P_{f(7UFO_1)}(2)|=52\). 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 1:0101100110100111010100010100100011011001110010111110110100000001000101000001001010100100000110001110110100010111010110100100011011111100000011011110110001101101010011100110011111000110010011011000110000100100010000100010100000
Pair \(Z_2\) Length of longest common subsequence
7UFO_1,6DIK_1 164 3
7UFO_1,1AHH_1 163 4
6DIK_1,1AHH_1 157 3

Newick tree

 
[
	7UFO_1:82.80,
	[
		1AHH_1:78.5,6DIK_1:78.5
	]:4.30
]

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 \((0.85)(0.8)(\frac{347 }{\log_{20} 347}-\frac{121}{\log_{20}121})=69.4\)
Status Protein1 Protein2 d d1/2
Query variables 7UFO_1 6DIK_1 90 68.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]